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authors for librarians v2018i1 volume 1, issue 1 from the editors we are excited to release this inaugural issue of communications of the blyth institute. the blyth institute has been in operation for eight years, and we have continued to expand our services to the academic community. our hope is that communications serves as a helpful platform both among the members of the institute and the wider community. 1 motivation for the journal prior to this journal, the blyth institute has facilitated research through conferences and edited volumes, including engineering and the ultimate: an interdisciplinary investigation of order and design in nature and craft and naturalism and its alternatives in scientific methodologies. both of these volumes contain groundbreaking work in a variety of fields. as the blyth institute has grown, we have also found the need to communicate early work and intermediate results in a formal, reliable method. originally, we considered merely publishing these on the website as technical reports. however, we recognized that many of our colleagues, especially those performing interdisciplinary work or those not currently affiliated with an academic institution, had similar needs. from this the idea for communications was born. 2 call for papers communications accepts papers in a wide variety of fields including most sciences, mathematics, and philosophy. we have a particular focus on non-reductionist perspectives (including criticisms of non-reductionist perspectives) in these various fields. additionally, we will often suggest areas which we think deserve more focus, and where papers of such focus will receive priority treatment in the submission process. currently, we are seeking papers in two areas. first, we are seeking papers related to non-reductionist approaches to economics and business. examples of such approaches can be found in chapter 14 (“other nonnaturalistic methodologies in modern practice”) of naturalism and its alternatives in scientific methodologies, as well as the note “the wealth pies of plato’s library” in the present issue. second, we are seeking papers that discuss the concept of finiteness and infinity, especially in relationship to the philosophy of mind. topics dealing in areas such as gödel incompleteness, turing oracles, intensional vs. extensional definitions, human creativity, and questions about the reality or non-reality of inifinities are all of interest. 3 the current issue the present issue sports a wide variety of topics, including evolution, computer science, mathematics, philosophy of science, and moral reasoning, as well as interdisciplinary papers connecting them together. we have not established a rhythm for publication, but our hope is to be able to publish at least twice-yearly. if you would like to subscribe to the journal, you can subscribe or purchase individual articles at journals. blythinstitute.org. sincerely, the editors v1i2 volume 1, issue 2 from the editors this marks our second issue of communications of the blyth institute (cbi). as usual, this issue of cbi includes papers on a diverse array of topics, including machine learning, consciousness, philosophy of science, and mathematics. issue focus the focus of this issue is philosophy of science. to that end, we have included papers on: • the shifts required for science in thinking about consciousness (rakover), • how to quantifying generalizations (bartlett and holloway), • uncovering hidden usage of theology in science (hunter and dilley and tafacory), • null hypothesis construction (hunter), • science education (dilley and tafacory), and • the nature of truth (koch). every endeavor of knowledge involves both epistemology (how do we know that something is true?) and ontology (what is the structure of truth?). these philosophical questions frame the outlines of how science works. while some believe that the ontology and epistemology of science are set in stone, in truth it is a continuously-changing enterprise— hopefully for the better. philosophy of science is used both internally (for scientists to analyze and adjust their own thinking) and externally (for non-scientists to judge the quality and applicability of the outputs of science). those who discount the value of philosophy to science simply show their ignorance of the subject. the basic rules of inference come from philosophy. the identity of indiscernibles, the principle of sufficient reason, and the law of non-contradiction are indispensible to scientific reasoning, but they originate in metaphysics. many of the advances of science, such as null hypothesis testing, are actually philosophical advances about the nature of epistemology. so, while many in the popular press wonder how useful philosophy is to science, the actual practice of science is bathed in philosophy. we are thankful to all of our contributors for maintaining high standards of academic excellence. criticism welcome however, the progress of any model requires criticism as well. if you have a comment or criticism of a paper published in cbi, we encourage you to submit a letter (or even a full rebuttal paper) for publication. more than anything, cbi exists to facilitate communication among researchers in a variety of fields, and that includes well-founded criticism. cross-field analysis and criticism is also encouraged. different disciplines bring different mindsets, and applying knowledge and perspectives from a diversity of fields helps to sharpen and refine ideas more effectively. future issue focus the actual focus of each of our issues is dependent on the submissions we receive and pass peer review. however, we are hoping to put together an issue focusing on machine learning and artificial intelligence in the near future. if you work in that area, we hope you consider us for publication. —the cbi editors v2018i1 56 letters and notes the logical possibility of halting oracles eric holloway doi: 10.33014/issn.2640-5652.1.1.holloway.3 a halting oracle is a kind of function that can determine whether any computer program will halt. it is commonly thought that halting oracles are logically impossible. this is due to the common proof presented for the halting problem, which is as follows. imagine we have a halting oracle function h (p, i), which returns true if program p halts on input i, and false otherwise. we can also have a function defined as g(p): if h (p, p) is true then loop forever, else halt. if we run g(g), then we end up with a contradiction, because if h (g,g) halts then g(g) will not halt, and visa versa. consequently, the function h is impossible. this proof introduces a confusion because it appears that a halting oracle is logically impossible. however, the proof only shows that it is impossible for a halting oracle to be a finite turing machine. it is still logically possible to have a halting oracle that is not a finite turing machine. to see that halting oracles are a logical possibility, we can construct our own halting oracle from logically possible components. first, note that all finite turing machines form a countable infinite set. this means that we can match each finite turing machine with a positive integer. imagine this as an infinitely long index, with a numbered entry for each turing machine. the second step is to note that each finite turing machine has a halting status. each machine either halts or runs forever. consequently, we can take the infinite index from the first step, and, for each turing machine, add an entry with its halting status. thus, our index now consists of three elements: an index number, the finite turing machine definition, and the machines halting status. the final step is to imagine a search machine that has access to this index. the difference between the search machine and a finite turing machine is that since the index is infinite the search machine is also infinite, and thus the search machine does not show up in the index itself. the operation of the search machine is to incrementally search the index for a given finite turing machine and return the finite machines halting status. since the set is countably infinite and each finite turing machine is paired with a finite number, the search machine is guaranteed to halt with the halting status for every finite turing machine. thus, the search machine is a halting oracle. now we can address the question whether a halting oracle is logically impossible. since the search machine is a halting oracle, then if the search machine is not logically impossible, neither is the general concept of a halting oracle. the search machine is composed of two main components. if neither component is logically impossible, then neither is their composition in the form of the search machine. the components are: 1. the countable infinite index of finite turing machine halting statuses 2. the search procedure countable infinite sets are used regularly in mathematics and are not logically impossible, although some branches of mathematics deny their existence as an axiomatic decision. thus, component #1 is not logically impossible. the search procedure can be encoded with a finite turing machine that counts upwards incrementally, and can call out to an external index to retrieve the finite turing machine definition and halting status. since the search performs an exact match with the input finite turing machine and the retrieved finite turing machine, then the match can be encoded as a finite turing machine as well. since finite turing machines are not logically impossible, then neither is component #2, the search procedure. finally, the combination of the infinite index and the search procedure is not logically impossible, since no further concepts are added. consequently, the search machine demonstrates that halting oracles are logically possible. v2018i1 volume 1, issue 1 letters and notes implications of two opposing variations of neutral theory jonathan bartlett doi: 10.33014/issn.2640-5652.1.1.bartlett.2 in evolutionary biology, neutral theory has been gaining more and more ground since it was originally proposed by motoo kimura in 1968 (kimura, 1968). it was originally proposed as a mathematical way of understanding the relationship between allele variations and population sizes in population genetics, but was later applied to molecular evolution as well (dietrich, 1994). popular theories sometimes shape the thinking about a subject far beyond what the technical aspects of the theory suggest. this is true both for popular and professional audiences, as even for professionals, popular principles oftentimes fill in the gaps in understandings (see bartlett (2017) for a discussion of this). while selection has previously stood in the gap for these types of understandings in biology, today neutral theory has begun to takes its place. interestingly, in the case of neutral theory, the theory implied by the data is actually significantly at odds with the larger interpretation and application of it. the question turns on whether neutral evolution is merely a description of the peculiar features that are found in the organisms present in the earth today, or if neutral evolution is due to general features of evolution itself (i.e., they would exist no matter how biology was configured). i will call the first theory “observational neutral theory” and the second one “comprehensive neutral theory.” in observational neutral theory, neutral theory merely points to observations about present mutations in present organisms. it makes no claims about evolution in general, evolution past, nor the requirements for neutral evolution to take place. it merely points out that most mutations we observe are nearly-neutral or of low effect (eyre-walker and keightley, 2007), and therefore selection has very little effect on which mutations survive in the population (sanford et al., 2007). genetic drift therefore becomes the dominant mode of observable evolution. selection, when it acts, is primarily purifying selection (dietrich, 1994). this type of neutral theory does not speculate on why this is the case—more to the point, the reason for why neutral evolution occurs is basically outside of its scope. that is, it leaves out the specific molecular requirements that would lend themselves to neutral evolution. in comprehensive neutral theory, the dominance of neutral evolution is not only in the observed present, but is also the key to all of evolution. that is, evolution needs no guidance from natural selection to do its work (though it may have some). according to this view, neutral mutations and genetic drift are all that is needed to get all of the precise mechanisms available within biology. the reason that this distinction is important is that i have found that, in conversation, many biologists free-float between the two theories. neutral theorists often start in the observational theory, beginning by saying that evolution as we observe it obeys the principles of neutral theory. since neutral theory is dominant in the process of evolution today, many neutral theorists then generalize to the comprehensive theory and say that because it is dominant today that neutral theory must have been equally dominant in the past. therefore, neutral evolution must be really powerful, because all of biology is the result of neutral evolution. however, one can then point out that the reason neutral evolution works in the present is because mutational hot-spots are contained in less-sensitive areas of the genome. when pressed, the neutral theorist quickly switches from a comprehensive theory back to an observational theory, usually citing natural selection as the reason for such a propitious distribution of hotspots. recognizing the distinction between the observational and comprehensive theories of neutral evolution is important for critical thinking about neutral theory. this is somewhat amusing because one of the supposed benefits of neutral theory is getting around problems of selectionism and adaptationism in evolution. however, when pressed on shortcomings in neutral theory, this is precisely where neutral theorists often go. comprehensive neutral theory is unworkable, because the machinery in cells and organisms are precise mechanisms. therefore, random wanderings in genome space will not produce them in any amount of time. my own viewpoint 52 letters and notes is that the observational neutral theory is a fairly accurate representation of what we know about modern evolution, but it needs to be underpinned by something other than selectionism for a foundational theory of how it came to be that evolution has such a neutral focus. one possibility is that neutral theory works precisely because organisms contain sufficient information to target mutations in areas that are less likely to be problematic—i.e., in areas where modifications are expected to occur and accounted for. however, this presupposes the existence of information within the cell to do the targeting. neutral theory cannot hoist itself up by its own petard to perform this, and neither can neo-darwinian selectionism. constructive neutral evolution (stoltzfus, 2012), abbreviated cne, is an attempt to get around this, but winds up falling into the same trap. it aims to be more comprehensive in the small scale, specifically accounting for complexity. it is interesting that the models of cne show how complexity can form, but leave out how those complexities turned functional—it is merely assumed that they often do. interestingly, this mirrors the same process described in this paper with earlier forms of neutral evolution, with researchers passively switching back-and-forth between whether the theory only describes a process or whether it is a comprehensive solution to the problem of complexity. a better research program for neutral theory is to recognize the limitations of neutral theory’s role in evolution, and determine the necessary conditions for neutral theory to work. the most rigorous descriptions of what makes evolution workable in a general sense focuses on the information present in organisms (marks ii et al., 2013; ewert and marks ii, 2017; dembski and marks ii, 2009; bartlett, 2010; dembsking and marks ii, 2010). as the evolutionary informatics lab points out, “information makes evolution possible” (evolutionary informatics lab, 2019). ultimately, either neutral theorists need to say that this introduction of information is beyond the reach of biology (similar to the stance of yockey (2000)) or, like intelligent design, propose a valid source or mechanism for such information to have been included into organisms (meyer, 2009). eternally punting to mechanisms known not to be able to produce the effect in question, however, does not make for an effective research program in the long term. bartlett, j (2010). “irreducible complexity and relative irreducible complexity: foundations and applications”. in: occasional papers of the bsg 15, pp. 1–10. bartlett, j (2017). “evolutionary teleonomy as a unifying principle for the extended evolutionary synthesis”. in: bio-complexity 2017.2, pp. 1–7. dembski, w a and r j marks ii (2009). “conservation of information in search: measuring the cost of success”. in: ieee transactions on systems, man and cybernetics a, systems and humans 5.5, pp. 1051–1061. dembsking, w a and r j marks ii (2010). “the search for a search: measuring the information cost of higher level search”. in: journal of advanced computational intelligence and intelligent informatics 14.5, pp. 475– 486. dietrich, m r (1994). “the origins of the neutral theory of molecular evolution”. in: journal of the history of biology 27.1, pp. 21–59. evolutionary informatics lab (2019). “frequently asked questions”. in: evolutionary informatics lab website. url: http://evoinfo.org/faq/. ewert, w and r j marks ii (2017). “conservation of information in coevolutionary searches”. in: biocomplexity 2017 (1), pp. 1–15. eyre-walker, a and p d keightley (2007). “the distribution of fitness effects of new mutations”. in: nature reviews genetics 8.8, pp. 610–618. kimura, m (1968). “evolutionary rate at the molecular level”. in: nature 217, pp. 624–626. marks ii, r j et al. (2013). biological information: new perspectives. world scientific. meyer, stephen (2009). signature in the cell. harperone. sanford, j et al. (2007). “using computer simulation to understand mutation accumulation dynamics and genetic load”. in: lecture notes in computer science 4488, pp. 386–392. stoltzfus, a (2012). “constructive neutral evolution: exploring evolutionary theorys curious disconnect”. in: biology direct 7.35. doi: 10.1186/17456150735. url: https://biologydirect.biomedcentral.com/ articles/10.1186/1745-6150-7-35. yockey, h (2000). “origin of life on earth and shannon’s theory of communication”. in: computers and chemistry 24.1, pp. 105–123. v1i1 54 letters and notes laplace, pierre-simon (2012). pierre-simon laplace philosophical essay on probabilities: translated from the fifth french edition of 1825 with notes by the translator. vol. 13. springer science & business media. levin, leonid a (1984). “randomness conservation inequalities; information and independence in mathematical theories”. in: information and control 61.1, pp. 15–37. menabrea, luigi federico and ada lovelace (1842). sketch of the analytical engine invented by charles babbage. romer, paul m (1992). “two strategies for economic development: using ideas and producing ideas”. in: the world bank economic review 6.suppl_1, pp. 63–91. solow, robert m (1957). “technical change and the aggregate production function”. in: the review of economics and statistics 39.3, pp. 312–320. suárez, fernando f and james m utterback (1995). “dominant designs and the survival of firms”. in: strategic management journal 16.6, pp. 415–430. turing, alan m (2009). “computing machinery and intelligence”. in: parsing the turing test. springer, pp. 23– 65. numberphile’s proof for the sum 1 + 2 + 3 + . . . jonathan bartlett and asatur khurshudyan doi: 10.33014/issn.2640-5652.1.1.bartlett.3 in 2014, youtube math vlogger numberphile upset the amateur math world by declaring that the sum of all the natural numbers (i.e., the positive integers, the infinite series 1 + 2 + 3 + . . .) is − 1 12 (haran and padilla, 2014; haran, 2015). while this is indeed the result of the riemann zeta function applied to −1, we will show here that it is not the sum of 1 + 2 + 3 + . . .. the standard summation which the riemann zeta function is based on is simple: ζ (x) = ∞! n=1 1 nx . (1) for x > 1, (1) is well defined and makes a convergent series. for x ≤ 1, (1) no longer converges. for x = −1, (1) is equivalent to the series under consideration, 1 + 2 + 3 + . . .. the question is whether or not ζ (−1) is still equivalent to the series implied by (1). if it is, then 1+2+3+ . . . is indeed equal to − 1 12 . according to the video, which uses a proof based on the one originally given by ramanujan, the proof that 1+2+3+. . . = − 1 12 can be shown by beginning as follows. first, start with the following series: s1 = 1 − 1 + 1 − 1 . . . (2) s2 = 1 − 2 + 3 − 4 . . . (3) s3 = 1 + 2 + 3 + 4 . . . (4) s1 has the well-known value of 1 2 and s2 has the well-known value of 1 4 . he then subtracts s3 − s2. doing this yields the series 0 + 4 + 0 + 8 . . .. the error comes next. this is claimed to be equivalent to the series 4+ 8+ 12 . . ., which would be 4s3. this gives the equation s3 − s2 = 4s3. because s2 = 1 4 , this can be then solved. s3 − 1 4 = 4s3 (5) 3s3 = − 1 4 (6) s3 = − 1 12 (7) as suggested the problem comes with stating that 0 + 4 + 0 + 8 + 0 + 12 . . . = 4 + 8 + 12 . . . . volume 1, issue 1 numberphile’s proof for the sum 1 + 2 + 3 + . . . 55 bartlett, gaastra, and nemati (2018) developed a technique, which we can term the bgn technique, that assigns hyperreal values to divergent sums. applying the bgn technique shows that, even though it may seem counterintuitive, adding zeroes in the middle of an infinite sum changes the value of the sum, therefore invalidating the proof. according to the method given in bartlett, gaastra, and nemati (2018), the sum of 1 + 2 + 3 . . . is the hyperreal value ω2 2 + ω 2 . the sum of 0+4+0+8+0 . . . is the hyperreal value ω2 2 + ω 2 − 1 4 , which, in fact, is the result of s3− 1 4 . note that both of these series are essentially the same value, as the lower-orders of infinity are essentially noise compared with the highest order term, which is ω2 2 . the reason why ζ (−1) = − 1 12 while the series (1) doesn’t is that ζ (−1) is evaluated using the zeta function’s analytic continuation (a modification of a function that expands its domain), not the series given in (1). the analytic continuation of ζ (the expanded expression that actually is valid for −1) is, according to lavrik (2011), π−x/2γ " x 2 # ζ (x) = 1 x(x − 1) + $ ∞ 1 % x−(1−x/2) + x−(1−(1−s)/2) & θ(x) dx, (8) where γ is the euler gamma function, and θ(x) is'∞ n=1 e−πn 2x . this is no longer identical to the original expression given in (1). however, the question still remains why physicists can use − 1 12 as a stand-in for the sum of all natural numbers. as haran and padilla (2014) point out, in several aspects of physics, such as for the casimir effect, when physicists need a sum of all natural numbers, the zeta function can act as a stand-in and yield valid results. while no conclusive reason for this has been established, vandegrift (2014) offers a numerical evaluation of a series that is very similar to the series 1+2+3 . . ., but is offset by a tiny complex component. vandegrift has suggested the possibility that lim ϵ→0 ∞! n=1 ne−ϵn cos(ϵn) = − 1 12 . (9) this sum would be nearly identical to 1 + 2 + 3 . . . in its beginning, but begin to diverge for higher values of n. we investigated this possibility and found the following results: 1. for an infinitesimal ϵ (where ϵ = ω−1), the series actually diverges. 2. interestingly, in the evaluation of the series expansion of (9), even though it diverges to infinity, there is a component of it that is − 1 12 .2 3. for a finite ϵ , a wide range of values will produce results near − 1 12 , though we did not yet find a value that produces this value exactly. ϵ ranging from 1 2 to 1 3750 seemed to be fairly close, while values outside this range started to stray. bartlett, j, l gaastra, and d nemati (2018). “hyperreal numbers for infinite divergent series”. in: arxiv 1804.11342. haran, b (2015). “this blog probably won’t help”. in: brady haran blog. url: http : / / www . bradyharanblog.com/blog/2015/1/11/this-blogprobably-wont-help. haran, b and t padilla (2014). “astounding: 1 + 2 + 3 + 4 + 5 + . . . = -1/12”. in: youtube numberphile channel. url: https://www.youtube.com/watch?v=wi6xtvzxww. lavrik, a f (2011). “zeta function”. in: encyclopaedia of mathematics. springer. url: https : / / www . encyclopediaofmath . org / index . php / zeta function. vandegrift, g (2014). “matlab/divergent series investigations”. in: wikiversity. url: https : / / en . wikiversity.org/wiki/matlab/divergent_series_ investigations. 2using the bgn technique, the expansion of the sum was found to be ( sin(1) e − cos(1) 2e ) ω2 + ( cos(1) 2e ) ω − sin(1) 12e − 1 12 where ω is the hyperreal infinite unit. notice the last part of this term is − 1 12 . it is unclear the connection between this value and the zeta function. nonetheless, it is interesting that − 1 12 appears there. login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians v2018i1 volume 1, issue 1 news blyth institute mobile microscopy lab makes appearances the blyth institute’s mobile microscopy laboratory has been touring homeschooling conventions in the oklahoma area. the goal of the lab is to provide students (and their parents) the ability to have a hands-on look at life at the tiniest levels, and to have experience with some of the tools that make modern discovery possible. during the lab sessions, blyth institute volunteers show students how to take samples, make simple stains, and view their samples under the microscope. the sessions are usually employ fairly standard types of samples, such as onion skin, pond water, and vegetable ferments. various samples of flowers and other objects are made available for viewing under the stereo microscope. there is a limit to the amount of actual lab work that can be down in a crowd, but getting students used to the methods and thought processes behind it can start them thinking about what goes in to the scientific discoveries they will learn during their education. am-nat business and technology conference information originally, the blyth institute had planned to do another alternatives to methodological naturalism conference focused on business and technology theory and applications. however, this idea is sufficiently new and different that we have had trouble sourcing talks for such a conference. we are still planning to do something along these lines, but instead of our normal conference format, we are currently planning on doing a series of introductory seminars to spark further interest in the topic. mindmatters: using technology instead of worshipping it the technology blog mindmatters (https:// mindmatters.ai) recently appeared on the scene. it is the news and popular content wing of the walter bradley center for natural and artificial intelligence. the blog’s authors include several members of the blyth institute. the topics are wide-ranging, but the focus is on artificial intelligence and its role within society. it deals with the good and the bad of technology, proper use and misuse, and the personal, moral, and spiritual impacts that technology can have. blyth institute press books now available online in addition to hosting the online version of this journal, https://journals.blythinstitute.org/ will also hold the digital editions of blyth institute press books, including engineering and the ultimate and naturalism and its alternatives in scientific methodologies. the blyth institute also recently registered with the doi network, so all papers and chapters will receive a doi. for those unaware, a doi makes referencing and linking scholarly material easier. new model of species relationships proposed in the latest issue of bio-complexity, winston ewert proposed a new model of species relationship—the dependency graph. his paper, “the dependency graph of life,” shows that the relationships among species based on their gene families better represents a dependency graph than a tree. ewert shows that, in absence of the proper model, dependency graphs look like trees when compared to random distributions (which is what they are normally compared against in the literature). this is why the tree hypothesis has such vigorous support—when compared against a ran58 news dom null model, the data looks like a tree. however, when compared against a dependency graph, the data looks exceptionally more like a dependency graph than a tree. while this is definitely an exciting development, this research is still in its early stages, and many questions are unanswered. further work will show what model of species relationships best fits the data. latest business trends combine ai and human creativity early work in ai had the long-term goal of replacing human creativity with machine intelligence. however, over the years, it is becoming increasingly evident that the best ai models actually include human input at various stages. for instance, in eric holloway’s “imagination sampling” paper (in naturalism and its alternatives in scientific methodologies, 2016), he suggested that ai could be augmented by including humans in exploring the hypothesis space. a new european software company takes this idea to the extreme. engineer.ai, for instance, is a new startup that uses an ai to help build new software projects, and incorporates human talent on an as-needed basis. some companies, such as iflytek, have been caught using humans instead of ais, at least in demos. to some extent, this isn’t even really a problem, as the user would not care whether the work is done by a computer or by a human. however, for investors, it is important to know if the core technology is computing, which is relatively cheap to source, or humans, who tend to be more expensive. in any case, for difficult jobs, we are finding more and more that humans and computers each have important but distinct roles. health risks of mutation accumulation recently, john sanford gave a talk at the nih on the question of whether or not mutation accumulation poses a health risk to humans. sanford’s population genetics simulator, mendel’s accountant, has shown repeatedly the problem of getting rid of slightly deleterious mutations through natural selection. below a certain threshold, deleterious mutations are essentially invisible to natural selection, and therefore, according to standard population genetic models, they accumulate in populations which eventually experience mutational meltdowns. in his nih talk, sanford discusses the medical implications of this result. the talk is available at https://www.youtube.com/watch?v=eqijnol9uh8 . blyth institute director releases new calculus book blyth institute director jonathan bartlett released his new calculus book titled calculus from the ground up, as well as a full solution manual. this book was developed while teaching calculus to homeschool co-op classes. being frustrated with calculus books that seemed to miss the actual beauty and wonder of calculus, bartlett decided to embark on a quest to write his own that would capture the aesthetics as well as the content of calculus. as an example, in the section on representing functions as series, the book uses this as a springboard to a general discussion of how to solve impossible problems. new types of journals starting to take hold while the internet brought many new methods of publication (online, open access, etc.), other innovations in academic publishing have gone relatively unnoticed. while the traditional journals remain the mainstay of published academic content, some other types of journals are starting to arise. quillette (https://quillette.com/) is a social issues journal founded in 2015 dedicated to a more free exchange of ideas not bound by typical norms. it includes topics ranging from why you should drop out of school to the way that trans activism negatively affects the political speech of women. next is the upcoming journal of controversial ideas. this journal is based on the fact that many researchers have been attacked and their academic freedom threatened due to the controversial nature of their research. this journal aims to provide an outlet for communicating valid but unpopular findings, where the researchers can use aliases to protect their privacy. on the science side is the journal inference: international review of science (https://inference-review. com/). the goal of this journal is be to science what art criticism is to art. essentially, the idea is that science needs critics as much as it does cheerleaders. since the internet volume 1, issue 1 the blyth institute 59 is awash in sites declaring just how much they love science (and every ridiculous paper and press release put out by science organizations), they are providing (among other things) a critical review of what is being published. finally, this journal is providing a way to solidify the frontend of science. journals used to provide more space for conjectural and early-stage ideas. communications of the blyth institute aims to prime the pump of research while still maintaining a solid review process. it remains to be seen whether these publications will succeed in their aim, if others will succeed in their place, or if, perhaps, some of the publications are altogether misguided. in any case, as traditional journals have closed themselves off from certain areas of inquiry and analysis, new and specialized journals are rising to fill the vacuum left behind. v1i2 80 letters and notes the data, the more they classify each sample incorrectly. russell, s and p norvig (2009). artificial intelligence: a modern approach. 3rd ed. pearson. the possibility of spontaneous generation of self-replicating systems gary prok doi: 10.33014/issn.2640-5652.1.2.prok.1 it has been glibly stated that given enough time, a universe of monkeys at typewriters could write hamlet. if this is true then perhaps the universe of particles could accidently assemble the right configuration of stuff to spark life. yet the universe today is not even old enough to allow all the resources in the visible universe to work together with the tiniest probability of success to randomly generate the first 200 characters of hamlet. a shorter 142-character string of the start of hamlet is a unique string of information which is of 10210 possible strings of 142 characters. 10210 random tries would give a chance of ! 1 − 1 e " , or ~63%, for generating this simple 142-character passage. this might be only for a fleeting instant at some corner of the universe, but nonetheless it would be spontaneously generated. adding another 58 characters to total 200 characters reduces the chance to a minuscule value. spontaneous generation of life it seems, would require even more resources or time. seth lloyd has estimated the computational capacity of the universe to be 10120 operations from the start to date, on a register of 1090 bits (lloyd, 2002). a register of 1090 bits contain nearly 1090 different 142-character length strings. so, the universe could generate at most 10210 tries to date. 10210 is approximately 2700, or all of the possible permutations of 700 bits. although this computational capacity cannot generate hamlet in its entirety by chance, or even the first 200 characters, perhaps it can be shown to be sufficient to spontaneously generate life. another bound was offered by dembski as 10150, or approximately all the possible permutations of 500 bits (dembski, 1998, pg. 213). this is more restrictive, but may be a more realistic estimate for practical things like the probability of spontaneous life. one way of quantifying the needed time and resources is to consider a simple proxy for life. a proxy for abiogenesis requires a simple system that allows a means for an information string to induce its own replication as well as a means to execute this replication. this proxy could be a simple system of things that operate on such things to make more such things. lambda calculus is a system of mathematical logic reduced to a minimal set of symbols and rules. expressions in lambda calculus can operate on other such expressions to generate more such expressions. furthermore, lambda calculus is a universal model of computation and is turing complete. it is enlightening to see how much information is needed to describe a simple self-replicating set of statements in lambda calculus. if a universe of monkeys or of particles can generate this simple set of statements, then perhaps it can do the same with material stuff and spark life. lambda calculus is considered to be a minimally simple programming language; it is hard to conceive of a simpler language. it was created by alonzo church as part of his research into the foundation of mathematics and uses three simple rules, yet it is capable of expressing any computation. its simplicity results in bloated expressions for simple concepts, like numbers, or “true” and “false”. its simplicity, however, also makes it a model for a system most likely to spontaneously generate. the fundamental concept allowed by lambda calculus is substitution. (λx.fx) is an expression in lambda calculus where ”λ” indicates that the next variable is a free variable to be substituted, “x” is the name of the free variable, and “.” indicates that what follows is an expression or function in which the free variable is to be substituted. the value or expression to be substituted for x is placed to the right of the expression. as an example, (λx.x2) y = y2, where y is substituted for x. this substitution is called abstraction. lambda calculus also allows for application, which is a function operating on an argument. a tutorial of lambda calculus is not included here, but is readily found elsewhere. lambda calculus can be efficiently encoded in binary; binary lambda calculus (blc) is an efficient way to encode expressions in lambda calculus into binary (tromp, 2007). blc uses de bruijn indices instead of variables, where the index value is a natural number indicating how many λs back the variable refers. λx.λy.xy is written as λ λ 2 1 with de bruijn indices (bruijn, 1972). three things that volume 1, issue 2 the possibility of spontaneous generation of self-replicating systems 81 then need to be encoded into binary are abstraction (λ), application, and natural numbers. the scheme is very simple: abstraction (λ) is encoded as 00 application is encoded as 01 natural number n is encoded as 111110. . . (where there are n 1s) λx.λy.xy is written as λ λ 2 1 with de bruijn indices, which in blc is 00 00 01 110 10 (spaces added for understanding). lambda expressions are executed by the process of betareduction. this means of execution can also be expressed in lambda calculus and encoded in blc. lambda calculus can express a list using the pair function. other lambda expressions can extract any particular element of a list. the following elements comprise a self-replicating system in lambda calculus: • the self-replicating combinator q; qq -> qq does not propagate on beta-reduction, it merely replaces itself. however, qe ((qe) nil) does propagate qe on betareduction, by creating a growing list of (qe), (qe), (qe). . . . (qe), nil (e is defined below). qe will propagate any expression, p; qe (p nil) will generate a growing list of p, p, p,. . . . p . • a beta-reduction engine is required. – if this engine were encoded into p, then a means to translate from the information space to machine space also would be required and the initial instance would have no machine with which to execute. – the least required total kolmogorov complexity would have the beta reduction engine simultaneously generated in the machine state, as opposed to being generated in the information media state and subsequently transcripted to the machine state. the engine would act like a single instance of a re-usable catalyst, operating on the growing list. a minimal self-replication system in lambda calculus would generate a growing list of copied expressions, like (qe), (qe), (qe). . . . (qe), nil. this would require: • a means to encode lambda calculus. blc is an efficient means. • the e combinator, encoded in an information media state, like dna/rna in life. • the self-replicating combinator q, encoded in the information media state. • a program for self-reduction – encoded in the machine state, like an enzyme protein assemblage in life. the total information requirement to generate the minimal proxy for abiogenesis is then: • e, which operates on a list and extends it by one element (based on larkin and stocks, 2004). e = λx. (λp.(λl.xxp(pair pl))) , which in blc is 000000111111111011101100000001011101011010 (42 bits long). • q, the self-application combinator. q = λx. xx which in blc is 00011010 (8 bits long). • the application of q to e, qe, which adds 2 bits. • nil, which is λz.λx.λy.x, adding 9 bits. • two more applications to create the expression qe ((qe) nil), adding 4 more bits • a beta-reduction engine in machine space to process ((qe) e nil). this would at a minimum require: a. a true statement: λx.λy.x (7 bits) b. a false statement: λx.λy.y (6 bits) c. an if-then-else statement: λz.λx.λy.zxy (15 bits) d. abstractions to delete and replace expressions (>~15bits each, or >~30bits). the bit count so far for a beta reduction engine is > 58. actual construction of the beta reducer could require many more. a beta-reduction engine in an abstracted lambda calculus has been found, which is longer than 200 bits (mogensen, 1994). an engine in blc would require a similar number of bits. so far we are up to many more than 123 bits, and likely more than 265 bits, for a randomly-formed pair of information strings, one in information space (dna/rna) and one in machine space (protein/enzyme) which allows the information string to propagate in a list. it may be possible to compress these relatively short strings. e in particular appears to be a compressible string, which 82 letters and notes might allow for a reduced bit count. however, adding a codec to the mix will certainly increase the bit count more than it offers in compressive bit-reduction. it is reasonable to think that a minimal basic precursor to abiogenisis of life would require two random assemblages with total information exceeding 265 bits. however, 265 bits is below the 500 bit dembski limit and below the 700 bit limit based on seth lloyd’s analysis. this analysis does not rule out the spontaneous, if fleeting, generation of a self-replicating system somewhere in the universe at some time in its past. the probability given the dembski limit is! 1 − 1 e (500/265) " , or ~85%. the probability given the 700 bit limit is ! 1 − 1 e (700/265) " , or ~93%. appending other features on to this analysis will require more bits. examples are: • a means for the information describing the betareduction engine in the machine space to be also expressed in the information space. • a means for the information expressed in the information space to be realized in the machine space, they way a genotype becomes a phenotype in life. • a means to operate on more than the first element in the list to allow population growth that approaches exponential. this will require information to describe recursion on the tail function. • a means to store the information and the betareduction engine in the physical world. although these are needed and may well push the information needs above 700 bits, they are beyond the scope of this analysis. this analysis does not rule out a single instance of the spontaneous generation of a self-replicating system somewhere in the universe. it does, however, suggest that this is an extraordinarily rare event. this analysis suggests that there is less than 50% likelihood that 10 self-replicating systems have spontaneously generated in the universe. given the vastness of the spacetime of the universe, an implication is that any evidence of extra-terrestrial life would be evidence of transpermia. bruijn, n g de (1972). “lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the church-rosser theorem”. in: indagationes mathematicae 75 (5), pp. 381– 392. url: http://alexandria.tue.nl/repository/ freearticles/597619.pdf. dembski, w a (1998). the design inference: eliminating chance through small probabilities. cambridge: cambridge university press. larkin, j and p stocks (2004). “self-replicating expressions in the lambda calculus”. in: proceedings of the twenty-seventh australasian computer science conference (acsc2004). ed. by v estivill-castro. dunein, new zealand, pp. 167–173. lloyd, s (2002). “the computational universe”. in: edge.org. url: https : / / www . edge . org / conversation/seth%5c_lloyd-the-computationaluniverse. mogensen, t (1994). “efficient self-interpretation in lambda calculus”. in: journal of functional programming 2.3. tromp, j (2007). “binary lambda calculus and combinatory logic”. in: randomness and complexity, from leibniz to chaitin. ed. by c s calude. world scientific publishing company, pp. 237–260. login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians v1i2 volume 1, issue 2 letters and notes exploring alternate notations for partial differentials jonathan bartlett doi: 10.33014/issn.2640-5652.1.2.bartlett.2 recent work has shown that differentials can be made more algebraically manipulable if the notation is improved (bartlett and khurshudyan, 2019). can this also be the case with the jacobian notation for partial differentials (i.e., ∂y ∂x )? the typical counterexample to why partial differentials could not be algebraically manipulable comes from an example similar to the following. take a three-variable equation, such as y = x2z. this equation has six partial derivatives. for this example, we will note that ∂y ∂x = 2xz and ∂y ∂z = x2. if partial differentials were algebraically manipulable, we should be able to find ∂z ∂x by simple algebraic manipulation: ∂z ∂x = ∂y ∂x ∂y ∂z = 2xz x2 = 2z x however, actually calculating the partial derivative of z with respect to x directly yields − 2z x . as was the case in bartlett and khurshudyan (2019), the reason for the contradiction is not a failure of the power of differentials, but merely in the notation. to understand this, let us look at where partial differentials come from. taking our original example, let us simply take the total differential. y = x2z d(y) = d(x2z) dy = x2 dz + 2xz dx. let’s say we wanted the partial derivative ∂y ∂x . a partial derivative between two variables means that no variation is allowed to happen in the other variables. in this case, the other variable is z. if no variation happens in z, that means that dz must be zero. therefore, we set dz = 0 and solve for the ratio of the other differentials, like this: ∂y = x2 (0) + 2xz ∂x ∂y = 2xz ∂x ∂y ∂x = 2xz now, when we solve for ∂y ∂z , we do the same process, but set a different differential to zero (i.e., dx). note that both of these derivatives involve ∂y, but they come from two different modifications to the original equation. therefore, the ∂y in ∂y ∂z is not the same ∂y that is in ∂y ∂x . indeed, the bottom differential gives us additional information about which ∂y is being discussed. that is why the notation ∂y ∂x cannot be separated—information about the numerator is contained in the denominator, and is therefore lost when the fraction is split. to resolve this situation, we merely need a notation that allows us to be more specific about which partial differentials we are dealing with. here we will describe two possible approaches, each with different implications. i don’t think either of these are the “best” system, and i hope that this discussion sparks additional ideas which combines the advantages of each system. it is also possible that the notation chosen to represent partial differentials is based on your own goals of how to manipulate them. the two systems will be based on subscripting our partial differentials. in system 1 (for lack of a better name), we will subscript the partial differentials with the variable that was allowed to freely move. in the system 2, we will subscript the partial differentials with the variables that were forced to not move. so, in system 1, instead of ∂y ∂x , we will now modify the notation to include the variables which were allowed to freely move. therefore, the partial derivative of y with respect to x will be ∂x y ∂x x . likewise, the partial derivative of y with respect to z will be ∂z y ∂z z . this notation can be further simplified by noting that, if a variable is allowed to freely vary, that is the same as being a total differential. therefore, ∂x x = dx. this simplifies our derivatives to ∂x y dx and ∂z y dz . this also means that a total derivative of a dependent variable is simply the sum of its partial differentials. dy = ∂x y + ∂z y in fact, we can actually carry pieces of the par78 letters and notes tial derivative around in the subscripts, by saying ∂x+z y = ∂x y + ∂z y. this can have benefit in large, multivariable equations, as the subscript can simply be added to as additional partials are added in. when all of the variables are included, then the partial differential is the same as the total differential. the drawback to system 1 is that it only fully works when y is a dependent variable, and all other variables are independent variables. if the other variables are have dependencies among them, the system breaks down. for instance, if x = f (z), then ∂x x is not equal to dx, and dy is not equal to the sum of its partials, depending on the particular formula those partials come from. the other system, system 2, takes this into account by, instead of subscripting which variables are allowed to freely vary, subscripts which differentials were forcibly set to zero. this system makes fewer requirements of the equation itself (because it specifies what we are doing to the equation), but also lends itself, as far as i can currently tell, to fewer simplification mechanisms. therefore, the partial derivative of y with respect to x (where dz = 0) would be specified as ∂z y ∂z x . this can get unweildy in equations with a large number of variables, as you would need to subscript every variable whose differential which was set to zero. in any case, both system 1 and system 2 allow for extending algebraic manipulability to partial differentials. the advantage of system 1 is that it has rules for interchanging partial and total differentials, but the disadvantage that you must know a priori which variables are dependent and independent. the advantage of system 2 is that you do not need the knowledge of which variables are dependent and independent, but building up total differentials from partial ones is more complicated. unfortunately, the notation for system 1 and system 2 are identical, so it would be confusing to use them both. another alternative would be to use set notation. so, using system 1, you could say ∂d∈x y ∂d∈x x , while system 2 would say, ∂d!z y ∂d!z x . basically, this uses set notation to say which elements were allowed to be modified. there are drawbacks here, too, as it makes it look like system 1 and system 2 are combinable, but i am not sure that they are. additionally, the notation itself is quite unweildy. the primary point of this exercise is to show that (a) the problem of the algebraic manipulability of partial differentials is primarily a notational problem, and (b) to start the conversation about what notation might possibly replace the current notation, and the benefits and drawbacks of each option. bartlett, j l and a zh khurshudyan (2019). “extending the algebraic manipulability of differentials”. in: dynamics of continuous, discrete and impulsive systems, series a: mathematical analysis 26.3, pp. 217–230. the unlearnable checkerboard pattern eric holloway doi: 10.33014/issn.2640-5652.1.2.holloway.1 in the history of machine learning, a famous upset was the disproving of the perceptron’s generality by use of the xor problem. there is no linear separator than can classify the points with 100% accuracy (russell and norvig, 2009, pg. 741). figure 1: difficulty of linear separation in an xor x1 x2 in response, the multilayer perceptron was invented, which eventually became the modern day neural network. however, the neural network, and other machine learning paradigms, still have a problem learning a tiled xor pattern called the checkerboard, see figure 3. the checkerboard classifications can be generated using a logic expression. to generate the classifications from 2n variables, we use the logic expression x1 ⊕ xn+1. here is an example with 4 variables, x1, x2, x3 and x4. the logic expression is x1 ⊕ x3. v1i2 volume 1, issue 2 news tackling research debt in the book indiscrete thoughts, gian-carlo rota wrote an essay titled “problem solvers and theorizers,” in which he divided up mathematicians into two types (rota, 2010). problem-solvers identify unsolved problems, then, with lazer-focus, attempt to be the first person to solve that problem. theorizers, on the other hand, take alreadysolved problems, and try to trivialize them, to make them obvious. in other words, the theorizer’s goal is to shed conceptual or philosophical light on a problem such that the solution becomes obvious once the problem is observed in the right way. over the last century, there has been a heavy shift, both in science and mathematics, away from theorizing towards problem-solving. for instance, most mathematical journals will not accept new proofs for already-proved theorems. the problem with this approach is that, while it solves more problems in the short term, it makes it more difficult to solve problems in the long term, as researchers must learn more complex systems than necessary (since there are fewer people around to trivialize them). the distill group (https://distill.pub/) has recognized this fact, and has given it a term—research debt. essentially, you can think of research as having two components—making discoveries and making discoveries understandable. making discoveries without making them understandable incurs “debt” within the whole system. just like normal debt, if the debt is unpaid, the interest payments show up in the fact that each researcher has more work to do to understand their field (olah and carter, 2017). the distill group is focused specifically on machine learning, and has organized both a journal and a prize. the journal is an interactive academic journal. that is, they go beyond typical pdfs that most online journals provide, and actually include simulations and interactive visualizations in their publications. the prize is $10,000 usd, and is given for researches in machine learning who, essentially, clarify things that we formally know but don’t intuitively understand, or for reframing problems in a much easier-to-understand way. nominations for the prize should be send to prize@distill.pub. new unified model of specified complexity formulated one of the problems within the intelligent design research community is a plethora of definitions and terms for very similar things. functional information (hazen et al., 2007), functional sequence complexity (durston et al., 2007), algorithmic specified complexity (ewert, dembski, and marks ii, 2014), algorithmic mutual information (milosavljevi, 1995), and other models all use fundamentally similar mathematics, but the profusion of models has made systematization difficult. in the latest bio-complexity, george montañez creates a unified mathematical model that can be used for all of these concepts (montañez, 2018). the model is sc(x) = − log2 ! r p(x) v(x) " . here, p(v) is the probability distribution of x, v(x) is a specification function (either discrete or continuous but uniformly positive), and r is a scaling factor where r ≥ v(ω) to normalize the distribution. the − log2() is applied to convert the probability into bits. additionally, a signficance level α can be applied by adding log2(α) to the result. montañez notes that specified complexity can lose some efficiency compared to precise probabilities, but that the benefit is that the calculation can be more easily utilized when precise probabilities are not known. the primary requirement for the application of specified complexity is the detachment principle, which states that the specification function must be determined prior to observing the data. for those with an interest in specified complexity, in 2016 the blyth institute put out a video tutorial on the mathematics of specified complexity (focusing on algorithmic specified complexity), available at https://youtu.be/ 5cwu_8ctddy. this obviously does not include the generalization found in the presently-discussed paper, but might 86 news provide a decent background for understanding the concepts within it. blyth institute develops improved notation for higher-order derivatives it is commonly known that, in standard calculus, while first-order differentials (such as dy and dx) can generally be manipulated algebraically, second-order and higher differentials (such as d2y and dx2) cannot be so manipulated. in order to manipulate them, special formulas such as faà di bruno’s formula must be used (the better-known special case of this formula is the chain rule for the second derivative). that is, one cannot just multiply and divide by higher-order differentials and expect to get back consistent and correct results. this surprising fact is generally left unexplained in standard textbooks. blyth institute director jonathan bartlett discovered that the reason for this stretches back well over a hundred years, when the formula for the second derivative (d2y dx2 ) was originally established. it turns out that a change in this notation will render the differentials for the second derivative to be fully algebraically manipulable, with no apparent drawbacks. the new notation, interestingly, was developed by using standard calculus rules for taking the derivative, and simply applying those same rules to the first derivative (which is already algebraically manipulable). if you take the first derivative seriously as a quotient (since dy dx is already in the form of a quotient), then simply applying the quotient rule and simplifying yields the improved formula for the second derivative. d2y dx2 − dy dx d2x dx2 faà di bruno’s formula (and the chain rule for the second derivative) is still valuable because it tells you how to manipulate the second derivative in certain cases (which is not altogether obvious), but it is no longer needed to justify the manipulations themselves, which are now just simple algebraic transformations. this was recently published in the paper “extending the algebraic manipulability of differentials,” published in the journal dynamics of continuous, discrete and impulsive systems, series a: mathematical analysis (bartlett and khurshudyan, 2019a). the paper lays the groundwork for future investigations into the nature of the differential. ara avetisyan and asatur zh. khurshudyan win prestigious science award this year, ara avetisyan and asatur zh. khurshudyan received the president prize of the republic of armenia in the area of “technical sciences and information technologies.” this award is issued by the republic of armenia for significant contributions to diverse areas of science and mathematics. avetisyan and khurshudyan won the award for their work on using green’s functions in control systems analysis, specifically for the monograph controllability of dynamic systems: the green’s function approach (2018). the official presentation of the award will be on june 10. the blyth institute has leaned on dr. khurshudyan for mathematical help for several projects, including the recently published papers “extending the algebraic manipulability of differentials” (bartlett and khurshudyan, 2019a) and “numberphile’s proof for the sum 1 + 2 + 3 + . . . ” (bartlett and khurshudyan, 2019b), as well as others which are still pending publication. the blyth institute also participated in developing the monograph for which the award was made, with director jonathan bartlett’s acting as the monograph’s editor. dr. khurshudyan said that he plans to use his part of the prize money to help fund scholarships for students in armenia. engineering working group launches for the past year, an informal group of engineers across many disciplines, together with biologists, scientists, medical researchers, and technologists, have been meeting together to explore the intersection between engineering and biology. the group hopes to enable a greater understanding of biological systems, generate better predictions of future discoveries, empower more productive research, and better understand the causal requirements underlying biological design. toward this end, a number of projects are either underway or in development, including a survey of engineering in the biology literature, detailed engineering models of the bacterial flagellum (and developing requisite reusable modvolume 1, issue 2 87 eling tools), a survey of repeatable and reversable adaptive mechanisms in biology, developing coherence metrics for engineered artifacts, and classification of control mechanisms in living systems. the group is planning to organize more formally in the near future, and will make announcements to this effect in the coming months. while this is not a blyth institute effort, anyone who would like to participate in this project can contact the blyth institute for more information. avetisyan, a s and a zh khurshudyan (2018). controllability of dynamic systems: the green’s function approach. newcastle: cambridge scholars publishing. bartlett, j l and a zh khurshudyan (2019a). “extending the algebraic manipulability of differentials”. in: dynamics of continuous, discrete and impulsive systems, series a: mathematical analysis 26.3, pp. 217–230. bartlett, j l and a zh khurshudyan (2019b). “numberphile’s proof for the sum 1 + 2 + 3 + . . . ” in: communications of the blyth institute 1.1, pp. 54–55. durston, k k et al. (2007). “measuring the functional sequence complexity of proteins”. in: theoretical biology and medical modelling 4.47. doi: 10.1186/1742-46824-47. ewert, w, w a dembski, and r j marks ii (2014). “algorithmic specified complexity”. in: engineering and the ultimate: an interdisciplinary investigation of order and design in nature and craft. ed. by j bartlett, d halsmer, and m r hall. blyth institute press, pp. 131– 151. doi: 10.33014/isbn.0975283863.7. hazen, r m et al. (2007). “functional information and the emergence of biocomplexity”. in: pnas 104.suppl 1, pp. 8574–8581. doi: 10.1073/pnas.0701744104. milosavljevi, a (1995). “discovering dependencies via algorithmic mutual information”. in: machine learning, pp. 35–50. montañez, g d (2018). “a unified model of complex specified information”. in: bio-complexity 2018.4. olah, c and s carter (2017). “research debt”. in: distill. url: https://distill.pub/2017/research-debt. rota, g c (2010). “problem solvers and theorizers”. in: indiscrete thoughts, pp. 45–46. login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians v2i1 volume 2, issue 1 news eric holloway publishes paper on specified complexity david nemati and blyth institute fellow eric holloway recently published a new paper in the journal biocomplexity (nemati and holloway, 2019). the paper, titled “expected algorithmic specified complexity,” explores the expected algorithmic specified complexity (asc) of a random variable, concluding that the expected asc is always less than zero. this is true both of random variables and of “processed” random variables—variables which have undergone some sort of transformation. this indicates that the existence of positive asc always counts as “surprise,” and therefore always requires explanation. new thinking on human origins this past year witnessed a plethora of new thinking on human origins. first up, new research by ola hössjer and ann gauger recently showed a unique model for looking at biodiversity (hössjer and gauger, 2019). essentially, they looked at the ways in which minor allele frequency distributions can arise, and how long di!erent distributions take to arise. new alleles essentially start out as one-o! events, arising as a mutation in a single individual and later spreading through the population or dying out (or somewhere inbetween). the frequency of these minor alleles can provide some amount of information about the history of the species in question. it takes time for an allele to spread through a population. therefore, initially, from an initially homozygous pair, the low-frequency side of the minor allele frequency spectrum will contain all of the new mutations. the mutations will take time to spread throughout the population. what hössjer and gauger discovered, though, is that a heterozygous initial pair creates an allele frequency spectrum that looks much older than it is. this is because an allele can actually start as either 25%, 50%, 75%, or 100% of the population before any mutations even occur. thus, the frequency spectrum will fill very quickly from the initial pair, and the initial heterozygosity will look equivalent to ancient mutations. using standard assumptions, hössjer and gauger calculated that the current allele frequency spectrum could be attained from an initial starting pair in 100,000–500,000 years. using other alternative assumptions about the nature of the starting pair could result in attaining the current allele frequency spectrum in an even shorter period of time. another interesting paper was done by nathaniel jeanson and ashley holland, which analyzed the human y chromosome (jeanson and holland, 2019). analyzing the human genome as a whole leads to a number of model-specific issues. if we imagine a starting pair for humanity, were the original chromosomes identical or did they house diversity? additionally, might the first human female have eggs that had additional diversity in their chromosomes? however, nearly all considerations of single-couple human origins have exactly one starting y chromosome, leading to fewer model-specific considerations. jeanson and holland aimed to improve the data available about y chromosome mutation rates by examining pedigree-based studies which used high-coverage sequencing. according to jeanson and holland, (a) a y chromosome molecular clock exists, and (b) it suggests a paternal history of the human race of about 4,500 years. finally, the year ended with the publication of joshua swamidass’s new book titled the genealogical adam and eve (swamidass, 2019). this book aims to show that the practical di!erence between popular and scientific conceptions of “adam and eve” are not too far o!. his viewpoint is that, although, according to the consensus view, there could be no single-couple origin of humans, there could be a single couple to whom all modern humans could trace their genealogies. communicating science through new venues new media becomes old media very quickly in the modern age. email was once the best technological way to communicate interpersonally. this is now often replaced with various social media platforms such as facebook, twitter, and others. likewise, youtube was once at the center of 40 news video-based media. while youtube is still the de facto destination for video content, it is useful to look at some of the newer players. first of all, some video is being distributed through apps on standard platforms. developing an app for roku, amazon fire, or apple tv is a new way to get content to users. additionally, streaming services such as twitch, and now mixer, are becoming the dominant social video platforms for the youth. science communicators should explore ways of reaching the public through these outlets. one possibility would be to play video games with scientists, discussing what they do while shooting zombies, or discussing the latest theories of the universe while racing nascar. growth opportunities are always with the latest technology. asserting a strong position while they are still unproven is the best way to establish leadership for the future. austrian society zentrum für biokomplexität & naturteleologie opens with special symposium a new austria-focused scientific society, zentrum für biokomplexität & naturteleologie, recently formed and held their first symposium. the symposium featured many european scientists and mathematicians, as well as a few from the united states as well. the organizers of the conference were günter bechly, a prominent german paleontologist who presently works as a senior scientist for the biologic institute, and siegfried scherer, a professor of microbiology and chair of microbial ecology at the technical university of munich. while the society is based in austria, the symposium itself was largely in english. many of the talks from the three day symposium are available on youtube, at https://www.youtube.com/playlist?list= plkakqujdyg2jhnqewqhnvtxz-37h0tjmb. breaking the weismann barrier and closing the loop for lamarckian evolution in multicellular organisms a recent review paper in the royal society shows that the weismann barrier is crumbling. in “the active role of spermatozoa in transgenerational inheritance,” sciamanna et al review the mounting evidence that there is a lamarckian feedback loop in dna inheritance (sciamanna et al., 2019). the paper reviews evidence that mammalian somatic tissues release rna-containing vesicles, and that these vesicles are then passed to epididymal spermatozoa. additionally, epididymal spermatozoa are known to be able to internalize foreign nucleic acids into their nuclei. this completes the communication channel between somatic cells and germ cells required for lamarckian inheritance. this communication channel was original proposed in the 1990’s. steele et al’s lamarck’s signature suggested that somatic mutations might be passed to germ line cells through an rna channel (steele, lindley, and blanden, 1999). after decades of work across multiple groups, evidence is mounting that steele’s hypothesis was largely correct. overcoming entrenched dogma about pseudogenes biologists have long known that not all non-coding dna is junk dna. however, pseudogenes have long been considered the standard bearer for the junk dna concept. since pseudogenes look like defective, non-coding copies of ordinary genes, it has been often assumed that these are evolutionary leftovers—genes which once coded for something, or a copy of a gene that once coded for something, but which some accident of mutation incapacitated its activity. while the evidence for the activity of pseudogenes has long been known, the idea that pseudogenes indicate junk dna has been ingrained in biologists. a group of researchers recently published a paper pointing out that the prejudices that biologists have about the status of pseudogenes as junk dna is impeding the progress of understanding the way that the genome functions (cheetham, faulkner, and dinger, 2019). references cheetham, s w, g j faulkner, and m e dinger (2019). “overcoming challenges and dogmas to understand the functions of pseudogenes”. in: nature reviews genetics. doi: 10.1038/s41576-019-0196-1. volume 2, issue 1 references 41 hössjer, o and a gauger (2019). “a single-couple human origin is possible”. in: 2019 (1), pp. 1–20. jeanson, n t and a d holland (2019). “evidence for a human y chromosome molecular clock”. in: answers research journal 12, pp. 393–404. nemati, d and e holloway (2019). “expected algorithmic specified complexity”. in: bio-complexity 2019 (2), pp. 1–10. sciamanna, i et al. (2019). “the active role of spermatozoa in transgenerational inheritance”. in: proceedings of the royal society b: biological sciences 286.20191263. steele, e j, r a lindley, and r v blanden (1999). lamarck’s signature: how retrogenes are changing darwin’s natural selection paradigm. basic books. swamidass, s j (2019). the genealogical adam and eve: the surprising science of universal ancestry. ivp academic. v2018i1 volume 1, issue 1 a proposed framework for cellular evolution albert d. g. de roos doi: 10.33014/issn.2640-5652.1.1.deroos.1 abstract this article shows how a good understanding of the design principles that underlie life is crucial in understanding its evolution. it gives concrete examples on how designs can be applied to evolution in the same way an engineer uses designs in creating building or bridges, or a software engineer that designs programs that can evolve. if we apply the notion of a design for evolution and realize that it is in its basis an evolving system of molecular machines, we can start to reverse engineer evolution and understand life. this article shows scenario’s for the origin of life and cellular life and how eukaryotic cells evolved to multicellular organisms. the driving force for evolution would be the intrinsic capability of the molecular machines to evolve and this basic tendency to evolve its ultimate goal. the scenarios that can be deduced following a design framework are drastically different from the theories that have been proposed so far. based on the premise that that evolution can be modeled on a design framework, we can deduce that life evolved inside-out and that ontology reflects phylogeny on a molecular basis 1 evolving machines 1.1 evolution of the eukaryotes in order to understand life and its evolution, we first have to see how living organisms function. the cell is the main building block of all organisms and is in itself a small molecular machine, illustrated nicely by the cell cycle. in higher multicellular organisms, the cells have specialized and formed into organs and limbs but the cell remains the main building block. the mechanistic organization of multicellularity can be easily seen when we look at development from a fertilized egg to an organism. the evolution of life starts with the evolution of the cell, specifically the eukaryotic cells that contain a nucleus and forms the basis of all higher life. this paper concentrates on the evolution of the eukaryotic cell, which includes not only all plants and animals, but also protists such as algae and yeast. 1.2 cells are molecular machines the basic premise underlying the study of design in evolution is that the eukaryotic cell is basically a small molecular machine where the components are formed by molecules. cell membranes are formed by lipid bilayers, the cytoskeleton is made up of protein fibers, our genetic material is made up of a double stranded helix. there is machinery that can assemble these materials illustrated by cell division showing a carefully orchestrated sequence of mechanical events. in this process of cell division, dna has to be replicated, the nuclear membrane dissolved, chromosomes condensed and aligned, the replicated chromosomes need to be pulled apart, the nuclear membranes reformed and the physical split of the two daughter nuclei. it is not hard to see this as a purely mechanistic process with many checkpoints, regulators, machinery, feed-back and feed-forward loops and self-assembly of machinery. the question for evolution is how this system evolved and how the molecular components were assembled over time. 1.3 development represents a mechanistic cycle just as the cycle of individual cells, the development of an organism from fertilized egg to the adult organism is also a purely mechanical process. based on the genetic blueprint containing the information for the protein components and the assembly of the organism, development consists of selfassembly, feedback and feedforward loops and self-learning systems. the sequence is put in motion be the fertilization of the egg until the adult organism where, several genes have to be activated at specific point in time of development. in humans, development involves the coordinated and timely activation of 100,000 genes over a period of more than 50 years. this process is tightly regulated with checkpoints and many other regulatory processes that check certain condition before progressing cell division and organ formation. the evolution of such a multicellular system adds another dimension to evolution, because we look at the assembly of the organism over time. 6 a proposed framework for cellular evolution 1.4 the life cycle as vehicle for evolution the life cycle of an organism is defined from the single cell or fertilized egg, all the way through development and ultimately to the rise of another new organism by fertilization. every life cycle has to end with the birth of a new organism and the organism should always reach the reproduction phase in order to complete the cycle. each step or life cycle has the potential to add extra functionality and thus evolve, but throughout evolution the development of fertilized egg to mature organism has to be fully functional. any functionality that would cause a cell or an organism to cease functioning and to interrupt the reproductive cycle would stop to exist. this essential functional continuity is an important (design) constraint for evolution implying that all the steps in evolution must each give rise to a fully functional organism or cell system. drastic redesigns are impossible in evolution as they would certainly break the functional continuity principle. 1.5 incremental development in line with the principle of functional continuity, evolution can be seen as the incremental expansion of an existing system. the components of the system are re-assembled during development and with every life cycle, there is the potential for new functionality. mutations in the genetic material can give rise to new sorts of protein that can give rise to new components of the system. all the changes that have occurred in evolution and that give rise to the specific developmental pattern that is encrypted in the genome of the cell, for eukaryotic cells mainly in the chromosomes in the nucleus. in this sense, evolution can be regarded as a molecular machine (an organism) that can self-assemble itself in each life cycle with the potential to add new functionality on top of the existing functionality. since the blueprint of the self-assembly is contained in the genome (dna), the expansion of the blueprint in time is what we call evolution. 1.6 the software development life cycle we can compare the stepwise evolution of the molecular machine we call life with the step-wise development of a software program. with each cycle in software development some extra programming for new functionality is done resulting into a new functional release. we want to create of system with many functional modules that has evolved from previous less complex stages. if we model evolution on building software, we would start with some simple code that creates a program but that we build incrementally. with each software cycle we would create a working product unto which to build further and each iteration of the software should be fully functional. in software development, we work with concrete design and design patterns in order to build complex software systems that continue to keep working with increasing complexity. in order to use the analogy of software design to evolution, we have to specify a similar framework or model that will represent evolution. 1.7 a concrete design paradigm for evolution the basic premise in this article is that a design framework similar to the concepts used in engineering and exemplified in complex it-systems and software development can be used to model evolution. the working hypothesis in the research presented here is that evolution can be modeled on the software design methodology ’design-by-contract’, the basic design underlying complex software systems. a strict implementation of design-by-contract is enforced by the condition that earlier ’contracts’ must always be respected otherwise the premise of functional continuity will be breached. evolution of such a system can then take place in different manners for instance by the creation of completely new functional modules build on top of others, or by hierarchical extension of existing interfaces. based on the same requirements, basically functional continuity in evolving systems, the concrete design patterns used in software development can therefore also be used for modeling evolution. 2 software design patterns there are many similarities between software design and evolution. except for a more general architecture of incremental development as we have seen as the basic principle behind evolution, several design patterns that are relevant for evolution can also be discerned in software development. here, some of them are described. mostly, they represent common patterns in engineering that are formally conceptualized in software design. 2.1 modularity in many ways, the requirements for the evolution of life are similar to those of modern software design. software systems often start small but soon extra functions are needed volume 1, issue 1 3. the origin of life 7 or existing ones need to be changed. as the system grows by adding new functions, it becomes more and more difficult to change the system. changes in one part may have an effect on other parts and can therefore have unintended consequences. this makes that we want to have a system that is robust yet flexible. in computer science, these requirements are usually implemented by having modular design in which function al modules communicate with each other through interfaces. by hiding the complexity within each module, we can reduce the overall complexity of the system. modularity is something we also expect in evolution as it allows independent evolution of subparts. 2.2 system expansion through design-by-contract the problems of increasing complexity in a system that needs to be robust, flexible and resilient have been addressed in software development by using the design-bycontract methodology. it works by dividing the system in functional modules that communicate with each other in a specified way, a sort of contract that both parties need to adhere to. the only thing a module has to know about other parts of the system is through this interface and as long as you do not change the way you communicate, each function can evolve independently. the reason that established interfaces cannot be changed is because downstream processes rely on that interface. if you change them, all processes that are dependent on it, may not work anymore. for evolution that we also see as an expanding system of functionalities, it means that all processes or functional modules that are added later in evolution will be dependent on earlier interface and therefore difficult to change. 2.3 encapsulation in software design, the term encapsulation is used when a functional layer is added as a layer on top of the old layer without replacing the old layer. this is for instance very useful when dealing with legacy systems that function correctly and that we do not want to replace. for instance, instead of using the old command-line interface in ms-dos, we can introduce a graphical windows layer on top that will translate the commands for us. another example is the internet itself that uses in its basis (and in its origin) a simple protocol that sends binary data over a network. once that was established, other layers were added to route the data through more complex networks and to give instructions to higher level systems. thus, by layering functionalities on top of each other, we can create complex systems that are robust as long as we keep existing (lower level) interfaces intact. for evolution, encapsulation would provide a way to keep existing functions by wrapping them with new, more modern functionality. legacy systemssystem that are developed using the designby-contract methodology leave older interfaces intact causing the system not only to be robust but also inflexible. older parts of the system cannot be changed anymore because of the dependencies of new functionality upon these older parts of the systems. many software systems contain old subsystems that were developed some long ago but could never be changed because the code is essential and changing it could cause them not too work anymore because of the many dependencies. in other words, the functional continuity of the entire system could not be guaranteed by redesigning the core part. an example is the old cobol code for banking systems that were developed in the 70s but are still in use until a complete redesign is warranted. in evolution, there is no redesign possible as it would breach the functional continuity that is needed. the risk of changing them for the stability of the systems prevents changing them. 3 the origin of life 3.1 the central dogma of biology in analogy with software development, if we want to unravel the origin of life we should first define the functional modules and their interfaces, in this case the molecular counterparts of modules and interfaces. as the basic structural entities underlying life, we can discern the double-stranded dna as the carrier of the genetic information, the singlestranded rna that can both function as a ribozyme and as a template for translation into proteins. the molecular machinery for dna replication, for transcription and for translation can be considered the functional modules. the interfaces between these three functional modules are the double-stranded dna helix with the four bases (atcg), and the single-stranded rna with the four rna bases (aucg) as template for translation into proteins. this configuration is called ’the central dogma of biology’. 3.2 evolution of the dogma of biology if we look at the dependency and the relations between the functional modules of the central dogma, we can deduce the sequence of evolutionary events. dna is transcribed into 8 a proposed framework for cellular evolution rna that functions as the code (interface) for the proteins translation, so double-stranded dna had to be first to have evolved. from this initial dna, single-stranded rna was derived which first functioned as catalytic rna. using the catalytic characteristics of single-stranded rna the first proteins were made using single-stranded rna (mrna). thus, we can directly reverse engineer the steps in evolution from the developmental steps, just by studying the interfaces and their dependencies. the general rule here is that we look at the flow in development steps (dsdna to ssrna to protein) to deduce the evolutionary steps. 3.3 double-stranded dna all life is based on double-stranded dna and it is therefore important to see how this double-stranded dna could have evolved in the first place. dna is composed of nucleotides that have the tendency to stick to other types of nucleotides. nucleotides can also form covalent bonds between them, so that they can form strands. the combination between single-strand formation and hydrogen-bonding between the nucleotides can make that the strands bind to complementary strands of dna forming a double-stranded dna. thus, the double-stranded dna can be formed based on the basic characteristic of nucleotides to form covalent bonds between nucleotides and hydrogen bonds between complementary nucleotides. nucleotides and their capability to form covalent bonds and their intrinsic tendency to form complementary strands can form the first interface for life. although it is thought that rna would precede dna as a prebiotic molecule, they have similar characteristics and a later change to dna would not affect any interfaces based on rna. 3.4 replication of dna replication of dna is based on the characteristic of dna that it can form its own template, but in order to replicate the strands have to be separated. the covalent bonds between the nucleotides that form the single-stranded dna are quite strong, but the hydrogen bonds between different strands can be broken more easily for instance by heating the double-stranded dna. this process is also called melting of dna and yields two separate strands of dna. the melting of dna can be done by an increase in temperature, but also through the action of proteins. as proteins were not present at the origin of life, melting by an increase in temperature is likely to be the first way of separating the two strands for replication. the day/night cycle may have provided the necessary heating and cooling of an original dna mixture for early life, similar to the pcr reaction in which dna is replicated in a laboratory. even though the replication process is now facilitated by proteins, its basic mechanism has not changed. 3.5 transcription of dna into rna if we look at the current events in the life cycle of an organism, we see that apart from serving as its own template for replication, single-stranded rna is also generated from the same template. mechanistically in an abiotic cycle, the formation of single stranded rna can be relatively easy accomplished by partially melting of the dna and the ’replication’ of the exposed single-stranded dna. this process is not fundamentally different from what happens in transcription where the dna is partial single-stranded (in the transcription bubble) so that genes can be transcribed. single-stranded rna is directly transcribed from the double-stranded dna and can function by itself as a catalyst (hence the term catalytic rna) or as a template for proteins in a separate process. throughout evolution, the transcription process has not been changed fundamentally and the interface (double-stranded dna that codes for single-stranded rna has not changed. 3.6 protein translation from mrna the input for protein translation by the ribosome is singlestranded rna, also called messenger rna. the ribosome is the machinery that does the translation and adds specific amino acids based on the genetic code to a growing chain of protein. as we have seen, ribozymes can also be derived from double-stranded dna and ribozymes could thus have been involved in the first translation to proteins. in fact, the ribosome has many rna components and can be considered a ribozyme in its core. for evolution, this also shows a logical sequence of events, where first ribozymes were derived from the double-stranded dna template which formed the machinery to start using singlestranded rna as a template for proteins. here we see that the same template (ssrna) can be used to evolve different functionalities while keeping existing interfaces intact. the evolution to protein generation can be seen as an independent functional module. 3.7 evolution of the dogma of biology if we look at the dependency and the relations between the functional modules of the central dogma, we can deduce the volume 1, issue 1 4. early genome building 9 sequence of evolutionary events. dna is transcribed into rna that functions as the code (interface) for the proteins translation, so double-stranded dna had to be first to have evolved. from this initial dna, single-stranded rna was derived which first functioned as catalytic rna. using the catalytic characteristics of single-stranded rna the first proteins were made using single-stranded rna (mrna). thus, we can directly reverse engineer the steps in evolution from the developmental steps, just by studying the interfaces and their dependencies. the general rule here is that we look at the flow in development steps (dsdna to ssrna to protein) to deduce the evolutionary steps. 3.8 the first legacy system we see that although the implementation of the functional modules has changed, their interfaces have not changed. dna replication is now much more efficient than in the early years with many more proteins and cofactors involved, but the basic interface (template-based replication) has not changed. although there were more modern and efficient functions implemented over time, its basic interfaces were kept intact. once the central dogma was established all subsequent functions, whether it is bacterial growth or the formation of multicellular organism would depend on the formation of catalytic rna and proteins. in all life forms, the central dogma still holds and can thus be considered the first legacy system. these basic interfaces simply could never change because it would break the rule of functional continuity. everything else is based on these original and additional layers of functionality have been built on top of this, as you would expect in a system that is based on a modular design based on design-by-contract. 4 early genome building design-by-contract divides a system into functional modules and their interfaces. the modules perform a certain task in the system and communication between modules is through defined interface. design-by-contract states that these basic interfaces cannot be changed once established and we applied this concept to the evolution of the central dogma. here we see how a complex genome can be formed based on the central dogma while applying designby-contract and the rule of functional continuity. 4.1 exon concatenation if we look at dna and its structure, there is a clear modularity at the gene level. the gene as a functional module that codes for a protein and its interface consists of the promotor with the start codon and the introns and the exons. within the gene, the different exons can also be regarded as functional modules as they can be combined to give different proteins when spliced into an intronless mrna. the splicing machinery as functional module has a clear interface: single-stranded rna with introns and exons are used as the input and messenger rna without introns is the result. intron splicing, or exon concatenation is a way to form complex (multi-exon) genes without changing the original interface. single-stranded rna is still derived from the double-stranded dna and the ribosome still works with the same template. the concatenation of exons creates new multi-exon proteins while leaving all other systems intact ensuring functional continuity. 4.2 exon and gene shuffling once the system has evolved multi-exon genes, further combinations of a limited number of functional and structural exon modules can create a large set of different proteins. introns and other non-coding sequences provide recombination points that make the shuffling of genes and exons feasible. higher level shuffling can be performed when complete protein modules composed of multiple exons are shuffled made possible by the modular structure of genes and exons. the exons are recognizable in the strands of dna by a nucleotide sequence in the intron that demarcates the exons and the entire exon modules would function in another gene. transfer of parts of genes with their promotor regions that demarcate the start of a gene, allow transferred genes to be transcribed without needing extra signals. the modular structure of genes thus allow for quick expansion of the genome and its concomitant expression of proteins. 4.3 posttranslational modifications the ribosome translates messenger rna into proteins and is unaware whether the mrna contains introns. alternative splicing and exon shuffling were able to diversify the number of proteins without affecting protein translation itself. also after translation, the cell has evolved mechanisms to expand the total number of functions of proteins by posttranslational modifications, for instance by adding several chemical groups. using the original machinery that transcribes mrna from dna and that translates mrna to 10 a proposed framework for cellular evolution proteins, an enormous diversity of proteins can be created without changing these basic steps. this is done by leaving the earlier interfaces intact in line with the design-bycontract paradigm and adding extra functionality on top of the existing system. 4.4 an expanding molecular system in eukaryotic cells, there are mechanisms for splicing and alternative splicing, but also for gene recombination and gene hopping. these mechanisms can be seen as the vehicles for the evolution of new proteins. active mechanisms for gene recombination could have quickly generated a diverse gene population with only a limited set of functional exon modules. there could also be many other active processes that are involved in an active expansion of the genome during evolution. crossing-over during meiosis in the germ line cells is mechanism that creates recombinations. there are enzymes (telomerases) that are involved in extension of the chromosomes and they could have created space for new proteins. facilitated by the modular structure of the genome, active recombination mechanisms can drive genome while maintaining functional continuity. in other words, due to active gene recombination mechanisms, the genome can be considered to be self-evolving. 5 the origin of the nucleus the nucleus is a membrane-enclosed organelle found in all eukaryotic cells. it contains most of the cell’s genetic material, organized as multiple long linear dna molecules in a complex with a large variety of proteins, such as histones, to form chromosomes. the genes within these chromosomes are the cell’s nuclear genome. the main structures making up the nucleus are the nucleolus, the nuclear envelope and the nucleoskeleton (which includes nuclear lamina). the structure and relationship between these functional units and the nucleus can give insight in the stepwise evolution of the nucleus. 5.1 the nucleolus as first replicating unit in the evolution of the nucleus, we start with replicating strands of dna that can produce ribozymes and proteins as we have discussed in the previous chapter. we can relatively easy start extending this system into a more complicated structure by adding a microenvironment of protein fibers, dna, ribozymes and ribosome components. proteins can give the dna structural support and that create a microenvironment that would facilitate duplication. the nuclear matrix, a scaffold of proteins could serve as such a protective layer around the dna and would lead to a structure that we now call the nucleolus. such a system that is based on the protein components that the early translation machinery can produce would be the first step to a primitive cell. this nucleolus would be composed of a pool of dna that produces its own individual environment. 5.2 the appearance of the nuclear lamina from the nucleolus as the first compartmentalized structure that contains dna, the next layer would be the extension of nuclear matric proteins around the nucleolus. the nuclear matrix is a scaffold of protein fibers that surrounds the nucleolus and this would create an additional (protective) protein layer that could create the environment for additional processes. on top of this fiber scaffold, the nuclear lamina can be formed as a distinct protein scaffold that can form a semi-permeable barrier resembling the current nucleus but without the nuclear membrane. at that moment, a primitive cell is formed that consists of a replicating chromosome embedded in permeable, multiple layers of protein scaffolding. since the proteins for the nuclear lamina originate from dna genes, the early genome can develop its own environment. 5.3 self-assembly of lipids on protein scaffold lipids play an important role in the biology of the cell and many chemical reactions take place with the help of lipids. also, lipids have the ability to form vesicles and membranes to form a specialized microenvironment. the evolution of lipid generating proteins could lead to microvesicles that could facilitate replication and these vesicles could be associated with the nucleolus and the nuclear matrix. at a high enough density and by the expression of certain nuclear lamina proteins, these vesicles could fuse on top of the nuclear lamina and form the first nuclear membrane. the evolutionary steps in the formation of the nucleus can be seen at cell division, where the nuclear membrane is dissolved into vesicles and reforms after the cell division. thus, by expressing a set of proteins, a self-assembly of lipids on the nuclear lamina the nucleus could have formed as the first membrane-surrounded cell. volume 1, issue 1 6. the eukaryotic cell 11 5.4 the nucleus as an independent organism the first ’cell’ with a membrane in evolution would in our model consist of the nucleus and would precede the eukaryotic cell with a plasma membrane. it would be an independent unit that contained all the information to replicate itself. if the dna is replicated, this nucleus could physically divide into two nuclei as we see with each mitosis. in this scenario we see the nucleus as an independent unit that can replicate itself into to other nuclei since each genome can generate its own proteins for the nuclear matrix and formation of a nuclear membrane. the independence of the nucleus as an independently replicating unit is seen in the development of drosophila. here, the nucleus of the fertilized egg divides numerous times within the cytoplasm, generating a large number of nuclei within a single cytoplasm. later, these nuclei organize themselves, mainly guided by an extranuclear network into mononuclear cells. the nucleus can then be seen as replicating itself into two within the cytoplasm and in principle independent from the division of the eukaryotic cell itself. 5.5 the nucleus as a legacy system the scenario presented here indicates that the nucleus evolved inside-out and started with the nucleolus upon which literary new layers of functions were added that resulting in the nucleus as an independent unit. we then see various structural and functional components in the nucleus that are functionally and structurally dependent on each other. next to the distinct entity of the nucleolus, we discern the larger nuclear matrix and finally the nuclear lamina as a protein sheath that encapsulates the chromosomes and ribosomes. during the evolution to the eukaryotic cell, the nucleus and all previous processes layers remain intact. the entire nucleus of eukaryotes can therefore be considered a legacy system that functionally stays intact during the entire path of eukaryote evolution. 6 the eukaryotic cell we saw that we can stepwise build up a simple proto-cell that evolved into a self-contained replicating unit: the nucleus as the first real cellular life. the next major step in the evolution of life was the evolution of the plasma membrane that surrounds the nucleus. from the distinct functional components we can deduce the evolutionary events to generate the main components of the eukaryotic cell. 6.1 formation of endoplasmic reticulum (er) the er membrane is contiguous with the nuclear membrane which means that it shares its membrane and their membranes can be seen as a single continuum. in evolution the transition to the er could be made when the nuclear membrane started ’blebbing’ into membrane lamellae into a special compartment which became later the er. membrane blebbing can occur by the expression of membrane proteins and therefore, this step could thus be evoked by the novel expression of a single new protein in evolution. the generation of a separate lipid environment outside of the nucleus would allow many new functions to evolve. for instance, protein translation could be done more efficiently at the er. the disassembly of ribosome subunits in the nucleus and the subsequent transport of these units to reassemble at the er illustrate this process. 6.2 the formation of a cytoskeleton the eukaryotic cell consists of the nucleus surrounded by the cytoskeleton which provides structure but also a microenvironment for cellular processes. a first step to such an extranuclear environment could be the extension of protein fibers from within the nucleus trough the nuclear pores. this would give the nucleus already protection and anchor points for specific energy-rich environments. later in evolution, when extranuclear (cytoplasmic) translation at the er could take place, the cytoskeleton could evolve into a more complex protein scaffold. the nucleus would be suspended in its own cytoskeleton that it generated from its genome. each nucleus would then have its cytoskeletal coat which would define the boundaries of the cell, similar to the drosophila cells in the syncytial blastoderm. 6.3 formation of the plasma membrane starting from a nucleus with an extracellular matrix and an er, the last step in the evolution of the eukaryotic cell could be the formation of a plasma membrane on top of the cytoskeleton. we see the dependency between the er and the plasma membrane as the er and the endomembrane system feed directly into the plasma membrane. within the eukaryotic cell, vesicles bud off from the er/golgi and fuse with the plasma membrane to increase the surface of the cell. a plasma membrane could have formed in evolution in two steps. first vesicles started budding of the er by expression of new proteins that facilitated budding. second, vesicles could start fusing onto the cytoskeleton to form 12 a proposed framework for cellular evolution a plasma membrane, also facilitated by the expression of novel proteins. 6.4 conclusion the design framework and the resulting new insight in the path of evolution can therefore present a new set of paradigms for new evolutionary theories. the first one is that evolution can be modeled on a design framework which enables us to deduce evolutionary events. the second is that life evolved inside-out and started by the stepwise formation of the nucleus and was followed by the formation of the er, the cytoskeleton and the plasma membrane. volume 2, issue 2 news blyth institute paper highlighted in mathematics magazine the standard notation for higher-order di!erentials (the liebniz notation) does not allow di!erentials to be used in an algebraic manner (multiply, dividing, canceling, etc.). last year, a blyth institute researcher published a new notation for di!erentials that allow them to be algebraically manipulable (bartlett and khurshudyan, 2019). recently, this paper was highlighted in mathematics magazine, a publication of the mathematics association of america (campbell and rosenthal, 2019), in their “reviews” section. the review validated the overall the results of the paper, saying, “the authors make a strong case for a clear and honest notation that facilitates working with di!erentials.” while the reviewers agreed with the fact that the new notation makes working with di!erentials more straightforward, they thought that, for teaching, it “is probably just as confusing for students as the shorthand expression.” blyth institute researcher publishes paper on active information in biology blyth institute director jonathan bartlett published a new paper earlier this year on using the concept of active information in biology. active information was originally developed for evolution simulations, such as avida and the ev system, to measure how much information the simulation writers added to the system (dembski and marks ii, 2009). essentially, active information was developed as a way of measuring “cheating” on the part of programmers trying to demonstrate natural selection with code. in “measuring active information in biological systems,” bartlett decided to turn the metric onto living organisms, to provide a mechanism to see how much their evolution was actually governed by darwinian mechanisms and how much of it was guided by mechanisms of variation built in to the organisms themselves (bartlett, 2020). while it has been known for a while that there are mutational mechanisms within genomes, it takes a lot of time and money to tease them out. essentially, this measurement can be used to determine whether a mutational mechanism is worth investigating, or if it should be just considered “spontaneous.” if an organism’s mutations displays significant active information for a selection pressure, this is good evidence that there is a mechanism worth discovering that is producing those mutations. a followup note on this paper by the author is available in this issue. new era of research in active information in addition to the applications of active information to biology in the previous news item, there has been a renewed interest in active information from other parties as well. so far, two other active information papers by daniel andrés díaz-pachón and robert j marks ii have been published in the journal bio-complexity. the first one extends active information into unbounded domains (díaz-pachón and marks ii, 2020b). the second one uses active information to compare neutral and selective evolution (díazpachón and marks ii, 2020a). additionally, active information has shown to be a useful concept generally in statistical investigations. a trio of authors from the biostatistics and engineering departments of university of miami published a paper describing the usage of active information in hypothesis testing and its relationship to type-i errors (díaz-pachón, sáenz, and rao, 2020). the same group also developed a general method of statistical mode-hunting using active information (díazpachón, sáenz, rao, and dazard, 2019) which has been utilized in data mining software such as primsrc (dazard et al., 2015). 50 news blyth institute assists with n95 mask shortage most people are aware that the covid-19 pandemic has caused a shortage in n95 masks. private citizens have stepped into the breach by 3d printing various types of ppe equipment on home 3d printers. the blyth institute has been helping out by helping individuals who are printing masks increase their printing capacity. we would like to thank everyone who is doing the printing for their hard work and e!orts in this time. we would especially like to thank the front-line medical workers for whom this equipment is made. thank you for standing in the gap for us all. references bartlett, j (2020). “measuring active information in biological systems”. in: communications of the blyth institute 2020.2, pp. 1–11. doi: doi:10.5048/bioc. 2020.2. bartlett, j and a zh khurshudyan (2019). “extending the algebraic manipulability of di!erentials”. in: dynamics of continuous, discrete and impulsive systems, series a: mathematical analysis 26.3, pp. 217–230. campbell, p j and e s rosenthal (2019). “reviews”. in: mathematics magazine 92.5, pp. 396–397. doi: 10 . 1080/0025570x.2019.1673628. dazard, j et al. (2015). “r package primsrc: bump hunting by patient rule induction method for survival, regression, and classification”. in: jsm proceedings, section for statistical programmers and analysts, pp. 650– 664. dembski, w a and r j marks ii (2009). “conservation of information in search: measuring the cost of success”. in: ieee transactions on systems, man and cybernetics a, systems & humans 5.5, pp. 1051–1061. doi: 10.1109/tsmca.2009.2025027. díaz-pachón, d a and r j marks ii (2020a). “active information requirements for fixation on the wright-fisher model of population genetics”. in: bio-complexity 2020.4, pp. 1–6. díaz-pachón, d a and r j marks ii (2020b). “generalized active information: extensions to unbounded domains”. in: bio-complexity 2020.3, pp. 1–6. díaz-pachón, d a, j p sáenz, and j s rao (2020). “hypothesis testing with active information”. in: statistics and probability letters 161. doi: 10.1016/j.spl.2020. 108742. díaz-pachón, d a, j p sáenz, j s rao, and j dazard (2019). in: applied stochastic models in business and industry 35.2, pp. 1–18. doi: 10.1002/asmb.2430. https://doi.org/doi:10.5048/bio-c.2020.2 https://doi.org/doi:10.5048/bio-c.2020.2 https://doi.org/10.1080/0025570x.2019.1673628 https://doi.org/10.1080/0025570x.2019.1673628 https://doi.org/10.1109/tsmca.2009.2025027 https://doi.org/10.1016/j.spl.2020.108742 https://doi.org/10.1016/j.spl.2020.108742 https://doi.org/10.1002/asmb.2430 about this journal the purpose of the journal paper submission policies other journal content from the editors annie crawfordannie crawfordmetaphor and meaning in the teleological language of biology introduction the history of teleology in the biological sciences teleological language is essential to biology if teleological language is essential to biology, then life must be teleological conclusion: life all the way down salvador cordovasalvador cordovafisher's fundamental theorem of natural selection isn't fundamental after all introduction: the problem of defining fitness absolute ``darwinian'' fitness vs. relative fitness mean and variance of relative fitnesses numerical examples to illustrate fisher's theorem discussion conclusion eric hollowayeric hollowaytutorial: bioinformatics basics introduction genetic code and sequence translation sequencing and assembly accessing data finding things with blast summary letters and notes eric hollowayyou cannot get meaning from randomness jonathan bartlettactive information is a specified complexity model eric hollowayevolution in the valley of illusions jonathan bartlettis active information applicable to biology? eric hollowayempirical active information news login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians v2i1 32 letters and notes for example, beings (as well as possible beings and things impossible of being) can be understood in the context of possible worlds. a “possible world” is a su!ciently complete description of possible states of a"airs described through chains of propositions. we may observe that things impossible of being, such as a square circle, have in them mutually inconsistent required core attributes; they cannot be realised in any possible world. possible beings would exist in at least one possible world were it actualised. for instance, a contingent being b that depends on c might exist in a world w and not in a closely neighbouring one w ! if c is present in w but not w !; c thus being an enabling, necessary causal factor for b. by contrast, a necessary being f will exist in all possible worlds, showing itself to be a framework element for such a world. a key insight is that for any world w to be distinct from w ! it requires some factor a in w that is absent in w !. we may then partition the factors of w as w = {a|¬a}. after partitioning, we will have two distinct groups—the factor a and all of the factors which are not a. the null set corresponds to zero. each particular set in the partition can be counted as the number one, and the combination of both partitions (even in a single world where a is an empty set) is two. thus, for any particular possible world w , the quantities 0, 1, 2 are necessarily present. taking the von neumann construction, immediately we find n, thence (using additive inverses) z, so also (taking ratios) q and (summing convergent power series) r; where z provides unit-stepped mileposts in r. that is, a structured core of quantities will be present in any w , and we may regard mathematics as the study of the logic of structure and quantity. extensions to the hyperreals r" follow by construction of some h that has as reciprocal h = 1 h closer to 0 than 1 n for any n in n. therefore, relationships and linked operations across such quantities will also be present, or may be constructed as needed. illustrating, after abraham robinson (robinson, 1966), hyperreals allow calculus to be treated as extensions of algebra in r". thus, while bare distinct identity and coherence focused on quantities will not cause things by the inherent potential or action of such entities, they instead are logical constraints on being and are tied to what can or must be or cannot be or happens not to be. so, too, we may see that the abstract logic model worlds that we may construct then lead to key entities that if necessary are framework to any possible world; thus applicable to our common world. by contrast, if certain quantities and relationships are merely part of the contingencies of some w !! that is close enough to our own, they may provide adequate analogies for modelling. as a result, we have good reason to expect that mathematical reasoning and core entities will in many cases be highly relevant to and have powerful predictive power for our common world. robinson, abraham (1966). non-standard analysis. amsterdam: north-holland publishing company. wigner, eugene (1960). “the unreasonable e"ectiveness of mathematics in the natural sciences”. in: communications in pure and applied mathematics 13.1, pp. 1–14. doi: 10.1002/cpa.3160130102. independence conservation and evolutionary algorithms eric holloway doi: 10.33014/issn.2640-5652.2.1.holloway.2 levin’s law of independence conservation leonid levin’s 1984 article (levin, 1984) is the first to this author’s knowledge to prove a fully stochastic conservation of information law. levin titled his law ’independence conservation’ which he considered fairly obvious, describing it as “torturing an uninformed witness cannot give information about the crime!” levin’s law is not well known, which is unfortunate since the more commonly known conservation laws are focused either only on the random or deterministic case. levin’s law is remarkable because it unifies both the random and deterministic cases, showing that the combination also cannot result in information increase. the second remarkable thing about his law is how easy it is to prove, given some preliminaries about algorithmic information. volume 2, issue 1 independence conservation and evolutionary algorithms 33 algorithmic information theory background first is required the notion of algorithmic information, which is defined on bitstrings. algorithmic information is the length of the shortest program that generates a particular bitstring. k (x) := min y |u (y)=x |y |. (1) the shortest program is itself known as the elegant program for that particular bitstring. each bitstring has a unique elegant program. y" := arg min y |u (y)=x |y |. (2) all programs either terminate after a fixed amount of time, or never terminate. all the programs in question are known as prefix free, which means that no terminating program begins another terminating program. algorithmic mutual information is the length of this program if we are also provided another bitstring as input, subtracted from the length if we are not provided the extra input bitstring. i (x : y) := k (y) # k (y |x). (3) unfortunately, this basic definition of algorithmic mutual information is only symmetric under a logarithmic error, because we have to mark where one bitstring starts and the other ends. this requires a number of bits logarithmic on the size of the shortest bitstring, which is x in this case. i (x : y) # i (y : x) = o(log(x)). (4) we can improve the definition of algorithmic mutual information to be completely symmetric under a constant that is independent of the bitstrings we are looking at, which in other words means we don’t have to worry about the constant and the algorithmic mutual information is symmetric as far as we are concerned. this improvement is to use the elegant program of the input bitstring instead of the bitstring itself. i"(x : y) := k (y) # k (y |x"). (5) since the elegant program halts once it has generated the input bistring, we know we can start on the next bitstring, so we avoid having to encode the bitstring length. this saves us from having to use the logarithimic term. i"(x : y) # i"(y : x) = o(1). (6) one final fascinating point on algorithmic information is that we can also use it to create a universal distribution. m(x) := 2#k (x) . (7) “universal” means is that we have a distribution that provides the highest probability for every bitstring possible, within a multiplicative constant, under the assumption that we are only dealing with computable generating sources for the bitstrings. m(x) $ p(x) "o(1). (8) the computable distribution assumption is a reasonable assumption for dealing with physical phenomena, since (as far as we know) everything physical can be modeled to theoretically perfect accuracy with enough computational resources. proving levin’s deterministic law alright, so now onto proving levin’s law. we first start with a simple lemma, that providing more information can only decrease conditional algorithmic information. in other words, the more we know about y, the less information we need to describe y. k (y |x) $ k (y |x, z) +o(1). (9) we now introduce another simple lemma that with a program to generate x, namely z which we execute with turing machine u to generate x, x = u (z), (10) 34 letters and notes we can generate both x and z. thus, the joint information is the same between z and x, z. k (z) = k (x, z) +o(1). (11) this also means to generate the triple {y, x, z} we only need y and z. k (y, x, z) = k (y, z) +o(1). (12) since it is the case that k (y |x, z) = k (y, x, z) # k (x, z). (13) then performing replacements to equation 13 with equations 11 and 12, we get k (y |x, z) = k (y, z) # k (z) (14) = k (y |z). (15) combining equations 9 and 14 shows us that x can never tell us more about y than z. k (y |x) $ k (y |x, z) (16) = k (y |z). (17) we can then use equation 16 to show running a program f on i does not increase mutual information with y. the notation u ( f .i) to mean we’ve run program f with input i using a universal turing machine u. first we decompose the mutual information. i"( f (i) : y) = i"(u ( f .i) : y) (18) = k (y) # k (y |u ( f .i)). (19) (20) now, we set z = f .i and x = u (z) = u ( f .i), and then apply equation 16 to equation 18. i"( f (i) : y) = i"(x : y) (21) = k (y) # k (y |x) (22) % k (y) # k (y |x, z) (23) = k (y) # k (y |z) (24) = i"(z : y) (25) = i"( f , i : y). (26) giving the final concise result, i"( f (i) : y) % i"( f , i : y). (27) this equation 27 states that executing function f on input i does not produce any more information about y than the function and input before they are executed. in other words, running a program doesn’t produce any information. proving levin’s random law now with the deterministic version out of the way, we can move onto the random version. the random version asks, what if we generate f randomly, could that result in an information gain? this question is based on the fact that generating f randomly will result in an f with a lot of algorithmic information, since it will be incompressible. so, even though running u ( f .i) doesn’t give us anything new, the initial selection of f may start us o" with a good amount of information about y. levin’s second step in proving the random law shows this intuition is false. to prove the second law, we will rely on the dominance property of the universal distribution in equation 8. ! f p( f )i"( f , i : y) = ! f p( f ) log2 m( f , i |y) m( f , i) (28) % ! f p( f ) log2 m( f , i |y) m( f )m(i) (29) % log2 ! f p( f )m( f , i |y) m( f )m(i) (30) % log2 " f m( f , i |y) m(i) (31) = log2 m(i |y) m(i) (32) = k (i) # k (i |y) (33) = i"(i : y) (34) volume 2, issue 1 crowdrank: a simple ranking algorithm for crowdsourced rating systems with uneven participation 35 which gives us the result that randomly generating an f is not expected to provide any information about y. ! f p( f )i"( f , i : y) % i"(i : y). (35) to wrap up the independency conservation law, we apply equation 27 to equation 35. ! f p( f )i"( f (i) : y) % ! f p( f )i"( f , i : y) % i"(i : y). (36) evolutionary algorithms what sort of impact, if any, does the law of independency conservation in equation 36 have on evolutionary algorithms? one of the simplest implications is that if there is a target area independently designated by y, then it is not possible to randomly evolve population i towards y without any fitness information. however, there are also implications even if there is fitness information provided for the evolution of i. let’s say that f represents one round of an evolutionary algorithm applied to i, which consists of the following steps: 1. crossover population 2. vary population 3. select population i is defined as a population of bitstrings selected at random. we then define y as the set of bitstrings rated at a certain level of fitness. part of f stays constant, and another part is varied randomly, such as mutation and which bitstring sections are crossed. we denote the random part as r. this gives us a surprising result. ! r p(r)i"( f (i, r) : y) % i"( f , i : y). (37) equation 37 states that each round of randomized evolution provides no further information about the fitness region y than already existed in the initial conditions of the original population i and the evolutionary algorithm f . thus, this equation proves that evolutionary algorithms cannot generate algorithmic mutual information, even in regards to regions specified according to fitness. levin, leonid a (1984). “randomness conservation inequalities; information and independence in mathematical theories”. in: information and control 61.1, pp. 15–37. crowdrank: a simple ranking algorithm for crowdsourced rating systems with uneven participation jonathan bartlett doi: 10.33014/issn.2640-5652.2.1.bartlett.3 introduction public rating systems are di!cult to score well. voting systems tend to simply favor what is already popular. averaging systems tend to have significant variance if there are not enough people scoring. for instance, let’s say that i run a songwriting contest and have 100 entries. i then put it out to a public vote on the internet to see who wins. most people are not going to listen to all 100 songs. if i do a simple “thumbs up” approach and count how many votes a song has, then whichever songwriter has the best existing following will simply tell their fans to vote for them, and it will simply devolve into a popularity contest. let’s say instead i do a rating system where you can rate a song between 0 and 100. now, songs by popular artists will actually be negatively weighted because they will have more visibility for negative ratings. it is not hard for a few votes to be all 100s, but it is hard for a thousand votes to be that way. thus, those who have fewer ratings have an advantage. v1i2 volume 1, issue 2 generalized information a straightforward method for judging machine learning models jonathan bartlett and eric holloway doi: 10.33014/issn.2640-5652.1.2.bartlett.1 abstract generalized information (gi) is a measurement of the degree to which a program can be said to generalize a dataset. it is calculated by creating a program to model the data set, measuring the active information in the model, and subtracting out the size of the model. active information allows gi to be usable with both exact and inexact models. 1 introduction in machine learning and other forms of statistical inference, the goal is to create a model that matches the data. a model is essentially a function which takes a certain number of inputs and generates an output value. the input is whatever parameters the statistical model is allowing, and the output is the prediction, classification, or whatever the model is meant to identify. as a simplified example, let’s say that you are a realtor and you want to know the impact of square footage and the year a home was built on its selling price. given a large amount of data, a machine learning package might find a way to model that data, so that, if you give it an input which is not in the set, the system will spit out for you what it thinks the selling price will be. 2 the problem of overfitting exact fits of models to data are not necessarily preferable in machine learning. such models are often said to be overfit. overfitting occurs because not all data is actually signal. nearly any dataset will contain some amount of noise. if your model makes an exact fit to the data, that means that much of your model is actually modeling the noise. modeling the noise actually causes poor performance as the model is extended out to new data points. for the purposes of this paper, noise can either be statistically random events (variations around a mean) or even non-noise features, but whose predictive inputs are not included in the set of inputs being modeled. in the realtor example above, let’s say that most homes in the 1,000-1,200 square feet area that were built in 1975 were selling for $150,000, but one house, which was 1,175 square feet, sold for $75,000, because the homeowner desperately needed to sell it quickly. if the model attempted to have an exact model, that particular data point would cause bad predictions for square footages for that year (and possibly surrounding years). thus, overfitting a model means that both data and noise are included in the model. the goal, therefore, is to find a way to tell if a given model matches the data in the correct way. to do this, we will explore the question of models from a philosophical standpoint, and use those results to come up with a mathematical definition of a good model. 3 what is a model? what is the goal of modeling? for most people, the goal of making a model is to enable prediction of points that we don’t have. for instance, in the real estate model example, the goal is to be able to determine, as best we can, what the unknown price points will look like. we already know what the existing points are. if all we wanted to do was know what different square footages in different years sold for in the past, we don’t need a model, we only need a lookup table. now, obviously, machines can’t predict the future. we do not expect our predictions to work if the very basis of what is happening in our dataset changes. for instance, we would not expect a model to continue to function if a community implemented price controls for homes. therefore, a model has an inherent presumption that future data will have the same essential patterns as current data. 14 generalized information 4 picking models there are innumerable ways to pick models. given any discrete dataset, there are literally infinite models that can be made to match them. therefore, given an infinite selection of choices, how does one decide which model is the best model for a given set of data? as an example, figure 1 shows a set of points. these points can be given by the following list of data pairs: (42, 21), (40, 20), (30, 15), (24, 12), (36, 18), (14, 7), (12, 6) (1) now, as mentioned, if we want to generate a model for these points, there are actually an infinite number of models to choose from. one model (shown in figure 2) can be given by the equation x7 − 198x6 + 16364x5 − 729288x4 + 18855360x3− 281625984x2 + 2241146880x − y7 + 99y6 − 4091y5+ 91161y4 − 1178460y3 + 8800812y2 − 35017920y− 7258507200 = 0. (2) another model (shown in figure 3) can be given by the equation, y = x 2 . (3) yet another model (shown in figure 4) can be given by the equation x7 − 198x6 + 16364x5 − 729288x4 + 18855360x3− 281625984x2 + 2241146880x − y9 + 100y8 − 4190y7+ 95252y6 − 1269621y5 + 9979272y4 − 43818732y3+ 92171520y2 − 57153600y − 7315660800 = 0. (4) keep in mind that all of these models are perfect fits to the original dataset, and there are infinitely more models available to choose from. while it may seem intuitively obvious which of these models should be chosen, more difficult cases make intuition more problematic. therefore, we have to establish specific criteria for choosing models. the one we intuitively think of as the best fit is (3) (figure 3). notice that this is also the shortest description of the data. one consistent theme of the theory of inductive inference through the ages is that, when deciding between two equally-explanatory theories, the shortest one is the best. this has been expressed by aristotle (“the more limited, if adequate, is always preferable”), ptolemy (“we consider it a good principle to explain the phenomena by the simplest hypothesis possible”), occam (“plurality must never figure 1: example set of data points figure 2: a basic curve model volume 1, issue 2 5. finding generalizations 15 figure 3: a line model figure 4: a complex curve model be posited without necessity”), and newton (“we are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances”). this principle is generally known by the name “occam’s razor” (borowski, 2012). the underlying strand in all of these is to never make something more complicated than necessary. while it may be difficult to judge between two models that explain different subsets of data (though we will tackle this question in section 7), if two theories are exactly equivalent in explaining known data, this principle definitely prefers the one that is simpler. keas (2018) provides a detailed account of how this criteria has worked in the history and philosophy of science. since computer models are encoded in bits, we actually have an objective way of measuring the size (and, correspondingly, the simplicity) of the model. therefore, if two models are equivalent in prediction, the one which can be encoded in the fewest bits is to be preferred. this ability to connect model size to occam’s razor was first identified by solomonoff (solomonoff, 1964a; solomonoff, 1964b). solomonoff induction has been used as the basis for a number of machine learning induction techniques, including pac learning, occam learning, and others (a comparison of the present approach with these is given in section 12). 5 finding generalizations the methods described in section 4 allows us to distinguish between two possible models. however, while it does allow us to determine if one model is better than another, it does not give any information about whether or not a model is a “good” model in an absolute sense. look again at figures 2 and 4. even if we didn’t have the model in figure 3, both of these seem ridiculously overcomplex for the given data. that is, neither of them is a good model for the given data, even if they are being compared against each other. to understand why this is the case, take a look at the data points given in (1). now, take a look at (2) and (4). in both of these cases, the equations are longer than the original data set.1 however, the equation that seems to be a better model is (3). in this case, at least from an initial look, the model is shorter than the data that is modeled. 1while we haven’t specified a specific mechanism for measuring these size of equations, for these particular equations, pretty much every means available for measuring their size will be longer than the original data set. 16 generalized information we will call a model that is shorter than the data that it is modeling a generalization. generalizations are important because only generalizations represent real learning. this can be understood just from thinking about the problem itself. for any given set of data points, the data points could be treated as a mapping of input to output. therefore, the data points themselves act as a model for themselves. since occam’s razor measures models comparatively, we already have the data points themselves as a one possible model for the data. therefore, any proposed model must be smaller than the data points themselves. we will call a model that is smaller than the data points themselves a generalization. this is the first iteration of the concept we will construct. generalized information (ig) is the difference between the size of the data points and the size of the model. therefore, in this first formulation, if d is the data and |d | is the size of the data in bits, and m is the model and |m | is the size of the model in bits, then ig = |d | − |m |. (5) this measures the amount of generalization that a model provides for its data.2 in this formulation, when ig is positive, m provides a generalization of d. when ig is zero or negative, m does not provide a generalization of d. 6 output prediction dimensionality the one thing to consider about the model given in the previous section is that, since it uses data points, it is ambivalent as to which direction the prediction occurs in. that is, given n-dimensional data, one can use the data points to arrive at results from any n − 1 dimensions given. so, if our data consisted of homes with the year that it was built, the square footage, and the price it sold at, we presumably would want to know the price based on the year it was built and the square footage. however, there is nothing preventing us from looking up the square footage based on the price and the year it was built, or looking up the year it was built from the price and the square footage. however, many machine learning models are non-reversible. that is, if the goal is to determine the final price, and the 2there are some important caveats here, but the goal is to focus on the philosophical underpinnings rather than technical minutiae. in any case, for this to be sound, all data should be given in prefix-free formats, and |d | will also have to include some constant number of bits to convert d from pure data into a model. model is trained to look for a final price, the model cannot be used to take a final price and square footage and solve for the year. in many machine learning systems, you would have to build separate models for each direction of the data. therefore, for an n-dimensional system, you would need n models of the training data in order to match the original success of the data points. this means that we need to modify (5) in order to account for this. for a simple version, you can simply divide |d | by the number of dimensions, which would lead to ig = |d | n − |m |. (6) however, more specifically, you can think of the dataset itself divided by dimensions, where each dimension has its own size specification. therefore, in most machine learning systems, the model is only able to output a single dimension, which we can consider the “output” dimension. therefore, we can be even more explicit about the model size based on this dimension, yielding ig = |dout | − |m |. (7) 7 dealing with fuzzier models not every model is an exact fit for data. however, not every model needs to be an exact fit. if the goal is to avoid modeling noise, then some amount of discrepancy between model and data needs to be allowed for. the goal, then is to transform the ideas present in (5) and (7) so that they continue to apply to noisy data. active information is a simple and straightforward way to measure the amount of information that a model models (dembski and marks ii, 2009). first we will understand active information on its own, original terms, and then we will apply this to the study of generalized information. 7.1 active information basics imagine that we are looking for a particular card in a standard deck—we’ll use the king of diamonds for this example. active information says that the endogenous information (iω) is the probability that we will find the card by random guessing, expressed in bits.3 the probability for finding the king of diamonds in a deck in a single random guess is 1 52 , which is approximately 5.7 bits. 3if p is the probability, − log2 (p) is the probability expressed in bits. volume 1, issue 2 8. a simplified example and application 17 now, let’s say that someone has outside knowledge of how this particular card deck is organized. they tell you (correctly) that the king of diamonds is one of the first four cards. now, we can create a directed search that picks one of the first four cards at random. this new search probability, termed exogenous information (is) is 1 4 , which is 2 bits. the active information (i+) is the amount of information that my search strategy applies to the problem at hand. active information is given simply as i+ = iω − is (8) if active information is positive, then the search strategy is helping you, but if active information is negative, then the search strategy is hurting you. 7.2 bitwise active information active information is normally applied to complete results—that is, the chance of guessing a number correctly, or guessing a number within a boundary of error, etc. however, active information can also be applied in a bitwise manner by simply applying active information to the probability of guessing each bit correctly. therefore, if we have a target bitstring of 01001100101, we can measure the amount of active information in a generated bitstring 01001100111. the endogenous information present in the first bitstring is simply the number of bits—11 bits (i.e., − log2 !" 1 2 #11 $ ). the exogenous information present in the algorithm that generated the second bitstring can be found by first looking at the probability. the second bitstring hit the target 10 11 times. therefore, the exogenous information is − log2 !" 10 11 #11 $ = 1.5 bits. therefore, the active information in the algorithm that generated the second bitstring is 11 − 1.5 = 9.5 bits. 7.3 applying active information to fuzzy models if we are going to allow for models which have a fuzzy relationship to the actual output, we need a mechanism of also discounting the allowed model size. active information can be applied by reducing the measured size of our output dimension based on the active information in the result. active information can be applied to models in the following way—it is the ability for a model to improve the guessing on data outcomes. imagine that the outcomes of the known dataset were guessed at.4 what is the probability of guessing the results at random? this represents iω. now, imagine that we use model m to improve our guessing. what is the new probability of guessing the result? this represents is . therefore, the amount of data that is modeled by our model is the active information, i+. when using this for a generalization, we only care about the size of the actual modeled information, i+. therefore, we can use this idea to transform (7) into a more nuanced equation, ig = i+ − |m | (9) we can see that, for the case where we have an exact model, (7) and (9) are equivalent.5 if our search allows for exact guessing, then there is no exogenous information in the search. in other words, is = 0. therefore, all that is left is iω, which, with only guessing, is the size in bits of the data. therefore, iω will be the size of the data itself (at least in the output dimension). for reversible models of n dimensions, the active information from each dimension can be summed up for a total model size, yielding ig = ! " % x∈n i+ (x)#$ − |m |. (10) 8 a simplified example and application to see how this works, imagine a dataset of 400 entries. each data point will be a simple boolean true/false bit, with the input being simply the index of the bit. for this dataset, random guessing will achieve a 50% probability of a correct answer for each bit, yielding an endogenous information of 400 bits for the whole dataset. program z1 reproduces the 400 bits exactly, and |z1 | is 260 bits. program z2 reproduces the 400 bits with 99% accuracy, and |z2 | is 190 bits. both of these programs generalize the data (|z1 | < 400 and |z2 | < 400), but which one generalizes the data better? 4note that we can use either regular active information or bitwise active information for this. 5to see this more explicitly, remember i+ = iω − is . iω will be the size of the result (the output dimension) in bits, which is simply |dout |. if the result is exact, then is = 0. thus, i+ = |dout | − 0 = |dout |. 18 generalized information for z1, ig = 400 − 260 = 140 bits. for z2, since z2 is not an exact match to the data, we need to calculate its active information. iω will be the same. since the model moves the probability for each bit to 99% accurate, the exogenous information (is) is − log2 " 0.99400 # ≈ 5.8 bits. therefore, the active information (i+) in this model will be i+ = 400 − 5.8 = 394.2 ≈ 394 bits. (11) therefore, since |z2 | = 190, the generalized information will be ig = 394 − 190 = 204 bits. (12) because the ig of z2 is greater than the ig of z1, this means that z2 is a better generalization of the data, even though it is less accurate. z1 is at risk of slight overfitting, because the gain in accuracy is more than offset by the increase in the complexity of the model. thus, generalized information allows weighing between generalization and accuracy in models. it provides a philosophically coherent scoring system which weighs together accuracy and model size to determine which models are to be preferred over others, and which models should even count as generalizations at all. 9 generalized information and knowledge let us write ig (m, d) as the amount of generalization a model m has about dataset d. in this framework, knowledge can be represented as the following limit: lim |dout |→∞ ig (m, d) = ∞ (13) in other words, if a generalization can be applied to a theoretical infinite number of data points, it is knowledge. note that this definition of knowledge does not require exactness, since generalized information does not require exactness. it merely requires that increasing the amount of data without bound also increases the amount of generalization of the model. under this system, classical physics, despite it not being an exact description of reality, is considered knowledge, because the same model continues to generalize more and more points as the dataset gets larger. additionally, we can be certain that if knowledge about a topic can be found, then, with a large enough sample size, it can be generalized through generalized information. that is, if we are able to form a model of an item of knowledge, then it is covered by a fixed size program. if knowledge is defined to be the continued applicability of a model to an infinite size of data, and the model is of a fixed size, then that means that we will have generalized information available in the limit. therefore, there is some quantity of data for which a knowledge-oriented model provides generalization. interestingly, this also means that, given enough data, the most size-efficient model is not even necessary. that is, if the ideal model is mi , but a poorly implemented model mp has the same accuracy but is inefficiently coded (i.e., it is coded using three times amount of code), given sufficient data, mp will also be a generalization. in short, if knowledge can be had through a model, it will show generalized information on a sufficiently large dataset. 10 why generalization works montañez (2017) points out that all machine learning systems work only because of the existence of a bias. he paints compression-based learning systems with skepticism because, in theory, for any particular arrangement of codes, the desired ordering of codes may put the longer ones first. what makes the present model different is that it does not approach machine learning with the assumption that the hypothesis space is adequate. instead, it presents a way of testing if a given hypothesis can be defensibly considered to have generalized the training data. for any particular mappings of codes to functions, the training data may not be sufficient to generalize. thus, the ability to find an appropriate hypothesis under generalized information may not be available. however, in section 9, we pointed out that, if an appropriate model exists at all, there will be some size of training data for which the model will provide compression. since montañez focused on finite sets of data,6 this would not be true for his system. a way of understand the relationship between generalized information and the results of montañez is to say that generalized information provides a way of knowing whether or not your dataset is sufficiently large to provide enough information to the hypothesis space to be confident that the hypothesis is doing its job. in other words, generalized in6section 3.1 of montañez (2017) says, “we limit ourselves to finite, discrete search spaces, which entails little loss of generality when considering search spaces fully representable on physical computer hardware within a finite time.” volume 1, issue 2 12. comparison with other machine learning systems 19 formation is able to detect whether or not the bias in the hypothesis space has sufficient mutual information with the training set in order to have confidence that a given hypothesis likely also shares some amount of mutual information with the underlying data set. it does not say anything about whether or not a given hypothesis space is sufficiently biased in order to do this with a particular size of training data, or even if the underlying structure to the system can be modeled with a finite model in the hypothesis space. generalized information does not say that a model that does not exhibit generalized information is incorrect. rather, it says that there is not sufficient data to know, based on the data itself, that it is true. for instance, if we are given only a single data point, since it is presumably based on some real phenomena, there is some model about that data point that is true. if a good model is selected, then that model will continue to be true for future data points. however, it is impossible to tell from that single point whether or not the model matches the data sufficiently. a given modeller may know from other information they know about the problem whether or not the model is correct, but not from the data itself. generalized information tells you the cutoff point for when you can know, based on the data itself, when generalization is occurring. 11 benefits of generalized information generalized information offers several benefits over other inferential models. as noted in section 4, generalized information is not the first inferential system to utilize occam’s razor as a foundation stone. however, generalized information offers several benefits, including: • it provides a minimum threshold for establishing whether a model is a valid generalization of the dataset. • the techniques are grounded philosophically—each step is the result of philosophical analysis of the goals we are trying to achieve. • the techniques are straightforward—only the most basic information theory mathematics are required to perform them. • the techniques are adaptable—it is not dependent on any particular type of model being used. • generalized information allows use of more data— generalizations can be made using the entire dataset.7 7in typical machine learning techniques, some of the data has to be additionally, while a thoroughly rigorous application of these ideas in software may require a good amount of programming effort,8 a “good enough” approach is fairly straightforward to implement. the amount of active information can be determined statistically, and the data size and model size can both be evaluated simply by checking storage size inside the program itself. 12 comparison with other machine learning systems the first thing to note about generalized information is that it is not necessarily in competition with other machine learning systems. in fact, generalized information does not specify either (a) the nature of training algorithm, or even (b) the nature of the model being used. generalized information, as such, is fully compatible with any training algorithm or any model. generalized information is only a test of the outcomes of a machine learning system. for instance, for a decision tree, generalized information would take into account the number and size of nodes (i.e., the model size) and compare it to its accuracy on the training data. however, some machine learning systems do provide opportunities for comparison. for instance, take the k-nearest-neighbor (knn) algorithm. for this algorithm, the model is the training data. therefore, according to generalized information, a naive implementation of knn cannot exhibit generalized information. however, knn could be tweaked to do so. for instance, one could establish a subset of training data that performs sufficiently well in order to be considered a generalization. many statistical tests have been established to compare two alternative models, and decide which one is more likely to be the true model, even based on model size. the vuong closeness test, for instance, compares two models, taking into account the number of parameters in each model. many other similar criteria are available, including the akaike information criterion, the bayesian information criterion, and others (sayyareh, obeidi, and bar-hen, 2011). in the machine learning field, the principle of solomonoff induction inspired several systems including pac-learning (valiant, 1984) and minimum description length (grünheld back in order to test the model on the data. since this technique focuses on generalization rather than prediction, all of the data can be used. 8here, i am considering such problems as converting all data values to prefix-free formats, identifying a fixed language for a model, establishing the program size for converting a dataset into a model to determine |d |, etc. 20 generalized information wald, 2005). these have very similar characteristics to the statistical criteria listed above, in that they base their model selection on some combination of model size and accuracy. there are three primary advantages to generalized information against all of these other criteria. 1. these criteria only work for parameterized models, while generalized information can operate with any type of model, as long as it can be evaluated for a size (which means any computer-implementable model). 2. these criteria are only relative comparisons. that is, they compare models against each other, not against some absolute standard. generalized information establishes a minimum criteria which must be achieved— the size of the training data itself. additionally, using active information, this size can be adjusted based on the degree of accuracy which is attained. 3. generalized information is a much more straightforward test. it is understandable by nearly anyone with the slightest background in information theory or computer programming, while the other tests require much more advanced knowledge of statistics. additionally, knowing why generalized information works can be done without hardly any mathematics, as this present paper demonstrates. interestingly, since generalized information is modelagnostic, all of these criteria could be extended with at least part of generalized information by constraining models to a maximum model size based on the size of the training data available and the accuracy of the model. 13 potential problems several potential problems exist with this framework. the first and most obvious one is whether or not limiting the size of the model to the size of the output dimension as discussed in section 6 is the correct procedure. while it appears to be correct from a variety of angles (i.e., reconstructing all output dimensions allows use of the entirety of the training data size), it does seem that the allowable model size should include some amount of size from the input dimensions, since, after all, it will be using those dimensions in calculating the output dimension. another one is calculating accuracy. that is, with a naive approach, all failures are equivalently failing. this is not an essential problem with the model, as it is based on the output encoding. a simple naive output encoding could be squished into a binary output, but this prevents one from knowing “how far” off the algorithm is. an alternative output encoding could put more weight on more significant figures, and less weight on less significant figures, such that results that are “near” can match more bits than those that are “far.” additionally, this model needs to be subject to empirical verification. currently, it exists only as an idea, and needs to be applied to specific problems to demonstrate that it can indeed prevent overfitting and demonstrate generalizations as claimed. 14 future applications of generalized information generalized information can be used anytime someone wants to judge between actual fits between model and data and post-hoc curve fitting. the primary target considered here is for machine learning models, however, it can be applied to a number of similar situations. for instance, this technique could be used as a replacement for p-values in statistical inference. p-values do not take into consideration the model size used to establish the inference. thus, generalized information can prevent the problem of p-value hacking in many statistical applications. that is, imagine that someone pulls in a huge number of datasets in order to hack a false statistical correlation. with generalized information, there would need to be sufficient information within the model to choose which statistics are to be used for correlation, thus depressing the p-value of the result. statistically, p < 0.05 should be roughly equivalent to ig > 4.322. finally, work needs to be done on establishing a baseline language for this type of modeling. in the limit (see section 9) it doesn’t matter what language is used for the model, as long as the language selection is independent from problem selection. however, for practical purposes, it would be helpful to have a unified, efficient language that could be used for general comparisons. acknowledgements the author would like to acknowledge robert marks, winston ewert, george montañez, andrew jones, george volume 1, issue 2 references 21 hunter, william dembski, and mike keas for feedback on early versions of this manuscript. references borowski, s (2012). “the origin and popular use of occam’s razor”. in: sciencia. url: https://www.aaas.org/ origin-and-popular-use-occams-razor. dembski, w a and r j marks ii (2009). “conservation of information in search: measuring the cost of success”. in: ieee transactions on systems, man and cybernetics a, systems and humans 5.5, pp. 1051–1061. grünwald, p (2005). “introducing the minimum description length principle”. in: advances in minimum description length: theory and applications. ed. by p grünwald, j myung, and m a pitt. mit press, pp. 3– 22. url: https://arxiv.org/pdf/math/0406077. pdf. keas, m n (2018). “systematizing the theoretical virtues”. in: synthese 195 (6). url: https://link.springer. com/article/10.1007/s11229-017-1355-6. montañez, g d (2017). “why machine learning works”. phd thesis. carnegie mellon university. sayyareh, a, r obeidi, and a bar-hen (2011). “empirical comparison between some model selection criteria”. in: communications in statistics—simulation and computation 40, pp. 72–86. solomonoff, r (1964a). “a formal theory of inductive inference, part 1”. in: information and control 7.1, pp. 1– 22. url: http://raysolomonoff.com/publications/ 1964pt1.pdf. solomonoff, r (1964b). “a formal theory of inductive inference, part 2”. in: information and control 7.2, pp. 224–254. url: http : / / raysolomonoff . com / publications/1964pt2.pdf. valiant, l g (1984). “a theory of the learnable”. in: communications of the acm 27.11, pp. 1134–1142. url: http://web.mit.edu/6.435/www/valiant84.pdf. volume 2, issue 2 evolution in the valley of illusions 41 there is no scaling constant at the beginning—the scaling constant is simply one. therefore, active information fulfills the requirements for a canonical specified complexity model. generalized information (gi) measures the amount of generalization that a model achieves for a dataset. gi allows for judging machine learning models in the face of model errors by using active information as a discounting mechanism (bartlett and holloway, 2019). the simplified form of gi is simply the di!erence between the active information and the program length in bits (!). "! = "+ ! !. (3) we can rewrite this as follows: "! = ! log2 ! #($) %($) " ! log2 (2"), (4) = ! log2 ! #($) %($) " ! log2 (2"), (5) = ! log2 ! 2" #($) %($) " . (6) as you can see, 2" serves as the scaling constant &. as mentioned before, # # d%($) = 1. since any program will have a length ! " 0, this means that 2" " 1. this means that gi also serves as a specified complexity model. bartlett, j and e holloway (2019). “generalized information: a straightforward method for judging machine learning models”. in: communications of the blyth institute 1.2, pp. 13–21. doi: 10 . 33014 / issn . 2640 5652.1.2.bartlett.1. dembski, w a and r j marks ii (2009). “conservation of information in search: measuring the cost of success”. in: ieee transactions on systems, man and cybernetics a, systems & humans 5.5, pp. 1051–1061. doi: 10.1109/tsmca.2009.2025027. montañez, g d (2018). “a unified model of complex specified information”. in: bio-complexity 2018 (4), pp. 1– 26. doi: 10.5048/bio-c.2018.4. evolution in the valley of illusions eric holloway doi: 10.33014/issn.2640-5652.2.2.holloway.3 evolutionary algorithms are inspired by the biological theory of evolution. these kinds of algorithms are called optimization algorithms. they are meant to find ’good enough’ solutions to problems by searching through a combination of possible solutions and evaluating each solution by some objective function. the two tenets of evolutionary theory is that change to the genome are performed without information about what makes a fit organism. the adjustment for fitness is made by the environment selecting organisms that manage to survive and reproduce. this simple procedure is assumed to be responsible for the extraordinarily complex biological organisms we see all around us (including ourselves) that greatly exceed anything humans can engineer. in fact, many cutting edge human inventions, such a sonar, electricity and motors have already been invented many millions of years ago by evolution. additionally, when consideration of time and oportunities to evolve have been taken into account, the equivalent computation is not too far out of reach of our modern super computers. thus, it would seem that we almost automatically create phenomenal inventions automatically just by copying the simple evolutionary process. with mendel’s discovery of genes, this simplified the situation even more. instead of having to deal with messy analogue systems, evolution was reduced to variations on discrete modules. these modules were simplified even more through the discovery of dna, and the institution of the fundamental dogma, which is that information only flows from the dna sequence to the organism. the organism is said to have no ability to reverse the flow of information to modify its dna in anticipation of environmental changes. this is a restatement of darwin’s notion that variation is random in that it occurs without any foresight. we now know the fundamental dogma is not quite airtight, and is in fact fairly leaky. the discovery of horizontal gene transfer shows that the dna can be edited directly in a variety of di!erent ways. so, there are potential ways for the flow of information to be reversed back into the genome. for example, at the rna level, viruses frequently modify their own genetic code, and this mechanism allows them to adapt to new species through a process known as zoonosis. https://doi.org/10.33014/issn.2640-5652.1.2.bartlett.1 https://doi.org/10.33014/issn.2640-5652.1.2.bartlett.1 https://doi.org/10.1109/tsmca.2009.2025027 https://doi.org/10.5048/bio-c.2018.4 https://dx.doi.org/10.33014/issn.2640-5652.2.2.holloway.3 42 letters and notes a simple evolutionary algorithm but, let’s return back to evolutionary algorithms. these algorithms are based on the original darwinistic formulation that mutation occurs randomly. the potential solutions are usually represented as binary strings, but sometimes the encoding is much more sophisticated. the algorithm usually use some mechanism that is considered to be evolutionary, such as randomly mutating bits in the binary string, combining multiple strings with crossover, or even some variants of horizontal gene transfer. then, once a new set of candidate solutions are created, their ‘fitness’ is measured with the objective function, and then a subset of the solutions are selected based on fitness for the next round. as an example, figure 1 shows a very simple evolutionary algorithm written in python, used to solve a bin packing problem. this particular problem has useful applications. for instance, if you want to optimize what todo tasks to do, where each task has a time cost and a value associated, and there is a limited amount of time to do the tasks. we can also imagine the evolutionary utility of solving this problem. when being chased by a predator, an animal needs to correctly rank its various actions appropriately to maximize survival probability. if the animal decides to perform an elaborate mating dance while being chased, it is a goner. so, this simple problem actually turns out to be key for the reproductive survival that drives evolution. building block hypothesis john holland, the inventor of the “genetic algorithm,” came up with a theory as to why these algorithms work. he thought that good solutions could be built up from worse solutions through the composition of “building blocks.” the thought was that the reliance on building blocks reduced the search space and thus allowed the algorithm to find good solutions more quickly. however, as the no free lunch theorem proves, while this hypothesis is valid for some scenarios, it is not valid in general, and building blocks in fact can bias an algorithm towards bad solutions. deceptive landscapes this problem of bias towards bad solutions is known as the “deceptive landscape.” in this scenario, the evolutionary algorithm is lead along a “road” of incrementally better and better solutions by minor modifications to previous solutions. however, eventually the road leads to a cli!, where any modification to the solution drastically lowers the solution fitness, resulting in a halt to any further searching. this is related to the problem of local optima, where if we envision the search landscape as a real, physical landscape, with hills and valleys, the search process can be a ball we are trying to roll to the lowest part on the landscape, but it can get stuck in dips that are still fairly high up on the hills. the usual approach to solve this problem is to jostle the ball a bit to get it out of the dip. the deceptive road is a variant where the ball falls into a really deep pit such that no amount of jostling can get it out, and the pit is still really high up on the hill. here is one example of a deceptive landscape that we can plug into our evolutionary algorithm. 99 options receive a reward of 1, but the last option gets a reward of 10,000,000. the last option is the only option needed, but we will see evolution drives the solution to ignore the enormous reward in favor of a more piddly reward. you can see the result in figure 2. durations = [1] * 99 + [ timeframe ] values = [1] * 99 + [ 10000000 ] this landscape makes it almost impossible for the evolutionary algorithm to find the optimal solution since the structure of the landscape biases the algorithm to add more elements to the collection when what it should be doing is removing all elements except the element with the highest score. what does this mean? in arguments for evolution, it is often assumed that as long as some genetic code generates a functional organ important for survival, the environment will select towards that code, and with enough opportunities the organism’s genome will make all the necessary random baby steps to get to the target. richard dawkins makes this argument in the blind watchmaker. on the other hand, this article shows that “survival benefit = generated by evolution” is not a forgone conclusion. one might think that since animals evolved then what we observe is merely the successful paths. but, this makes the fallacy of a"rming the consequent, that because a implies b, then observing b implies a. we can only draw this conclusion if evolution is the only possible explanation; essentially a tautalogy. however, if we start o! with the a priori assumption that evolution is the only possible explanation, then we have crossed over from the realm of science to dogmatism. volume 2, issue 2 evolution in the valley of illusions 43 figure 1: python evolutionary algorithm from random import randint cnt = 100 durations = [ randint (1, 10) for _ in range (cnt)] values = [ randint (1, 10) for _ in range (cnt)] timeframe = 400 def fitness ( solution ): total_duration = 0 for i, d in zip(solution , durations ): if i == 1: total_duration += d if total_duration > timeframe : return -1 total_value = 0 for i, v in zip(solution , values ): if i == 1: total_value += v return total_value def mutate ( individual ): pos = randint (0, len( individual )-1) new_ind = [v for v in individual ] new_ind [pos] = randint (0, 1) return new_ind genome = [ randint (0, 1) for _ in range (cnt)] print (’start fitness : ’ + str( fitness ( genome ))) iterations = 300 for _ in range ( iterations ): new_genome = mutate ( genome ) if fitness ( new_genome ) > fitness ( genome ): genome = new_genome print (’ending fitness : ’ + str( fitness ( genome ))) 44 letters and notes figure 2: a deceitful landscape 0 200 400 600 800 1000 0 2 0 4 0 6 0 8 0 1 0 0 iteration f itn e ss 0 200 400 600 800 1000 0 2 0 4 0 6 0 8 0 1 0 0 iteration f itn e ss s im ila ri ty 0 2 0 4 0 6 0 8 0 1 0 0 genome fitness similarity to optimal is active information applicable to biology? jonathan bartlett doi: 10.33014/issn.2640-5652.2.2.bartlett.2 active information was originally introduced in 2009 by william dembski and robert marks ii (dembski and marks ii, 2009). active information identifies how much information that a search has compared to a “random search.” introduced in the context of information science, it was originally utilized towards identifying information sources in various computerized forms and simulations of evolution. the reason why active information works is because there is no general “best” algorithm for searching. a search that is good in one context will be terrible in another. there might be a best search for a particular situation, but not one that serves all situations equally. in fact, it turns out that, for any particular search situation, a random search has average performance characteristics compared to any other search algorithm. therefore, for any search situation, we have the capability of determining what the average success rate for a search should be (note that the success rate is how many times the search algorith has to “look” before finding a successful hit). if we simply perform a random search and measure successes, we can determine the average value. in terms of statistics, this average value is the expected value for the success rate for a search strategy chosen arbitrarily. that is, if the search strategy is chosen arbitrarily, we would expect that the success rate should be roughly equivalent to that of a random search. active information measures the distance between the success rate that we actually observe and the success rate that we would expect from an arbitrarily chosen search strategy. if this is measured prior to selection a!ecting the success rate, we can then measure the distance between the success rate that the cell’s own mutational machinery is having and the success rate that we would expect from arbitrary mutation strategies. this will tell us the amount of information that the cell’s mutational machinery has for finding a solution in a given selective process. recently, i demonstrated how this could be measured in biological systems, giving examples for how di!erent types of systems might be measured (bartlett, 2020). since this is a fairly new approach for thinking about mutations in the genome, there are many confusions about what is actually being claimed and proposed. this note intends to clarify, explain, and defend the notions presented in the paper. addressing misconceptions i want to start by clarifying that active information does not (a) hold that mutations form a uniform random distribution, (b) hold that mutations should form a uniform random distribution, or (c) hold that standard evolutionary theory holds that mutations should form a uniform random distribution. instead, active information attempts to simulate a uniform random distribution of mutations in order to get an expected value for the success rate of other mutational strategies. this follows not from evolutionary theory but rather from information theory, which states that such a search will give you the expected value for the success rate of other searches. this distinction is critical and forms the basis of the logic of applying active information to biology. another important clarification is that, as stated in the paper, it does not matter if evolution is ontologically a search. https://dx.doi.org/10.33014/issn.2640-5652.2.2.bartlett.2 about this journal the purpose of the journal paper submission policies other journal content from the editors annie crawfordannie crawfordmetaphor and meaning in the teleological language of biology introduction the history of teleology in the biological sciences teleological language is essential to biology if teleological language is essential to biology, then life must be teleological conclusion: life all the way down salvador cordovasalvador cordovafisher's fundamental theorem of natural selection isn't fundamental after all introduction: the problem of defining fitness absolute ``darwinian'' fitness vs. relative fitness mean and variance of relative fitnesses numerical examples to illustrate fisher's theorem discussion conclusion eric hollowayeric hollowaytutorial: bioinformatics basics introduction genetic code and sequence translation sequencing and assembly accessing data finding things with blast summary letters and notes eric hollowayyou cannot get meaning from randomness jonathan bartlettactive information is a specified complexity model eric hollowayevolution in the valley of illusions jonathan bartlettis active information applicable to biology? eric hollowayempirical active information news 44 letters and notes figure 2: a deceitful landscape 0 200 400 600 800 1000 0 2 0 4 0 6 0 8 0 1 0 0 iteration f itn e ss 0 200 400 600 800 1000 0 2 0 4 0 6 0 8 0 1 0 0 iteration f itn e ss s im ila ri ty 0 2 0 4 0 6 0 8 0 1 0 0 genome fitness similarity to optimal is active information applicable to biology? jonathan bartlett doi: 10.33014/issn.2640-5652.2.2.bartlett.2 active information was originally introduced in 2009 by william dembski and robert marks ii (dembski and marks ii, 2009). active information identifies how much information that a search has compared to a “random search.” introduced in the context of information science, it was originally utilized towards identifying information sources in various computerized forms and simulations of evolution. the reason why active information works is because there is no general “best” algorithm for searching. a search that is good in one context will be terrible in another. there might be a best search for a particular situation, but not one that serves all situations equally. in fact, it turns out that, for any particular search situation, a random search has average performance characteristics compared to any other search algorithm. therefore, for any search situation, we have the capability of determining what the average success rate for a search should be (note that the success rate is how many times the search algorith has to “look” before finding a successful hit). if we simply perform a random search and measure successes, we can determine the average value. in terms of statistics, this average value is the expected value for the success rate for a search strategy chosen arbitrarily. that is, if the search strategy is chosen arbitrarily, we would expect that the success rate should be roughly equivalent to that of a random search. active information measures the distance between the success rate that we actually observe and the success rate that we would expect from an arbitrarily chosen search strategy. if this is measured prior to selection a!ecting the success rate, we can then measure the distance between the success rate that the cell’s own mutational machinery is having and the success rate that we would expect from arbitrary mutation strategies. this will tell us the amount of information that the cell’s mutational machinery has for finding a solution in a given selective process. recently, i demonstrated how this could be measured in biological systems, giving examples for how di!erent types of systems might be measured (bartlett, 2020). since this is a fairly new approach for thinking about mutations in the genome, there are many confusions about what is actually being claimed and proposed. this note intends to clarify, explain, and defend the notions presented in the paper. addressing misconceptions i want to start by clarifying that active information does not (a) hold that mutations form a uniform random distribution, (b) hold that mutations should form a uniform random distribution, or (c) hold that standard evolutionary theory holds that mutations should form a uniform random distribution. instead, active information attempts to simulate a uniform random distribution of mutations in order to get an expected value for the success rate of other mutational strategies. this follows not from evolutionary theory but rather from information theory, which states that such a search will give you the expected value for the success rate of other searches. this distinction is critical and forms the basis of the logic of applying active information to biology. another important clarification is that, as stated in the paper, it does not matter if evolution is ontologically a search. https://dx.doi.org/10.33014/issn.2640-5652.2.2.bartlett.2 volume 2, issue 2 is active information applicable to biology? 45 many incorrectly reject the application of the mathematics of search to evolution on the basis that evolution isn’t truly a search for anything. whether or not that is true is irrelevant. evolution (or at least certain situations in evolution) matches the mathematical preconditions of a search, and, therefore, search mathematics applies whether or not it is a search ontologically. if an organism is undergoing selective pressure, we can define a “successful search” as an organismal configuration that relieves that selective pressure beyond a certain threshold. this is easiest to understand and measure when the selection is lethal. the search space (the genome), the search activity (mutation), and the search target (any genome configuration that relieves the selection pressure) are clearly defined. also note that some people incorrectly believe that the mathematics of search imply that we are looking for a specific target (i.e., dna sequence), or that we know what the target(s) (dna sequences) are ahead-of-time. this is not the case either. we merely have to have a well-defined definition of the target. in this case, it is a genome configuration that relieves the selective pressure. we identify it not by sequence (since we don’t know what sequence(s) that will be) but by result (relieving the selective pressure). methodological concerns one potential concern is that we are excluding the e!ects of the active information supplied by natural selection. the general method presented does not fall prey to that criticism, as it focuses on single-generation results (thus not allowing for natural selection to work). however, it is true that, if trying to apply active information to biology in some other way, this could be an issue. pachón and marks ii (2020) presents a way of calculating the active information of selection, which may point towards a way of measuring the active information in the biological system in experiments where selection also supplies active information as well. the active information supplied by selection may actually be a contributing factor to the success of e. coli developing the cit+ mutation described in “relative active information” section of bartlett (2020). further research will be required to determine how much of an impact this has on the calculation. another potential issue with the measurement technique presented in bartlett (2020) is that, to replicate to a population size adequate to perform the study, variation in the genome will already be introduced prior to the study in question. this might already introduce variety in the population that needs to be accounted for either experimentally or mathematically. a simple way to adapt for this is to begin with a replica plating technique to filter out colonies that already have a successful hit. how targeted is somatic hypermutation? bartlett (2020) also shows how, using certain assumptions, the active information calculation can be simplified. one particular simplification was given for the somatic hypermutation process. essentially, if it can be shown that a particular mutational system occurs by restricting the targets of mutation, and that the shortest mutational targets are contained within this restricted space, then a simplified calculation can be used based on the size of the genome, the size of the restricted mutational space and the number of mutations required to hit a target. some have called into question whether or not the somatic hypermutation process actually fits the given criteria. for instance, there is evidence that sometimes activation-induced deaminase (aid), the mechanism behind somatic hypermutation, sometimes hits targets outside of the space suggested by this characterization (see, for instance, álvarez-prado et al. (2018)). what is at issue is not the relevance of the simplified formulas to situations matching the criteria, but of whether or not the specific case of somatic mutation matches the criteria. additionally, the goal of the formula (and, in fact, any formula) is to generalize, so whether or not this criticism successfully prevents applying the simplified formula will depend on the quantity of exceptions. álvarez-prado et al. (2018) itself does not specifically address these issues, as it is itself working with a modified mutational process intended to identify potential aid targets from a biochemical perspective. in fact, the paper itself shows that the mutational process with all components intact actually removes the vast majority of “misses.” the biochemistry of aid acting alone targets a number of regions (275 identified by the paper), but the combination of aid with the other components of the mutational process limits the actual mutated targets (i.e., targets with an actual final sequence change) to only a handful (liu et al., 2008). since the mathematics of the process are based on orderof-magnitude reductions in search space, it is unlikely that having a handful of additional targets would actually significantly change the results, especially if they occurred at a lower frequency than those in the primary targeted area. thus, while it is certainly possible to be more precise in the measuring of active information of somatic hypermutation, 46 letters and notes it seems that being used as a simplified measurement is still well-justified. in fact, such papers as álvarez-prado et al. (2018) show how important the targeting is (justifying the criteria for using the formula), by showing the prevalence of cancerous e!ects of mistargeted mutations. isn’t this already well-known? one criticism is that we already knew that there are targeted mutations without active information. this is at least partially true. while there are groups who recognize this reality, many evolutionary biologists do not. in fact, i’ve talked with several practicing biologists (evolutionary, molecular, and otherwise) who were shocked to find out even that such phenomena existed. some were familiar with somatic hypermutation as a general idea, but had not mentally linked it to the question of directed mutation. many biologists still believe (and most textbooks still teach) that mutations are uncorrelated with their fitness e!ects. this could wind up being true or false in the general case. active information provides a mechanism for measuring this question from the data. however, the more important goal is not to determine the existence of such phenomena, but rather to be able to measure the phenomena. currently, directed mutations are only known after we know the mechanism in detail. the goal of active information is to provide a measurement prior to knowing the mechanism (in fact, specifically to see if there is a mechanism worth finding). there are some who agree that mutations are not uncorrelated with fitness, but don’t believe that comparing against a random background is a correct way to quantify the phenomena. however, i have not heard any such critic present an alternative means of quantifying directedness. i think the mathematics of active information (and the biological application of it) is su"ciently sound for experimental use. however, if there is a better means of quantification, i would be interested in comparing the two. additional notes the mathematics of bartlett (2020) are a little hard to follow, so i wanted to present a combined formula here. the meanings of the components of the formula are given in bartlett (2020). !+max = log2 ! "!1 #!1 " ! log2 #$ % "!2 #!2 ! "!1 #!1 (1 !$!) !$$ $! $! (1 !$$) &' ( (1) !+min = log2 ! "!1 #!1 " ! log2 #$ % "!2 #!2 ! "!1 #!1 (1 !$!) $! (1 !$$) &' ( (2) additionally, a supplementary spreadsheet to assist calculating active information using the techniques found in the paper is available (supplement 1), with example possibilities provided to give a feel for how di!erent outcomes a!ect active information.1 álvarez-prado, á f et al. (2018). “a broad atlas of somatic hypermutation allows prediction of activationinduced deaminase targets”. in: journal of experimental medicine 215.3, pp. 761–771. doi: 10.1084/ jem.20171738. bartlett, j (2020). “measuring active information in biological systems”. in: communications of the blyth institute 2020.2, pp. 1–11. doi: doi:10.5048/bioc. 2020.2. dembski, w a and r j marks ii (2009). “conservation of information in search: measuring the cost of success”. in: ieee transactions on systems, man and cybernetics a, systems & humans 5.5, pp. 1051–1061. doi: 10.1109/tsmca.2009.2025027. liu, m et al. (2008). “two levels of protection for the b cell genome during somatic hypermutation”. in: nature 451, pp. 841–846. doi: 10.1038/nature06547. pachón, d a díaz and r j marks ii (2020). “active information requirements for fixation on the wright-fisher model of population genetics”. in: bio-complexity 4, pp. 1–6. doi: doi:10.5048/bio-c.2020.4. 1supplement 1 is available online at https://journals. blythinstitute.org/ojs/index.php/cbi/article/view/68/66. https://doi.org/10.1084/jem.20171738 https://doi.org/10.1084/jem.20171738 https://doi.org/doi:10.5048/bio-c.2020.2 https://doi.org/doi:10.5048/bio-c.2020.2 https://doi.org/10.1109/tsmca.2009.2025027 https://doi.org/10.1038/nature06547 https://doi.org/doi:10.5048/bio-c.2020.4 https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/68/66 https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/68/66 about this journal the purpose of the journal paper submission policies other journal content from the editors annie crawfordannie crawfordmetaphor and meaning in the teleological language of biology introduction the history of teleology in the biological sciences teleological language is essential to biology if teleological language is essential to biology, then life must be teleological conclusion: life all the way down salvador cordovasalvador cordovafisher's fundamental theorem of natural selection isn't fundamental after all introduction: the problem of defining fitness absolute ``darwinian'' fitness vs. relative fitness mean and variance of relative fitnesses numerical examples to illustrate fisher's theorem discussion conclusion eric hollowayeric hollowaytutorial: bioinformatics basics introduction genetic code and sequence translation sequencing and assembly accessing data finding things with blast summary letters and notes eric hollowayyou cannot get meaning from randomness jonathan bartlettactive information is a specified complexity model eric hollowayevolution in the valley of illusions jonathan bartlettis active information applicable to biology? eric hollowayempirical active information news v1i2 volume 1, issue 2 the conscious unit (cu) model a preliminary outline of a new approach to consciousness sam s. rakover doi: 10.33014/issn.2640-5652.1.2.rakover.1 abstract the present paper attempts to handle the question how an unconscious mental state (ms) is transformed into a conscious-ms, by developing an outline of a new model, the conscious unit (cu) model. the essential assumption of this model is as follows: in the cognitive system exists an inborn, special linking-mechanism that connects a ms to a cu, i.e., a unit of consciousness (or a stream of such units when represented by the ms is complex). as a result, the individual becomes aware (conscious) of the ms representation. this model was applied successfully to certain empirical observations and to several problems, which were directed toward the higher-order (ho) theories of consciousness [especially the higher-order thought (hot) theory]. 1 introduction explaining consciousness is a core issue that has baffled philosophers and psychologists for decades. there is currently no accepted theoretical solution to this issue and the various existing explanatory attempts are under continuing debate (see carruthers, 2016; gennaro, 2004, 2017; macphial, 1998; rakover, 2007; gulick, 2017). the present paper discusses the following two related sub-questions: what makes a mental state (ms) a conscious-ms? how is an unconscious-ms transformed into conscious-ms? before beginning this discussion, i will clarify two important concepts: ms and consciousness. for the present paper a ms is described in the most general way by employing the following delineation of representation. a system t represents a system o, when t’s symbols and their relations map certain aspects of o and their relation. a ms can represent either an individual’s external world or inner private world. for example, a blue and red parrot can be represented in one’s cognitive system by a hypothetical internal symbol (the representation can be pictorial or propositional but it cannot be a tiny bird in one’s head), the content of a book, and even a chimera of a male body with a parrot’s head singing the aria casta diva from norma by bellini (e.g., goldstein, 2011; rakover, 1990). these representations mediate between the external world (the stimulus situation) and the individual’s response. consciousness is a very complex and controversial concept (e.g., gennaro, 2004, 2017; gulick, 2017). in comparison, the emotion of fear has, under different conditions, several behavioral expressions (escape, freeze, or attack) (e.g., rakover, 1975), but except in the extreme case where a patient is not aware of an object that is detected easily by a normal person, no such behavioral response exists for consciousness. for the present paper i will refer to consciousness as it is expressed by the following example. it takes a few seconds to become conscious of the environment in which i exist in, my body’s posture, some of my emotions and thoughts that are running through my mind (i am also aware of part of my consciousness) and above all, i am conscious of being alive, i.e., i have the most basic component of consciousness: the aliveness-feel. this feel gives meaning to the representations. in view of this, i propose that what differentiates a human being from a robot is not the human’s behavior, which can be imitated by a robot, but the aliveness-feel that a human being experiences but which a robot does not. given these clarifications, i will now discuss the above two questions. they have received elaborated answers in higher-order (ho) theories of consciousness which appeal to certain cognitive system ignoring brain neurophysiology. essentially, these theories are variations on the following basic idea: a ms becomes a conscious-ms when it is related by a higher-order ms. for example, my ms (desire to drink hot tea) becomes conscious-ms when i think about my desire (i become aware of my desire to drink hot tea). two important theoretical variations of ho theories are these: the higher-order thought (hot) is based on the idea that higher-order ms is interpreted as a thought (e.g., rosenthal, 2004), whereas the higher-order perception (hop) interprets higher-order ms as a perceptual state (lycan, 2004). the ho theories have encountered several objections (e.g., byrne, 1997; carruthers, 2016; gennaro, 2004, 2017). al6 the conscious unit (cu) model figure 1: abbreviations and nomenclature ms mental state cu conscious unit linkage cu/ms a connection between a ms and a cu or a stream of cus when the thing represented by the ms is complex is made by an inborn special cognitive-mechanism link-condition the cu is linked to a ms when the link-condition is realized in the cognitive system connecting-system the connections among ms, cu and the link-condition linking-mechanism an inborn special mechanism that connects a cu to a ms stm (ltm) short-term (long-term)-memory ho (lo) mental state higher-order (low-order) mental state ho theories higher-order theories hop theory higher-order perception theory hot theory higher-order thought theory train ride the example situation demonstrating the concepts related to the cu though these theories suggested replies to these objections, the polemics continues. this paper concentrates on hot because the major part of the dispute targets hot. the objections to this theory can be understood intuitively, and most of these disagreements can be generalized to other ho theories. the present paper offers a preliminary cu sketch-model that can propose explanations for certain empirical observations and solutions for some of the objections aimed against hot. it also sheds new light on the two questions raised above. this cu model is not developed on marr’s (1982) realization (neurophysiological) level or the algorithm level, but rather on the functional level. on this level, the model is characterized in terms of its goals; how the model operates (e.g., the stages in the information processing); and the rationale and justification on which it is based. the cu model is developed primarily as an explanation for the following core empirical observation, called the "train ride": david traveled from town a to town b by a train. he sat in his compartment and thought about the goals of his travel requiring him to get off the train at b-station and meet the secretary of dr. arnold, miss smith, who offered him a new job (this thought is called the goal). the journey took about two hours and during that time david focused on a detective novel he was reading, and ignored the goal. at b-station david got off the train, thought about the goal, and was also aware that he was thinking of the goal. he was happy to see a lady holding a banner on which his name was written and immediately realized that she must be miss smith, the secretary of dr. arnold. to explain the behavior of david on the train ride the present cu model attempts to answer the following questions: what makes the goal conscious (i.e., the ms (the goal) conscious)? how is the unconscious the goal transformed into a conscious one at the end of the journey? and how was it possible for david to be aware of his awareness? in the next section the uc sketch-model is presented and the core observation is accounted for. then it will examine if it can tackle several objections presented to the hot. if it can provide simple and straightforward answers to several problems with the hot, this will support the suggestion that the cu model is worthwhile. finally, the advantages vs. disadvantages and the model justifications will be discussed by describing the fundamental reasons and considerations motivating the development of the cu model. volume 1, issue 2 2. the conscious unit (cu) model: a preliminary sketch 7 figure 2: notation for representing mental states and consciousness ms(cat) a mental state representing a cat cu/ms(cat) a cu linked to the ms representing a cat ms*[cu/ms(cat)] the cu/ms(cat) is represented by a different symbol or by a different representing state called ms*(ms # ms*) cu/ms*[cu/ms(cat)] since the new ms*[cu/ms(cat)] is in the link-condition, a cu is linked to ms*[cu/ms(cat)], i.e., cu/ms*[cu/ms(cat)] 2 the conscious unit (cu) model: a preliminary sketch the cu model is based on several assumptions which should be viewed as theoretical statements evaluated in terms of the degree of success in proposing sound explanations for different observations, and also to respond to certain objections raised against other consciousness theories (hot). no theory that describes how brain activity can be transformed into the processes of consciousness exists (e.g., chalmers, 2007). furthermore, i have no knowledge of any association between certain neurophysiological activity in the brain and what i term the conscious unit. the cu model is based on purely theoretical concepts and can be evaluated in terms of its explanatory usefulness. assumption (1). the conscious unit (cu). the individual becomes conscious (aware) of the content represented by a ms in the following way. there is an inborn special cognitive linking-mechanism that connects to a ms a unit of consciousness (cu) or a stream of cus when the content represented by the ms is complex, called "linkage cu/ms". that is, when the linkage cu/ms is activated, the individual enters the state of being conscious of the thing represented by the ms. one possible interpretation of cu is as follows. cu may be viewed as the rudimentary aliveness-feel. when this unit or a stream of units are linked to a ms, the thing represented by it becomes conscious and meaningful. assumption (2). the link-condition. the cu is linked to a ms when a certain condition is realized in the cognitive system called the "link-condition”. five sub-assumptions construct the connections among ms, cu and the linkcondition called the "connecting-system": (a) the cu can be linked to ms only when the ms enters, or is in the link-condition; (b) the cu cannot be linked to a ms more than once. (without this sub-assumption the same ms can be bestowed with cu infinitely.) (c) when the link-condition ceases, the cu previously linked to ms is now removed from that ms and it becomes unconscious (a re-entrance of that ms to the link-condition re-grants it cu)1; (d) the linking of cu to ms or its removal from ms is automatic, unconscious and a very fast cognitive operation; (e) at a given time, the link-condition can encompass a limited number of mss. [usually one ms (e.g., a thought, an image, a view) at a time.] assumption (3). the entrance of a new-ms to the linkcondition. this situation is associated with three possibilities: (a) the new-ms acquires a cu. thus the individual becomes conscious (aware) of what is represented by that ms; (b) since the link-condition encompasses a limited number of mss, the previous cu/ms makes room for the new-ms and loses its cu. thus the individual ceases to be aware of the previous ms; (c) if the new-ms supplements the information of the previous cu/ms, both the new and the previous mss are linked to cus. thus the individual becomes conscious of both mss as parts of a whole picture. here are two examples. first, i see a white-house in front of me (i am aware of the white-house). i turn around and see a black cat (i am now aware of the black cat). i do not continue to be conscious of the white-house but only of the black cat. (usually, in daily life, i do not experience an afterimage. furthermore, i do not develop the belief that the white-house disappears, since when i turn 1can assumption 2c be gradual? theoretically the answer can be yes, but for the sake of simplicity the link-condition is dichotomized. furthermore, this assumption fits the fact that one is conscious of object a but when one turns the head she instantly becomes conscious of object b and not of a. 8 the conscious unit (cu) model around i see the house again and also i have the memory of seeing this house before.). the cu is removed from the ms (white-house) and it is transformed into an unconscious ms. secondly, i see a person before me, who says "what’s up my dear friend?" after a second i become aware that this is my good buddy from the army whom i haven’t seen for many years, and i respond "hey dan, it’s good to see you, how are you?" in this second case the conscious information about dan’s identity (good buddy) is added to the information about the person i see in front of me, i.e., it supplements the conscious information about that person. assumption (4). cu simplicity and ms complexity. the cu is a uniform rudimentary unit. however, conscious awareness changes in quality and degree as a result of changes in the thing represented by the ms. for example, one’s consciousness of a cat is different from one’s consciousness of a dog; and one’s degree of awareness of the center of a landscape picture is higher than of one’s awareness of the picture’s margins. a cu can be linked to a ms composed of one salient element (e.g., a black spot on a white wall) or of many elements (e.g., landscape). in the latter case, a cu is linked to each element of the landscape view in a way similar to a stream of electrons running through the tv screen to build an entire picture. furthermore, one may affect the thing represented by a ms (e.g., landscape) by several simple manipulations, such as narrowing eyes, staring, and concentrate one’s attention. assumption (5). competition between external and internal mss. when two mss, one from the external world and one from the individual’s inner world, enter the link-condition, only the external ms is linked with cu. however, certain manipulations can change or block this linkage. for example, if i see a cat and, at the same time, the face of a movie star is retrieved from my long-term memory, only the cat is linked to cu. however, if i stare (have a glazed look) or close my eyes and concentrate on the appropriate retrieved memory, i can consciously remember the movie star’s face. assumption (6) awareness of consciousness. one can be aware of one’s consciousness in the following way, as illustrated by an example. i consciously see a cat, i.e., my ms(cat) is linked to cu [i.e., cu/ms(cat)]. i can be aware of being conscious of a cat (according to subassumption (2b) a ms cannot grant a cu more than once) if the cu/ms(cat) is represented by a different symbol or by a different representing state called ms*, i.e., ms*[cu/ms(cat)]. since ms*[cu/ms(cat)] is in the link-condition, a cu is linked to ms*[cu/ms(cat)], i.e., cu/ms*[cu/ms(cat)]. this means that i am aware of being conscious of a cat. this situation of being aware of awareness can be achieved by concentrating my inner attention on the cu/ms(cat). usually, one becomes aware of seeing a cat by 1) concentrating attention on being aware of the cat, 2) by using a language to represent this event, e.g., by thinking: i am aware that i am consciously seeing a cat. given the description of the cu sketch-model, i shall attempt (a) to interpret david’s behavior in the train ride in terms of the model and (b) to show that the cu model may suggest simple and straightforward explanations for some of the objections to the hot. 2.1 the train ride according to assumptions (1), (2) and also (4) (since the present observation deals with complex mss) one may understand that david becomes conscious of the goal (he has to get off the train at b-station and meet miss smith, the secretary of dr. arnold who has offered him a new job), since this thought was in the link-condition and the cu has been attached to it. that is, the connecting-system has been activated. (note that the sketch-model does not provide an explanation of how the connecting-system has been executed by specifying the appropriate mechanisms. it is a description on the functional level. as mentioned no theory exists that details the connection between the neurophysiological activity of the brain and this specific processes of the mind.) these assumptions and assumption (3) may account for the fact that david is not conscious of the goal while traveling in the train, since he is aware of the novel’s new information and the goal makes room for the new information. when the train stops at b-station the goal re-enters the link-condition and it is re-granted cu (see assumption 2c). the end of the train ride is as follows: "at b-station david thought about the goal, got off the train and was thinking that he was thinking of the goal. he was happy to see a lady holding a banner on which his name was written and he immediately thought that she must be miss smith." the situation in which david is aware of his awareness can be handled by assumption (6) and the fact he believes that the woman with the banner is miss smith can be treated by assumptions (3), (4) and (5), which deal with new vs. old mss and the relation between external (the lady with the banner) and internal information (the stored information about miss smith). 2.2 objections to the hot in this section i present several interesting objections presented to hot and show how the cu sketch-model can effectively cope with them. these disagreements are still in dispute (for other disagreements see byrne, 1997; carvolume 1, issue 2 2. the conscious unit (cu) model: a preliminary sketch 9 ruthers, 2016; gennaro, 2004, 2017). note that my intention is not to critically survey these objections, but to emphasize that, because of the straightforwardness of the present model’s explanations, it may be perceived as receiving methodological support. (1) logical problems: since a ms becomes a conscious-ms by its relation to a higher-order thought (hot), a question arises: how has hot itself become a conscious-ms? this question leads to an infinite regress. when hot is conscious, the problem of circularity arises since consciousness is explained by the fact that one is conscious. a possible reply is to suggest that hot is unconscious. unfortunately, however, the assumption about unconsciousness raises other problems, which i do not see how they can be solved. it has been proposed that when two unconsciousmss are related [the ho mental-state is related to a lowerorder (lo) one] the lo mental state becomes conscious (e.g., gennaro, 2004, 2017). given this, and the reasonable hypothesis that there is a huge amount of unconsciousmss, one may wonder how it is that one’s mind is not flooded with conscious-mss caused by random relations among these unconscious-mss. furthermore, if one accepts that a conscious-ms is not created randomly, then one has to develop a very sophisticated unconscious mechanism which matches two relevant unconscious-mss (one of them ho and the other lo) without any inner conscious guidance. in my view, this is difficult, if not impossible, to achieve. by contrast, the cu sketch-model is not bothered by these objections because the linking of the cu to a ms is carried out by an inborn automatic process, the activation of the connecting-system. hence no need exists to attempt to avoid infinite regress and circularity. the connecting-system (especially sub-assumption 2e) has certain similarities to the well-known metaphors of shortterm-memory (stm), the inner visual spotlight, and dennett’s (1991) cartesian theater. the major focus of these metaphors is to deal with the fact that a limited amount of information can be encompassed in consciousness. while the two first metaphors are anchored to experimental results (e.g., free recall in the case of stm and the distribution of spatial attention in the case of the visual spotlight) dennett’s cartesian theater is a sarcastic concept used to point out the fact that in the end, the explanation of conscious perception is based on a homunculus who sits in a tiny theater in the head and consciously watches what is staged there. nevertheless, the present model is different from these metaphors because it is essentially founded on a functional process. first, the cu sketch-model does not locate the link-condition anywhere in the mind/brain – it is delineated theoretically; secondly, as mentioned above, the model does not attempt to suggest a theory of how consciousness emerges from the neurophysiology of the brain – it assumes that a rudimentary innate cu is linked to a ms under a certain condition, the link-condition. note that the assumption about cu can be viewed as a necessary condition for conferring consciousness, since only when a ms is in the link-condition is it attached to the cu. (2) necessary and sufficient conditions: these objections suggest that hot is not a necessary or a sufficient condition for phenomenal consciousness. it is unnecessary, since phenomenal consciousness can occur without high-order thoughts; it is not sufficient, since high-order thoughts can, and does, occur without phenomenal consciousness. [note that “phenomenal consciousness” is referred to in the literature by similar expressions such as “qualitative property of consciousness,” “qualia,” "what it is like" (e.g., nagel, 1974), “hard problem of consciousness” (e.g., chalmers, 1996).] necessary condition – animal consciousness: today many animal behavior researchers agree that at least the “supreme” animals (e.g., apes, dogs, cats, dolphins, etc.) have phenomenal consciousness, meaning they are conscious of the information detected by their senses (e.g., seeing, hearing, touching) and their emotions (e.g., pain, fear, pleasure by tickling) (see allen and trestman, 2016; rakover, 2007; seager, 2004). the problem for hot is that these mss have to be enhanced with consciousness by hots, but there are major doubts whether animals (also infants) possess such advanced higher-order mss. how one can explain the consciousness attributed to animals without having hots has sparked a hot dispute. what i would like to do here is not critically review this controversy, but show that the cu sketch-model can handle this problem quite straightforwardly. since it is assumed that cu is rudimentary, uniform and innate, in accordance with the evolution theory one may suggest that the connecting-system can be found also in animals’ cognitive systems, hence these animals may have consciousness (e.g., rakover, 2007). but, as mentioned, it is doubtful that animals possess the ability of selfconsciousness or of being aware of awareness. for example, continuing debate exists whether gallup’s mirror test can provide unequivocal experimental results that indicate selfrecognition in animals (e.g., a chimpanzee recognizes itself in the mirror) (see e.g. allen and trestman, 2016; gallup, jr., 1998; povinelli, 1998). according to the cu sketchmodel [assumption (6)], to be aware of awareness another system for representing the cu/ms is required. while empirical observations indicate emotions and sensory informa10 the conscious unit (cu) model tion are conscious in animals, it is difficult to find experimental evidence that support the hypothesis that animals can be aware of their awareness. while a human can use his/her natural language to represent a cu/ms, a similar language has not been found in animals. sufficient condition – phenomenal consciousness: according to hot, the ho mental state relates to the lo mental state and thereby the lo mental state acquires the qualitative property of consciousness. this raises the following problem: how can hot handle the possibility that one thinks that one now sees a red flour when in fact one sees a white wall? the hot may find this question hard to deal with, perhaps because the question is anchored to the request to give a complete explanation of how consciousness is generated, whereas hot aims only to explain how an unconscious-ms becomes a conscious one. the present model deals with this question in two parts. in the first one the present model does not provide an answer how consciousness arises from the neurophysiology of the brain. the present answer is similar to hot’s answer. but the second part of the answer emphasizes that the cu model presents some new and interesting information regarding the question how an unconscious-ms is transformed into a conscious one. this helps the present model skip over some of the potholes into which the hot has stumbled. first, while according to hot consciousness depends on the relationship between two mental states (ho and lo), according to the present model the relationship between cu and ms depends on the connecting-system. given this, it doesn’t matter what kind of ms is at issue (ho or lo mental states) since the same cu is linked to any ms when the link-condition is realized. according to the cu sketch-model, the difference between a ho and lo mental states lies not in the conscious experience itself (since the same cu is linked to any ms) but in the content, in what is represented by these two different mss. secondly, it seems that there is a point of similarity between hot and the present model, assumption (6). but this is only a seeming similarity. the situation "i am thinking that i am conscious of that beautiful cat" is not interpreted as illustrating that i am conscious of the beautiful cat since this ms was related by a higher-order thought; instead, according to the present model, it is interpreted as a cu/ms that was represented by ms* that was linked to a cu. 3 disadvantages vs. advantages and the cu model justifications disadvantages: as mentioned above, the present model does not provide an explanation of how consciousness arises from the neurophysiology of the brain. nor does it provide a neurophysiological explanatory foundation for cu and link-condition. as stated, the best way to conceive these assumptions is as theoretical statements which provide us with efficient explanations. the cu sketch-model was constructed on the functional level by a description of how it has to operate. advantages: first, as can be seen from the above, the cu sketch-model has succeeded in explaining certain empirical observations and also several objections leveled at hot. secondly, the cu sketch-model is based on six basic assumptions that raise several important questions regarding their rationales. the answers to these questions will highlight the qualities of the present model. i will now deal with the following fundamental queries. question (1): why is the transformation of an unconsciousms into a conscious-ms done by linking a cu to a ms? the answer is based on the assumption that the linkingmechanism (see assumption (1)) bestows consciousness on each ms. the bestowal of consciousness depends on the realization of a specific condition (the link-condition) in the cognitive system. this bestowal can be achieved in the following two possible ways. first, the linking-mechanism bestows on a ms consciousness that varies in quality and intensity. the change in conscious experience is matched to the complexity in quality and intensity of what is represented by that ms. secondly, the linking-mechanism bestows on each ms the same unit of consciousness (cu). if so, how does the model explain the changes in the conscious experience? the changes do not originate from consciousness itself but from the changes in the content (quality and degree) represented by a ms. given these two options, the second was chosen as the infrastructure for the present model for the following reasons. simplicity. to develop a theory that will match variations in consciousness to variations in the thing represented by a ms is more complex than constructing a theory that links each ms with the same cu (when the changes in conscious experience are determined by the complexity of the reprevolume 1, issue 2 3. disadvantages vs. advantages and the cu model justifications 11 sented). consciousness uniformity. since the same cu is linked to any ms, the thing represented by that ms is unified to a higher degree in this case than in the case where various qualities and degrees of consciousness are linked to that ms. the reason is that the same cu creates in the perceiver’s mind a uniform conscious-feel of the thing represented by that ms (e.g., one perceives a whole picture of a landscape which includes a house, trees, a lake, ducks and birds). generalization. since the second option paves the way for the development of a possible durable linking-mechanism for consciousness grant, one may propose the following. according to the evolutionary approach, it possible to suggest that supreme animals may also possess the connectingsystem, and therefore have phenomenal consciousness. according to the present model, this proposal rests on animals also having the ability to represent the world, i.e., they have mss which can be linked to a cu. aliveness-feel. it is simpler to interpret a cu as an aliveness-feel than a complex consciousness that varies over the dimensions of quality and degree (intensity). furthermore, this interpretation can be generalized to animals and one may propose that the crucial difference between an animal and a machine is, while an animal can be endowed with an aliveness-feel a machine cannot. question (2): why assume the link-condition? if the cu sketch-model consisted only of the linkingmechanism (without the link-condition) one would not be able to explain the following objections: first, the same ms can be conscious at one moment and unconscious at another; secondly, if the activation of the linking-mechanism were non-stop (since the link-condition does not exist) the result would be that the cognitive system would be flooded with conscious mss. the condition of the link-condition provides appropriate answers to these objections: it explains both the linkage to ms and the removal of a cu from that ms by restricting these operations to the cases where ms enters the linkcondition and where the ms is not under that condition. question (3): why does the link-condition handle only a limited number of mss? the link-condition is a theoretical construct which allows the linking-mechanism to join a cu to a ms. in a given time, it can handle a limited number of mss. this restriction is based on the following observations and experimental results. first, if the link-condition allowed the linkage of cu to many mss, one’s mind would be flooded with many cu/mss that would interfere with conducting appropriate behavior, and one’s chances of survival would plummet. this is called information overload. secondly, many instances indicate that one can be aware of limited visual information. consider the following case. i am aware of all the items that appear in visual field a. when i turn my head i am aware of all the items in visual field b but no longer of those in visual field a. in this case, the domain of consciousness is restricted: it can encompass only what is represented by ms (field a) or ms (field b). however, according to assumption (3), if i see a face in front of me, i am conscious of the following mss: i am aware of that face; i am also aware that i saw this face in the past, and that i cannot remember the name of the face’s owner. that is, in this case different cu/mss are joined together to form a unified conscious picture. thirdly, the present restriction may be viewed as analogous to the well-known hypothesis that the short-term memory (stm) can handle limited chunks of information (about four). although there are several criticisms of the distinction between the stm and long-term memory (ltm), most researchers accept that the stm is limited in capacity and can preserve information for about 20 seconds. by contrast, the ltm stores an infinite amount of information for many years (see sternberg, 2009). despite this similarity, it is important to emphasize the following crucial difference. while the stm is conceived metaphorically as a storage with limited space, the link-condition is a theoretical construct, which can be viewed as part of the cognitive system, and its function is to allow the cu linking to a ms. (note that as a storage, the stm is not granted cognitive operations; these are bestowed on the “working memory.”) question (4): when two mss (one representing the external world and the other one’s internal world) enter the link-condition, why is the cu linked to the external ms and not to the internal ms? if the external ms were not preferred to the internal ms, the following intolerable possible situation would be created in the cognitive system: the mind would be flooded with a huge number of internal unconscious-mss that immediately would be transformed into conscious ones. the assumption regarding the preference of the external over the internal ms prevents the occurrence of this undesirable possibility, simply because a live creature receives continuously external stimulations that are represented in the cognitive system by their appropriate mss. if the external stimulation was reduced or blocked, as in the case with the experiments in “sensory deprivation,” the chances of unconscious-ms ap12 the conscious unit (cu) model pearing in the link-condition and being transformed into conscious-ms would increase. and indeed, the results of experiments in sensory deprivation in which the sensory stimulation of seeing, hearing, touching, etc. is reduced or blocked show detrimental effects such as visual hallucinations, disorientation in time and space, inability to concentrate and think clearly, and restless behavior (see zubek, 1969). in light of the above, one may propose that, although the present paper has not offered a theory of consciousness anchored to the neurophysiological level, but only to the functional level, the cu sketch-model has succeeded in explaining particular empirical observations and also in solving certain problems connected with other theories. acknowledgements i am grateful to jonathan bartlett and two anonymous reviewers who read the paper and made helpful suggestions. references allen, c and m trestman (2016). “animal consciousness”. in: the stanford encyclopedia of philosophy. ed. by e n zalta. byrne, a (1997). “some like it hot: consciousness and higher-order thoughts”. in: philosophical studies 86, pp. 103–129. carruthers, p (2016). “higher-order theories of consciousness”. in: the stanford encyclopedia of philosophy. ed. by e n zalta. chalmers, d j (1996). the conscious mind: in search of a fundamental theory. new york: oxford university press. chalmers, d j (2007). “the hard problem of consciousness”. in: the blackwell companion to consciousness. ed. by m velmans and s schneider. blackwell. dennett, d c (1991). consciousness explained. boston: little, brown, and co. gallup, jr., g (1998). “animal self-awareness: a debate— can animals empathize? yes.” in: scientific american 9, pp. 66–71. gennaro, r j (2004). “higher-order theories of consciousness: an overview”. in: higher-order theories of consciousness: an anthology. ed. by r j gennaro. amsterdam/philadelphia: john benjamins. gennaro, r j (2017). “consciousness”. in: internet encyclopedia of philosophy. goldstein, e b (2011). cognitive psychology. 3rd ed. wadsworth: cengage learning. gulick, r van (2017). “consciousness”. in: the stanford encyclopedia of philosophy. ed. by e n zalta. lycan, w g (2004). “the superiority of hop to hot”. in: higher-order theories of consciousness: an anthology. ed. by r j gennaro. amsterdam/philadelphia: john benjamins. macphial, e m (1998). the evolution of consciousness. oxford: oxford university press. marr, d (1982). vision: a computational investigation into the human representation and processing of visual information. san francisco: w. h. freeman. nagel, t (1974). “what is it like to be a bat?” in: philosophical review 83, pp. 435–450. povinelli, d j (1998). “animal self-awareness: a debate— can animals empathize?” in: scientific american 9, pp. 72–75. rakover, s s (1975). “tolerance of pain as a measure of fear”. in: learning and motivation 6, pp. 43–61. rakover, s s (1990). metapsychology: missing links in behavior, mind and science. new york: paragon/solomon. rakover, s s (2007). to understand a cat: methodology and philosophy. amsterdam/philadelphia: john benjamins. rosenthal, d m (2004). “varieties of higher-order theory”. in: higher-order theories of consciousness: an anthology. ed. by r j gennaro. amsterdam/philadelphia: john benjamins. seager, w (2004). “a cold look at hot theory”. in: higher-order theories of consciousness: an anthology. ed. by r j gennaro. amsterdam/philadelphia: john benjamins. sternberg, r j (2009). cognitive psychology. 5th ed. wadsworth: cengage learning. zubek, j p (1969). sensory deprivation: fifteen years of research. new york: appleton-century-crofts. login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? 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bb � mqm`2/m+ibp2 2k2`;2mi t`qt2`iv q7 i?2 #bqhq;b+�h bi`m+im`2b i?�i /2}m2 ?mk�mm2bbx a7 bi bb i`m2 i?�i 2tbbi2m+2+qmb+bqmbm2bb �m/ b/2mibiv 2tbbi � t`bq`b iq ?mk�m hb72 bm bqk2 7q`k q7 m2q@sh�iqmb+ `2�hkě q` tqbbb#hv bm � t�mi?2bbib+ mmbp2`b2ě�i h2�bi i?`22 bmi2`m�h +qm~b+ib �`bb2x *qm~b+i or, � s`bq`b bb � sqbi2`bq`b *hmmm h2�mb ?2�pbhv qm �vm _�m/ 7q` /2}mbm; ?bb �tbqkb #mi /2t�`ib 7`qk _�m/ r?q i�m;?i i?�i +qmb+bqmbm2bb �m/ kq`�hbiv �`2 � tqbi2`bq`bx h?bb /bbibm+ibqm bb +`bib+�h 7q` *hmmm �b ?2 ?qt2b iq bmbi�bm ?bb +qkkbik2mi iq #qi? q#d2+ibp2 kq`�hbiv �m/ 7`22 rbhhx >2 r`bi2bǳ�i i?2 2m/ q7 i?2 /�vkq`�hbiv bb �#qmi 7`22 rbhh+?qb+2b�m/ /2+bbbqmbx h?2b2 i?bm;b �hh 2tbbi rbi?bm qm` +qmb+bqmbm2bb u98vxǵ >2`2 bb r?2`2 i?2 bm+q?2`2m+2 }`bi k�mb72bibx "v /2}mbibqm� t`bq`b k2�mb i?�i kq`�hbiv kmbi 2tbbi bm/2t2m/2mi q7 �mv t2`bqmƕb 2tt2`b2m+2x u2i*hmmm �hbq t`2bmk2b i?�i kq`�hbiv 2tbbib i?`qm;? i?2 2t2`+bb2 q7 qm2ƕb 7`22 rbhhx :bp2m i?2b2 +h�bkbkq`�hbiv kmbi �hbq #2 � tqbi2`bq`b #2+�mb2 bi /2t2m/b mtqm ?qr 2�+? bm/bpb/m�h t2`bqm 2t2`+bb2b i?2b` 7`22 rbhhx *hmmmƕb t`2bmttqbbibqm q7 � t`bq`b kq`�hbiv k�v #2 t`2b2`p2/ b7 ?2 �bbmk2b 7`22 rbhh bb �hbq �m 2tt`2bbbqm q7 i?2 � t`bq`b mmbp2`b�h +qmb+bqmbm2bbx >qr2p2`i?bb �bbmktibqm h2�/b iq � b2+qm/ +qm~b+i 7q` ?qr *hmmm /2}m2b b/2mibivx *qm~b+i ok, am/bpb/m�hbiv bb �m ahhmbbqm 6q` *hmmm+qmb+bqmbm2bb bb mqi � t`qt2`iv q7 t2`bqm?qq/#mi �m 2k2`;2mi t`qt2`iv q7 i?2 t?vbb+�h `2�hk i?�i 2tbbi2/ #2@ 7q`2 �mv bm/bpb/m�hx h?�i bb iq b�v�hh ?mk�mb b?�`2 bm i?2 qm2 mqm`2/m+ibp2 � t`bq`b mmbp2`b�h +qmb+bqmbm2bbx �i i?2 b�k2 ibk2*hmmm �`;m2b i?�i i?2 i2`k ǳaǵ bb �m 2tt`2bbbqm q7 `�ibq@ m�h i?qm;?i r?b+? 2bi�#hbb?2b qm2ƕb bt2+b}+ b/2mibiv rbi?bm i?2 mmbp2`b�h +qmb+bqmbm2bb2bx "mi 2p2m b7 ǳaǵ 2bi�#hbb?2b kv t2`@ bqm�h 2tbbi2m+2bi `2k�bmb �m 2tbbi2m+2 qmhv rbi?bm i?2 h�`;2` �tbqk q7 2tbbi2m+2x ai b22kb iq 7qhhqr 7`qk *hmmmƕb qrm /2}mb@ ibqmb i?�i i?2 t2`+2tibqm q7 bm/bpb/m�hbiv�m/ #v 2ti2mbbqm 7`22 +?qb+2bb qmhv �m bhhmbbqmx h?bb +`2�i2b �i h2�bi qm2 bb;mb}+�mi bmi2`m�h +qm~b+ib 7q` *hmmmƕb �tbqkbx *hmmm �`;m2b i?�i i?2 +qmb2[m2m+2b q7 qm` /2+bbbqmb �`2 2tt2`b@ 2m+2/ qmhv rbi?bm i?2 `2�hk q7 t2`bqm�h +qmb+bqmbm2bbr?b+? mq qi?2` t2`bqm +�m q#b2`p2x am +qmi`�bi*hmmm b�vb i?�i r2 +�m q#b2`p2 2tbbi2m+2x u2i7q` *hmmmkq`�hbiv /q2b mqi k�mb72bi bm i?2 �tbqk q7 2tbbi2m+2x >qr2p2`b7 2�+? t2`bqmƕb +qmb+bqmbm2bb bb � b?�`2/ � t`bq`b `2�hbiv?qr bb bi #2vqm/ kv tqr2`b q7 q#b2`p�ibqm\ a7 a +�m ?�p2 �r�`2m2bb q7 kv qrm +qmb+bqmbm2bb�m/ i?�i +qmb+bqmbm2bb bb ib2/ iq i?2 mmbp2`b�hi?2m #v /2}mbibqm a kmbi �hbq ?�p2 �++2bb iq mm/2`bi�m/bm; i?2 +qmb+bqmbm2bb q7 qi?2`b #2+�mb2 i?2v iqq �`2 ib2/ iq i?2 b�k2 mmbp2`b�h �tbqkx 1p2m kq`2b7 +qmb+bqmbm2bb bb �m 2k2`@ ;2mi t`qt2`iv q7 2tbbi2m+2?qr /q2b bi `2k�bm bm/2t2m/2mi q7 2tbbi2m+2 �b bi `2h�i2b iq kq`�hbiv\ h?bb bm+q?2`2m+2 h2�/b iq https://dx.doi.org/10.33014/issn.2640-5652.3.1.miller.1 about this journal the purpose of the journal paper submission policies other journal content from the editors sam s rakover and baruch cahlonsam s rakover and baruch cahlonwhen is explanation transitive? a methodological note introduction explanatory-transitivity discussion acknowledgments robert j. marks iirobert j. marks iitiling efflorescence of expanding kernels in a fixed periodic array: generalizing the flower-of-life introduction other expanding kernels properties of expanding kernels of varying periodicity analysis conclusions appendices letters and notes eric hollowaydeciding a bitstring of 1s is non-random is impossible in general jonathan bartlettproving the derivative of sin(x) using the pythagorean theorem and the unit circle j r millera response to clunn's axioms of morality jorge fernandezis information content a single, static quantity? news volume 2, issue 2 empirical active information 47 empirical active information eric holloway doi: 10.33014/issn.2640-5652.2.2.holloway.4 active information is the log ratio of the performance of a search with (!) and without (") information about the target it is searching for, using the notation of self information # ($) = ! log2 $, #+ = log2 ! " (1) = # (") ! # (!). (2) as proven in bartlett (2020), active information is a canonical specified complexity, and therefore by montañez (2018), pr(#+ > %) " 2!! . (3) this is posed in an ideal setting where we know both of these performance values. however, in the empirical setting, although we can perhaps take the baseline as a given value, we must infer the performance of the search with target information by observation. in this case, we will only consider a search across binary strings. all finite domains can be cast as binary strings, so the proof here is general enough for all finite domains, although perhaps not always the most convenient representation. we’ve observed & bits and of those ' are zeros. we can think of this in terms of a prediction task, where ones correspond to correct predictions and zeros correspond to incorrect predictions. for sake of demonstration we set ' " &/2, (4) which we can always guarantee by flipping the prediction if more than half are incorrect. from the assumption in (4) we define the probabilities $ = '/& (5) ( = 1 ! '/& (6) such that $ " (. we want to figure out what kind of prediction accuracy we can expect on unseen data, and we want to err on the side of caution and not be over optimistic. stated more formally, what is the bernoulli distribution probability ) of ones that generated this sequence, based on a certain confidence probability of *? first, here is an upper bound on the binomial quotient tail derived from the binomial cumulative distribution: "! #=0 " & + # $$%(&% " "! #=0 " & + # $#(%!# " 1 (7) "! #=0 " & + # " $!$%(!&% (8) = 2%' ($) . (9) the left hand side of (7) is derived by keeping the probability constant during the summation, instead of changing as + is incremented. this guarantees the left hand side is a lower bound on the binomial cumulative distribution, since we’ve selected the smallest probability in the summation and kept it constant. the jump from $!$%(!&% in (8) to 2%' ($) in (9) is based on the entropy function: , ($) = !$ log2 $ ! ( log2 ( (10) 2' ($) = $!$(!& . (11) now, let us return to our goal of estimating the accuracy on unseen data. the estimate can be wrong in two ways. 1. too low. if so, then great! 2. too high. if so, we want to know the probability the estimate is too high. so, stated more formally, we want to pick an ) for our estimate such that any bernoulli distribution with a smaller probability " of generating a one, i.e. 0.5 " " < ) , will have a probability less than * of generating ' or fewer zeros. in other words, * is the probability we’ve over estimated our model accuracy. the probability * is thus: * = "! #=0 " & + # (1 ! ))#)%!# " "! #=0 " & + # )% (12) " 2%' ($))% (13) log2 * " &(, ($) + log2 )). (14) the substitution to get the right hand side in (12) is the same sort of reasoning used to get the left hand side in (7), except reversed. in (7) the goal was to get a lower bound https://dx.doi.org/10.33014/issn.2640-5652.2.2.holloway.4 48 letters and notes on the cumulative distribution. in (12) the goal is to get an upper bound. so, we pick the largest probability in the summation, )%, which is larger than (1 ! ))#)%!# because ) # 0.5. the reduction from (12) to (13) is based on the substitution from (9). the use of the logarithm in (14) measures the probability in bits to make the formula a bit easier to manipulate. now, we want to derive ) from a predefined value for *, for example * = 2!(. this means we need to pick a value for ) such that the right hand side of (14) evaluates to !-. if we substitute in ) = 2!' ($)!(/%, (15) we achieve just that result, log2 * " &(, ($) + log2 (2!' ($)!(/%)) (16) = &(, ($) ! , ($) ! -/&) = !-. (17) as long as &, ($)+< & then from (15) ) > 0.5, and we are able to predict better than 50/50 odds. here we can also see why our very first assumption in (4) is necessary. if ' > &/2 then since the entropy function , ($) is symmetrical we can substitute in a value for $ such that (15) gives us a estimate that is higher than the observed accuracy rate, i.e. ( < ) , which is a contradiction since the estimate is a lower bound and so should be lower than the observed accuracy. now we can finalize our concept of empirical active information per sample by substituting in ! = ) for (1) and setting = 0, #)+ = # (") ! , ($). (18) and as at the beginning, the probability bound still applies. pr(#)+ > %) " 2!! . (19) bartlett, jonathan (2020). “active information is a specified complexity model”. in: communications of the blyth institute 2.2. montañez, george d (2018). “a unified model of complex specified information”. in: bio-complexity 2018. about this journal the purpose of the journal paper submission policies other journal content from the editors annie crawfordannie crawfordmetaphor and meaning in the teleological language of biology introduction the history of teleology in the biological sciences teleological language is essential to biology if teleological language is essential to biology, then life must be teleological conclusion: life all the way down salvador cordovasalvador cordovafisher's fundamental theorem of natural selection isn't fundamental after all introduction: the problem of defining fitness absolute ``darwinian'' fitness vs. relative fitness mean and variance of relative fitnesses numerical examples to illustrate fisher's theorem discussion conclusion eric hollowayeric hollowaytutorial: bioinformatics basics introduction genetic code and sequence translation sequencing and assembly accessing data finding things with blast summary letters and notes eric hollowayyou cannot get meaning from randomness jonathan bartlettactive information is a specified complexity model eric hollowayevolution in the valley of illusions jonathan bartlettis active information applicable to biology? eric hollowayempirical active information news login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians volume 2, issue 2 tutorial: bioinformatics basics eric holloway doi: 10.33014/issn.2640-5652.2.2.holloway.1 1 introduction bioinformatics can appear to be a daunting field, since it combines the complex science of biology with the complex theory of computer science. however, the basics are surprisingly simple. essentially, bioinformatics is the discipline of analyzing symbol strings. the symbol strings represent dna, rna, and protein sequences, with each symbol representing a component of the molecule. the strings are analyzed by extracting the structure within the strings and comparing the relationships between the strings. the dna and rna strings are composed with four di!erent symbols and protein strings have twenty di!erent symbols. 2 genetic code and sequence translation the letters of dna and rna strings are called nucleotides. the dna letters are g (guanine), a (adenine), t (thymine), c (cytosine). the rna letters are g, a, u, c. it is almost directly copied from dna, except the t is turned into u (uracil). the protein letters are a, c, d, e, f, g, h, i, k, l, m, n, p, q, r, s, t, v, w, y. see figure 1 for their meanings. each protein letter is translated from three rna letters. each group of three rna letters is called a codon. the translation table is known as the genetic code. the start and stop symbols are used to mark where a gene begins and ends. figure 1 shows the standard mapping between codons and amino acids. a single biological dna sequence is a molecule, and this molecule is called a chromosome. 3 sequencing and assembly these symbol strings are digital abstractions, and show how fundamental the notion of information is to biology. the process of extracting these abstractions is called sequencing. to extract genetic sequences, current technology must first break a long sequence into many little fragments, usually on the order of a few hundred nucleotides long or tens of proteins long. once these fragments are digitized, then they must be reassembled back into the full genome. this assembly process is very computationally intensive and error prone. sometimes the full genome cannot be assembled, and the best that can be done is to construct larger fragments. the fragments are known as reads. a collection of fragments is known as a run. when the fragments are pieced together into a longer fragment, this is known as a contig. if the full genome is put together, this is known as an assembly. if there are gaps, but the contigs are lined up against a known genome, this is called a sca!old. 4 accessing data the data for each step in the process is usually stored in databases, so that experiments and assembly can be reproduced by other scientists. the databases described in this article are the databases maintained by the national center for biotechnology information, since these are what the author is most familiar with. all items of data in the database have a unique id number known as an accession. once you know the accession for a piece of data, you can use ncbi’s tools to download the data. the main tool you can to search for an accession and download the data is ncbi’s website: www.ncbi.nlm.nih. gov/. if you want to access data from the command line for an automated workflow, there are a couple command line tools available. https://dx.doi.org/10.33014/issn.2640-5652.2.2.holloway.1 www.ncbi.nlm.nih.gov/ www.ncbi.nlm.nih.gov/ 36 tutorial: bioinformatics basics amino acid symbol codon alanine a gcu, gcc, gca, gcg asparagine/aspartic acid b aau, aac, gau, gac cysteine c ugu, ugc aspartic acid d gau, gac glutamic acid e gaa, gag phenylalanine f uuu, uuc glycine g ggu, ggc, gga, ggg histidine h cau, cac isoleucine i auu, auc, aua lysine k aaa, aag leucine l cuu, cuc, cua, cug, uua, uug methionine m aug asparagine n aau, aac proline p ccu, ccc, cca, ccg glutamine q caa, cag arginine r cgu, cgc, cga, cgg, aga, agg serine s ucu, ucc, uca, ucg, agu, agc threonine t acu, acc, aca, acg valine v guu, guc, gua, gug tryptophan w ugg tyrosine y uau, uac glutamine/glutamic acid z caa, cag, gaa, gag start aug stop uaa, uga, uag figure 1: the standard codon table volume 2, issue 2 5. finding things with blast 37 4.1 file format the main file format used for dna and protein sequences is the fasta format. the format is pretty straightforward. there are metadata lines and lines that contain the genetic data. the metadata lines start with the > character, and can be used to break up multiple reads in a run file. the rest of the lines contain dna or protein letters. sometimes, there are extra letters that stand in for multiple possible dna letters. most often this is the letter n, which means any dna letter can go in that particular spot. it signifies a sequencing error. see the next section for an example of this file format. 4.2 sequence read archive the initial read data is stored in ncbi’s sequence read archive (sra): www.ncbi.nlm.nih.gov/sra. to access this data there is the sra-toolkit: github.com/ncbi/sratools. here in an example session of using the toolkit to then download a run. $ fas tq !dump !!f a s t a !z drr001793 | head !n 8 >drr001793 . 1 fc30uf2aaxx: 6 : 1 : 1 0 : 1 4 5 3 l ength=35 accagctatcaccgagtttnnntatcctttcaccc >drr001793 . 2 fc30uf2aaxx: 6 : 1 : 1 0 : 1 6 9 2 l ength=35 tattatttaactgataattannctagatatattat >drr001793 . 3 fc30uf2aaxx: 6 : 1 : 1 0 : 1 8 9 6 l ength=35 agaccaattcattaattttttntttattatactat >drr001793 . 4 fc30uf2aaxx: 6 : 1 : 1 0 : 1 8 4 5 l ength=35 aaaggcagagtacattaagacnatagatttagttt you can see from the above the downloaded file consists of lines of dna spaced with identifier lines. each of these lines of dna is a read. 4.3 eutils the assembled genomes and proteins can be accessed with the eutils web api. the documentation for the api is available at https://www.ncbi.nlm.nih.gov/books/ nbk25500/. there is a python library available for using eutils in python available at https://pypi.org/project/ eutils/. additionally, there are also command line tools for eutils, and a great tutorial on them is available at https://www.ncbi.nlm.nih.gov/books/nbk179288/. the general workflow for eutils is a query tool returns an xml report, which is then fed to a data access tool to retrieve the record. eutils is the most versatile tool, since it can access data from all the di!erent ncbi databases of processed genetic data. 4.4 datasets finally, ncbi has recently released a beta version of a more user friendly search and data access tool called datasets: ncbi.nlm.nih.gov/datasets. the tool’s main feature is the ability to download many pieces of data altogether in a single ’bag’. the idea is to make accessing data like a grocery shopping store, where you fill your cart with data items, and then check them all out at once. there is also a command line tool that can be used for programmatic workflows. 5 finding things with blast blast (basic local alignment search tool) is the google of bioinformatics, hosted at the national center for biotechnology information. you can enter dna or an amino acid sequence into the tool, and blast will search the ncbi databases for matches. since dna is mutated—with swapped, deleted, and added nucleotides—there is never an exact match. blast searches heuristically using a variant of the edit distance with a substitution matrix, representing the probability one nucleotide mutates into another nucleotide. there are four main variants of blast, representing the four possible combinations of dna and amino acid searches. 1. blastn: enter dna sequence to find dna sequence 2. blastx: enter dna sequence to find amino acid sequence 3. tblastn: enter amino acid sequence to find dna sequence 4. blastp: enter amino acid sequence to find amino acid sequence 5.1 blast interface the basic interface is straightforward, and the web interface at https://blast.ncbi.nlm.nih.gov/blast.cgi is www.ncbi.nlm.nih.gov/sra github.com/ncbi/sra-tools github.com/ncbi/sra-tools https://www.ncbi.nlm.nih.gov/books/nbk25500/ https://www.ncbi.nlm.nih.gov/books/nbk25500/ https://pypi.org/project/eutils/ https://pypi.org/project/eutils/ https://www.ncbi.nlm.nih.gov/books/nbk179288/ ncbi.nlm.nih.gov/datasets https://blast.ncbi.nlm.nih.gov/blast.cgi 38 tutorial: bioinformatics basics self descriptive. you enter a reference to a sequence, such as the accession number, or paste the sequence itself. a specific subrange of the sequence can be queried. to constrain the search, di!erent database can be searched, ranging from databases of carefully currated genomes to user submission databases. searches can be within specific organisms, or exclude specific organisms. the search sensitivity is tuned by setting the expect threshold, which will return only matches that do not exceed the expected number of random matches. the results come back with metadata expressing in which genetic data the match was found, an ’e’ score based on the logarithm of probability of matching, and what percentage of the returned sequence matches the query. the text of the sequence itself is also returned, along with any associated publications. 5.2 example: finding the top2a protein the simplest way to find a known protein is through the ncbi search bar, available from the ncbi front page at ncbi.nlm.nih.gov. typing in top2a will bring up an information card, with links to the known orthologs in other species as well as a prepopulated blast search. you can then run the blast search to retrieve matches. note, you can only exclude results at the taxonomic level, so if there is another protein that is similar, it will show up in the search as well. 6 summary as you can see, while the user interface for accessing data may be a bit complicated, and the naming convention for various aspects of genetic data obscure, the fundamentals are straightforward. and, once you know that genetic data is composed into dna, rna, and protein sequences, you just need to download the data to start analyzing it from the comfort of your living room. the ncbi website is a good pathway to becoming a bioinformatics scientist, all without the need for an expensive lab and fancy equipment. all you need is a computer with an internet connection and the mind between your ears. ncbi.nlm.nih.gov about this journal the purpose of the journal paper submission policies other journal content from the editors annie crawfordannie crawfordmetaphor and meaning in the teleological language of biology introduction the history of teleology in the biological sciences teleological language is essential to biology if teleological language is essential to biology, then life must be teleological conclusion: life all the way down salvador cordovasalvador cordovafisher's fundamental theorem of natural selection isn't fundamental after all introduction: the problem of defining fitness absolute ``darwinian'' fitness vs. relative fitness mean and variance of relative fitnesses numerical examples to illustrate fisher's theorem discussion conclusion eric hollowayeric hollowaytutorial: bioinformatics basics introduction genetic code and sequence translation sequencing and assembly accessing data finding things with blast summary letters and notes eric hollowayyou cannot get meaning from randomness jonathan bartlettactive information is a specified complexity model eric hollowayevolution in the valley of illusions jonathan bartlettis active information applicable to biology? eric hollowayempirical active information news v2i1 volume 2, issue 1 hyperreal numbers for infinite divergent series jonathan bartlett, logan gaastra, and david nemati doi: 10.33014/issn.2640-5652.2.1.bartlett-et-al.1 abstract treating divergent series properly has been an ongoing issue in mathematics. however, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. the infinities that resulted from divergent series led to contradictions within the real number system, but these contradictions are largely alleviated with the hyperreal number system. hyperreal numbers provide a framework for dealing with divergent series in a more comprehensive and tractable way. 1 the problem of infinite series historically, infinities have led to many problems in mathematics. infinities, when not handled carefully, easily lead to contradictions and indeterminacies. therefore, caution has always been urged when dealing with infinite series. this is especially true with divergent infinite series. convergent infinite series generally behave unproblematically similar to the value that they converge to. given a series that converges to 2 and another series that converges to 3 then the sum of the values of the series will be 5 and their product will be 6. therefore, the nature of these series can be summarized into a single number. with divergent series, this is not so straightforward. a lack of agreement on the rules for handling infinities had led to numerous problems with handling divergent series. if a series diverges to infinity, is it greater than or equal to some other series that diverges to infinity? can the terms of the series be rearranged? can their spacing be modified? is 1 + 1 + 1 + . . . equivalent to 1 + 0 + 1 + 0 + 1 + 0 + . . .? lack of answers to questions like this have stifled work in divergent series, and have caused many mathematicians to think of divergent series as invalid entities to work with rigorously. 2 working with infinities many paradoxes exist with infinities. for instance, are there the same number of positive even integers as positive integers? there are an infinity of them, but does that make them the same? it seems pretty obvious that, on a number line, positive integers occur twice as often. however, there are an infinite amount of both. cantor’s solution to this problem is to separate out the final quantity of a set (the cardinality) from the arrangment of a set (its ordinality). the cardinal numbers do not behave in any way similar to real numbers. the ordinals, on the other hand, behave in many ways similar to real numbers. however, cantor’s own system for ordinal arithmetic is difficult to use, and doesn’t translate well between transfinite and regular real arithmetic. the hyperreal number line has many similarities to cantor’s ordinals, operating essentially at the level of “ordinal” in cantor’s system. however, the hyperreal number line o!ers a way to do arithmetic with infinities in a way that very closely matches real arithmetic through the use of the transfer principle (henle and kleinberg, 2003). the transfer principle states that any first-order proposition that is true for the reals is also true for the hyperreals. this means that the standard arithmetic principles for dealing with real numbers will apply to hyperreal numbers as well. the hyperreal number line operates with an infinite unit, !, that represents an order of infinity.1 the way it is usually handled, ! isn’t a specific number in the typical sense, but rather more of a benchmark of infinity. previous work has shown that hyperreal numbers could be a potential solution to how values of divergent series can be represented (gaastra, 2016).2 the present paper will build on this original idea and establish a system for using 1the choice of character/typography for the unit varies with the author. for instance, keisler uses h (keisler, 2012). ! was chosen because of its historical connection with ordinal-type infinities. 2other work worth mentioning in this area are (paterson, 2018a) and (paterson, 2018b). in the current work, we will use a notation similar to (keisler, 2012) to notate hyperreal values, and show how infinite series can be simplified to them. paterson did the opposite, by notating hyperreal values with the infinite sum that represents them. 8 hyperreal numbers for infinite divergent series hyperreal numbers to assign values to infinite series. 3 hyperreals and partial sums the vast majority of issues with divergent series comes with the transition from partial sums to infinite sums. as long as a series remains a partial sum, arithmetic with the series is unproblematic. therefore, it would be beneficial to develop a system which matched the partial sum behavior of finite sums, but allowed the result to be generalized to infinity. the value of a partial sum of an infinite sequence of a given length is sensitive to the order of the terms in the infinite sequence. imagine summing the first n terms of an infinite sequence. the result will not be the same with di!erent orderings of the infinite sequence. for instance, if i did a partial sum of the first n terms of an infinite sequence, then reversed the infinite sequence, the partial sum of the first n terms of the reversed sequence will not necessarily match the original partial sum. however, within the first n terms, rearrangements can occur without consequence. if the extent of the partial summation is unknown, then it is also unknown the extent to which numbers can be reordered. for the same reason, tacking on zeroes to the beginning of the series can potentially change the partial sum. therefore, although adding zeroes to the beginning of a series has the appearance of being a null operation, because doing so modifies the value of finite partial sums, it can also lead to long-term changes in behavior. additionally, changing the number of terms in a partial sum alters the value. adding together the first n numbers of a sequence will often yield a di!erent value than adding together the first m numbers of the sequence. in short, partial sum behavior is well-behaved, wellunderstood, and well-regulated. by understanding divergent series in terms of partial sums extended into the hyperreals, we will be able to deal with them more rigorously and uniformally. to understand many of the rules that will be developed for infinite series, imagine that the rules are being built for merely doing partial sums to an unknown parameter k, where k at least acts like a particular finite value, but is larger than any particular list index referenced by any finite manipulation of the series. some of these formulas will be further reducible due to the nature of the hyperreals, as will be discussed in section 7. 4 pinning down ! since ! operates as a benchmark instead of a number, the first task is to identify the benchmark to associate ! with. this is actually to some extent an arbitrary decision. any infinitely large value could be used to establish a baseline !. however, the value that seems most natural for ! (especially for summation) is the size of the set of positive integers. therefore, ! will be used to refer to the total quantity of positive integers.3 ! = |n| = ! i!n 1 (1) because of this, the notation used will be more specific when writing summations. instead of summing to the ambiguous infinity, ", a summation to the specific infinity of all positive integers, !, will be used. therefore, the series 1 + 2 + 3 + . . . will be written as !! i=1 i (2) (1) will establish the starting benchmark for relationships among the di!erent series. 5 the standard summation because partial sums are dependent on length and order, it is important to establish an o"cial standardization of summation. that is, !" i=1 will be di!erent from !" i=0 . even though it looks like series with these types of sums will have an identical number of terms (after all they both have infinite terms), using this methodology the latter one will actually have more elements than the former. this is due to the principle established in section 3. if, instead of ! being infinite, pretend that ! was just an ordinary finite integer parameter. examine the series !! i=1 1. (3) 3there are some objections to equating a hyperreal number to a cardinal number such as |n |. the specific identity of ! with |n | is for conceptual convenience. alternatively, simply treating ! as an arbitrary (but unchanging) benchmark of infinity leads to the same results. volume 2, issue 1 6. simple arithmetic and geometric series 9 if ! represented an integer (say, 5) instead of ", it would be obvious that this sum represents a di!erent value from the series !! i=0 1. (4) equation 3 would represent the value 5 while equation 4 would represent the value 6. therefore, it is clear that having matching indices matters. in fact, our ability to sum divergent series will sometimes depend on having summations with equivalent numbers of terms. therefore, a “standard” starting point for summation will need to be established in order to ensure that like entities are being compared and reasoned about. since ! has been defined as being the size of the set of all positive integers, it makes sense to start at 1. for the purposes of this paper, the “standard” way of summing will be to start with 1 and proceed to !. 6 simple arithmetic and geometric series 6.1 arithmetic series arithmetic series take the form n! i=1 a + (i # 1)d. (5) the sum of an arithmetic series, given a starting value a, the number of elements n, and distance between elements d, can be given by the formula n! i=1 a + (i # 1)d = n 2 (2a + (n # 1)d) . (6) to find the sum of an infinite arithmetic series, ! is used for n, forming a hyperreal value. that reduces the formula to !! i=1 a + (i # 1)d = !a + !2d 2 # !d 2 . (7) therefore, to find the summation of the series 1+1+1+ . . ., one must only substitute in the correct parameters. since the starting value is 1 and the distance between terms is 0, this yields !! i=1 1 = ! · 1 + ! 2 · 0 2 # ! · 0 2 (8) = ! + 0 # 0 (9) = !. (10) it is intuitively obvious that since there are ! 1s added together that the sum of them would add up to !, as would be true for any finite value as well. this matches the value given by equivalent considerations in (1). the arithmetic series 1+ 2+ 3+ . . . can be calculated using hyperreals as well. !! i=1 i = ! · 1 + ! 2 · 1 2 # ! · 1 2 (11) = !2 2 + ! 2 . (12) the next arithmetic series to examine is 1+3+5+ . . ., which can be similarly calculated. !! i=1 (2i # 1) = ! · 1 + ! 2 · 2 2 # ! · 2 2 (13) = !2. (14) thus, the value of 1 + 3 + 5 + . . . is equal to (1 + 1 + 1 . . .)2. interestingly, as noted in section 3, there is nothing intrinsically infinite about the behavior of ! in these series. for instance, if ! was replaced with 5, the results would hold. that is, (1 + 1 + 1 + 1 + 1)2 = (1 + 3 + 5 + 7 + 9) = 25. even though the sums are divergent, summing them has a very well-defined behavior within the combined hyperreal/partial sum methodology presented here. 6.2 geometric series geometric series take the form n! i=1 ar i#1, (15) where n is the number of terms, a is the starting term, and r is the common ratio. a value for a geometric series can be given by the formula n! i=1 ar i#1 = a 1 # rn 1 # r . (16) because an infinite series will have ! terms, n can be replaced with !. let us begin by looking at the series 1+ 2+ 4+ 8+ . . .. the value of this series can be given by the formula !! i=1 2i#1 = 1 · 1 # 2! 1 # 2 (17) = 2! # 1. (18) 10 hyperreal numbers for infinite divergent series divergent geometric series will generally have the same form. convergent series are also interesting. the series 1+ 1 2 + 1 4 + . . . can be plugged into the formula to yield !! i=1 1 2 i#1 = 1 · 1 # 1 2 ! 1 # 1 2 (19) = 2 # 2 · #1 2 $! (20) 7 generalizing to the principal value in most discussions of hyperreal numbers, the halo of a number is considered the hyperreal values which are infinitely close to a standard real number. however, this definition is too focused on real numbers. we will consider the order of a hyperreal value to be its largest exponent of !. this is the most significant term of the hyperreal value. we will call this most significant term the principal value of the hyperreal. the halo (also known as a monad) of a hyperreal consists of all of the hyperreals which have the same principal value.4 we will use the $ operator to denote two hyperreals which share the same principal value.5 therefore, the halo of a hyperreal number consists of all of those numbers which share the same principal value. many people use “infinitely close” as a colloquialism to describe two hyperreals which share the same principal value. however, technically it is not correct, since, when dealing 4most texts on hyperreal numbers define the halo or monad of x to be all of the values y for which x # y is infinitesimal (loeb and wol!, 2015, pg. 21) (goldblatt, 1998, pg. 52). however, defined in such a way, the infinitesimals !#1 and 2!#1 are within a monad. using principal values, !#1 and 2!#1 are in the same galaxy, but not the same monad. you would have to have a term of lower-order infinity to be within a monad, such as !#1 and !#1 + !#2. this seems to be the essence of what the other texts are getting at, but, since most mathematics focuses on the reals, their definitions were entirely based on using reals as a starting point. here, since we will have results in the hyperreals, we need definitions that are equally useful when the final result is a hyperreal number. 5in practice, $ can be replaced with =, as it denotes equality to the extent normally practiced in mathematics. for instance, the di!erential d (xy) is often stated as being equal to x dy + y dx, but really it is just the principal value. the actual value is x dy + y dx + dy dx. the dy dx term is always discarded because it is infinitely less significant than the other pieces. even when discarding this term, the equality sign is used. therefore, while the present paper will be pedantic about asserting exact equality or mere principal value, for most general purposes equality can be asserted even when only stating the principal value. with infinities, two hyperreals which di!er by multiple infinities can be considered “infinitely close.” that is, !2+5!, !2 # 12!, and !2 + 23 all share the same principal value, !2. they are infinitely apart, yet, colloquially, they can be considered “infinitely close” because their di!erences are infinitely less significant than their similarities. when dealing with hyperreals, the principal value is the main one of concern. so, for instance, while 1 + 2 + 3 + . . . is exactly described by !2 2 + ! 2 , its principal value is just !2 2 . therefore, the formula given in (7) can actually be simplified to !! i=1 a + (i # 1)d $ ! 2d 2 (21) if d ! 0.6 interestingly, we can see that, while the exact value of the hyperreal associated with a series depends on the starting point, the principal value depends only on the distance chosen, provided that d ! 0. geometric series can use similar considerations. you may have noticed that the hyperreal given for the series 1 + 1 2 + 1 4 + . . . in section 6 is 2 # 2 · % 1 2 &! . typically, this series is thought to converge to 2. in fact, its principal value is 2, because % 1 2 &! is an infinitesimal. the use of principal values allows for a great amount of simplification for hyperreal values and formulas. as an example, the ratio between two given arithmetic series can be solved for very simply. s1 = !! i=1 a1 + (i # 1)d1 $ !2(d1) 2 s2 = !! i=1 a2 + (i # 1)d2 $ !2(d2) 2 s1 s2 $ !2 (d1) 2 !2 (d2) 2 = d1 d2 (22) in other words, the principal value of the ratio of two arithmetic series is simply the ratio of the distances. 6when d = 0, then the !2 term goes to zero, and the series simplifies to a ·! instead. volume 2, issue 1 8. series manipulation rules for finite subsets 11 8 series manipulation rules for finite subsets many attempts to manipulate divergent series have resulted in contradictions, to the extent that many suggest that it is best to not attempt to do so. the reason for these contradictions, however, lies in the treatment of the infinite nature of the number of values. in the real system, " is considered a boundless number. that is, there is not "+1 that is distinct from ". likewise, "#1 is also infinity. essentially, within the real numbers, " is used largely like an ambiguous infinite value, essentially saying that “the real numbers can’t handle this value.” if, instead, the hyperreal numbers are used, then ! and ! + 1 are distinct quantities, despite the fact that they are both infinite. the rules for manipulating series come from these ideas. see section 11 for a possible exception to these rules. 8.1 finite term addition to begin with, it is possible to easily add a scalar value to a series, provided that it is added to one of the particular terms of the series. in other words, suppose the value a is added to the series 1 + 2 + 3 + . . .. this can be written as a + !! i=1 i (23) or as a + (1 + 2 + 3 + . . .). (24) to integrate a into the series, a can be added to any distinct position. the series could read as (a + 1) + 2 + 3 + . . . (25) or 1 + 2 + (a + 3) + . . . . (26) all of these yield the same value for the final series, as long as partial sums are taken starting after the index where a is added. additionally, a can be spread across multiple finite terms. for instance, half of a could be added to each of the first two terms, yielding a + (1 + 2 + 3 + . . .) = ' 1 + a 2 ( + ' 2 + a 2 ( + 3 + . . . . (27) in fact, there is no reason why the same amount would have to be distributed to each position. a + (1 + 2 + 3 + . . .) = # 1 + 2 5 a $ + # 2 + 3 5 a $ + 3 + . . . (28) 8.2 finite term insertion and removal because this method of summation is based on partial sums, it should be apparent that inserting and removing terms will in fact alter the summation. for instance, let’s begin with the arithmetic sum 1+1+1+ . . .. it may seem intuitive that one should be able to freely add or remove a 1 from this sum without a!ecting the sum. in this particular series, the exact hyperreal value does change, but not the principal value. again, remember that, as mentioned in section 3, this conception of summation will be based on partial sums. so, let us begin by considering the partial sum k! i=1 1. (29) if k is a finite number, then adding one to this sequence will in fact alter its value. additionally, removing a 1 from this sequence will also alter its value. therefore, k! i=1 1 ! 1 + k! i=1 1. (30) likewise, k! i=1 1 ! k! i=0 1 ! k! i=2 1. (31) because performing these operations will change the value for any partial sum of k terms for a finite k, they will also change the value for a hyperreal k such as !. however, for these particular series, the principal value will be the same, because ! $ ! + 1 $ ! # 1. additionally, a more surpising fact is that removing a term from a sequence also changes its value if it does not also change the number of terms being summed. consider the series 1 + 2 + 3 + . . . = !! i=1 i. (32) this series is not equal to the series 1 + !! i=1 (i + 1). (33) 12 hyperreal numbers for infinite divergent series although it does have the same principal value in this case. in other words, (1 + 2 + 3 + . . .) ! 1 + (2 + 3 + 4 + . . .) (34) but (1 + 2 + 3 + . . .) $ 1 + (2 + 3 + 4 + . . .). (35) the reason for this is readily apparent when considering how these work in terms of partial sums. if the parameter k was used instead of !, then it is apparent that the value of (33) actually has an extra term compared to (32). that is, it is obvious that 5! i=1 i ! 1 + 5! i=1 (i + 1). (36) this can also be seen in the results of applying the arithmetic series formula to the two series. for (1 + 2 + 3 + . . .) the formula yields !2 2 + ! 2 . however, for (2+ 3+ 4+ . . .) the formula yields !2 2 + 3 2!. now, terms can be removed without even a!ecting the exact hyperreal value if they are replaced by zeroes in the sequence, or if the sequence starting index is moved appropriately. in other words, (1 + 2 + 3 + . . .) = 1 + (0 + 2 + 3 + . . .) = 1 + !! i=2 i. (37) this can be easily proved using the principle derived in section 8.1. for instance, to move the 1 outside of the series, 1 + #1 can be added to the series. 1 + #1 + (1 + 2 + 3 + . . .) = 1 + ((1 + #1) + 2 + 3 + . . .) = 1 + (0 + 2 + 3 + . . .) (38) 8.3 finite term rearrangement as can be deduced from sections 8.1 and 8.2, any number of finite terms in a series can be rearranged in position. that is, for any given series member with a value of a, a # a can be added to the series, applying the #a such that it cancels out the value of the series member. after doing this to several series members, the inverse operations can then be applied to move these values to any finite position in the series. doing this will preserve the partial summing behavior of the series for all partial sums after the members which have been manipulated. 9 more advanced series while basic formulas for divergent series of arithmetic and geometric series can be established using the standard formulas, more advanced series require the use of discrete integral calculus7 to establish the formulas for such series. doing so leads to very interesting results. 9.1 cesàro sums and oscillating series oscillating series have an interesting history of treatment within mathematics. the standard series to consider is grandi’s series: 1#1+1#1+ . . .. or, written more formally, "! i=1 (#1)i+1. (39) partials sums for this series can be found by performing a discrete integral. n! i=1 (#1)i+1 = 1 2 (#1)n+1 + 1 2 . (40) what is particularly interesting about this formula is that the cesàro sum of the infinite series ( 1 2 ) is present in the formula. now, consider the oscillating series #1 + 1 # 1 + . . .. this series has the formula "! i=1 (#1)i . (41) a discrete integral of the partial sums yields the formula n! i=1 (#1)i = 1 2 (#1)n # 1 2 . (42) note that in this as well, # 1 2 is the cesáro summation of the infinite series. this leads to the conjecture that, in evaluating infinite series using integral formulas, (#1)" = 0, (43) at least for additive o!sets of !. for instance, in the case of grandi’s series, using the ! notation, the infinite series would include (#1)!+1. the other series includes (#1)! . according to the present conjecture, both of these simplify 7also known as symbolic summation. see, for instance, chapter 2 of graham, knuth, and patashnik (1994). volume 2, issue 1 9. more advanced series 13 to 0, at least for the purpose of creating formulas for infinite series based on partial sums. this can be understood probabilistically. since we have no information about what sign #1! will have, we can say that #1! = ±1. (44) since both of these possibilities are equally probable, the limit towards infinity resolves to their average, or zero. also, since we have no information about the sign of #1! , we have equally little information about the sign of #1!+1, or any other variation on ! which is not biased towards evenness (e.g., 2!). the expression #1x has an oscillation pattern very similar to sin(x). since (paterson, 2018a) showed that sin(!) = 0 in the surreal numbers, it is possible that a similar proof may be found for #1! = 0 along similar lines in the hyperreals. 9.2 other oscillatory behavior because (a) discrete integration can be used to find formulas for series involving partial sums, and (b) the behavior of (#1)" (for infinities without bias towards evenness) is conjectured to be zero, the behavior of a wide variety of oscillatory behaviors can be deduced. raising #1 to the ith power can produce all sorts of oscillatory behavior. as has been seen with grandi’s series, this can produce a series of values that go back-and-forth across a mean value (the mean value can be changed by adding, and the back-and-forth can be changed by multiplying). however, (#1)i can also be expanded to blank out members of a series. for instance, to blank out every other member of a series, the formula ((#1)i + 1) 2 (45) can be used. this simplifies to 1 where i is even and 0 when i is odd. therefore, by multiplying a given formula by (45), odd-indexed terms of the given formula will be zeroed out. for instance, take the series 1 + 2 + 3 + . . .. this series can be converted to the series 0+2+0+4+0+6+ . . . by applying (45). this gives the series !! i=1 i · ' ((#1)i + 1) 2 ( . (46) the discrete integral yields n! i=1 i · ' ((#1)i + 1) 2 ( = 1 8 % 2n2 + 2n(#1)n + 2n + (#1)n # 1 & (47) when n = ! the formula runs into a problem with simplifying this through the conjecture (43) because it yields an indeterminate form. the term 2n(#1)n becomes an indeterminate form of the type ! · 0. this can be resolved, however, through l’hospital’s rule. lim n%" 2n (#1)#n = 2 # ln(#1)(#1)#n = # 2 ln(#1) (#1)n . (48) now (43) can be applied without ambiguity, simplifying it to zero. therefore, for n = !, (47) simplifies to n! i=1 i · ' ((#1)i + 1) 2 ( = 1 8 % 2n2 + 2n # 1 & . (49) this means that the value of this sum in the hyperreals is 1 4! 2 + 1 4! # 1 8 $ 1 4! 2. interestingly, this is a di!erent result than for the simple series 2+4+6+ . . .. since 2+4+6+ . . . is a simple arithmetic series, we can determine the hyperreal sum using (7). !! i=1 2 + (i # 1)2 = !2 + ! $ !2. (50) this is a di!erent result than what was obtained for 0+ 2+ 0 + 4 + 0 + 6 + . . ., which was 1 4! 2, indicating that the two series have di!erent behaviors. 9.3 1 # 2 + 3 # 4 + . . . euler’s sum for the series 1#2+3#4+ . . . can be confirmed using this method as well. this series can be given the value n! i=1 i(#1)i#1 = 1 4 % #2n(#1)n + (#1)n+1 + 1 & . (51) using (43) and (48) this simplifies to 1 4 . interestingly, this is a series that is not changed even in its exact hyperreal by prepending a zero to the function. n! i=1 (i # 1)(#1)i = 1 4 % 2n(#1)n + (#1)n+1 + 1 & . (52) likewise, (43) allows this to reduce to 1 4 . 14 hyperreal numbers for infinite divergent series 10 whole series manipulation rules in addition to manipulation of finite partial sums of a series, certain operations can (and can’t) be performed to the series as a whole. in this section, some of these operations will be considered. 10.1 scalar multiplication because of the distributivity of multiplication, multiplication of a series by a scalar value will distribute the scalar multiplication to every term. 2(1 + 2 + 3 + . . .) = (2 · 1 + 2 · 2 + 2 · 3 + . . .). (53) or, written as a formula, n !! i=1 f (i) = !! i=1 n f (i). (54) 10.2 whole series addition adding two series together is equivalent to a term-by-term addition of the series. since the method presented here is based on partial sums, term-by-term addition only works when the lower and upper bounds of the terms are identical. therefore, ! " !! i=1 f (i)#$ + ! " !! i=1 g(i)#$ = !! i=1 f (i) + g(i). (55) however, ! " !! i=0 f (i)#$ + ! " !! i=1 g(i)#$ ! !! i=1 f (i) + g(i) (56) because the limits of summation di!er. again, to see why this is the case, imagine replacing ! with a fixed scalar such as 5. in (56), the left-hand addend would have a di!erent number of terms than the right-hand addend. 10.3 series spacing as noted in section 8.2, adding or removing elements of a series, even if they are zero, has an e!ect on the sum of the resulting series. this e!ect can be calculated using the considerations discussed in section 9. for instance, the series 1 + 1 + 1 + . . . can be spaced out by adding in zeroes, to make 1 + 0 + 1 + 0 + . . .. a variation of the oscillatory pattern in (45) can be used to give the series the formula n! i=1 ((#1)i+1 + 1) 2 . (57) the discrete integral of this yields the formula 1 2 n + 1 4 (#1)n+1 + 1 4 (58) using conjecture (43) this reduces to the hyperreal value 1 2! + 1 4 $ 1 2!. this is a slightly di!erent value (but with the same principal value) than for the series 0 + 1 + 0 + 1 + . . .. this series can be represented as n! i=1 ((#1)i + 1) 2 = 1 2 n + 1 2 (#1)n # 1 4 . (59) using conjecture (43), the hyperreal value for this is 1 2! #1 4 $ 1 2!. if (58) and (59) were added, it should be equivalent whether they are added term-by-term (section 10.2) or by summing their relevant values. summing term-by-term it is apparent that (1 + 0 + 1 + 0 + . . .) + (0 + 1 + 0 + 1 + . . .) = (1 + 1 + 1 + 1 + . . .). (60) the value of this series was deduced to be ! in (3). likewise, if the values for each series are added the result is #1 2 ! + 1 4 $ + #1 2 ! # 1 4 $ = !. (61) 11 ongoing and future work 11.1 proving #1" = 0 the first obvious point of future work is the proof of the conjecture in (43). work on this proof is ongoing and is promising. 11.2 representing infinitesimal values in general, the methods in this paper are about representing infinite values using a series of finite terms. however, it volume 2, issue 1 references 15 may also be possible to write an infinitesimal value in a similar way. while it is outside the scope of the present paper, there is some evidence that, for instance, the series 1 + #1 + 0 + 0 + 0 + 0 + . . . (with the zero repeating forever) represents an infinitesimal value. this means that the rules established in section 8 are limited to cases where the principal value is finite or infinite. 12 conclusion here a method of summation was presented that uses the structure of the hyperreal numbers to represent values for divergent series. this methodology was shown to be stable across a variety of di!erent scenarios. one unproven, but seemingly correct, conjecture was relied upon for this formulation. future work will focus on proving (43). 13 acknowledgements i wanted to take a moment to thank stanley schmidt. i was thinking on this problem at the same time i was reading his life of fred books to my children. the fundamental idea for this method of summation came from thinking about gaastra’s original presentation (gaastra, 2016) while reading life of fred: kidneys to my children, when fred was using the formula for arithmetic series (schmidt, 2012). additionally, the infinite by a. w. moore provided some help to the imagination in his discussion of the löwenheimskolem theorem. the basics of the discussion was to point out that there was little in the theory of infinities that were really unique to infinity. even finite sets can look “infinite” in some ways to other sets. the techniques and ideas explored in section 3 were based largely o! of thinking about infinities as much more tame and finite-like than is normally considered. finally, i want to thank jessica hastings, whose interest in the “wheat and chessboard” problem(weisstein, 2018) originally introduced me to the concepts in discrete calculus. references gaastra, l (2016). “omega: how hilbert’s infinite hotel can be used to evaluate divergent series”. in: grcc student mathematics seminars. url: https://www. youtube.com/watch?v=nlwh9oyiqye. goldblatt, r (1998). lectures on the hyperreals: an introduction to nonstandard analysis. springer. graham, r l, d e knuth, and o patashnik (1994). concrete mathematics. new york: addison-wesley. henle, j m and e m kleinberg (2003). infinitesimal calculus. dover publications. keisler, j (2012). elementary calculus: an infinitesimal approach. second. dover books. loeb, p a and m p h wol! (2015). nonstandard analysis for the working mathematician. second. london: springer. paterson, d a (2018a). “banishing divergence part 1: infinite numbers as the limit of sequences of real numbers”. in: arxiv 1108.5081v1. url: https://arxiv.org/abs/ 1108.5081. paterson, d a (2018b). “banishing divergence part 2: limits of oscillatory sequences and applications”. in: arxiv 1108.4952v1. url: https://arxiv.org/abs/ 1108.4952. schmidt, s (2012). life of fred: kidneys. polka dot publishers. weisstein, e w (2018). “wheat and chessboard problem”. in: mathworld—a wolfram web resource. v2i1 volume 2, issue 1 letters and notes divergent series and its assigned value in a hyperreal context bas van der reijden doi: 10.33014/issn.2640-5652.2.1.reijden.1 abstract this letter discusses the deep connection between the infinite sum of natural numbers and the value ! 1 12 . aside of more widely known facts, we consider a nontrivial way in which we show the veracity of this connection; more precisely this concerns the bgn method (bartlett, gaastra, and nemati, 2020) applied on the so-called damped oscillated abel summed variant of the series. moreover, we have found a generalization of this method which ‘correctly’ assigns finite values to other divergent series. we conclude with some questions concerning whether and how we can analytically relate our hyperreal terms to frame the method in a more justifiable and applicable context. background it is obvious that the sum of natural numbers 1+2+3+ · · · tends to infinity and can thus not be equal to ! 1 12 . there does however exist some connection between this series and value and it is highly probable that this connection is implicitely used (i.e. ‘under the hood’) in e.g. physics (which often turns out to be perfectly justifiable, as can be shown by various experiments). the first evidence of this connection is retrieved when one considers the riemann zeta function ! (s). it is known that ! (s) is equal to ! 1 12 when s = !1 and it is interesting that one retrieves the sum of natural numbers when one ‘plugs in’ s = !1 at the defining series of the riemann zeta function !" k=1 1 k s . plugging s = !1 in the above series is unfortunately not justifiable (given that ! (s) is only equal to this series when #(s) > 1) but it remains an interesting thing to mention. another evidence of the connection can be revealed when figure 1: smoothed partial sums !n k=1 k with a yintercept of ! 1 12 . one considers the ‘smoothed version’ of the partial sums!n k=1 k, see also tao, 2010. it turns out that these smoothed partial sums have the same behaviour as the regular partial sums (i.e. they have the same asymptotic expansion) and thus tend to infinity when n $ ". however, one probably recognizes the constant value in its asymptotic expansion, which is (according to tao (2010)) given by cn2! 1 12+o( 1 n ) (with c some coe!cient of little importance in this case). moreover, it is given that ! 1 12 is attained when one looks at the intersection with the y-axis in figure 1. damped oscillations the first two evidences we mentioned are quite widely known but a more unknown fact can be observed when one considers a damped oscillating variant of the series 1 + 2 + 3 + · · · , namely "" k=1 ke!k! cos(k" ). (1) 30 letters and notes this variant was also discussed in a previous letter (bartlett and khurshudyan, 2019). in this letter it was also mentioned that, in the context of hyperreal numbers by introducing # := " (i.e. by appying the bgn method on it), (1) can be written in a closed-form expression (or at least as an approximation of it). it remained however still unclear which value/magnitude the infinitesemal quantity " must be1 in order that the bgn method applied on (1) equals the ‘appropriate’ value ! 1 12 ; only numerical evidence was given. in particular, it was shown that if " = 1 " , the computing software “wolfram mathematica” will include the constant ! 1 12 in its bgn expression (which is similar to the observation of the previous paragraph). at the time that bartlett and khurshudyan (2019) was written, it only seemed clear that there is a numerical evidence that (1) equals ! 1 12 when we take " in a su!ciently small interval. recently, we have found that sugiyama (2014) (section 2.3) provides a more theoretical derivation of this matter. although the website and its choice of words are somewhat vague and confusing, the derivation seems correct. in this derivation there is being made use of a so-called ‘damped oscillated abel summation method’, which is a kind of generalization of the more common abel summation method used to assign finite values to divergent series. in this article, this method of ‘damped oscillated abel summation’ is consequently used on a larger class of divergent series as well; furthermore it turns out that the ‘damping’ and ’vibrating’ constant should not be necessarily equal to each other. we thus in fact have that (see also section 5.2 and section 6.1 of sugiyama (2014), we here write " instead of x) !" k=1 k i can be transformed to (letting i % 1 be an integer) "" k=1 k ie!k! cot ! 2i+2 cos(k" ) and "" k=1 k ie!k i+1 2 ! cos(k i+1 2 " ) and consequently taking the limit " $ 0 yields the ‘appropriate’ assigned value; we also numerically verified this2. it remains of course interesting how this damped oscillated abel summation method can be stated in our more ‘detailed’ hyperreal context; i.e. in which we know the exact values of " (possibly in terms of #) in order that the bgn method assigns the ‘appropriate’ value to a divegent series. unless it is still untrivial which values " must have in order that the mentioned method assigns this value, we can however say from equation (5.57) in sugiyama (2014) that in 1in relation to " 2by again letting ! be in a su!ciently small interval general 1 ! must be a lot smaller than # (this was also shown by numerical experiments: if we set " = 0.01, # must be a lot larger than 100). conclusion in conclusion, we can thus say that the connection between the often assigned value of a divergent series is hidden in its asymptotic expansion. furthermore, some slight variations (performed in the context of hyperreals) of the terms in the divergent series will alterate its asymptotic expansion in such a manner that that the bgn method assigns the ‘desired value’ to it. as it is at this point still untrivial when equality holds, and how in this case " and # thus must be related, remains an interesting topic for further research. to state this in a more general and mathematically way: consider a divergent series with bgn expansion a(" (#))#2 + c + o(1/#) (here a is a value dependent of " which is in turn dependent of # and c is the ‘appropriate’ value we want to have), the question is now which variations (in terms of " (#)) we have to make in order to make a(" (#))#2 equal to zero. bartlett, j, l gaastra, and d nemati (2020). “hyperreal numbers for infinite divergent series”. in: communications of the blyth institute 2.1, pp. 7–16. bartlett, j and a khurshudyan (2019). “numberphile’s proof for the sum 1+2+3+...” in: communications of the blyth institute 1.1, pp. 54–55. sugiyama, k (2014). new proof that the sum of natural numbers is -1/12 of the zeta function. url: https : / / xseek qm . net / regularization _ e . htm # _toc524947400 (visited on 11/16/2019). tao, t (2010). the euler-maclaurin formula, bernoulli numbers, the zeta function, and real-variable analytic continuation. url: https://terrytao.wordpress. com/2010/04/10/the-euler-maclaurin-formulabernoulli numbers the zeta function and real-variable-analytic-continuation/ (visited on 01/07/2019). v2i1 volume 2, issue 1 on the logic of being and wigner’s astonishment regarding the applicability of mathematics 31 do mutation rates match the kelly criterion? jonathan bartlett doi: 10.33014/issn.2640-5652.2.1.bartlett.2 the kelly criterion defines an optimal betting strategy for games that have a defined risk and payo!. it was developed by john kelly, jr. at bell labs (kelly, 1956). given a bet with a probability of success p and a payout of b, the kelly criterion tells you the size of your bet compared to your overall bankroll. the kelly criterion is given as pb + p ! 1 b (1) this formula can be derived from a formula for an expected total payo! of the bet given by the equation t = a(1 + b f )np (1 ! f )n (1!p) (2) where t is the total winnings, a is your starting amount, n is the number of trials, and f is the bet size. optimizing for t yields equation 1. many researchers have discussed the concept of mutations in populations as “bet hedging.” (philippi and seger, 1989; bartlett, 2008; simons, 2011; grimbergen et al., 2015) since the kelly criterion allows one to at least theoretically calculate the optimum bet size for each configuration, it might be possible to calculate various optimum mutation rates at di!erent sites and compare them to their optimal size according to the kelly criterion, or an adjusted version of it. most analysis of bet hedging has merely checked to see if the hedging strategy is empirically beneficial (childs, metcalf, and rees, 2010; simons, 2011) or potentially evolvable (king and masel, 2007). applying the kelly criterion may be able to help determine how optimal organisms’ various bet hedging strategies are. one possible experimental approach would be to provide organisms with a long-term, continually-varying environment. after many generations, it would be interesting to check if the mutation rates for adaptive switching between environments had any relation to the theoretical considerations of the kelly criterion, or any other theoretical hedging system. bartlett, j l (2008). “statistical and philosophical notions of randomness in creation biology”. in: creation research society quarterly 45, pp. 91–99. childs, d z, c j e metcalf, and m rees (2010). “evolutionary bet-hedging in the real world: empirical evidence and challenges revealed by plants”. in: proceedings fo the royal society b: biological sciences 277, pp. 3055– 3064. doi: 10.1098/rspb.2010.0707. grimbergen, a j et al. (2015). “microbial bet-hedging: the power of being di!erent”. in: current opinion in microbiology 25, pp. 67–72. kelly, j l (1956). “a new interpretation of information rate”. in: the bell system technical journal 35, pp. 917–926. url: http://www.herrold.com/ brokerage/kelly.pdf. king, o d and j masel (2007). “the evolution of bethedging adaptations to rare scenarios”. in: theoretical population biology 72, pp. 560–575. doi: 10.1016/j. tpb.2007.08.006. philippi, t and j seger (1989). “hedging one’s evolutionary bets, revisited”. in: trends in ecology and evolution 4.2, pp. 41–44. simons, a m (2011). “modes of response to environmental change and the elusive empirical evidence for bet hedging”. in: proceedings of the royal society b: biological sciences 278.1712, pp. 1601–1609. doi: 10.1098/rspb. 2011.0176. url: https://royalsocietypublishing. org/doi/10.1098/rspb.2011.0176. on the logic of being and wigner’s astonishment regarding the applicability of mathematics gordon e mullings doi: 10.33014/issn.2640-5652.2.1.mullings.1 the nobel prize winning physicist, eugene wigner, famously posed a powerful challenge (1960) by asking why is mathematics so e!ective, especially in the physical sciences (wigner, 1960). it is possible that the reason for the e!ectiveness of mathematics is not because mathematics is in any way causative, but instead because mathematics studies the structure of logical possibility and constraint. when plugged into a possible world, mathematics gives us the tools to analyze the logically possible outcomes. therefore, when a possible world that is expressed mathematically su"ciently aligns with reality, mathematics becomes e!ective at expressing relationships and outcomes. 32 letters and notes for example, beings (as well as possible beings and things impossible of being) can be understood in the context of possible worlds. a “possible world” is a su"ciently complete description of possible states of a!airs described through chains of propositions. we may observe that things impossible of being, such as a square circle, have in them mutually inconsistent required core attributes; they cannot be realised in any possible world. possible beings would exist in at least one possible world were it actualised. for instance, a contingent being b that depends on c might exist in a world w and not in a closely neighbouring one w " if c is present in w but not w "; c thus being an enabling, necessary causal factor for b. by contrast, a necessary being f will exist in all possible worlds, showing itself to be a framework element for such a world. a key insight is that for any world w to be distinct from w " it requires some factor a in w that is absent in w ". we may then partition the factors of w as w = {a|¬a}. after partitioning, we will have two distinct groups—the factor a and all of the factors which are not a. the null set corresponds to zero. each particular set in the partition can be counted as the number one, and the combination of both partitions (even in a single world where a is an empty set) is two. thus, for any particular possible world w , the quantities 0, 1, 2 are necessarily present. taking the von neumann construction, immediately we find n, thence (using additive inverses) z, so also (taking ratios) q and (summing convergent power series) r; where z provides unit-stepped mileposts in r. that is, a structured core of quantities will be present in any w , and we may regard mathematics as the study of the logic of structure and quantity. extensions to the hyperreals r# follow by construction of some h that has as reciprocal h = 1 h closer to 0 than 1 n for any n in n. therefore, relationships and linked operations across such quantities will also be present, or may be constructed as needed. illustrating, after abraham robinson (robinson, 1966), hyperreals allow calculus to be treated as extensions of algebra in r#. thus, while bare distinct identity and coherence focused on quantities will not cause things by the inherent potential or action of such entities, they instead are logical constraints on being and are tied to what can or must be or cannot be or happens not to be. so, too, we may see that the abstract logic model worlds that we may construct then lead to key entities that if necessary are framework to any possible world; thus applicable to our common world. by contrast, if certain quantities and relationships are merely part of the contingencies of some w "" that is close enough to our own, they may provide adequate analogies for modelling. as a result, we have good reason to expect that mathematical reasoning and core entities will in many cases be highly relevant to and have powerful predictive power for our common world. robinson, abraham (1966). non-standard analysis. amsterdam: north-holland publishing company. wigner, eugene (1960). “the unreasonable e!ectiveness of mathematics in the natural sciences”. in: communications in pure and applied mathematics 13.1, pp. 1–14. doi: 10.1002/cpa.3160130102. independence conservation and evolutionary algorithms eric holloway doi: 10.33014/issn.2640-5652.2.1.holloway.2 levin’s law of independence conservation leonid levin’s 1984 article (levin, 1984) is the first to this author’s knowledge to prove a fully stochastic conservation of information law. levin titled his law ’independence conservation’ which he considered fairly obvious, describing it as “torturing an uninformed witness cannot give information about the crime!” levin’s law is not well known, which is unfortunate since the more commonly known conservation laws are focused either only on the random or deterministic case. levin’s law is remarkable because it unifies both the random and deterministic cases, showing that the combination also cannot result in information increase. the second remarkable thing about his law is how easy it is to prove, given some preliminaries about algorithmic information. login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians v1i2 volume 1, issue 2 the random design argument an example of science under theological influence cornelius hunter doi: 10.33014/issn.2640-5652.1.2.hunter.1 abstract the “random design argument” is a popular mode of justification, used to prove that scientific theories are true. the first part of this argument is that, if god had designed x, the features of x would approximate randomness. the second part of this argument is that random design can therefore be used, in the form of a null hypothesis, as a proxy for design. if the null hypothesis can be falsified, then design is falsified and contingency is confirmed. the random design argument has two important problems that have gone unrecognized. first, though presented as a finding of empirical science, it relies on theological claims. second, though presented as a null hypothesis, there is no justification that random design is the logical complement of the scientific theory in question. despite its failings, the random design argument has a long history of use for justifying and proving scientific hypotheses. this paper documents several areas where the random design argument has been used (both currently and historically) as well as the logical problems with the argument. 1 introduction in his book the evidence for evolution, alan rogers employs contrastive reasoning to argue that evolutionary theory is far superior to creationism. regarding the universal genetic code, he explains that as with human language, the genetic code is arbitrary. nothing forces us, for example, to use the word “bird” for animals with wings and feathers. rogers concludes: “different species could have different genetic codes just as easily as different human populations speak different languages. but they don’t. every living thing—from the smallest microorganism to the largest whale—makes protein using essentially the same arbitrary code. what sense does this make, unless all these forms of life evolved from a single ancestor?” (rogers, 2011, pg. 31) the two key premises in rogers’ argument are that the genetic code is arbitrary, and that it is universal. in other words, the code’s design space is unconstrained (most any code would work), but in practice the code is highly constrained (all species have essentially the same code). there is a stark contrast between the potential and the actual. the different species “could have different genetic codes . . . [b]ut they don’t.” this for rogers is powerful evidence against independent creation and for evolution. but why? superficially this appears to be a weak argument. rogers’ argument appears to amount to the following logical flow. if the species evolved, then it is plausible, or likely, that the genetic code is identical or highly similar across the species. but if the species were independently created, then the genetic code could vary across the species. an interlocutor would be delighted. clearly this argument does not rule out creationism. the argument does not even show that creationism is unlikely. yes, god could create different genetic codes in the different species, but we could just as easily state that god could create the same genetic codes in the different species. superficially, the argument does not seem to serve rogers’ purpose. the argument seems to be at best, trivial, and at worst, invalid, for the conclusion— that the evidence makes no sense except on evolution—does not follow from the premises. to make matters worse, the above example from rogers is not a rare exception. this argument—that the finding of a single characteristic in an otherwise unconstrained design space, where many alternative designs are possible, is evidence for evolution—is not uncommon (as we shall see in the following sections). furthermore, not only is this argument not uncommon, it is presented as powerful and decisive. have evolutionists made a terrible mistake in committing to, and promoting, an invalid argument? in this paper i demonstrate this is not the case. this evolutionary argument, as exemplified by rogers above, can be seen to be perfectly valid once the context is understood. the key to rogers’ argument is the underlying evolutionary premise that if the species were independently created, then their designs would fill the design space. the potential should be realized in the actual. there should be no gratuitous repetitions of a design. instead, designs should be scattered throughout the design space, leaving no dis24 the random design argument cernable gaps or patterns. exceptions can arise only if the design space is functionally constrained. that is, if only certain designs will work then, of course, some level of repetition will be required. that is why it is significant for rogers that the “[d]ifferent species could have different genetic codes.” [emphasis added] in other words, the design space is not constrained, and so under independent creation there is no reason why the species should not have varied genetic codes. but they do, and so contingency is implicated. mark ridley makes the argument more explicit in his evolution textbook. after explaining that the code is unconstrained, he concludes that “[t]he universality of the genetic code is important evidence that all life shares a single origin.” for it is “similar between species, but would not be if the species had independent origins.” (ridley, 1993, pgs. 48–49) here ridley makes explicit the expectation for independently created species. they must fill the design space. clearly this argument entails non empirical content. the origins and details of the underlying metaphysics are beyond the scope of this paper. i will merely refer to the argument as the “random design argument.” (following hunter, 2007 & hunter, 2014) the form of the random design argument is as follows: 1. god would create the fullest creation without gaps. 2. we observe arbitrary or idiosyncratic patterns which do not fill the full range of possibilities. that is, they do not fill the naturally available design space. 3. such patterns would not have been divinely intended, and so must have arisen via contingent events. step 1 states that a divinely designed world would have no unnecessary gaps. therefore, such a world would not be limited to a particular, single, design where multiple designs are possible. a divine design would explore the entire range. step 2 acknowledges that we find limitations in nature’s designs which do not seem to be necessary. that is, there are designs that could exist which do not exist. this suggests that nature has gaps, and its designs are arbitrary. step 3 concludes that this falsifies divine design, and therefore is strong evidence for contingency. evolutionists often express this argument qualitatively, as exemplified by rogers and ridley above. but it also lends itself conveniently to a powerful quantitative form: null hypothesis testing. if it could be shown that random design is false, then contingency could be declared to be true. as we shall see in section 2, mathematical techniques were developed in the early eighteenth century to perform this type of test. in the twentieth century, the modern discipline of statistics formalized null hypothesis testing. (fisher, 1935) the null hypothesis is the opposite of the hypothesis in question. that is, the null hypothesis is what is expected if the hypothesis in question, referred to as the alternate hypothesis, is false. if the null hypothesis can be shown to be statistically false, then the alternate hypothesis is declared true. in this simple form, the null hypothesis is rejected if its probability, computed as the so-called p value, is sufficiently small. when the null hypothesis is rejected, then the alternate hypothesis is accepted. this simple null hypothesis test presents a dichotomy, and for it to function properly it is crucial that no other explanations are possible. that is, there must be only one alternate explanation. otherwise, the test presents a false dichotomy. twentieth century null hypothesis testing formalized the earlier mathematical techniques developed in the eighteenth century (though i know of no connection between the two). as we shall see, the development of null hypothesis testing further bolstered this approach of statistically falsifying a model of what we expect of nature under random design. we will see in sections 2 and 3 that random design became the null hypothesis in cosmology and biology, respectively, even before such statistical tests were formalized in the early twentieth century. the random design model was represented by hypothetical designs that filled the design space and had no gaps. the design space should be full, with the designs appearing not at merely a few locations within the space, but rather throughout the space, at random. as we will see, the random design null hypothesis test was, and remains today, an extremely powerful and influential argument for contingency. today, it is a fixture of evolutionary reasoning that is common across numerous academic authors. finally, section 4 provides the conclusions of this study. 2 the influence of the random design argument in cosmological evolution isaac newton explained the solar system with his new physics and law of universal gravitation. the planets revolved about the sun, and the moons about their respective planets, according to the gravitational force and laws of motion. it was a grand unification of what had been volume 1, issue 2 2. the influence of the random design argument in cosmological evolution 25 aristotle’s two, very different, sub and superlunar regions. this new view of the cosmos was simple and stunning, and newton went on to make a series of arguments for why the solar system exhibits design rather than a naturalistic origin. first, newton argued that while his laws explained the operation of the solar system, they could not explain the origin of the solar system: the planets and comets will constantly pursue their revolutions in orbits given in kind and position, according to the laws above explained; but though these bodies may, indeed, persevere in their orbits by the mere laws of gravity, yet they could by no means have at first derived the regular position of the orbits themselves from those laws. (newton, 1687, pg. 440) newton also made an argument from what we might call fine-tuning. in order for the planets to fall into their concentric orbits about the sun, their velocities would need to fall into certain ranges, as he explained in a letter to richard bentley in 1692: nor is there any natural cause which could give the planets those just degrees of velocity, in proportion to their distances from the sun and other central bodies, which were requisite to make them move in such concentric orbs about those bodies. (danielson, 2000, pg. 228) finally, newton repeatedly argued that the patterns found in the solar system revealed design. specifically, while the comets exhibited random orbits, the planets and their moons exhibited consistent patterns. if the comets revealed what could be expected from the action of blind natural processes, the planets revealed a stark contrast of consistency. for while comets move in very excentrick orbs in all manner of positions, blind fate could never make all the planets move one and the same way in orbs concentrick, (newton, 1718) as william derham later reported, newton specifically noted that the planets revolve about the sun in the same direction, and that “their orbits have all the same inclination.” (manuel, 1968, pg. 127) newton was, of course, well aware that the planetary orbits did not share the exact same inclination angle. but they are sufficiently similar to form, at least roughly, a plane in which the planets travel as they orbit the sun. in comparison with the comets, whose orbits were at seemingly random inclination angles and in no relation to each other, the planets exhibited a striking pattern and similarity. but for what purpose was this pattern? newton’s argument that the solar system patterns revealed common design could be turned on its head. for the patterns could just as easily be seen as the result of a common mechanism. this was the view of mathematician and scientist daniel bernoulli in his award-winning 1734 essay on the origin of the solar system at the paris academy. bernoulli contrasted the inclination angles of the planets with a random design where the planetary orbits were inclined at random angles. if the planetary orbits had fallen into place by chance, it would be highly improbable that they would just happen to lie in practically the same plane. bernoulli gave three different calculations, all of which showed the odds were astronomical. he picked the middle result of the three, which was that the odds of such a coincidental alignment are 1,419,856 to 1. bernoulli arrived at this value by dividing the range of possible orbital inclination angles into 17 bins. the orbital inclination angles of the six known planets all fell into the same bin. if the planetary orbits were inclined at random angles, the chances of them all falling into the same bin would be 1 in 176−1, or 1 in 1,419,856. this is highly improbable so bernoulli argued that the sun’s atmosphere was the cause of the alignment of the planetary orbits. he who would deny this, concluded bernoulli, “must reject all the truths, which we know by induction.” (bernoulli, 1734) bernoulli’s 1734 paper is an example of what today would be referred to as null hypothesis testing, long before fisher’s formalization of this method in the twentieth century. the null hypothesis, in this case, states that the planetary orbits, and in particular their inclination angles, are randomly distributed over the space. the striking consistency of the planetary orbits is highly unlikely on this null hypothesis. therefore, bernoulli rejected it, and concluded his alternate hypothesis must be true, that the orbits were formed by the sun’s atmosphere. bernoulli’s paper was an early example of the random design argument. immanuel kant used similar reasoning twenty years later in his ambitious and expansive cosmological treatise.1 kant’s approach was a blend of mechanical principles and metaphysics. (shea, 1986, pg. 119) regarding the solar system, kant’s random design argument now added ten moons in addition to the six planets, and 1kant did not mention bernoulli, but he did make use of bernoulli’s 17 divisions of inclination angle in discussing the volume of space that would contribute matter to the forming planets. (kant, 1755, pgs. 53– 56) 26 the random design argument included additional orbital parameters: the axial rotation, and revolution about the sun, in addition to the orbital inclination angle. these movements have a continuous shared direction: of the six main planets and the ten satellites, not a single one moves, either in its forward motion or in its axial rotation, in any other direction than from west to east. moreover, these directions are so precisely coordinated that they deviate only a little from a common plane, and this plane, to which everything is related, is the equatorial plane of the body which rotates on its axis at the central point of the entire system in exactly the same direction and which has become, through its predominant power of attraction, the reference point for all motions and thus necessarily participates in them as precisely as possible. (kant, 1755, pg. 117) kant claimed this argument provided “proof that the collective movements arose and were determined in a mechanical way in accordance with general natural laws,” (kant, 1755, pg. 117) but he exaggerated the precision and consistency of these orbital parameters. indeed, he was well aware of variations in the orbital inclination angle, and struggled to explain them.2 nonetheless, kant was highly confident for he had, as he next explained, disproven the null hypothesis (to use modern statistical parlance). to elucidate on the proof, kant focused on the question of why the planets revolve about the sun in the same direction, for “it is clear that here there is no reason why the celestial bodies must organize their orbits precisely in one single direction, unless the mechanics of their development had determined the matter.” (kant, 1755, pg. 118) if they were arranged by the “immediate hand of god” then we would expect them to reveal deviations and differences. thus, god’s choice would not have the slightest motive for tying them to one single arrangement, but would reveal itself with a greater freedom in all sorts of deviations and difference. (kant, 1755, pg. 118) in kant, the random design argument is clear. the planets reveal a pattern rather than a random arrangement. therefore, the planetary orbits must have originated not by the immediate hand of god but by natural processes. kant 2kant appealed to qualitative, ad hoc, explanations for variations in orbital parameters such as eccentricity and inclination. (kant, 1755, pgs.48–49) argued the solar system arose from a condensing cloud of particles. kant was sure that the solar system arose via a mechanical sequence of natural laws. for kant, these arguments demonstrated the reality of a mechanistic origin so clearly that we can entertain “no doubts about it.” (kant, 1755, pg. 117) this was proof that the solar system arose mechanistically in accordance with general natural laws. in addition to bernoulli and kant, buffon and laplace proposed their own theories for the origin of the solar system. buffon replaced bernoulli’s solar atmosphere idea with a comet that collides with the sun, spewing forth solar material that would later condense to form the planets. buffon concluded that “it is therefore extremely probable, that the planets were originally parts of the sun.” (buffon, 1749, pg. 80) laplace replaced buffon’s idea with his nebular hypothesis. the nebular hypothesis called for a cloud of material about the sun that rotates and condenses to form the planets and sun. it was, claimed laplace, the “true system of the world.” (quoted in brush, 1996, pg. 22) in spite of their theoretical differences, both buffon and laplace used the random design argument, with their own refined versions of bernoulli’s calculation, to support their confident conclusions. buffon found that “by the doctrine of chances” the odds of such a coincidental alignment of the planetary inclination angles would be 7692624 to 1. (buffon, 1749, pg. 65) laplace made several calculations, eventually finding the odds of the solar system’s patterns to be 537 million to 1 if they had arisen by chance: laplace was familiar with newton’s opinion that the regular motions of the planets proved their divine design. we know he was acquainted with daniel bernoulli’s prize essay of 1734 on the subject, since in an earlier paper he had cited bernoulli’s method for calculating the probability that n bodies all move in the same one of two possible directions if their motions are selected by chance: 2(−n+1). in that paper laplace had applied the method to six planets and ten satellites, finding the probabilities to be 2−15 = 1/32768. by 1796 he had made the coincidence even more unlikely by including the seventh planet, uranus (discovered by william herschel in 1781), as well as four more satellites, saturn’s rings, and the rotations of five planets, the sun, the moon, and one of saturn’s satellites (iapetus). thus of the 30 known motions in the solar system, all are in the same direction. if these motions had been determined by chance, the probability that at least one of them would be different from the rest is extremely high (1 − 2−29). (brush, 1996, pg. 21) volume 1, issue 2 2. the influence of the random design argument in cosmological evolution 27 in the ideas of bernoulli, kant, buffon and laplace the random design argument was key. they established a random design argument tradition, using what today is referred to as a null hypothesis to argue against design and arrive at what was virtually a proof of their respective contingency hypotheses. in this tradition, the hypotheses were underdetermined and in most cases opposing or even mutually exclusive. but confidence was extremely high, not from theoretical successes but from the clear refutation of the null hypothesis. laplace could on the one hand be supremely confident and even assure napoleon of his contingency theory (brush, 1996, pg. 20) while, on the other hand, have nothing more than an underdetermined, untested, overarching notion of how the solar system actually arose. indeed, laplace failed to explain new observations such as the anomalous orbits of uranus’ moons, discovered by herschel: laplace was aware when he first published his theory that herschel had found the two satellites of uranus to have orbits in a plane nearly perpendicular to the plane of the ecliptic. in 1798 herschel announced that the satellites of uranus have retrograde motion. while this amounted to only a slight revision of his earlier result—the orbit plane is still nearly perpendicular but is tilted in the other direction—it was still [herschel explained] “a remarkable instance of the great variety that takes place among the movements of the heavenly bodies” since previously all known motions took place in the same direction. (brush, 1996, pg. 21) this was a remarkable variation, and it highlights a crucial aspect of this random design reasoning. the use of what we refer to today as null hypothesis testing allowed one to obviate the scientific activity of developing and deriving models, mathematical relationships, and mechanisms. instead, a dichotomy is drawn: either the design of the solar system is random, or else the solar system arose by a yet to be determined contingency. the alternate hypothesis does not specify any particular mechanism, that is the subject of after-the-fact theorizing. various mechanisms can be hypothesized or dropped, as needed. as we have seen, bernoulli, buffon, kant, and laplace each presented different mechanisms with complete confidence. investigations of possible mechanisms would be viewed as a sign of scientific progress, no matter how often they turn out to be flawed. meanwhile anomalies, such as the two satellites of uranus with perpendicular orbits, would be viewed as curiosities and grounds for further scientific research. they do no harm to the underlying null hypothesis rejection, for the most they can do is slightly nudge the statistics. furthermore, such anomalies can simply be ignored in the null hypothesis calculation, as laplace did. (brush, 1996, pg. 22) this approach of rejecting the random design null hypothesis made the science more of a statistical exercise than of providing specific and falsifiable models and mechanisms to adequately explain natural phenomena. to summarize these eighteenth century theories of the origin of the solar system, these theories included or promoted the following six important elements for our purposes. 1. the random design argument is not limited to objects, but also applies to design parameters. in this case, it was not the celestial bodies such as planets and moons themselves that were of concern so much as their orbital parameters. the direction of their revolutions about the sun, the direction of their spin, and the inclination angle of their orbits about the sun were of concern. newton referenced these parameters in his design arguments and now they had become subject to random design testing. 2. nature should present a full continuum of values of these orbital design parameters. those values should randomly fill the design space. the motivation here was from pattern, not mechanism. in other words, these new theories for the origin of the solar system were not motivated by the finding of a compelling, explanatory mechanism, but rather by the patterns found within the solar system structure. 3. this new tradition, based on the random design argument, produced highly underdetermined theories. whereas newtonian physics could claim a rather tight, mathematical, cause and effect relationship between forces and motion, this new tradition produced broad, phenomenological theories which did not provide detailed descriptions of the outcomes. while this is to be expected of such phenomenological hypotheses they, in fact, did not even account for the very observables, such as the planetary inclination angles, of concern to this tradition. that is, the different hypotheses of bernoulli, buffon, kant, and laplace, did not provide specific forces or causes that would result in, or explain, the observed variation in inclination angles, in any sort of direct sense. the solar atmosphere, a comet striking the sun, and a condensing cloud were meant to explain the common design parameters, but they did not provide any specific causes that would produce the variation in inclinations angles of the planetary orbits. 4. the contingency mechanisms were unrelated to the random design reasoning that had underwritten them. bernoulli’s solar atmosphere hypothesis, for example, 28 the random design argument did not derive in any way from his statistical calculations. the same is true for buffon’s, kant’s and laplace’s hypotheses. this new tradition consisted of a confirmation step (the falsification of the random design null hypothesis) which was entirely disjoint from the derivation of the mechanism. by falsifying design, the scientist was free to speculate about the mechanism, in spite of theoretical problems. 5. in spite of the theoretical shortcomings, and the dramatic differences between the different theories, bernoulli, buffon, kant, and laplace each had the utmost confidence in the veracity of their respective theories. each of these theoreticians produced high-level, phenomenological theories with theoretical shortcomings. and each lacked theoretical details. looking back, it seems obvious that each theory was merely one of several possibilities. indeed, stephen brush has pointed out that those early hypotheses, as well as those from the following centuries, fell into two broad categories: monistic and dualistic. monistic theories describe the sun and planets as originating from a common phenomenon (e.g., a condensing cloud) whereas dualistic theories have them originating from distinct, separate phenomena (e.g., the sun forms first, and later a comet strike produces the planets). brush points out the solar system origin problem remains unsolved simply because there has continued to be a switching in preference between these two mutually exclusive categories. (brush, 1996, pg. 4) but the high confidence of bernoulli, buffon, kant, and laplace did not arise from any theoretical success. it is not as though they had produced highly detailed theories that convincingly explained what we observe. instead, their high confidence was a result of the random design tradition. 6. the spectacular failure of the random design null hypothesis had a significant impact on the philosophy of science within this tradition. given that it was interpreted as an undeniable proof against design of the solar system, it relieved scrutiny of the scientific theories for its origin. bernoulli, buffon, kant, and laplace could proclaim full confidence in their respective theories with little or no demonstration that their mechanisms actually could, in fact, create the solar system. and shortcomings in their mechanisms—whether known at the time or discovered later—were viewed more as interesting research problems rather than evidences against the theory. this made the theories more robust to scientific failures and resistant to falsification. orbits that violated the expected pattern were of little concern. they could always be explained by contingent events, something which newton himself called upon to explain the variations in the inclination angles of the planetary orbits. if the choice was between contingent events and random design, then contingent events were the obvious preference since the random design null hypothesis had been shown to be false. so the spectacular failure of the null hypothesis served to underwrite substantial speculation in science. explanations could be fairly vague and failures could be accommodated as research problems. these theories of the origin of the solar system are important for their influence on eighteenth century thought but, as we shall see next, they are also important because this new philosophy of science would emerge in the confirmation of biological theories of origin, particularly in the twentieth century. 3 the influence of the random design argument in biological evolution in advancing his theory of evolution charles darwin made a wide range of arguments. many of those arguments referred to patterns in the biological world which, darwin argued, would not be expected under independent creation. indeed, one of his strong arguments was from the mere existence of similarities between the different species which he summarized in chapter 13 of origin: what can be more curious than that the hand of a man, formed for grasping, that of a mole for digging, the leg of the horse, the paddle of the porpoise, and the wing of the bat, should all be constructed on the same pattern, and should include the same bones, in the same relative positions? (darwin, 1859, pg. 434) darwin’s rhetorical question highlights the role of the random design argument in this interpretation of the evidence. there should be no such obvious pattern. instead, these anatomical designs should fill the design space: we never find, for instance, the bones of the arm and forearm, or of the thigh and leg, transposed. hence the same names can be given to the homologous bones in widely different animals. (darwin, 1859, pg. 434) darwin found these seemingly arbitrary patterns throughout biology: volume 1, issue 2 3. the influence of the random design argument in biological evolution 29 we see the same great law in the construction of the mouths of insects: what can be more different than the immensely long spiral proboscis of a sphinx-moth, the curious folded one of a bee or bug, and the great jaws of a beetle?—yet all these organs, serving for such different purposes, are formed by infinitely numerous modifications of an upper lip, mandibles, and two pairs of maxillæ. analogous laws govern the construction of the mouths and limbs of crustaceans. so it is with the flowers of plants. (darwin, 1859, pgs. 434– 435) as with the shared inclination angles of the planetary orbits, these shared features could not be explained “by utility or by the doctrine of final causes.” (darwin, 1859, pg. 435) in other words, darwin argued the design space was largely unconstrained. other designs were possible. it is a testament to the acceptance of random design thinking that darwin could so casually suggest reversing “the bones of the arm and forearm, or of the thigh and leg,” as though such wholesale restructuring would have no functional effects. darwin could not know that the bones of the arm and forearm, or of the thigh and leg, could be transposed with no loss of utility. for our purposes here, the point is that the expectation that nature ought to fill the design space parallels the eighteenth century random design interpretation of cosmology, this time applied to the biological world. after darwin this tradition was taken for granted. here is how mark ridley explains this argument, updated to include the universal genetic code: homologous similarities between species provide the most widespread class of evidence that living and fossil species have evolved from a common ancestor. the anatomy, biochemistry, and embryonic development of each species contains innumerable characters like the pentadactyl limb and the genetic code: characters that are similar between species, but would not be if the species had independent origins. (ridley, 1993, pgs. 48–49) similarly, jerry coyne restates this idea that the anatomies of different species should share no common patterns and should be unique: there is no reason why a celestial designer, fashioning organisms from scratch like an architect designs buildings, should make new species by remodeling the features of existing ones. each species could be constructed from the ground up. (coyne, 2009, pg. 54) this argument from similarities across the species is ubiquitous and appears in a variety of contexts. whales are mammals and, as this example points out, would be unlikely to sport mammalian characteristics under the random design hypothesis. clearly there is a pattern at work: the probability of mammalian characteristics (such as having hair and feeding their young with milk, as well as a number of defining skeletal characteristics) arising in a separate, unrelated lineage is a pretty big stretch. (venema and mcknight, 2017, pg. 14) it is “a pretty big stretch” because the expectation is random design. likewise, the fossil record should be random rather than exhibiting patterns: “so the appearance of species through time, as seen in the fossils, is far from random.” (coyne, 2009, pg. 29) these are longstanding, powerful arguments for evolutionary contingency, based on the failure of random design in nature. these qualitative interpretations of the biological world have been augmented with more quantitative arguments. with the formalization of statistical testing, more data, and more computational power, the random design argument has been incorporated into biological studies in more sophisticated and subtle ways. the remainder of this section presents three such cases. 3.1 protein sequences and evolutionary trees in 1982 david penny and co-workers presented influential arguments for evolution that fall squarely within the random design argument tradition. penny used five proteins (cytochrome c, hemoglobin a, hemoglobin b, fibrinopeptide a and fibrinopeptide b) to infer the evolutionary relationships between eleven different species (rhesus monkey, sheep, horse, kangaroo, mouse, rabbit, dog, pig, human, cow, and ape). (penny, foulds, and hendy, 1982) just as visible features, such as the heart, vary from species to species, so too proteins, such as hemoglobin a, vary from species to species in their amino acid sequence. the penny et. al. random design null hypothesis stated that the protein relationships between species are random. for example, the cytochrome c protein is highly similar between the 30 the random design argument human and ape. according to the null hypothesis, this tells us nothing about how the other four proteins compare between the human and ape. of course this random design null hypothesis fails spectacularly. protein differences between species tend to be correlated. penny et. al. expressed this failure quantitatively using evolutionary trees. first, they used the five proteins, one at a time, to construct five different evolutionary trees. according to the random design null hypothesis, these trees should bear no particular similarity. the evolutionary tree derived by comparing one protein across the different species should bear no relation to the evolutionary tree derived by comparing a second protein across those species. the protein sequence differences should be random and so the resulting evolutionary trees that are computed, from those differences, are also randomly related, according to the null hypothesis. of course this was not true. each of the five proteins, independently, produced similar trees. the different evolutionary trees, based on the different proteins, did show some significant differences. one of the trees showed the dog relatively far from the human (9 species distant out of a possible 10) whereas others show the dog relatively close to the human (3 species distant out of 10). and the same is true for the mouse. yet the results were far from a random sampling of the space of all possible evolutionary trees. the null hypothesis was clearly false, and the paper concluded, “there is thus a strong divergence away from random towards the trees being very similar.” (penny, foulds, and hendy, 1982, pg. 200) for penny this provided “strong support” for the theory of evolution. a follow up study found that with those eleven different species, “the probability of randomly selecting trees this similar is 5.37×105.” (penny and hendy, 1986, pg. 408) the null hypothesis was falsified and the trees “were much more similar than would be expected by chance.” (penny and hendy, 1986, pg. 403) as one textbook explained, “the key observation was that the trees for all five proteins are very similar,” and there is no reason for this if the species were “separately created.” (ridley, 1993, pg. 52) this example illustrates the importance of the random design argument in the evaluation and confirmation of evolution. the random design tradition has become a textbook norm. in a later 2013 study penny and co-workers used an updated approach with more data and even more powerful results were obtained: “combining results for all 51 genes gives a p value for our non-evolutionary null model of ≈ 2× 1019.” (white, zhong, and penny, 2013) that result was for one of their eight data sets. combining all eight data sets resulted in a p value of 10132: even on our conservative test, the probability that chance could produce the observed levels of ancestral convergence for just one of the eight datasets of 51 proteins is ≈ 1 × 1019 and combined over 8 datasets is ≈ 1 × 10132. (white 2013) the chance null hypothesis was clearly false and it seemed that evolution and common ancestry were undeniable: by comparison, there are about 1080 protons in the universe, hence the probability that the sequences could have been produced by a process involving unrelated ancestral sequences is about 1050 lower than picking, among all protons, the same proton at random twice in a row. (white 2013) according to this random design argument, the molecular differences, across different species are expected to fill the design space at random. this is the null hypothesis and it is extremely unlikely given the patterns in the molecular sequence data. given the failure of the null hypothesis, the alternate hypothesis is taken to be true. as one textbook concluded, referring to penny, foulds, and hendy (1982): penny et. al. suggested that this pattern is so compelling that the [null] hypothesis of separate ancestry should be emphatically rejected as being incompatible with the data. while science rarely deals with certainty, it is fair to say that evolution from common ancestry is now supported beyond any reasonable doubt. (baum and smith, 2012, pg. 23) thus the random design argument has not only provided a null hypothesis for use in justifying evolutionary theories, it has done so in striking fashion. the assumption that molecular sequences should exhibit random variations has produced astronomical improbabilities and high confidence in the alternate hypothesis; namely, evolution. 3.2 systematics it has been known since antiquity that the species fall into groupings and in the eighteenth century linnaeus used a hierarchical structure to organize the species. species were volume 1, issue 2 3. the influence of the random design argument in biological evolution 31 grouped into genera, genera were grouped into orders, orders were grouped into classes, and classes were grouped into kingdoms. this nonrandom pattern was yet another failure of random design, and so another argument for evolution: the several subordinate groups in any class cannot be ranked in a single file, but seem rather to be clustered round points, and these round other points, and so on in almost endless cycles. on the view that each species has been independently created, i can see no explanation of this great fact in the classification of all organic beings. (darwin, 1859, pgs. 128–129) in recent decades this taxonomic failure of the random design null hypothesis has been quantified for many different sets of species and characters. the consistency index (ci), for example, measures the degree of consistency between (i) a set of character data, from a set of species and (ii) the tree used to describe their evolutionary history. for example, consider two groups of species that are distant on the evolutionary tree, and yet one of the species, in one of the groups, surprisingly shares a few of its character states with the species in the other group. these type of inconsistencies, sometimes striking, are not uncommon in biology (morris, 2004), and ci measures how prevalent they are in a data set. ci ranges from 0-1, with a value of 1 indicating an entirely consistent data set, and a value of 0 indicating an entirely inconsistent data set. note that even randomized character data have some consistencies just by chance, and so produce ci values greater than 0. as a test of evolution and common ancestry, a random ci measure is used as the null hypothesis. in other words, the character data are first randomized, and then the ci value is computed. this process is repeated many times to establish the distribution of ci values that can be expected in the randomized case. the real ci values (based on the actual character data) are often far from 1 due to inconsistencies between the species. in fact, the real ci values are often closer to the randomized ci value than to 1. but nonetheless, the real ci values are outside the range of randomized ci values. (archie, 1989; faith and cranston, 1991) in other words, though far from 1, the real ci values do not fall within the typical range of randomized values. the null hypothesis can be rejected, and this is cited as powerful evidence for the evolution and common ancestry of the species. the strength of the evidence rests not on the absolute ci values, and proximity to a value of 1, but rather on the ci values relative to their respective randomized values: when we sequence the same gene from multiple species and subject it to this statistical [ci] test, we generally find huge differences between the observed ci and the [randomized] ci predicted under separate ancestry. (baum and smith, 2012, pg. 21) for example, salamandridae is a family of salamanders consisting of true salamanders and newts. data on 40 characters from these species (wake and ozeti, 1969) yielded a relatively low ci value of .596. when the data were randomized,3 however, the ci value ranged from .422-.463. though far from 1, the actual ci value was well outside of the range of values resulting from randomized data, and thus interpreted as powerful evidence for evolution and common ancestry. 3.3 evolution of primates my final example of the influence of the random design argument in the biological sciences is a systematic study of the evidence for common ancestry within the primate species. (baum, 2016) this study gathered several different, large scale, data sets, including molecular, morphological, and biogeographical data. these data were then used in several different tests of common ancestry, using separate ancestry as the null hypothesis. as in the previous examples, the general approach is to construct a model of the null hypothesis, compare the empirical data to the null hypothesis, and compute the p value to determine if the null hypothesis can be rejected. exceedingly small p values indicate that the null hypothesis (separate ancestry) can be rejected, and so the alternate hypothesis (common ancestry) is accepted. the study performed tests both at the species and the family level. figure 1 summarizes the five species-level tests. as in our earlier examples, in each of these tests the null hypothesis expects no pattern. it represents what would result from a randomized version of the observed data. a typical technique, as described in section 3.2, is to rearrange the character state data so they are randomized for each species. 3the randomization process is as follows. for each of the 40 characters, there is a character state which is observed for each species. these data can be arranged in a matrix where each row represents a species, and each column represents a character. in the randomization process the character state data in each column are moved to a randomly selected row. therefore, the set of character state data in each column is not changed, but the data are rearranged, as they are randomized for each species. 32 the random design argument figure 1: summary of the five species-level tests used to reject the null hypothesis of separate ancestry test name null hypothesis procedure agreement within a single data matrix randomize character state data and measure pattern similarity (consistency) between the different characters. phylogenetic autocorrelation in a single character randomize character state data and compare with the evolutionary tree derived from dna sequences. testing for autocorrelation in the presence of potential covariates randomize character state data and focus on two characters. assume that other characters are independent, and so do not help to explain how the character compares with the evolutionary tree derived from dna sequences. agreement between the trees estimated from different datasets updated version of penny, et. al., 1982 test, described above in section 3.1 compute the difference (or distance) between evolutionary trees, each derived from a single gene, using evolutionary trees that are randomly generated for each gene, for the species in question. this is equivalent to deriving the evolutionary trees using randomized gene sequences. deficit of derived character states in fossils for both extant and extinct species, measure the distance to the root of the evolutionary tree. on average, the null hypothesis expects no difference. volume 1, issue 2 4. conclusions 33 some of these tests were run repeatedly with different data sets, resulting in more than merely five p value results. and as in our earlier examples, the computed p values for most of the tests were exceedingly small. this was true for the tests run at the family level as well. for example, many of the p values were less than 10−−300. given these infinitesimal p values, the authors overwhelmingly rejected the separate ancestry null hypothesis. following penny, the authors explained that for several of the tests the separate ancestry null hypothesis was less likely than the probability of picking the correct atom at random among the estimated 1080 atoms in the known universe. echoing daniel bernoulli and the eighteenth century cosmological evolutionary theories discussed in section 2, the authors explained the essence of this approach. even a single character can provide strong evidence for common ancestry if its observed states, in different species, is a small subset of its possible states: in principle, a single characteristic that could exist in very many alternative states can provide evidence of [common ancestry] when the states seen in a clade, or life as a whole, occupy a smaller subset of state space than would be expected under [separate ancestry]. (baum, 2016, pg. 1362) this is the random design argument. if there is no reason to think the character state could not take on “very many alternative states,” and yet it occupies “a smaller subset of state space,” then the null hypothesis can be rejected. just as the planetary inclination angles occupied a small subset of the possible values and so proved cosmological evolution, so too biological characters that occupy a small subset of the possible values prove biological evolution. the authors suggest this random design philosophy of science may find broader application in the historical sciences: by looking across different historical sciences and the sources of evidence that they use in support of accepted claims, we may hope that a general theory of statistical history may emerge. thus, we hope that this article will not just stimulate further philosophical and statistical research on evidence for [common ancestry], but also on broader questions in historical inference. (baum, 2016, pg. 1362) 4 conclusions the random design argument is an important tradition in the history of science. the fundamental idea is that nature’s designs should fill the design space, otherwise contingency is implicated. over the past three centuries the random design argument, and in particular testing of the random design null hypothesis, has provided for an extremely powerful philosophy of science. it is a solution to the ageold difficulty of how to prove a scientific theory. if a null hypothesis can be constructed which complements the theory in question (the alternative), such that the two theories are the only two possible explanations, then falsifying the null hypothesis is equivalent to proving the alternative. if the null hypothesis has a probability of less than 10−10 then the alternative certainly qualifies as a “fact,” by any reasonable understanding of that term. this paper shows how the random design argument has motivated this philosophy of science. the following five points summarize this move. 1. god, if he was directly responsible for creation, should fill the design space. objects within nature, and their design parameters, have a range of possibilities, and nature should fill that capacity. genuine possibilities should not go unfulfilled. this is the null hypothesis. 2. the null hypothesis, by definition, complements the alternate hypothesis. the null hypothesis and the alternate hypothesis span the space of possible hypotheses. they are mutually exclusive and there are no other possible explanations. 3. rejection of the null hypothesis implies that the alternate hypothesis is a fact. contingency, both in cosmology and biology, has been proven to be a fact by the failure of the respective null hypotheses. 4. this philosophy of science obviates mechanism. the alternate hypothesis can be proven to be true even though it lacks specific or detailed mechanisms. the development and testing of the scientific mechanisms can come later and can sustain many failures. indeed, mechanisms that are proposed typically do not even explain the very data used to reject the null hypothesis. variations in the planetary inclination angles, or variations in the species hierarchical structure, are not explained by the condensing nebula or common ancestry hypotheses, respectively. additional, ad hoc, contingent events and causes are required. 5. this philosophy of science, with its rejection of the null hypothesis, leads to exceptionally high confidence. the alternate (i.e., contingency) hypothesis simply must be 34 the random design argument true, in spite of ambiguities, lack of specifics, or failures. the validity of the statistical reasoning behind these five points is dependent on one special property of the null hypothesis. as stated above, the null hypothesis must be the complement of the alternate (contingency) hypothesis. there can be no overlap and no gap between the two hypotheses. this is crucial and its impact to the validity of the reasoning should not be underestimated. the power of this philosophy of science lies in its ability to (i) craft relatively simple, tractable null hypotheses which can be evaluated and rejected, while (ii) credibly maintaining the premise that it is a legitimate null hypothesis; that is, that it is the complement of the alternate hypothesis. the assumption that if the planetary inclination angles, or the species’ characters, do not fully populate the possible range of values, then they must have arisen via contingent events, is underwritten by an underlying theological assumption, not by empirical science. this is an example of how a nonscientific idea influences not merely theory development, but theory evaluation and even theory confirmation. the origin and details of this theological assumption are beyond the scope of this paper. in the past century historians have increasingly demonstrated how nonscientific influences have played a role in the development of scientific theories. less attention has been paid to the influence of nonscientific ideas on theory evaluation. why are certain theories held with such high confidence? how are they known to be facts? this paper has explored one such example of how the random design argument has contributed to the high confidence in some scientific theories, and how that confidence relies on theological assumptions. from the perspective of empirical science, such confidence is not warranted. references archie, j w (1989). “a randomization test for phylogenetic information from systematic data”. in: systematic zoology 38, pp. 239–252. baum, d et al. (2016). “statistical evidence for common ancestry: application to primates”. in: evolution 70, pp. 1354–1363. baum, d and s smith (2012). tree thinking: an introduction to phylogenetic biology. new york: w. h. freeman. bernoulli, d (1734). “physical and astronomical researches on the problem proposed for the second time by the academie royale des sciences de paris”. in: recueil des pièces qui ont remporté les prix de l’académie royale des sciences, vol. 3. trans. by richard j. pulskamp. paris: jombert. url: http://cerebro.xu.edu/math/ sources/danbernoulli/1734%5c_planets%20and% 20comets.pdf. brush, s (1996). nebulous earth: the origin of the solar system and the core of the earth from laplace to jeffreys. cambridge: cambridge university press. buffon, g l c (1749). “of the formation of planets”. trans. by william smellie. in: natural history: general and particular 1.1. coyne, j (2009). why evolution is true. new york: viking. danielson, d (2000). the book of the cosmos. new york: basic books. darwin, c (1859). the origin of species. london: john murray. faith, d and p cranston (1991). “could a cladogram this short have arisen by chance alone—on permutation tests for cladistic structure”. in: cladistics 7, pp. 1– 28. fisher, r (1935). the design of experiments. edinburgh: oliver and boyd. hunter, c (2007). science’s blind spot. grand rapids: brazos. hunter, c (2014). “darwin’s principle: the use of contrastive reasoning in the confirmation of evolution”. in: hopos 4, pp. 106–149. kant, i (1755). allgemeine naturgeschichte und theorie des himmels [universal natural history and theory of heaven]. trans. by ian johnston. arlington, va: richer resources. manuel, f (1968). a portrait of isaac newton. cambridge, ma: belknap. morris, s c (2004). life’s solution: inevitable humans in a lonely universe. cambridge: cambridge university press. newton, i (1687). the principia. trans. by andrew motte. new york: prometheus books. newton, i (1718). opticks. london. url: http://www. newtonproject . sussex . ac . uk / view / texts / normalized/natp00051. penny, d, l foulds, and m hendy (1982). “testing the theory of evolution by comparing phylogenetic trees constructed from five different protein sequences”. in: nature 297, pp. 197–200. penny, d and m hendy (1986). “estimating the reliability of evolutionary trees”. in: molecular and biological evolution 3, pp. 403–417. ridley, m (1993). evolution. boston: blackwell. volume 1, issue 2 references 35 rogers, a (2011). the evidence for evolution. chicago: university of chicago press. shea, w (1986). “filled with wonder: kant’s cosmological essay, the universal natural history and theory of the heavens”. in: kant’s philosophy of physical science. ed. by r e butts. dordrecht: d. reidel. venema, d and s mcknight (2017). adam and the genome: reading scripture after genomic science. grand rapids: brazos. wake, d and n ozeti (1969). “evolutionary relationships in the family salamandridae”. in: copeia 1969, pp. 124–137. white, w t j, b zhong, and d penny (2013). “beyond reasonable doubt: evolution from dna sequences”. in: plos one 8 (e69924). v2018i1 volume 1, issue 1 simplifying and refactoring introductory calculus jonathan bartlett doi: 10.33014/issn.2640-5652.1.1.bartlett.1 abstract first year calculus is often taught in a way that is very burdensome to the student. students have to memorize a diversity of processes for essentially performing the same task. however, many calculus processes can be simplified and streamlined so that fewer concepts can provide more flexibility and capability for first-year students. 1 introduction while the exact set of topics in any particular calculus book or course may vary, the general method of calculus training has been essentially set in stone for the last hundred years. nonetheless, there are many issues with this methodology that have been insufficiently addressed over the years. these issues range from the sequencing of topics to the content of the topics themselves. a well-recognized phenomena in computer programming is known as “code debt.” code debt occurs when new ideas and changes get incorporated into a program, but the rest of the program doesn’t change sufficiently to take these new ideas and changes into account. because of this, there winds up being a lot of duplication and confusion over the right ways of doing things. it is known as code debt because eventually, to relieve the tension, future work will have to be done to the rest of the system to bring it back into alignment. to relieve code debt, computer programmers engage in in a process known as “refactoring.” the idea behind refactoring is to reconceptualize the whole of the computer program in order to discover which facilities are the core, distinguishable pieces and which ones are merely a variant or permutation of those pieces. the present goal of the paper is to begin a similar process of refactoring the subject of calculus and the way that it is taught. 2 proof mechanisms and learning calculus calculus books and courses are often written so that each step of the development of calculus can be proved. most books begin with limits, and then calculus is then proved using limits. unfortunately, most calculus students are not yet ready for limits, and limits often wind up being a confusing side-challenge that derail students before they have even begun to study the subject in depth. in nearly any subject, students do best when proofs occur after the core content is learned. as an example, consider children learning a language. children learn english (or any other language) long before they learn the grammar of english. in fact, most students can speak english perfectly well without ever learning the rules (grammar) that govern english. even when learning foreign languages, immersive approaches (i.e., those in which the language precedes the grammar of it) tend to work most effectively (gonzálezlloret and nielson, 2015). of course, mathematical learning is not identical to language learning. part of mathematics is proof, so learning proof tools is certainly an important part of mathematics. additionally, with most technical subjects, having a grounding in the “why” aspects certainly helps one to learn the intuitions behind the “how.” however, even when the proofs help build an intuition, there is a difference between teaching an intuition behind an idea by proving its truth and trying to get students to construct their own proofs ex nihilo. therefore, the sequencing in this method will focus on first making the intuitive understanding work, and then only later establish proofs. the primary target of this reasoning is limits. most of the time, limits are introduced before any of the problems it is intended to solve, which makes the subject confusing in the first place. if a student has grown up doing the simple calculation f (3) when f (x) = x2, it makes no sense to transform this into limit notation, lim x→3 x2. this is simply seen by the student as extra steps which have no perceptible benefit. 18 simplifying and refactoring introductory calculus students see the new notation, a bunch of rules, and are asked to put them together to solve trivial problems that they could solve using the normal rules of algebra. therefore, they start to get lost because they are bombarded with extra notation for nothing. they can’t grasp at what this could possibly be for, and are lost before they ever really start. at minimum, the concept of limits should be introduced to solve the problem of having “holes” in a graph rather than for expressions that are easily calculated without limits. this at least provides a good context for why students should bother with them. in my own classes, i have moved limits to the end of the course altogether. some want to introduce limits to establish a formal definition of continuity. however, it is much more straightforward to new students to introduce continuity as “being able to draw a graph without picking up your pencil” than to talk about limits. students understand drawing without picking up your pencil much better than limits. after a whole year of talking about continuity in terms of whether or not you pick up your pencil (and why that is important to calculus), you can say that, as another benefit of limits, we get a more formal definition of what it means to have a continuous graph. thus, the explicit justification for the derivative using limits occurs long after the students learn the derivative and learn to use it well. this has the additional advantage of including l’hospital’s rule as part of the general discussion of limit behavior, rather than having to revisit limits again after derivatives. 3 introducing the derivative in this method, derivatives are introduced through extensive practical work on evaluating slopes between two points on a graph. given a graph of, say, y = x2, what is the slope between the points x = 1 and x = 2? basic algebra is used to to find the slope from two points, using the standard formula m = y1 − y0 x1 − x0 . next, we discuss what it means to find the slope at a point. we talk about the problems of finding a slope at a single point (the formula we have reduces to 0 0 ), and then discuss methods of getting around that. i suggest estimating the slope at the point using two points that are close together. several problems are worked for getting the distance between the two x locations closer and closer (x = 1 and x = 1.1, then move to x = 1 and x = 1.0001). eventually, we try to make a formula that expresses the “general idea” of a slope between two points on a given line. if we are looking at two points where the x values are 0.01 away from each other, we eventually come up with the formula m = (x+0.01)2−x2 (x+0.01)−x to match their existing knowledge of the slope formula. after solving a few of these, i then suggest that we introduce a parameter to represent the distance. this way, we can decide later how close we want the points to be. if we call our parameter h, then the formula becomes m = (x+h)2−x2 (x+h)−x . this simplifies to m = 2x + h. so, to find the slope between any two points that are h = 0.01 away from each other, we simply use the formula. we then make h smaller and smaller and smaller to get a “more exact” value of the slope at a point. i then ask them to think about if there is any way to abuse this formula in order to find a formula for the slope at a single point. at this point, students are ready to understand that if i set h to 0 that the slope is equivalent to the slope at a particular point. i then generalize this with functions, using f (x) to represent the function we want the slope of, and show that basic simplifications give us the formulat for the derivative, y′ = f (x + h) − f (x) h . i then say that, for any particular f (), after getting rid of h in the denominator through simplification, we can simply substitute 0 for h in the resulting expression. i do mention that h is not really zero, but in fact really close to it. nonetheless, i tell them that the formal justification for treating h as zero will come later in the course, and that for now they should treat it as a value that is sufficiently close to zero that it can be treated as such, but sufficiently far away from zero that it doesn’t produce divide-by-zero errors. doing this helps students start building intuitions around these types of situations, which will help us refine them in our formal discussions of limits later on. 4 derivatives vs. differentials there are two potential operators to use for teaching differential calculus. the first, and more commonly used, is the derivative operator, which can be written as dx () or as d dx (). this is commonly spoken of as “taking the derivative with respect to x.” the problem with this operator is that it becomes very volume 1, issue 1 4. derivatives vs. differentials 19 confusing for students when they get to derivatives of implicit functions. the reason for this is that, when applied to implicit functions, derivatives are spitting out other derivatives rather than simple answers. and, in fact, it does this for some variables and not others. for instance, the derivative x with respect to x is 1, but the derivative of y with respect to x is dy dx . this assymetry causes confusion. while the derivative operation is perfectly consistent and solves the necessary problems, a much clearer way to teach students all types of derivatives is to instead focus on the differential operator, d(). the differential operator is similar to the derivative, but it does not treat any variable specially. there is no variable that the derivative is being taken with respect to. instead, whichever variable(s) are in the expression always comes out at the end as a differential. to understand the differences, we will apply the operators to both an explicit and an implicit function. the explicit function will be y = x3 and the implicit function will be xy = 5. using the d dx () operator, the explicit function is straightforward. d dx (y) = d dx (x3) dy dx = 3x2. however, the implicit function is unintuitive for students. d dx (xy) = 5 x dy dx + y = 0 the product rule, which is supposed to have some amount of symmetry to it, now seems to have no symmetry whatsoever. however, when taking differentials, the operations are much more straightforward. first, the explicit function. d(y) = d(x3) dy = 3x2 dx as you can see, this is identical to the d dx () operation except that the result is not divided by dx. this localizes the differentials to the contexts where they occur. as we will see shortly, this simplifies a lot of reasoning about complicated derivatives. here is the differentiation of the implicit function. d(xy) = d(5) x dy + y dx = 0 this is functionally identical to the implicit derivative. however, it maintains the symmetry of the product rule itself. additionally, it required no extra rules for the student for the handling of y vs. x. they are both treated identically in the differentiation step. to convert the result of differentiation into a derivative, the student merely needs to solve for dy dx using normal algebra rules. therefore, all derivatives become a two-step process: 1. find the differential of the equation. 2. solve for the derivative you are interested in. this way, the process for finding dy dx is the same as for finding dx dy . there are no funny steps. you merely differentiate both sides and then solve for the particular derivative (ratio of differentials) that you want. it does not matter if the equation is implicit, explicit, or, as we will see shortly, multivariate, the process is identical. even though going through the differential is slightly more complicated for simple equations, overall i have found that students find the separation of finding differentials and then finding derivatives to be much easier to process over a wider variety of problems. interestingly, this is the way the original leibnizian calculus was developed. the process focused on differentials rather than derivatives, and did not focus on finding ratios of differentials or worrying about identifying independent variables (bos, 1974). as mentioned in section 3, i do start with the traditional derivative, as it is much more concrete. however, i do attempt to pivot very quickly from derivatives to differentials. another possible mechanism for doing this was pioneered by thomson (1910). in this method, differentials are introduced first, basically as almost-discrete differences. essentially, the question is asked, given, say, y = x2, if i added a number named dy to all the y variables, i would have to compensate by adding some other number dx to all the x variables. this possibility is also explored, but not very fully, by dray and manogue (2010). future work may entail discovering which approach is more beneficial to students— starting with slopes as a concrete tie-in to algebra and then pivoting to differentials, or starting more directly with differentials at the very beginning. 20 simplifying and refactoring introductory calculus 5 treating differentials algebraically because we are solving for the derivative instead of calculating it directly, we must be willing to treat differentials algebraically. although in the 19th century this was frowned upon, developments in the 20th century have shown that differentials can be thought of as algebraic units. abraham robinson’s formal description of the hyperreals and the introduction of non-standard analysis provides sufficient justification for treating differentials algebraically (robinson, 1974; henle and kleinberg, 2003; keisler, 2012). essentially, differentials are treated as hyperreal values—values which exist on the number line but which are not contained by the reals. although differentials can be treated algebraically, they can’t actually be solved for as specific numbers. eventually, to get a number that can be evaluated or calculated, the differentials have to be in ratio with each other. however, for intermediate steps, there is no problem with treating differentials such as dx and dy exactly as you would the variables x and y. they can be multiplied, divided, cancelled, etc. treating differentials as algebraic units is very intuitive for students who have studied and practiced the algebraic treatment of unknowns for quite some time. additionally, the ability to treat differentials algebraically improves the comprehension of topics such as related rate problems. in related rate problems, dt springs up as if from nowhere. books often teach this as “taking the derivative with respect to t,” but this is confusing since there is no t. i have found that students are much less confused by an algebraic approach. we simply take the differential the same way we always have, but then we divide both sides of the equation by dt. this works simply because, algebraically, we can divide by any value we wish as long as we divide by the same thing on both sides of the equation, even if it is a new unknown. again, by using differentials instead of derivatives, we have transformed a number of processes that students find unintuitive into a single process where the intuition is supplied by the student’s knowledge of algebra. 6 multivariable calculus this method of using differentials instead of derivatives also simplifies some aspects of multivariable calculus. take the equation z2 = xy. this can be easily converted into differentials. d(z2) = d(xy) 2z dz = x dy + y dx this can then be solved algebraically for any derivative that is desired. for instance, dy dz can be found. 2z dz = x dy + y dx 2z dz − y dx = x dy 2z x dz − y x dx = dy 2z x − y x dx dz = dy dz what this means is that the rate at which y changes with respect to z not only depends on the actual values of x, y, and z, but that it also depends on the rate at which x changes with respect to z. many calculus books skip over this idea, probably because when differentials are not treated independently, these processes are very complicated. however, with dealing with differentials instead of derivatives, these ideas arise very naturally from the notation. 7 partial derivatives/differentials this treatment of differentials also leads to a very straightforward way of defining partial differentials and derivatives. total derivatives define the relationships between changes in all parts of the system. but what happens if you want to hold some pieces still, and only find the way that one variable influences another when treated by itself? in order to do that, we would say that the other variables don’t change. another way of saying that these variables don’t change is to say that their differentials are zero. in other words, to convert from a multivariable differential (as in section 6) to a partial differential is to merely set the other differentials which aren’t under consideration to zero. for instance, section 6 ended with the equation dy dz = 2z x − y x dx dz . to understand the relationship between the changes in y and z if everything else is kept constant, we merely need to set the differentials of everything else (dx in this case) to volume 1, issue 1 8. higher order differentials and derivatives 21 zero. doing this results in the equation dy dz = 2z x − y x dx dz ∂y ∂z = 2z x − y x 0 dz = 2z x − 0 = 2z x therefore, the partial derivative of y with respect to z is 2z x . note, however, that partial differentials cannot always be treated algebraically. this is not due to a failing of the concept of partial derivatives, but merely of their notation. for our original equation, ∂y can refer to two different entities in the ratios ∂y ∂z (where dx = 0) and ∂y ∂x (where dy = 0). information about which particular ∂y is being spoken about is contained in the denominator, and therefore splitting the numerator from the denominator results in a loss of information.1 8 higher order differentials and derivatives performing derivatives by taking differentials first also has benefits down the road, as it allows students to understand other notations more fully. the liebniz notation for the second derivative ! d2y dx2 " has long baffled many students. most books take a “just use it and don’t ask questions” approach.2 however, recent advances have shown that the standard notation for higher-order derivatives is not only baffling, it is in a very real sense incorrect (bartlett and khurshudyan, 2018). to understand the issues, first recognize that differentials are actually a shorthand. when you take the differential of a composite function, you always wind up with a differential of the inner function. for instance, d(sin(x2)) = cos(x2) d(x2) = cos(x2) 2x dx. 1a possible solution to this problem would be to subscript partial differentials with the list of differentials which were allowed to change. this is cumbersome, but allows for an algebraic treatment of partial differentials. so, for instance, ∂y ∂z would be written as ∂yz y ∂yz z and ∂y ∂x would be written as ∂yx y ∂yx x . doing this makes it clear ∂yz y is a distinct algebraic entity from ∂yx y. this is the subject of a current paper in progress from the present author. 2bartlett and khurshudyan (2018) gives several examples of textbooks taking this approach. however, the last term, dx, stands in the same relationship to 2x as d(x2) does to cos(x2). it is the differential of the interior function. therefore, dx actually is just a shorthand for d(x). since it is irreducible, it is shortened to just dx. this shortening happens both to reduce reading and writing effort, and also to mark the fact that this differential cannot be further reduced. nonetheless, dx is actually a composite—an operator and an operand.3 but what do d2y and dx2 mean? the latter is straightforward enough. dx2 is simply a shorthand for (d(x))2. however, d2y (with the superscript after the differential operator) actually means applying the differential operator twice. in other words, while dy is short for d(y), d2y is a shorthand for d(d(y)). to see how this plays out, imagine the equation y = x3. (1) let’s start by taking the differential of this equation twice. y = x3 d(y) = d(x3) dy = 3x2 dx first differential d(dy) = d(3x2 dx) d2y = 3x2 d2x + 6x dx2 second differential (2) this result may seem surprising, but allow for an explanation. the term 3x2 d2x seems like it is out of place, but it is not. since 3x2 dx is the product of 3x2 and dx, the product rule has to be used to resolve the next differential. therefore, since d(uv) = u dv + v du, while one of the outputs is the anticipated 6x dx2, there is also another one, 3x2 d2x. if x is the independent variable, this term goes to zero because d2x goes to zero (see bartlett and khurshudyan (2018) and bos (1974) for an explanation of why), and the result looks like it is expected to under typical understandings of calculus. however, if x is not an independent variable, the term is vitally important. without keeping the term, the second differential would not be algebraically manipulable. keeping the term then allows higher order differentials to remain as algebraically manipulable terms. now, let us divide the whole thing by dx2. doing so yields d2y dx2 = 3x2 d2x dx2 + 6x (3) 3to emphasize this, i usually typeset dx such that the d is in roman type and the x is in italic. this is similar to the way that other functions such as sin x are typeset. 22 simplifying and refactoring introductory calculus however, this has more terms than what we normally expect from a second derivative. this is because the second derivative comes from the following sequence of steps: 1. take a differential 2. divide by dx 3. take another differential 4. divide by dx because the derivative is the combination of steps 1 & 2, the second derivative simply repeats those steps. however, if you take the differential twice in a row before dividing by dx2, then you wind up with a strange-looking answer, as we did in equation 3. a few things to note about equation 3: 1. the left-hand side has the form that we normally associate with the second derivative. 2. the right-hand side does not have the form that we normally associate with the second derivative. it has an extra term in it. 3. the reason for this is that, even though it is normally associated with the second derivative, the left-hand side is not the correct notation for the derivative of the derivative of y. 4. in other words, the equation given by equation 3 is correct as far as it goes (both sides are in fact equal), but it is not the second derivative, because the notation we have come to associate with the second derivative actually refers to a different quantity altogether. according to bartlett and khurshudyan (2018), the full notation for the second derivatives should be d2y dx2 − dy dx d2x dx2 . (4) this can be deduced simply from taking two derivatives of y. the first derivative is obviously dy dx . the second derivative is found by taking the differential of dy dx and then dividing by dx. d # dy dx $ dx = dx d(dy)−dy d(dx) dx2 dx = dx d(dy) − dy d(dx) dx3 = dx d(dy) dx3 − dy d(dx) dx3 = d(dy) dx2 − dy dx d(dx) dx2 (5) by noting that d(dy) = d(d(y)) = d2y and d(dx) = d(d(x)) = d2x we can see that this is equivalent with equation 4. so how does this square with equation 3? if we subtract 3x2 d2x dx2 from both sides of equation 3, it will result in d2y dx2 − 3x2 d2x dx2 = 6x. if you recognize 3x2 as being the first derivative (i.e., dy dx ) it is apparent that the left-hand side of this equation is the same as the improved form of the second derivative listed in equation 4. because we are using this form of the second derivative, this formula can be algebraically rearranged to yield a wide variety of results. we can rearrange the terms to find the second derivative of x with respect to y (instead of the second derivative of y with respect to x). or, it can be combined with other formulas and differential formulas (say, the relationship of x to some variable t) to algebraically accomplish a change of variables. previously, this was only available using specialty formulas such as faà di bruno’s formula. thus, teaching using leibnizian differentials confers numerous advantages for higher order differentials: 1. the notation is clearer, because there is a definitive reason for the way that the notation looks. 2. the notation allows differentials to be modified algebraically, which was not previously possible for higher order derivatives. 3. because the notation is algebraically manipulable, the notation allows for students to easily find relationships that previously required memorized formulas. 9 getting rid of logarithmic differentiation logarithmic differentiation is the process taught by most calculus textbooks for taking the derivative of functions of the form uv . essentially, what is taught is to use logarithms to remove the exponent, and then take the derivative now that the exponent is removed. the problem with this is that it is needlessly complicated, and forces the student volume 1, issue 1 10. hyperreals for limit analysis 23 to use different processes depending on the derivative in question.4 before learning logarithmic differentiation, the student had a more-or-less unified process for taking derivatives: 1. look at the form of the function. 2. find the corresponding rule (memorized or from the book). 3. apply the rule. however, logarithmic differentiation breaks that process, adding extra steps in some circumstances. if the mathematics required this, that would be one thing. however, there is actually a rule available for forms of the type uv which is rarely mentioned even in the appendices of most calculus books. the rule is d(uv ) = vuv−1du + ln(u)uvdv (6) this formula can be derived in many ways. the most straightforward is to first set z = uv and then differentiate both sides using logarithmic differentiation (logarithmic differentiation is useful to prove the formula for uv but after that it is fairly useless because you can just apply the formula). doing this yields z = uv ln(z) = ln(uv ) ln(z) = v ln(u) d(ln(z)) = d(v ln(u)) 1 z dz = v u du + ln(u)dv dz = zv u du + z ln(u)dv dz = v uv u du + ln(u) uvdv dz = v uv−1du + ln(u) uvdv this is a decent proof for first-year calculus. however, a more interesting proof can be found by simply recognizing that a total differential is the sum of its partials. so, the partial differential of uv with v kept constant is v uv−1du and the partial differential of uv with u kept constant is ln(u)uvdv. therefore, the total differential is merely the sum of these, as you can see in equation 6. probably due to its rarity of actually appearing in textbooks, this rule has been given a variety of names, the 4the process of logarithmic differentiation is necessary in the proof of some important rules, but not in their usage. two most common being the generalized power rule and the functional power rule. logarithmic differentiation does have some unique uses, but these are mostly upper-level ideas. for instance, logarithmic differentiation can be used to convert products of sequences (which are difficult to integrate) into a sum of sequences (which tend to be easier). for instance, logarithmic differentiation allows us to say that if y = n% j=1 f (x, j) then y′ = y n& j=1 d(ln( f (x, j))) (7) logarithmic differentiation is also sometimes used to simplify complicated fractions, exponents, and even products, but, since there are already rules for all of these, the “simplification” usually just makes learning the process more difficult for students. students need unified processes more than they need tricks to make things easier. conceptual simplicity is usually preferable to speed of computation. 10 hyperreals for limit analysis ϵ-δ proofs have long been the bane of calculus students. while they do present an interesting mathematical technique, the retention rate for understanding ϵ-δ proofs is so low as to hardly be worth doing (katz and polev, 2017). instead, the method which helps students understand the process of limits the most is to use the hyperreal number line. on the hyperreal number line, ϵ is the unit of the infinitesimal (not the same as the ϵ in ϵ-δ proofs). to take a righthanded limit, the student merely replaces x with x + ϵ everywhere it occurs in the expression. this “looks at” the function immediately to the right of the point in question— an infinitely small step to the right. the left-handed limit is found by subtracting ϵ . as an example, the expression x2−25 x−5 cannot be evaluated at x = 5 because it results in a zero in the denominator. however, any value except 5 will work. therefore, if we bump x an infinitely small amount to the right, the divideby-zero problem will no longer exist. therefore, to find 24 simplifying and refactoring introductory calculus lim x→5+ x2−25 x−5 , we merely replace x with x + ϵ . this yields lim x→5+ x2 − 25 x − 5 = (x + ϵ )2 − 25 x + ϵ − 5 = x2 + 2xϵ + ϵ2 − 25 x + ϵ − 5 = (5)2 + 2(5)ϵ + ϵ2 − 25 (5) + ϵ − 5 = 25 + 10ϵ + ϵ2 − 25 ϵ = 10 + ϵ this is infinitely close to 10. therefore, the limit is 10. additionally, i have found from experience that limits are best taught at the end of a year of calculus rather than at the beginning. teaching about hyperreal numbers and then using them in limits provides a good way to make many of the intuitions developed over the first year of calculus more rigorous. 11 the integral as an infinite sum one more change that improves calculus for first-year students is redefining the integral from an area to an infinite sum. this is a very subtle difference, but one that i have found to be important. finding the area under a curve is one particular usage of the integral. however, more generally, the integral is used as a tool of summation. using the idea of the integral as a tool of summation helps explain the usage of the integral as the area under the curve, but the converse is not true—explaining the integral as the area under the curve does not help students imagine other uses of the integral such as arc lengths and volumes of revolution. when the integral is defined as an infinite sum of infinitely small pieces, then it is straightforward to then say that what is to the right of the integral defines what each individual small piece that we are adding together looks like. figure 1 lists several different sorts of things we can add together using integrals. in each of these, the integral represents the infinite sum of well-defined infinitely small objects. if the integral is defined as an infinite sum, this makes an intuitive connection for the student. however, if the integral is defined as the area under the curve, jumping out of this to understand how the area under the curve can be reconfigured as one of the other operations is quite confusing. additionally, defining the integral as an infinite sum allows for the integral to be more easily defined in multivariable situations. the reason for this is that, as an infinite sum, the integral is adding up all of the differences that occur into a total difference. this works just a straightforwardly for multivariable differentials as it does for single variable differentials. for instance, let’s say we have the equation dz = dy + dx. the integral of this is just z = y + x + c. as an “area under the curve” this makes no sense. however, as an “infinite sum” this makes perfect sense. if dz represents the sum of dy + dx, then the total sum will be the difference of y+ x+c evaluated at two points. so, traveling from x = 2, y = 3 to x = 7, y = 4 will give a sum total of (7 + 4 + c) − (2 + 3 + c) = 11 + c − 5 − c = 6. therefore, treating the integral as an infinite sum not only helps students generalize the integral to various integrationrelated formulas, but it also helps students generalize the integral into a multivariable version, and similarly to complex number situations. the area under the curve can be seen as a particular, easyto-understand instance of infinite summation. one other benefit of treating the integral as an infinite sum is that it makes the notation more clear. some introductory texts, when defining the integral as the area under the curve, simply use the integral form as a pro forma way of specifying the variable of integration. for instance, it will often be explained like this: ' formula to be integrated(!!!!!!!!!!!!!!!!!)*!!!!!!!!!!!!!!!!!+ x3 + 2x2 − 3x + 5 dx*+() variable of integration however, doing it this way needlessly restricts the usage of integration to only area under the curve, and makes the other uses of it harder to understand. 12 resistance to hyperreals the primary reason that these methods are not more widespread is the lack of enthusiasm for the hyperreal number system. this comes from two sources. the first is a historical bias against infinities and infinitesimals, with volume 1, issue 1 12. resistance to hyperreals 25 figure 1: summations using integration general geometry infinitesimal geometry formula integral area under the curve ultrathin rectangles height · width , y dx arc length line length (x1 − x0)2 + (y1 − y0)2 , dx2 + dy2 revolution about x ultrashort cylinders π r2h , π y2 dx revolution about y ultrathin shells (curved boxes) height · length · thickness , y 2πx dx infinitesimals actually having the stronger of the negative biases. the primary bias against infinitesimals comes from the fact that they were used long before they were proved. before rigorous means of working with infinitesimals were established, many critics pointed to the inconsistent ways in which infinitesimals were handled as proof that they were non-entities. in some circumstances, infinitesimals were treated as zero and thrown away, and, in other circumstances, they were used in denominators and were therefore treated as non-zero entities which could also be used for algebraic cancelling. in the latter half of the twentieth century, robinson’s hyperreal number system made these operations rigorous with the hyperreal number system (robinson, 1974). however, by that time, the damage from hundreds of years of skepticism had already taken its toll. the most classic recrimination against infinitesimals was done by george berkeley, in his famouse quote: and what are these fluxions? the velocities of evanescent increments? and what are these same evanescent increments? they are neither finite quantities nor quantities infinitely small, nor yet nothing. may we not call them the ghosts of departed quantities? (berkeley, 1734)5 additionally, even though the hyperreal number system has been shown to be usable as a consistent system for the inclusion of infinities and infinitesimals, it is not the only viable candidate. cantor’s transfinite number system (cantor, 1915), surreal numbers (knuth, 1974), dual numbers (wolfe, 2014), and other systems have all been proposed for extending the real number line into infinities and infinitesimals. while the hyperreals are the most widespread, it is not the only system available. this lack of standard convention has prevented a lot of building on any one foundation. 5in modern terminology, fluxions refer to derivatives, and evanescent increments refer to infinitesimals. finally, there is also a philosophical distrust of hyperreal numbers based on general concerns over infinities and infinitesimals. both infinities and infinitesimals have troubled certain schools of mathematicians. these concerns can be divided into ontological concerns and epistemological concerns. the ontological concern is about whether infinities exist and/or are needed in mathematics. this concern stems from the line of mathematicians following in the footsteps of leopold kronecker. kronecker opposed cantor’s theory of infinities because kronecker only admitted mathematical concepts which could be constructed in a finite number of steps from the natural numbers (dauben, 1990). david hilbert’s program was similar to kronecker’s. however, hilbert was not actively opposed to infinity per se, but believed that infinities were ideals and the natural numbers were reality. therefore, hilbert believed that any true statement about natural numbers that were proved with infinity could also be proven without them. infinities weren’t invalid, they were just superfluous. thus, hilbert’s program was to define a finite set of axioms which were consistent and complete, and could prove any valid theorem without explicitly relying on any concepts of infinity (zach, 2016). gödel later proved that hilbert’s program was unworkable, but the motivations and concerns behind it remain today. even for mathematicians who accept cantor and gödel’s infinities, a continued concern about over-reliances on infinities and infinitesimals remains. for the epistemological concern, i cannot point to any one bright source. however, this concern stands as a subtext to many conversations i have had regarding hyperreal numbers, infinities, and infinitesimals. essentially, the idea is that since we cannot point to anything that is infinitely small or infinitely big in the world around us, it is not safe to make solid assertions about such entities, as those assertions cannot be tested. our minds (and therefore our proofs) can always fail, therefore, building on premises which can only be proved logically and not physically is dangerous. 26 simplifying and refactoring introductory calculus while these concerns are understandable, the long-term payoff will come from helping students see the concepts of the infinite and infinitesimal more clearly, and that will only come from practice and familiarity with the concepts. the infinite should not be feared, in fact, mathematics is one area which allows us to grapple with the infinite on a much more rigorous basis. 13 conclusion by making a few modifications to the way that calculus is taught, students can be presented a more unified, holistic system. this is both easier to use and easier to understand. having a single process and expanding out its usage to more and more complex cases is much more straightforward than having to reinvent the system at every step, and forcing students to memorize different processes for different situations. the changes proposed here include: • separating differentiation from finding the derivative. this allows the unification of explicit differentiation, implicit differentiation, and multivariable differentiation. additionally, it helps explain (and correct) the notions of higher-order differentials. • treating differentials algebraically. this is an extension of the separation of finding differentials and derivatives. additionally, when done correctly, it improves the usability of higher-order differentials and derivatives. • using a rule for uv instead of logarithmic differentiation. instead of forcing students to use different types of processes for different forms, teaching the generalized power rule allows students to take the differential of uv directly, just as with every other form. • using hyperreals for limits. hyperreals allow for a more intuitive approach to limits. additionally, moving limits to the end of a first-year course allows students to develop intuitions around the derivative first before seeing the formal proof of their validity. • treating integrals as infinite sums. treating the integral as an infinite sum instead of an area under a curve allows for easier generalization of the concept of the integral into various geometric situations (and even non-geometric situations). additionally, this allows for a more straightforward generalization of integration into the inclusion of multiple variables. the goal is to simplify introductory calculus while simultaneously making it more powerful. this is accomplished by (using computer science terminology) “refactoring” calculus into pieces that are more easily recombined, adapted, and applied to various situations. since differentials can always be transformed into derivatives by algebraic rearrangement, nothing is lost in their treatment as individuated entities. these ideas have been incorporated into a new text on calculus (bartlett, 2018), and future study is needed to fully assess the impact of these ideas (both positive and negative) on the teaching of calculus. references bartlett, j (2018). calculus from the ground up. broken arrow, ok: bp learning. bartlett, j and a z khurshudyan (2018). “extending the algebraic manipulability of differentials”. in: arxiv 1801.09553. in review. url: https://arxiv.org/ abs/1801.09553. berkeley, g (1734). the analyst. bos, h j m (1974). “differentials, higher-order differentials, and the derivative in the leibnizian calculus”. in: archive for history of exact sciences 14.1, pp. 1– 90. url: https://link.springer.com/article/10. 1007/bf00327456. cantor, g (1915). contributions to the founding of the theory of transfinite numbers. trans. by p e b jourdain. dover publications. url: https://www.maths. ed.ac.uk/~v1ranick/papers/cantor1.pdf. dauben, j w (1990). georg cantor: his mathematics and philosophy of the infinite. princeton university press. dray, t and c a manogue (2010). “putting differentials back into calculus”. in: the college mathematics journal 41.2, pp. 90–100. gonzález-lloret, m and k b nielson (2015). “evaluating tblt: the case of a task-based spanish program”. in: language teaching research 19.5. url: https:// www.academia.edu/6763175/evaluating_tblt_the_ case_of_a_task-based_spanish_program. henle, j m and e m kleinberg (2003). infinitesimal calculus. dover publications. katz, m and l polev (2017). “from pythagoreans and weierstrassians to true infinitesimal calculus”. in: journal of humanistic mathematics 7.1. url: http: //scholarship.claremont.edu/cgi/viewcontent. cgi?article=1368%5c&context=jhm. keisler, h j (2012). elementary calculus: an infinitesimal approach. dover publications. volume 1, issue 1 references 27 knuth, d (1974). surreal numbers. addison-wesley professional. robinson, a (1974). non-standard analysis. north-holland publishing company. thomson, s p (1910). calculus made easy. new york: macmillan company. url: http://www.gutenberg. org/ebooks/33283. wolfe, alan (2014). “dual numbers and automatic differentiation”. in: the blog at the bottom of the sea. url: https://blog.demofox.org/2014/12/30/dualnumbers-automatic-differentiation/. zach, r (2016). “hilbert’s program”. in: the stanford encyclopedia of philosophy. ed. by edward n. zalta. spring 2016. metaphysics research lab, stanford university. url: https : / / plato . stanford . edu / archives/spr2016/entries/hilbert-program/. login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? keep me logged in login register subscription login to access subscriber-only resources. information for readers for authors for librarians j3 g2ii2`b �m/ lqi2b q?�i bb bb;mb}+�mi �#qmi i?bb t`qq7 bb i?�i bi `2hb2b 2mib`2hv qm i?2 #�bb+běi?2 svi?�;q`2�m i?2q`2ki?2 mmbi +b`+h2i?2 /27@ bmbibqm q7 bbm2 �m/ +qbbm2i?2 /2}mbibqm q7 i?2 `�/b�m k2�bm`2 q7 �m �m;h2i?2 /bbi�m+2 7q`kmh��m/ i?2 tqr2` `mh2x � 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h2�`mbm; i?�i ǵ?2` m�k2 bb am@ b�mƕ r2 rqmh/ b�v i?�i r2 ?�p2 ǵ�+[mb`2/ bm7q`k�ibqmƕx h�f2m i?�i r�v�m bmbi�m+2 q7 bm7q`k�ibqm m�im`�hhv h2�/b iq � bbm@ ;h2bi�ib+ [m�mibiv q7 bm7q`k�ibqmx h?mbb7 �bf2/ ?qr km+? bm7q`k�ibqm bb +qmi�bm2/ bm h2�`mbm; i?�i � ~bt q7 � 7�b` +qbm vb2h/2/ � ǵ?2�/bƕi?2 ivtb+�h �mbr2` bb ǵr #bi q7 bm7q`k�ibqmƕ u! log2 ! 1 2 " = 1 #bivx a2�bqm2/ bm7q`k�ibqm i?2q`bbib �`2q7 +qm`b2�r�`2 i?�i i?2`2 bb kq`2 iq bi i?�m i?�ix u2i 2p2m i?qb2 bm/bpb/m�hb mbm�hhv qt@ 2`�i2 rbi?bm � t�`�/b;k i?�i bb kqbi q7i2m mqi �b +qkt`2?2m@ bbp2 �b bi m22/b iq #2 iq �//`2bb i?2 7mhh bm7q`k�ibqm tb+im`2x h?mbǵr #biƕ k2`2hv bm/b+�i2b i?2 mmk#2` q7 tqbbb#h2 bi�i2b u21 = 2 bi�i2bvx �hqm2i?bb mmk#2` bb bm/bz2`2mi `2;�`/bm; /22t2`bb;mb}+�mi �bt2+ib q7 bm7q`k�ibqm bm+? �b k2�mbm;x h?2`2 bb �m �ii`b#mi2 �#qmi bm7q`k�ibqm i?�i bb 2p2m kq`2 7mm@ /�k2mi�h i?�m i?qb2 +qmbb/2`�ibqmbx a �k bt2+b}+�hhv `272``bm; iq i?2 7�+i i?�i #27q`2 bm7q`k�ibqm k�v #2 k2�bm`2/ bi kmbi }`bi k�mb72bi �b � bt2+b}+ fbm/ q7 bm7q`k�ibqm�m/ i?�i k�m@ b72bi�ibqm �hr�vb q++m`b rbi?bm � }t2/ +qmi2tix a7 �mv +`bib+�h 2h2k2mi q7 i?2 +qmi2ti bb +?�m;2/i?2 bm7q`k�ibqm i?�i bb https://doi.org/10.33014/issn.2640-5652.1.1.clunn.1 https://doi.org/10.33014/issn.2640-5652.1.1.clunn.1 https://dx.doi.org/10.33014/issn.2640-5652.3.1.fernandez.1 about this journal the purpose of the journal paper submission policies other journal content from the editors sam s rakover and baruch cahlonsam s rakover and baruch cahlonwhen is explanation transitive? a methodological note introduction explanatory-transitivity discussion acknowledgments robert j. marks iirobert j. marks iitiling efflorescence of expanding kernels in a fixed periodic array: generalizing the flower-of-life introduction other expanding kernels properties of expanding kernels of varying periodicity analysis conclusions appendices letters and notes eric hollowaydeciding a bitstring of 1s is non-random is impossible in general jonathan bartlettproving the derivative of sin(x) using the pythagorean theorem and the unit circle j r millera response to clunn's axioms of morality jorge fernandezis information content a single, static quantity? news oqhmk2 jabbm2 k g2ii2`b �m/ lqi2b k. smxxh2 obbm�hbx�ibqmb q7 "qqh2�m 6q`kmh�2 1`b+ >qhhqr�v .pa, ryxjjyr9fbbbmxke9y@8e8kxjxkx?qhhqr�vxr "�+f;`qmm/ am i?2 +qkt�`bbqm #2ir22m ?mk�m �m/ +qktmi�ibqm�h bmi2hhb@ ;2m+2q7i2m ibk2b i?2 +qkt�`bbqm bb mqi bi`�b;?i7q`r�`/ #2@ +�mb2 ?mk�mb +�m tqbb2bb /qk�bm fmqrh2/;2 bm�++2bbb#h2 iq i?2 t`q;`�k i?2v �`2 +qkt2ibm; rbi?x hq t`qpb/2 � h2p2h th�v@ bm; }2h/bi bb ?2ht7mh iq ?�p2 ?mk�mb �m/ +qktmi2`b +qkt2i2 bm � /qk�bm r?2`2 #qi? bi�`i rbi? 2[m�h /qk�bm fmqrh2/;2�m/ i?2 /qk�bm bb r2hh mm/2`biqq/x pm2 bm+? /qk�bm bb #qqh2�m 7q`kmh�2x h?2b2 7q`kmh�2 �`2 b2ib q7 #qqh2�m p�`b�#h2b i?�i �`2 +qk#bm2/ rbi? i?2 �l. u!vp_ u"v�m/ lph u¬v hq;b+�h qt2`�iq`bx 1�+? #qqh2�m 7q`kmh� k�tb iq � bt2+b}+ i`mi? i�#h2x � i`mi? i�#h2 bb i?2 `2bmhi q7 i`vbm; �hh i?2 tqbbb#h2 t2`kmi�ibqmb 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�m/ rbi?qmi mqbb2 �//2/x jk g2ii2`b �m/ lqi2b u�v :m2bb i?2 #hm2 #bix u#v �mbr2` iq tmxxh2x 6b;m`2 r, smxxh2 rbi? 9 p�`b�#h2bx u�v :m2bb i?2 #hm2 #bix u#v �mbr2` iq tmxxh2mq mqbb2x 6b;m`2 k, smxxh2 rbi? 9 p�`b�#h2b �m/ r #bi q7 mqbb2x oqhmk2 jabbm2 k k. smxxh2 obbm�hbx�ibqmb q7 "qqh2�m 6q`kmh�2 jj u�v :m2bb i?2 #hm2 #bibx u#v �mbr2` iq tmxxh2x 6b;m`2 j, smxxh2 rbi? 3 p�`b�#h2bx u�v :m2bb i?2 #hm2 #bibx u#v �mbr2` iq tmxxh2mq mqbb2x 6b;m`2 9, smxxh2 rbi? 3 p�`b�#h2b �m/ ry #bib q7 mqbb2x about this journal the purpose of the journal paper submission policies other journal content from the editors eugenio darbesioeugenio darbesioa corollary of the conant-ashby theorem applied to abiogenesis robert sheldonrobert sheldoncomets, water, and big bang nucleosynthesis introduction benefits of a magnetized big bang and dark matter comets consequences of primordial comets analysis conclusions acknowledgments robert j marks iirobert j marks iisolution of the grazing goat problem: a conflict between beauty and pragmatism background grazing goat problem solution grazing goat problem inversion final thought letters and notes eric holloway2d puzzle visualizations of boolean formulae jonathan bartlettthe products of hyperreal series and the limitations of cauchy products tom and elizabeth siewertfollowing the science news login | communications of the blyth institute skip to main content skip to main navigation menu skip to site footer current archives about about the journal submissions editorial team privacy statement contact search search register login home / login subscription or article purchase required to access item. to verify subscription, access previous purchase, or purchase article, log in to journal. username * required password * required forgot your password? 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h2bb ;2iibm; i?2 t`qi2bmb bmiq i?2 +q``2+i hq+�ibqm bm i?2 2v2btqix q2 rqmh/ r2h+qk2 �hi2`m�ibp2 kq/2hbft`qtqb�hb iq bkt`qp2 q` +`bib+bx2 i?bb kq/2hx ǳ6qhhqr i?2 a+b2m+2ǵ bb ;qq/ �/pb+2#mi i?2 ?m`/h2b iq 1pq@ hmibqm �i i?2 +2hhmh�` h2p2h �`2 bm#bi�mib�hx q2 b?qmh/ +�`27mhhv r2b;? �hh i?2 /�i� u#qi? 7q` �m/ �;�bmbiv #27q`2 r2 �++2ti 1pqhmibqm �b � p�hb/ k2+?�mbbk 7q` i?2 7q`k�ibqm q7 +qkth2t hb72x *qhhbmbrq`i?"`v�m ukyyevx ǳh?2 6h�rb bm ami2hhb;2mi .2bb;mǵx am, *2mi2` 7q` �k2`b+�m s`q;`2bbx m`h, ?iitb,ffrrrx �k2`b+�mt`q;`2bb x q`; f bbbm2b f `2hb;bqm f m2rb f kyyefy9fryfrnj9fi?2@ 7h�rb@ bm@ bmi2hhb;2mi@ /2bb;mfx g2mbfb_ 1 ukykrvx h?2 1x +qhb hqm;@i2`k 2tt2`bk2mi�h 2pq@ hmibqm t`qd2+i bbi2x m`h, ?iit,ffkvtqx+bbxkbmx2/mf 2+qhbx _�ibqm�h qbfb ukyr3vx .�rfbmbƕ q2�b2hx m`h, ?iitb , f f `�ibqm�hrbfbxq`;frbfbf.�rfbmbnr2�b2hx ab2r2`i1 � �m/ h � ab2r2`i ukyrdvx ǳh?2 l22/ 7q` � zm�m@ ib}�#h2 jq/2h q7 1pqhmibqmǵx am, cqm`m�h q7 "bq ammqp�ibqm ex8ttx e38ĝen9x https://www.americanprogress.org/issues/religion/news/2006/04/10/1934/the-flaws-in-intelligent-design/ https://www.americanprogress.org/issues/religion/news/2006/04/10/1934/the-flaws-in-intelligent-design/ https://www.americanprogress.org/issues/religion/news/2006/04/10/1934/the-flaws-in-intelligent-design/ https://www.americanprogress.org/issues/religion/news/2006/04/10/1934/the-flaws-in-intelligent-design/ http://myxo.css.msu.edu/ecoli http://myxo.css.msu.edu/ecoli https://rationalwiki.org/wiki/dawkins_weasel https://rationalwiki.org/wiki/dawkins_weasel about this journal the purpose of the journal paper submission policies other journal content from the editors eugenio darbesioeugenio darbesioa corollary of the conant-ashby theorem applied to abiogenesis robert sheldonrobert sheldoncomets, water, and big bang nucleosynthesis introduction benefits of a magnetized big bang and dark matter comets consequences of primordial comets analysis conclusions acknowledgments robert j marks iirobert j marks iisolution of the grazing goat problem: a conflict between beauty and pragmatism background grazing goat problem solution grazing goat problem inversion final thought letters and notes eric holloway2d puzzle visualizations of boolean formulae jonathan bartlettthe products of hyperreal series and the limitations of cauchy products tom and elizabeth siewertfollowing the science news oqhmk2 jabbm2 r ab am7q`k�ibqm *qmi2mi � abm;h2ai�ib+ zm�mibiv\ jn i?2 }m�h bbbm2 �//`2bb2/ ?2`2bm `2;�`/bm; *hmmmƕb +h�bk i?�i q#d2+ibp2 kq`�hbiv 2tbbibx *qm~b+i oj, p#d2+ibp2 jq`�hbiv bb am#d2+ibp2 �++q`/bm; iq *hmmmi?2 ;q�h q7 ?bb rq`f bb iq 2bi�#hbb? 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i?�i 2mibivx �hi2`m�@ ibp2hvr?2m � bb;m�h bmi2`�+ib rbi? � `2+2bp2` bi k�mb72bib bm /bz2`2mi r�vb /2t2m/bm; qm i?2 +qkt`2?2mbbp2 +qmi2tix h?mbi?2 t`qtbk�i2 +�mb2ěi?2 bb;m�h ui?2 ǵbbƕ q7 bqk2 bm7q`k�ibqmvě/q2b mqi k�mb72bi �b bm7q`k�ibqm u#2+qk2 bm@ 7q`k�ibqmv bm � bbm;h2bi�ib+ �m/ mmp�`vbm; r�vx h?�i bb i?2 #�bbb 7q` bi�ibm; i?�i bm7q`k�ibqm mqi bq km+? bb bqk2i?bm; #mi `�i?2` #2+qk2b bqk2i?bm;x 6m`i?2`kq`2i?bb t?2mqk2mqm �hr�vb ?�tt2mb 7q` �hh 2mibib2b u�hh `2+2bp2`bvěhbpbm; q` mqm@ hbpbm;c m�im`�h q` �`ib}+b�h ui2+?mqhq;b+�hvx about this journal the purpose of the journal paper submission policies other journal content from the editors sam s rakover and baruch cahlonsam s rakover and baruch cahlonwhen is explanation transitive? a methodological note introduction explanatory-transitivity discussion acknowledgments robert j. marks iirobert j. marks iitiling efflorescence of expanding kernels in a fixed periodic array: generalizing the flower-of-life introduction other expanding kernels properties of expanding kernels of varying periodicity analysis conclusions appendices letters and notes eric hollowaydeciding a bitstring of 1s is non-random is impossible in general jonathan bartlettproving the derivative of sin(x) using the pythagorean theorem and the unit circle j r millera response to clunn's axioms of morality jorge fernandezis information content a single, static quantity? 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q7 gb72x a+?qhi2m. g ukyryvx 1p2`v :qq/ e2v jmbi #2 � jq/2h q7 i?2 gq+f bi pt2mb uh?2 *qm�mi � �b?#v h?2q`2k _2pbbbi2/vx oqb2�h#2`i ukyyevx ǳ"bqhq;b+�h 6mm+ibqm �m/ i?2 :2m2ib+ *q/2 �`2 ami2`/2t2m/2miǵx am, *?�qbaqhbiqmb�m/ 6`�+@ i�hb k3x9x pqm l2mk�mmc urneevx h?2q`v q7 a2h7@_2t`q/m+bm; �m@ iqk�i�x l`#�m�, lmbp2`bbiv q7 ahhbmqbb s`2bbx qb2m2`l urn93vx *v#2`m2ib+b, p` *qmi`qh �m/ *qkkmmb+�@ ibqm bm i?2 �mbk�h �m/ i?2 j�+?bm2x jah s`2bbx https://doi.org/10.1126/science.7973651 about this journal the purpose of the journal paper submission policies other journal content from the editors eugenio darbesioeugenio darbesioa corollary of the conant-ashby theorem applied to abiogenesis robert sheldonrobert sheldoncomets, water, and big bang nucleosynthesis introduction benefits of a magnetized big bang and dark matter comets consequences of primordial comets analysis conclusions acknowledgments robert j marks iirobert j marks iisolution of the grazing goat problem: a conflict between beauty and pragmatism background grazing goat problem solution grazing goat problem inversion final thought letters and notes eric holloway2d puzzle visualizations of boolean formulae jonathan bartlettthe products of hyperreal series and the limitations of cauchy products tom and elizabeth siewertfollowing the science news oqhmk2 jabbm2 k l2rb 1m;bm22`bm; 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i?2 g�bi lmbp2`b�h *qkkqm �m+2biq`ǵx am, "bq1bb�vb 9jxdx /qb, ryxryykf#b2bxkykryyyy9x s�hh2mj c �m/ l c j�ixf2 ukyyevx ǳ6`qk h?2 p`b;bm q7 at2+b2b iq i?2 q`b;bm q7 #�+i2`b�h ~�;2hh�ǵx am, l�im`2 _2@ pb2rb jb+`q#bqhq;v 9xryttx d39ĝdnyx /qb, ryxryj3f m`kb+`qr9njx _b+?�`/bh ukykrvx ǳh?qk�b *�p�hb2`@akbi? urn9kĝkykrvǵx am, l�im`2 8njtx rnyx /qb, ryxryj3f/9r83e@ ykr@ yrk8y@rx hqm`c ukykrvx �//`2bbbm; �#bq;2m2bbb �m/ *qkkqm jbb+qm@ +2tibqmbx m`h, ?iitb,ffrrrxvqmim#2x+qkfth�vhbbi\ hbbi4sgagqm/rn39ikh>"pcw6vmg�y[ptr`a".`x q�`k2`/�ko . ukykyvx >mk�m g2�`m, j�+?bm2 g2�`mbm; kq/2hb b?qmh/ th�v #v i?2 `mh2bhbi2`�hhvx m`h, ?iitb, ff;bi?m#x+qkffq�mbm;f?mk�m@h2�`mx q2bm#2`;a urnedvx ǳ� jq/2h q7 g2tiqmbǵx am, s?vbb+�h _2@ pb2r g2ii2`b rnxkrttx rke9ĝrkeex /qb, ry x rryj f s?vb_2pg2iixrnxrke9x qbhh2ii6 _ 2i �hx umx/xvx ǳ>b;?@t2`7q`k�m+2 #`�bm@iq@i2ti +qkkmmb+�ibqm pb� ?�m/r`bibm;ǵx am, l�im`2 8nj uvttx k9nĝk89x /qb, ryxryj3fb9r83e@ykr@yj8ye@kx https://www.cs.hmc.edu/~montanez/pdfs/allen-2020-castro-consensus.pdf https://www.cs.hmc.edu/~montanez/pdfs/allen-2020-castro-consensus.pdf https://www.cs.hmc.edu/~montanez/pdfs/allen-2020-castro-consensus.pdf https://doi.org/10.1016/j.cub.2015.07.055 https://doi.org/10.3389/fmicb.2021.639396 https://doi.org/10.3389/fmicb.2021.639396 https://doi.org/10.1016/j.isci.2021.102395 https://doi.org/10.1016/j.isci.2021.102395 https://www.theguardian.com/science/2021/jul/28/richard-lewontin-obituary https://www.theguardian.com/science/2021/jul/28/richard-lewontin-obituary https://www.theguardian.com/science/2021/jul/28/richard-lewontin-obituary https://doi.org/10.1038/s41467-021-23573-3 https://doi.org/10.1038/s41467-021-23573-3 https://doi.org/10.1098/rspb.2006.3531 https://doi.org/10.1126/science.abe0511 https://doi.org/10.1126/science.abe0511 https://doi.org/10.1016/j.tim.2020.01.005 https://cerncourier.com/a/steven-weinberg-1933-2021/ https://cerncourier.com/a/steven-weinberg-1933-2021/ https://doi.org/10.1091/mbc.e16-07-0509 https://doi.org/10.1091/mbc.e16-07-0509 https://doi.org/10.33014/issn.2640-5652.2.1.holloway.1 https://doi.org/10.33014/issn.2640-5652.2.1.holloway.1 https://arxiv.org/abs/1609.00904 https://doi.org/10.1089/ast.2015.1464 https://doi.org/10.1089/ast.2015.1464 https://doi.org/10.1038/scientificamerican0978-212 https://www.nybooks.com/articles/1997/01/09/billions-and-billions-of-demons/ https://www.nybooks.com/articles/1997/01/09/billions-and-billions-of-demons/ https://www.nybooks.com/articles/1997/01/09/billions-and-billions-of-demons/ https://doi.org/10.1002/bies.202100004 https://doi.org/10.1038/nrmicro1493 https://doi.org/10.1038/nrmicro1493 https://doi.org/10.1038/d41586-021-01250-1 https://doi.org/10.1038/d41586-021-01250-1 https://www.youtube.com/playlist?list=plilwudw_84t2thbvjzfyula0qvxwribdr https://www.youtube.com/playlist?list=plilwudw_84t2thbvjzfyula0qvxwribdr https://github.com/koaning/human-learn https://github.com/koaning/human-learn https://doi.org/10.1103/physrevlett.19.1264 https://doi.org/10.1103/physrevlett.19.1264 https://doi.org/10.1038/s41586-021-03506-2 about this journal the purpose of the journal paper submission policies other journal content from the editors eugenio darbesioeugenio darbesioa corollary of the conant-ashby theorem applied to abiogenesis robert sheldonrobert sheldoncomets, water, and big bang nucleosynthesis introduction benefits of a magnetized big bang and dark matter comets consequences of primordial comets analysis conclusions acknowledgments robert j marks iirobert j marks iisolution of the grazing goat problem: a conflict between beauty and pragmatism background grazing goat problem solution grazing goat problem inversion final thought letters and notes eric holloway2d puzzle visualizations of boolean formulae jonathan bartlettthe products of hyperreal series and the limitations of cauchy products tom and elizabeth siewertfollowing the science news volume 2, issue 2 fisher’s fundamental theorem of natural selection isn’t fundamental after all salvador cordova doi: 10.33014/issn.2640-5652.2.2.cordova.1 abstract fisher’s fundamental theorem of natural selection (ftns) was called “biology’s central theorem” (fisher, 1930, pgs. 36–37; brockman, 2011; royal society, 2020). ftns might possibly have been accorded this status for decades because fisher himself declared his own theorem to be fundamental to biology (fisher, 1930, pgs. 36–37). however, the idea that fisher’s theorem is biology’s central theorem is by-and-large a myth promoted by popular science writers like richard dawkins (brockman, 2011). joseph felsenstein, when delivering the 2018 fisher memorial lecture declared that ftns was “alas, not so fundamental” (felsenstein, 2018; felsenstein, 2017, pg. 94). one may be hard-pressed to find a biology textbook or biology student who can explain how ftns helps them understand biology. even the meaning and proof of the ftns have remained contentious even to this day (price, 1972; basener and sanford, 2018). not only does ftns do little to nothing to explain biological evolution, but like most population genetic and evolutionary literature, ftns relies on a definition of fitness in terms of population growth rates rather than the biophysical notions of fitness which are more in line with the common-sense intuitions of the medical and engineering communities. from the perspective of the biophysical (rather than the population growth) notion of fitness, natural selection might be more accurately described as an agent against the increase of complexity rather than an agent for it. thus, metaphorically speaking, some sort of anti-weasel model of natural selection might better describe how selection actually works in nature rather than dawkins’ weasel or other man-made genetic algorithms. however, the main focus of this article is to provide some pedagogical insights through simple numerical illustrations of fisher’s theorem. the hope is that this will show the general irrelevance of ftns to the question of the evolution of complexity by means of natural selection, and thus show that fisher’s theorem is not so fundamental after all. 1 introduction: the problem of defining fitness in order to understand the meaning of fisher’s fundamental theorem of natural selection, it is helpful to understand the definition of fitness which fisher was using. this is not so trivial a problem because in a 2009 paper on fitness, allen orr quipped, “biologists have o!ered a staggering number of definitions of fitness” (orr, 2009), and worse richard lewontin lamented, “it is not entirely clear what fitness is” (lewontin, 2003). andreas wagner went even further: however, fitness is hard to define rigorously and even more di"cult to measure. . . an examination of fitness and its robustness alone would thus not yield much insight into the opening questions. instead, it is necessary to analyze, on all levels of organization, the systems that constitute an organism, and that sustain its life. i define such systems loosely as assemblies of parts that carry out well-defined biological functions. (wagner, 2005, pg. 1) ironically, “systems loosely as assemblies of parts that carry out well-defined biological functions” sounds remarkably similar to michael behe’s definition of irreducible complexity: “a single system composed of several well-matched, interacting parts that contribute to the basic function of the system” (behe, 1996, pgs. 39–40). the population-genetic/evolutionary biology definition of fitness seems disconnected, if not o!ensive, to common sense notions of fitness used by the medical and engineering community. for example, in the medical sense, sickle cell anemia is a heritable trait that can lead to sickness, but it is viewed as a “beneficial” adaptation in the populationgenetic/evolutionary sense. natural selection could selectively favor loss of optical structure in gammarus minus (an aquatic creature that dwells in caves) or tusks in elephants. allen orr used the example of gammarus minus https://dx.doi.org/10.33014/issn.2640-5652.2.2.cordova.1 26 fisher’s fundamental theorem of natural selection to chide daniel dennett’s naïve views of natural selection when orr pointed out: in reality, selection “sees” only brute birth, death, and reproduction, and knows nothing of design. selection—sheer, cold demographics—is just as happy to lay waste to the kind of design we associate with engineering as to build it. consider the eyes of cave organisms who live in total darkness. if eyes are expensive to make, selection can wreck their exquisite engineering just as surely as it built it. an optic nerve with little or no eye is most assuredly not the sort of design one expects on an engineer’s blueprint, but we find it in gammarus minus. whether or not this kind of evolution is common, it betrays the fundamental error in thinking of selection as trading in the currency of design. (orr, 1996) in fact “reductive evolution” (loss of genes and function) rather than “constructive evolution” appears to be the dominant mode of evolution throughout most of geological history (wolf and koonin, 2013), but punctuated with episodes of complexification that have no clear mechanistic explanation. reductive evolution has also been confirmed by direct observation in the field and in the laboratory to be the dominant mode of evolution (behe, 2010). this is in contrast to a widespread and long-standing historic and present belief that natural selection generally leads to increase in complexity, and the basis for these beliefs not rooted in empiricism but either conjecture or computer simulation far removed from actual experiments (darwin, 1859; adami, ofria, and collier, 2000; vaughan, 2019). amusingly, the paucity of direct examples of complexity increase and the abundance of complexity decrease by natural selection was unwittingly highlighted by sharon moalem’s book, survival of the sickest, where he argues why we need birth defects like tay-sach’s disease on account of natural selection (moalem, 2008). furthermore, moalem went on to celebrate the facts of disease as evidence of darwin’s genius. there are a variety of the notions of the term, “fit,” and the population genetic/evolutionary definition (elaborated below) seems idiosyncratic relative to historical and common notions of the word. an aircraft is “fit” to fly, a submarine is fit to operate underwater, a car is fit to operate on land, a spaceship in space, etc. none of these notions of fit need be conflated with reproductive success. biophysicists have established eyes are fit to sense and count individual photons (bialek, 2015), that bacteria can count individual molecules (bialek, 2012), that sharks are fit to sense electric fields in conditions at the extreme limit permissible by physics (angier, 2010), and birds are fit to fly and navigate thousands of miles via compasses that leverage quantum spin chemistry (ritz, adem, and schulten, 2000; rubenstein and hack, 2013). although the definition and treatment of fitness in the population-genetic/evolutionary sense may seem irrelevant if not repugnant to common sense notions of fitness in the medical and engineering sense, one cannot understand fisher’s theorem without understanding the populationgenetic/evolutionary definition of fitness. therefore, the next section will be devoted to elucidating the populationgenetic/evolutionary definition of fitness. the stated definitions follow from conventions used in joseph felsenstein’s graduate-level textbook, evolutionary theoretical genetics (felsenstein, 2017). the population-genetic definition of fitness arises in the context of a highly idealized model that approximates some real world populations in an exponential growth stage. the notion of fitness in this simplest of models can be extended, with a modest amount of amendment, to definitions used by a large amount of population genetics literature. however, the staggering amount population genetics literature that uses such simplistic definitions does not at all imply these population genetic models are accurate or useful. felsenstein points out: fisher’s and wright’s one-locus equations turn out to be approximations, sometimes bad ones. . . the mathematical tools at hand have not revolutionized our understanding of the evolutionary process. . . many evolutionists will fail to find the clear and simple messages that population genetics theory once seemed to promise. (felsenstein, 1989) unfortunately, many preliminaries are needed to provide a cursory understanding of the terminology associated with the population-genetic/evolutionary definitions of fitness required to understand fisher’s theorem. one must suffer through some of the math in order to understand what fisher’s theorem means. volume 2, issue 2 2. absolute “darwinian” fitness vs. relative fitness 27 2 absolute “darwinian” fitness vs. relative fitness because populations can grow exponentially, it is possible that a single molecular change in one organism can result in immense macroscopic consequences for the population. for example, in the evolution of bacteria or viruses, the emergence of a novel mutational change in their genomes can result in their epidemic spread which has very noticeable e!ects on the macro scale. in light of the exponential growth of such populations, there is reasonable justification for choosing an exponential function for modeling growth of populations such as these, and this leads to the beginning of a mathematical definition of fitness in the sense of population genetics. the exponential growth function arises out of one of the most elementary di!erential equations: ! (") = d! (") d" (1) where !(") is the size of the population and is a function of time. one of the simple solutions to this di!erential equation is: ! (") = #$! (2) where # is a constant. a slightly more complex di!erential equation that is traditionally related to population growth is %! (") = d! (") d" (3) where % is a constant. a solution for ! (") under the constraint of (3) is: ! (") = #$"! (4) where # again is also a constant. % is customarily called the continuous growth constant and # the initial population size. this equation can serve as an idealization of exponentially growing populations. note that for " = 0, ! (0) = # (5) a discrete version of (4) can be synthesized by defining the following constant which we’ll call the absolute fitness or darwinian fitness: & ! $" (6) [it bears mentioning that calling & “darwinian fitness” might be a misnomer, since lewontin argues implicitly that describing fitness in this way violates the spirit of what darwin meant by fitness. lewontin said, “darwin’s sense of fit has been bypassed” by using reproductive schedules themselves rather than the functional aspects of an organism in relation to its environment (lewontin, 2003)]. we can then define the size of the population '(() as a function of the number of generations ' (() ! ' (0)& # (7) where ( is a non-negative integer representing a particular generation cycle of the population, and '(0) is the initial size of the population in generation zero. the assumption is that in such a population, all parents have their children simultaneously at the same time, and & represents the average number of children each parent has, and for simplicity it is assumed & is constant for all time. if we restrict the values of " to be only discrete points such that " = (, and noting that ' (() is defined in terms of & # , we can relate ' (() to the continuous time version of population size ! ("). in other words, if we assume " has integer values and that the units of time are stated in generations rather than seconds or years, so that " = 1 corresponds to the amount of time for one generation, " = 2 is the amount of time for two generations, etc., then under these constraints we can then make this relation: & # = {$"}# = {$"}! = $"! . (8) if further we let the constant ' (0) = #, then ' (0)& # = #$"! (9) again, there is an implicit assumption laid out so far; namely every parent of generation k will bear all their o!spring for generation k+1 simultaneously. 28 fisher’s fundamental theorem of natural selection if we have a population composed of ) sub populations that each obey the above simple model, we can extend (7) to cover multiple sub populations. with * " {1, 2, . . . )}, the size '$ (() of each the * sub populations in generation ( is: '$ (() = '$ (0)& # $ (10) note that capital “'” is used to designate absolute population numbers. depending on the context, '$ can describe individuals and/or alleles. for the sake of simplicity, we will discuss the special case where the number of individuals is the same as the number of alleles, namely a haploid asexual population where only one gene locus is considered. aspects of this simple special case will not hold true for diploid populations but is used primarily for pedagogical purposes. the total population 'tot for a given generation is straight forwardly stated as the sum of the sizes of the individual * sub populations: 'tot (() = %! $=1 '$ (() (11) the proportion, the relative frequency, or simply frequency +$ (() (lower case p), of alleles/individuals of a given subpopulation * that appear in the total population in generation k is: +$ (() = '$ (() 'tot (() (12) +$ (() is often called the gene frequency, although strictly speaking it is more properly called the allele frequency. in a somewhat analogous manner, instead of absolute fitness &$ of each of the individuals of a sub population, we can state the relative fitness ,$ of each of the individuals. because absolute fitness is designated with a capital & , it is customary to designate relative fitness with a lowercase ,. a method of defining relative fitness, though not the only way, is to take the highest absolute fitness value found in a total population and designate it as the reference absolute fitness &ref. we can then define relative fitness ,$ for each subpopulation in relation to &ref as follows: ,$ ! &$ &ref (13) for example, if &1 4.0 &2 3.0 &3 2.0 then &ref = 4.0, thus: ,1 1.0 ,2 0.75 ,3 0.50 3 mean and variance of relative fitnesses for an arbitrary generation (, we can define a mean of the relative fitnesses , (() as: , (() ! %! $=1 +$ (() ,$ (14) we can also define the variance of relative fitnesses var (, (()) for a given generation ( as: var (, (()) ! %! $=1 {+$ (() ,2 $ } # , (()2 (15) also let us define the change of mean relative fitnesses !, (() as: !, (() ! , (( + 1) # , (() (16) this definition of !, (() may or may not be in agreement with other texts, but it will nevertheless be su"cient to derive a proof of fisher’s fundamental theorem of natural selection in the discrete generation single locus haploid case. when it is said, “the fitness of the population is increasing,” it usually means , (() is increasing. qualitatively, it simply means the individuals with the highest reproductive rate are occupying a larger and larger proportion of the population. if there is only 1 type of individual with the highest fitness, a fitness increase means that the population is asymptotically approaching a state of being homogeneous. volume 2, issue 2 4. numerical examples to illustrate fisher’s theorem 29 with these concepts now defined, we can now examine some numerical examples that give insights into fisher’s fundamental theorem of natural selection. 4 numerical examples to illustrate fisher’s theorem repeating the example in section 2, suppose we have the following scenario defined by the given boundary conditions specified by tables 1 and 3; let us call it scenario 1. table 1 lists the given absolute fitness values for the sub populations. &1 4.0 &2 3.0 &3 2.0 table 1: absolute fitness values of subpopulations (scenario 1) the given values in table 1 result in the computed relative fitness values for table 2: ,1 1.0 ,2 0.75 ,3 0.50 table 2: relative fitness values (scenario 1) the given initial absolute individual/allele populations at generation 0 are listed in table 3: '1 (0) 1 '2 (0) 2 '3 (0) 7 table 3: absolute individual/allele populations at generation 0 (scenario 1) which results in the computed relative population frequencies in table 4: +1 (0) 0.1 +2 (0) 0.2 +3 (0) 0.7 table 4: relative population frequencies (scenario 1) given the boundary conditions defined by tables 1 and 3, the following values were computed over 5 generations for scenario 1 and listed in table 5. [tables 1 through 5 were from given and computed values used in the associated supplementary spreadsheet, supplement 1.1] one should readily observe that the last two columns of table 5 have identical values! this is an illustration of fisher’s fundamental theorem of natural selection in the simplest discrete generation, single locus, haploid model. the statement of the fisher’s theorem in the discrete generation model is: !, (() = var (, (()) , (() (17) and is illustrated by the fact the last two columns are identical. running more generations, the mean fitness ,(() will approach 1.0, meaning the population will asymptotically approach homogeneity. ironically a condition where all members of a population are all clones of each other might be deemed to actually be unhealthy since diversity of alleles in a population can help a species’ survivability since an environmental change might eliminate some individuals carrying a certain allele but not others. it must be emphasized (17) is not the most general form of fisher’s theorem despite the fact barton and queller refer to it as fisher’s theorem (barton et al., 2007; queller, 2017). lessard and ewens would call this the discrete generation case (ewens and lessard, 2015) for only one locus (albeit they use fairly di!erent math symbols to describe the theorem). the most general statement fisher’s theorem was for the continuous generation case and for multiple loci (price, 1972). that said, below is the proof the discrete (17) version of fisher’s theorem for the haploid single locus case which follows almost exactly a proof provided in joseph felsenstein’s graduate textbook, evolutionary theoretical genetics (felsenstein, 2017), but with some clarifying notation added. 1supplement 1 is available online at https://journals. blythinstitute.org/ojs/index.php/cbi/article/view/67/64. https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/67/64 https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/67/64 30 fisher’s fundamental theorem of natural selection generation (() ,(() var (, (()) !, (() var(& (#)) & (#) 0 0.6000000 0.0275000 0.0458333 0.0458333 1 0.6458333 0.0360243 0.0557796 0.0557796 2 0.7016129 0.0420135 0.0598813 0.0598813 3 0.7614943 0.0429713 0.0564303 0.0564303 4 0.8179245 0.0387825 0.0474157 0.0474157 5 0.8653403 0.0316793 0.0366091 0.0366091 table 5: scenario 1 (5 generations) 4.1 proof of (17) starting from (10), the following must also hold by simple substitution of ( + 1 for (: '$ (( + 1) = '$ (0)& #+1 $ (18) thus, in light of (10) and (18): '$ (( + 1) = '$ (0)& #+1 $ = '$ (0)& # $ &$ = '$ (()&$ (19) using this result we can say by extending (11) and (12): +$ (( + 1) = '$ (( + 1) 'tot (( + 1) = '$ (( + 1)"% $=1 '$ (( + 1) (20) however, in light of (19), (20) can be restated as: +$ (( + 1) = '$ (( + 1)"% $=1 '$ (( + 1) = &$'$ (()"% $=1&$'$ (() (21) we can simultaneously divide the numerator and denominator of (21) by 'tot ((), and given (12), instead of relating +$ (( + 1) in terms of the absolute sizes '$(k) of the * sub populations, we can express it in terms of the frequency of individuals (or alleles) +$ in total population: +$ (( + 1) = &$ +$ (()"% $=1&$ +$ (() (22) referring back to equation (13), if we divide the numerator and denominator of (22) simultaneously by &ref, we scale the absolute fitnesses down to relative fitnesses: +$ (( + 1) = ,$ +$ (()"% $=1 ,$ +$ (() (23) the term in the denominator is equal to the mean of the relative fitnesses , ((), thus +$ (( + 1) = ,$ +$ (() , (() (24) by way of extension, equation (14) must hold true also for using ( + 1: , (( + 1) = %! $=1 +$ (( + 1) ,$ (25) substituting the righthand side of (24) for +$ (( + 1) into (25) yields , (( + 1) = %! $=1 ,$ +$ (() , (() ,$ = %! $=1 +$ (() ,2 $ , (() (26) subtracting , (() from the right hand side and left hand side: , (( + 1) # , (() = # %! $=1 +$ (() ,2 $ , (() $ # , (() (27) since , (() = , (()2 , (() (28) we can state (27) alternatively as: volume 2, issue 2 5. discussion 31 , (( + 1) # , (() = %"% $=1 +$ (() ,2 $ & # , (()2 , (() (29) the numerator of (29) is the same as the variance var (, (()) from (15), thus , (( + 1) # , (() = var (, (()) , (() (30) noting equation (16) we have !, (() = var (, (()) , (() (31) this completes the proof of the discrete-generation, haploid, one-locus case of fisher’s theorem. it is worth mentioning many, if not all, texts will not use the notation here, especially the explicit statement of a variable’s dependence on generation (. but the dependence on ( is emphasized here for clarity. 4.2 how much di!erence does it make? now suppose we have the following scenario defined by the boundary conditions described by tables 6 and 7; let us call it scenario 2. the absolute fitness and absolute population numbers need not be stated explicitly for scenario 2 because (23) enables the computation of values for table 8 with only relative fitnesses and the initial allele/population frequencies. one can simply assume there exists some absolute fitness values and initial absolute population sizes that will yield tables 6 and 7. the relative fitness values which are constant for every generation are listed in table 6: ,1 1.00000 ,2 0.53125 ,3 0.53125 table 6: relative fitness values (scenario 2) the initial allele frequencies at generation 0 are listed in table 7: +1 (0) 0.146666666 +2 (0) 0.426666667 +3 (0) 0.426666667 table 7: initial allele frequencies (scenario 2) given the boundary conditions defined by tables 6 and 7, the following values were computed over 5 generations for scenario 2 and listed in table 8. [tables 6 through 8 were from given and computed values used in the associated supplementary spreadsheet (supplement 2).2] what is noteworthy is that for generation 0, the entries for both scenario 1 and scenario 2 are identical! however, at generation 5, the mean fitness in scenario 1 is 0.8653403 whereas for scenario 2 it is 0.9073945. this illustrates the obvious fact that di!erent sets of relative fitness values ,$ can possibly result in identical mean fitness and variance values for some generations but not others. this shows that fisher’s theorem, in and of itself, cannot predict the trajectory of population structure. this is owing to the simple fact that infinite sets of numbers can share the same mean and variance somewhat analogous to how several different curves with di!erent trajectories can share a point in a 2d plane. ewens and lessard highlighted this fact as a part of a generally negative assessment of fisher’s theorem (ewens and lessard, 2015). it shows fisher’s theorem adds no greater insight to population trajectory than provided by the relative fitness values ,$ themselves and the relative initial allele frequencies +$ (0). thus, fisher’s fundamental theorem of natural selection adds no additional insight into the evolution of complexity, not only for the reasons stated by ewens and lessard, but also due to the definition of fitness used, namely fitness defined in terms of population growth rather than biophysical complexity. 5 discussion the di"culty of establishing the relevance fisher’s theorem to real-world questions about the evolution of complexity should be apparent because fisher’s theorem could just as well be applied to the increase of fitness due to loss of complexity. the numerical illustrations above have no indication whether the fitness values are due to gain or loss of complexity. it would appear dawkins lionizing and mythologizing of fisher’s theorem is exactly that, since fisher’s theorem doesn’t directly establish that biological complexity must necessarily increase. 2supplement 2 is available online at https://journals. blythinstitute.org/ojs/index.php/cbi/article/view/67/65. https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/67/65 https://journals.blythinstitute.org/ojs/index.php/cbi/article/view/67/65 32 fisher’s fundamental theorem of natural selection generation (() ,(() var (, (()) !, (() var(& (#)) & (#) 0 0.6000000 0.0275000 0.0458333 0.0458333 1 0.6458333 0.0405816 0.0628360 0.0628360 2 0.7086694 0.0516877 0.0729363 0.0729363 3 0.7816056 0.0546763 0.0699538 0.0699538 4 0.8515594 0.0475469 0.0558351 0.0558351 5 0.9073945 0.0348330 0.0383880 0.0383880 table 8: scenario 2 (5 generations) the above discrete-generation version of fisher’s theorem can be generalized to a continuous multi-locus diploid version of fisher’s theorem. fisher described his theorem for the continuous case where the continuous case does not require dividing var (, (()) by ,(() in relating “rate of increase in fitness” to “genetic variance in fitness.” the proof of the most general version is substantially more di"cult, but was demonstrated by george price in 1972 (price, 1972), and thus not repeated here. an amusing historical anecdote regarding fisher’s theorem is that he did not use su"cient rigor to describe his own fundamental theorem. for decades people accepted ftns as true even though they did not understand it. it could be speculated this perpetuated its mythical status as biology’s central theorem, even though population geneticists rarely, if at all, used ftns after fisher first introduced it. he stated his theorem in this way without rigorously defining the terms mathematically: "the rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time." (fisher, 1930, pgs. 36–37) these vague words lead george price to observe in 1972: it has long been a mystery how fisher (1930, 1941, 1958) derived his famous ‘fundamental theorem of natural selection’ and exactly what he meant by it. . . also, he spoke of the ‘rigour’ of his derivation of the theorem and of ‘the ease of its interpretation’. but others have variously described his derivation as ‘recondite’ (crow & kimura, 1970), ‘very di"cult’ (turner, 1970), or ‘entirely obscure’ (kempthorne, 1957). and no one has ever found any other way to derive the result that fisher seems to state. hence, many authors (not reviewed here) have maintained that the theorem holds only under very special conditions, while only a few (eg. edwards, 1967) have thought that fisher may have been correct – if only we could understand what he meant! (price, 1972) however, as with the discrete-generation version, the most general version of fisher’s theorem su!ers the same problems in terms of its lack of adding any further insight to the population’s trajectory than already specified by the requisite boundary conditions. as with the discrete single locus haploid case, the most generalized ftns adds no insight to the details of the evolution of biological systems in terms of the common sense notions of fitness used in the medical and engineering disciplines. amazingly, the original generalization of ftns clarified by price does not include e!ects of the infusion of additional mutations over time. basener and sanford demonstrated that given enough mutations, mean fitness will never maximize (basener and sanford, 2018). further, apart from even adding mutations, patrick moran and richard lewontin demonstrated that fitness is not guaranteed to maximize if epistasis and gene linkage are modeled. grodwohl characterized these shocking mathematical developments as “the rise and fall of fitness maximization” (grodwohl, 2016). in light of the fact that most “beneficial” mutations are loss of function, then the individual with the highest fitness could be the one that has lost function, rather than gained it. this suggests that even in the existing framework of population genetics, natural selection could just as well eliminate function out of a population rather than construct it. thus, fisher’s theorem could just as well be used in models where natural selection facilitates destruction of function, and such destruction of function has direct observational confirmation in the field and in experiments as the overwhelming cause of beneficial mutations (behe, 2010). volume 2, issue 2 references 33 it is also worth mentioning that ronald brady, j. g. ollason, and others point out the tautologous and inadequate definition of fitness in evolutionary biology, such that it has no utility in helping determine the veracity of evolutionary theory (brady, 1979; ollason, 1991). dawkins’ weasel program (dawkins, 1986, pgs. 46–51) metaphorically describes how evolution is conceived in the minds of some and has been augmented and extended to teach evolution as part of an outreach program (christensen-dalsgaard and kannewor!, 2009). independent of the scholarly value of dawkins’ weasel, metaphorically speaking an anti-weasel model of evolution by natural selection might be a more valid description of how certain, if not most, organisms evolve by natural selection. 6 conclusion fisher may have envisioned that his fundamental theorem of natural selection was proof that evolutionary progress is inevitable. however, fisher’s theorem is perfectly consistent with the view that reductive evolution is the dominant mode of evolution. and if direct observation of the ubiquity of reductive evolution can be extrapolated to the past, then complexity decrease by natural selection would be the norm, and thus complexity increase from simple bacteria to complex multicellular eukaryotes must come about by a mechanism other than natural selection. an anti-weasel model of natural selection might more accurately describe the operation of natural selection in the wild. beyond that, on many levels fisher’s theorem has been given a negative assessment by ewens and lessard, was criticized by price for not being understandable and to be incompletely derived and proven, and declared by felsentein as being not-so-fundamental afterall. all of these considerations are in stark contrast to dawkins’ characterization of fisher’s theorem as biology’s central theorem. references adami, c, c ofria, and t c collier (2000). “evolution of biological complexity”. in: proceedings of the national academy of science 97.9, pp. 4463–4468. doi: 10.1073/pnas.97.9.4463. angier, n (2010). “seeing the natural world with a physicist’s lens”. in: the new york times november 1, 2010. barton, n h et al. (2007). evolution. cold spring harbor: cold spring harbor press. basener, w f and j c sanford (2018). “the fundamental theorem of natural selection with mutations”. in: journal of mathematical biology 76, pp. 1589–1622. doi: 10.1007/s00285-017-1190-x. behe, m j (1996). darwin’s black box. new york: touchstone, pp. 39–40. behe, m j (2010). “experimental evolution, loss-offunction mutations, and “the first rule of adaptive evolution””. in: the quarterly review of biology 85.4, pp. 419–445. doi: 10.1086/656902. bialek, w (2012). biophysics: searching for principles. princeton, nj: princeton university press. bialek, w (2015). more perfect than we imagined: a physicist’s view of life. url: https://www.cornell. edu/video/william-bialek-physicists-view-oflife. brady, r h (1979). “natural selection and the criteria by which a theory is judged”. in: systematic biology 28.4, pp. 600–621. doi: 10.2307/sysbio/28.4.600. brockman, j (2011). “who is the greatest biologist of all time?” in: url: https : / / www . edge . org / conversation/armand_marie_leroi-who-is-thegreatest-biologist-of-all-time. christensen-dalsgaard, j and m kannewor! (2009). “evolution in lego: a physical simulation by natural selection”. in: evolution: education and outreach 2, pp. 518–526. doi: 10.1007/s12052-008-0099-7. darwin, c (1859). “organs of extreme perfection and complication”. in: on the origin of species by means of natural selection, or the preservation of favoured races in the struggle for life. dawkins, r (1986). the blind watchmaker. oxford university press. ewens, w j and s lessard (2015). “on the interpretation and relevance of the fundamental theorem of fundamental theorm of natural selection”. in: theoretical population biology 104, pp. 59–67. doi: 10.1016/j. tpb.2015.07.002. felsenstein, j (1989). “mathematics vs. evolution: mathematical evolutionary theory”. in: science 246.4932, pp. 941–942. doi: 10.1126/science.246.4932.941. felsenstein, j (2017). theoretical evolutionary genetics. seattle, wa. url: http : / / evolution . genetics . washington.edu/pgbook/pgbook.html. felsenstein, j (2018). fisher memorial lecture 2018. url: https://www.youtube.com/watch?v=zf3nimvbbdw. fisher, r a (1930). “the genetical theory of natural selection”. in: doi: 10.5962/bhl.title.27468. grodwohl, j b (2016). ““the theory was beautiful indeed”: rise, fall, and circulation of maximizing methods in population genetics (1930–1980)”. in: journal https://doi.org/10.1073/pnas.97.9.4463 https://doi.org/10.1007/s00285-017-1190-x https://doi.org/10.1086/656902 https://www.cornell.edu/video/william-bialek-physicists-view-of-life https://www.cornell.edu/video/william-bialek-physicists-view-of-life https://www.cornell.edu/video/william-bialek-physicists-view-of-life https://doi.org/10.2307/sysbio/28.4.600 https://www.edge.org/conversation/armand_marie_leroi-who-is-the-greatest-biologist-of-all-time https://www.edge.org/conversation/armand_marie_leroi-who-is-the-greatest-biologist-of-all-time https://www.edge.org/conversation/armand_marie_leroi-who-is-the-greatest-biologist-of-all-time https://doi.org/10.1007/s12052-008-0099-7 https://doi.org/10.1016/j.tpb.2015.07.002 https://doi.org/10.1016/j.tpb.2015.07.002 https://doi.org/10.1126/science.246.4932.941 http://evolution.genetics.washington.edu/pgbook/pgbook.html http://evolution.genetics.washington.edu/pgbook/pgbook.html https://www.youtube.com/watch?v=zf3nimvbbdw https://doi.org/10.5962/bhl.title.27468 34 fisher’s fundamental theorem of natural selection of the history of biology 50.3, pp. 571–608. doi: 10. 1007/s10739-016-9449-4. lewontin, r (2003). “four complications in understanding the evolutionary process”. in: santa fe institute bulletin 18.1. url: https://sfi-edu.s3.amazonaws. com/sfiedu/production/uploads/publication/ 2016/10/31/winter2003v18n1.pdf. moalem, s (2008). survival of the sickest. new york: harper perennial. ollason, j g (1991). “what is this stu! called fitness?” in: biology and philosophy 6, pp. 81–92. doi: 10.1007/ bf02426827. orr, h a (1996). “dennett’s strange idea”. in: boston review 21.3. url: https : / / bostonreview . net / archives/br21.3/orr.html. orr, h a (2009). “fitness and its role in evolutionary genetics”. in: nature reviews genetics 10, pp. 531– 539. doi: 10.1038/nrg2603. price, g r (1972). “fisher’s ‘fundamental theorem’ made clear”. in: annals of human genetics 36.2, pp. 129– 140. doi: 10.1111/j.1469-1809.1972.tb00764.x. queller, d c (2017). “fundamental theorems of evolution”. in: the american naturalist 189.4, pp. 345–353. doi: 10.1086/690937. ritz, t, s adem, and k schulten (2000). “a model for photoreceptor-based magnetoreception in birds”. in: biophysical journal 78.2, pp. 707–718. doi: 10.1016/ s0006-3495(00)76629-x. royal society (2020). “ronald fisher”. in: url: https : //makingscience.royalsociety.org/s/rs/people/ fst00034451. rubenstein, d i and m a hack (2013). “migration”. in: encyclopedia of biodiversity. ed. by s a levin. second edition. elsevier, pp. 309–320. vaughan, n (2019). “evolution of biological eye in computer simulation”. in: 2019 ieee congress on evolutionary computation (cec). doi: 10.1109/cec.2019. 8790284. wagner, a (2005). robustness and evolvability in living systems. new jersey: princeton university press. wolf, y i and e v koonin (2013). “genome reduction as the dominant mode of evolution”. in: bioessays 35.9, pp. 829–837. doi: 10.1002/bies.201300037. https://doi.org/10.1007/s10739-016-9449-4 https://doi.org/10.1007/s10739-016-9449-4 https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/publication/2016/10/31/winter2003v18n1.pdf https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/publication/2016/10/31/winter2003v18n1.pdf https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/publication/2016/10/31/winter2003v18n1.pdf https://doi.org/10.1007/bf02426827 https://doi.org/10.1007/bf02426827 https://bostonreview.net/archives/br21.3/orr.html https://bostonreview.net/archives/br21.3/orr.html https://doi.org/10.1038/nrg2603 https://doi.org/10.1111/j.1469-1809.1972.tb00764.x https://doi.org/10.1086/690937 https://doi.org/10.1016/s0006-3495(00)76629-x https://doi.org/10.1016/s0006-3495(00)76629-x https://makingscience.royalsociety.org/s/rs/people/fst00034451 https://makingscience.royalsociety.org/s/rs/people/fst00034451 https://makingscience.royalsociety.org/s/rs/people/fst00034451 https://doi.org/10.1109/cec.2019.8790284 https://doi.org/10.1109/cec.2019.8790284 https://doi.org/10.1002/bies.201300037 about this journal the purpose of the journal paper submission policies other journal content from the editors annie crawfordannie crawfordmetaphor and meaning in the teleological language of biology introduction the history of teleology in the biological sciences teleological language is essential to biology if teleological language is essential to biology, then life must be teleological conclusion: life all the way down salvador cordovasalvador cordovafisher's fundamental theorem of natural selection isn't fundamental after all introduction: the problem of defining fitness absolute ``darwinian'' fitness vs. relative fitness mean and variance of relative fitnesses numerical examples to illustrate fisher's theorem discussion conclusion eric hollowayeric hollowaytutorial: bioinformatics basics introduction genetic code and sequence translation sequencing and assembly accessing data finding things with blast summary letters and notes eric hollowayyou cannot get meaning from randomness jonathan bartlettactive information is a specified complexity model eric hollowayevolution in the valley of illusions jonathan bartlettis active information applicable to biology? eric hollowayempirical active information news j9 g2ii2`b �m/ lqi2b h?2 s`q/m+ib q7 >vt2``2�h a2`b2b �m/ i?2 gbkbi�ibqmb q7 *�m+?v s`q/m+ib cqm�i?�m "�`ih2ii .pa, ryxjjyr9fbbbmxke9y@8e8kxjxkx#�`ih2iixr �#bi`�+i *�m+?v t`q/m+ib �`2 mb2/ iq i�f2 i?2 t`q/m+ib q7 +qm@ p2`;2mi b2`b2bx >2`2r2 b?qr i?2 hbkbi�ibqmb q7 i?bb �tt`q�+? bm /bp2`;2mi b2`b2bx �hi2`m�ibp2 �tt`q�+?2b �m/ 7q`kmh�b 7q` /bp2`;2mi b2`b2b �`2 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"=1 " "! #=1 % # &"" #+1 # . ukv 6q` +qmp2`;2mi b2`b2bi?2 *�m+?v t`q/m+i bb 2[mbp�h2mi iq i?2 t`q/m+i q7 # �m/ 'x >qr2p2`2p2m rbi? ?vt2``2�hbi?2 *�m+?v t`q/m+i bb mqi 2[mbp�h2mi iq i?2 t`q/m+i q7 # �m/ ' b7 # �m/ ' �`2 /bp2`;2mix hq mm/2`bi�m/ r?vbi bb bktq`i�mi iq `2+q;mbx2 i?2 b?�t2 q7 i?2 *�m+?v t`q/m+i 7q` }mbi2 b2`b2bx ak�;bm2 i?�i # �m/ ' �`2 }mbi2 b2`b2b rbi? " 2h2k2mibx am i?�i +�b2bi bb 2�bv iq `2+q;mbx2 i?�i i?2 bmk /q2b mqi rq`fx g2i mb bk�;bm2 irq b2`b2b rbi? bbt 2h2k2mibx h?2 *�m+?v t`q/@ m+i 7q` bm+? � b2`b2b rqmh/ #2 # · ' = 6! "=1 " "! #=1 % # &"" #+1 # . ujv 6b;m`2 r b?qrb r?�i i?bb rqmh/ hqqf hbf2x 1�+? bi`bt2 q7 i?2 };m`2 `2t`2b2mib qm2 bi2`�ibqm i?`qm;? i?2 qmi2`kqbi bmkk�@ ibqmx lqib+2?qr2p2`i?�i i?2`2 �`2 mq bi`bt2b t�bi i?2 +2mi2` bi`bt2x am qi?2` rq`/b�hh q7 i?2 p�hm2b t�bi i?2 +2mi2` bi`bt2 �`2 mqi +qmbb/2`2/ bm i?2 }m�h bmkk�ibqmx h?bb bb q#pbqmbhv t`q#h2k�ib+ 7q` }mbi2 bmkbx q?v bb bi mqm@ t`q#h2k�ib+ 7q` +qmp2`;2mi b2`b2b\ https://dx.doi.org/10.33014/issn.2640-5652.3.2.bartlett.1 oqhmk2 jabbm2 k h?2 s`q/m+ib q7 >vt2``2�h a2`b2b �m/ i?2 gbkbi�ibqmb q7 *�m+?v s`q/m+ib j8 6b;m`2 k, h?2 _2+i�m;mh�` s`q/m+i q7 # �m/ ' %1 %2 %3 %4 %5 %6 &1 %1&1 %2&1 %3&1 %4&1 %5&1 %6&1 &2 %1&2 %2&2 %3&2 %4&2 %5&2 %6&2 &3 %1&3 %2&3 %3&3 %4&3 %5&3 %6&3 &4 %1&4 %2&4 %3&4 %4&4 %5&4 %6&4 &5 %1&5 %2&5 %3&5 %4&5 %5&5 %6&5 &6 %1&6 %2&6 %3&6 %4&6 %5&6 %6&6 6q` � +qmp2`;2mi b2`b2b�b i?2 bm/2t �tt`q�+?2b bm}mbivi?2 p�hm2 q7 i?2 i?2 i2`k �tt`q�+?2b x2`qx a7 vqm hqqf �i 6b;m`2 rbi bb 2pb/2mi i?�i i?2 i2`kb i?�i �`2 #2bm; b;mq`2/b7 bi bb � +qmp2`;2mi b2`b2b?�p2 �i h2�bi qm2 kmhibthb+�m/ q7 i?2 i2`k �i � m2�`@x2`q p�hm2x h?2`27q`2bm � +qmp2`;2mi b2`b2b�hh q7 i?2 i2`kb #2bm; b;mq`2/ �`2 m2;hb;b#h2x >qr2p2`i?�i bb mqi i`m2 q7 � }mbi2 b2`b2bx q?2m t2`7q`k@ bm; ?vt2``2�h bmkk�ibqmbi?2 p�hm2b �m/ k�mbtmh�ibqmb �`2 bbkbh�` iq }mbi2 b2`b2bmqi m2+2bb�`bhv bbkbh�` iq +qmp2`;2mi b2`b2bx lqm@*�m+?v s`q/m+ib �m �/p�mi�;2 q7 *�m+?v t`q/m+ib bb i?�i bi /2}m2b � r�v q7 mm/2`bi�m/bm; i?2 #2?�pbq` q7 � b2`b2b bm i2`kb q7 � mqm@i`bpb�h k�mbtmh�ibqm q7 i?2 t`2pbqmb b2`b2bx ai bb q#pbqmb i?�i r2 +qmh/ `2t`2b2mi i?2 kmhibthb+�ibqm q7 ?vt2``2�h b2`b2b # �m/ ' �b # · ' = " !! 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"=1 " !! #=1 %" & # # . u8v h?bb?qr2p2`bb mqi �b mb27mh �b bi +qmh/ #2x abm+2 bi #�bb@ +�hhv ;q2b i?`qm;? 2p2`v 2h2k2mi q7 ' #27q`2 +qmbb/2`bm; 2p2m i?2 b2+qm/ 2h2k2mi q7 #t�`ib�h bmkb rbhh mqi t`qpb/2 km+? bm7q`k�ibqm �#qmi i?2 #2?�pbq` q7 i?2 t`q/m+i �b � r?qh2x � kq`2 bm7q`k�ibp2 7q`kmh� +�m #2 7qmm/ #v i`�+bm; t�i?b �b qmihbm2/ bm 6b;m`2 kr?b+? r2 rbhh +�hh i?2 `2+i�m;mh�` k2i?q/x h?bb bb bm +qmi`�bi rbi? i?2 *�m+?v kmhibthb+�ibqm k2i?q/r?b+? bb i`b�m;mh�``2kqpbm; ?�h7 q7 i?2 i2`kb 7`qk +qmbb/2`�ibqmx am � `2+i�m;mh�` t`q/m+i�i 2�+? bm/2t q7 i?2 qmi2` bmk�hh q7 i?2 bm/b+2b bm #qi? # �m/ ' mt iq i?�i bm/2t �`2 +qmbb/2`2/x 6b;m`2 j, (1 + 1 + 1 + . . .) · (1 + "1 + 0 + 0 + 0 + . . .) r r r r r r r r r r r r r @r "1 "1 "1 "1 "1 "1 y 0 0 0 0 0 0 y 0 0 0 0 0 0 y 0 0 0 0 0 0 y 0 0 0 0 0 0 h?bb k2i?q/ +�m #2 `2t`2b2mi2/ #v i?2 7q`kmh� # · ' = !! 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s`q#h2k :2ib �m 1t�+i aqhmibqmǵx am, zm�mi� j�;@ �xbm2x m`h, ?iitb , f f rrr x [m�mi�k�;�xbm2 x q`; f k�i?2k�ib+b�m@ bqhp2b@ +2mim`b2b@ qh/@ ;`�xbm;@ ;q�i@t`q#h2k@2t�+ihv@kykyrkynfx lhhbb+?am;q ukykyvx ǳ� *hqb2/@6q`k aqhmibqm iq i?2 :2q@ k2i`b+ :q�i s`q#h2kǵx am, j�i?2k�ib+�h ami2hhb;2m+2` 9kttx rĝ8x /qb, ryxryydfbyyk3j@ yky@ ynnee@ yx m`h, ?iitb,ffhbmfxbt`bm;2`x+qkf�`ib+h2fryxryydw k6byyk3j@yky@ynnee@yx https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.190.4817%5c&rep=rep1%5c&type=pdf https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.190.4817%5c&rep=rep1%5c&type=pdf https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.190.4817%5c&rep=rep1%5c&type=pdf https://www.tandfonline.com/doi/pdf/10.1080/00029890.1999.12005066?casa_token=v9kvgbh4exmaaaaa:cvldnruzour9iw14739ru3bm_kzj7n5pponbfhtgjwsevq9poahmss7ojin_ttljs54txxgiotm0 https://www.tandfonline.com/doi/pdf/10.1080/00029890.1999.12005066?casa_token=v9kvgbh4exmaaaaa:cvldnruzour9iw14739ru3bm_kzj7n5pponbfhtgjwsevq9poahmss7ojin_ttljs54txxgiotm0 https://www.tandfonline.com/doi/pdf/10.1080/00029890.1999.12005066?casa_token=v9kvgbh4exmaaaaa:cvldnruzour9iw14739ru3bm_kzj7n5pponbfhtgjwsevq9poahmss7ojin_ttljs54txxgiotm0 https://www.tandfonline.com/doi/pdf/10.1080/00029890.1999.12005066?casa_token=v9kvgbh4exmaaaaa:cvldnruzour9iw14739ru3bm_kzj7n5pponbfhtgjwsevq9poahmss7ojin_ttljs54txxgiotm0 https://www.tandfonline.com/doi/pdf/10.1080/00029890.1999.12005066?casa_token=v9kvgbh4exmaaaaa:cvldnruzour9iw14739ru3bm_kzj7n5pponbfhtgjwsevq9poahmss7ojin_ttljs54txxgiotm0 https://doi.org/10.1109/taes.1978.308550 https://doi.org/10.1109/taes.1978.308550 https://ieeexplore.ieee.org/document/4102075 https://ieeexplore.ieee.org/document/4102075 https://www.quantamagazine.org/mathematician-solves-centuries-old-grazing-goat-problem-exactly-20201209/ https://www.quantamagazine.org/mathematician-solves-centuries-old-grazing-goat-problem-exactly-20201209/ https://www.quantamagazine.org/mathematician-solves-centuries-old-grazing-goat-problem-exactly-20201209/ https://doi.org/10.1007/s00283-020-09966-0 https://link.springer.com/article/10.1007%2fs00283-020-09966-0 https://link.springer.com/article/10.1007%2fs00283-020-09966-0 about this journal the purpose of the journal paper submission policies other journal content from the editors eugenio darbesioeugenio darbesioa corollary of the conant-ashby theorem applied to abiogenesis robert sheldonrobert sheldoncomets, water, and big bang nucleosynthesis introduction benefits of a magnetized big bang and dark matter comets consequences of primordial comets analysis conclusions acknowledgments robert j marks iirobert j marks iisolution of the grazing goat problem: a conflict between beauty and pragmatism background grazing goat problem solution grazing goat problem inversion final thought letters and notes eric holloway2d puzzle visualizations of boolean formulae jonathan bartlettthe products of hyperreal series and the limitations of cauchy products tom and elizabeth siewertfollowing the science news v2i1 volume 2, issue 1 how to explain behavior: author precis sam s. rakover doi: 10.33014/issn.2640-5652.2.1.rakover.1 abstract this is an author precis of the book how to explain behavior: a critical review and a new approach by sam s. rakover (2018, lexington). the precis has two sections. the first, basic methodological origin-points, treats the fundamental ideas and premises concerning explanation and understanding. the second section outlines the book’s arrangement, and summarizes the content of each chapter. 1 introduction this section describes the infrastructure on which i built the entire book. it covers matters from the philosophy of explanation in general to explanations in psychology more particularly. i start the discussion by emphasizing the following two general cornerstone ideas in scientific research methodology (citations are taken from einstein & infeld, 1938/1950. see also popper, 1959/1995): (a) the scientific attempt is to explain and understand reality: "the purpose of any physical theory is to explain as wide a range of phenomena as possible. it is justified in so far as it does make events understandable." (p. 43) "all the essential ideas in science were born in dramatic conflict between reality and our attempts at understanding." (p. 280) (b) scientific knowledge is provisional: "there are no eternal theories in science. it always happens that some of the facts predicted by a theory are disproved by experiment. every theory has its period of gradual development and triumph, after which it may experience a rapid decline." (p. 77) now i move on to discuss several methodological ideas that are more specific to the subject of the book: (1) to o!er an explanation for the studied phenomenon, a suitable scientific procedure has to be used. to propose explanations one has to know how, that is, scientists need a justified procedure for giving an explanation that is appropriate for the given phenomenon under scrutiny, just as they need a procedure suitable for making an observation or performing an experiment. in a way similar to the justifications for the use of the procedure of an experiment that are based on several logical, epistemological, ontological considerations, so the procedure for giving scientific explanations is justified by various considerations—logical, epistemological, ontological, and so on up to common-sense considerations of daily life. a model of scientific explanation is not like a scientific theory, but is like a set of rules, norms, on how to behave. from this perspective it follows that an explanation model, procedure, may not be tested empirically like a theory (which is subject to an empirical test) but is evaluated by theoretical considerations and the degree of match of the procedure to the field under study. (2) a theory (or a hypothesis, model, law, mechanism) in itself is not able to propose an explanation. to explain a phenomenon, suitable explanatory information is needed. in science this information is provided by a theory, hypothesis, model and so on. however, the theory in itself is not able to explain the occurrence of the studied phenomenon. for the theory to do this, it has to function in the framework of a procedure created to provide scientific explanations. (3) the functioning of an explanation-procedure is based on rational relations. rational relations are of di!erent kinds: from logical, mathematical, statistical and causal to practical. to propose a scientific explanation based on non-rational relations is impossible because what one will get is fortuity and chaos. (4) a procedure of explanation is an integral part of the 18 how to explain behavior: author precis methodology of science and is closely connected especially to a procedure of empirical testing. the methodology of science is a collection of methods/procedures for research whose main purpose is to bring about understanding of the world. explanation-procedures are indissolubly bound to a procedure for empirical testing, such as the hypothetico-deductive (h-d) method (see hempel, 1965, 1966). without an empirical test we will never be able to know if the given theory is false or true. however, it should be stressed (as mentioned above) that scientific research never ends, and anyone who believes that a certain theory is wholly correct in fact drops out of the empirical science game (see popper, 1972, 1959/1995). (5) the scientific explanation is an attempt to approximate the hidden process involved in the occurrence of the studied phenomenon. this can be expressed by the following three basic assumptions: (a) there exists in nature some kind of unknown real-process (urp) that is responsible for the occurrence of the studied phenomenon under certain conditions. (note that except for the assumption regarding reality, the rest is unknown.); (b) science proposes a theory (hypothesis, model, mechanism) which tries to approximate the urp and its function, thereby giving a reasonable explanation for the studied phenomenon; (c) the proposed theory is based on the scientific knowledge collected in the area under discussion. the degree of proximity of this theory to the urp is estimated by the degree of success/failure of this theory. the approach here (and of course in the entire book) is realistic in the broad sense. that is, i perceive science as a system that attempts to answer the question how nature (inanimate, plant and animal) functions by suggesting a theory that attempts to decipher nature’s code: how it is built, how it works, and according to what. (6) to date no one has been able to develop a theory that will describe and explain the connection between neurophysiological activity in the brain and consciousness, i.e., no one has succeeded in developing a mind/body theory. this carries the following implications: (a) behavior cannot be explained solely by mechanistic explanations (which are accepted in the sciences, in behaviorism, in cognitive psychology, and in physiological psychology), because it neglects conscious behavior; (b) to propose a better account of behavior one must consider the conscious aspect explanatorily. this may be done as follows: (1) a procedure must be developed for proposing mentalistic explanations (e.g., explanations based on one’s will and belief); (2) it has to be shown that a procedure for mentalistic explanation meets the accepted methodological requirements of science; (3) a theoretical framework has to be developed that allows coherent use of these two kinds of explanation (mechanistic, mentalistic). this account will be better than a purely mechanistic explanation. idea (6) is one of the most important ideas sustaining the present book. chapter 5 summarizes the empiricaltheoretical arguments showing that the mind/body theory has not yet been developed, and chapter 6 describes in detail (a) methodological dualism (md), which shows that like the mechanistic explanation, the mentalistic explanation meets the methodological requirements of science, and (b) the multi-explanation framework (mef), which allows one to construct a coherent theory in any psychological domain based on these two kinds of explanation: the mechanistic and the mentalistic. the book does not aim to o!er another solution for the mind/body or consciousness/brain problem. quite the reverse: the goal is to circumvent this problem, thereby to achieve another goal, but no less important, namely to improve the explanation of behavior. this purposeful e!ort takes place within the framework of science by constructing an argument showing that a mentalistic explanation can be encompassed by the accepted methodological framework of science. 2 chapter summaries the book’s seven chapters plot a course of study from chapter 1, on the relation between explanation and understandvolume 2, issue 1 2. chapter summaries 19 ing, to chapter 7, on a general procedure for giving explanations for the behavior of the individual. chapter 1 discusses the relation between explanation and understanding. the prevalent view from 1948 (the year hempel and oppenheim published their influential paper) was that scientific understanding was based on scientific explanation. about fifty years later the literature began to suggest that scientific understanding was not built entirely on explanation, as it had additional sources such as the ability of the scientist herself. the article by lipton (2009) even proposed the idea of understanding without explanation. in the spirit of that article i proposed a relatively new approach, namely the dual theory of understanding, which posits a certain non-dependence between explanation and understanding. first, scientific understanding is based on consciousness of the scientific content associated with the phenomenon under study. hence a sophisticated robot may be imagined that will supply an appropriate explanation for a given phenomenon without understanding the significance of the explanation. accordingly, while giving an explanation is a mechanical rational process, understanding the explanation requires a human’s consciousness. secondly, even before 1948 (e.g., in antiquity), the human being tried to understand the world and himself by means of certain procedures that di!ered from the explanationprocedures (models) known today. the chapter sets forth several illustrations of procedures for an understanding of that kind: a match between the phenomenon under study and some scheme that exists in the individual’s cognitive system; understanding person a when person b gets into person a’s shoes; the passage of a square through a round hole when the diagonal of the square is smaller than the diameter of the circle; etc. these procedures are based on the underlying assumption that there is some unknown real-process (urp) that is responsible for the appearance of the phenomenon in question (in ancient times and even today god represents urp). the chapter also suggests that compared with understanding, explanation is interwoven with scientific knowledge based on the development of a rational scientific methodology, which emphasizes for instance the importance of the development of a scientific model. as an example, the chapter considers the model developed by rakover & cahlon (1989) called the "catch model." it is intended to reproduce from a witness’s memory the picture of the accused’s face. the phenomenon whose understanding is being sought is presented as the "reality-model," and what explains it (the reality-model) is a "theoretical-model" (hence the catch model is based on two sub-models: the reality-model and the theoretical-model). chapter 2 reviews critically nine models of explanation discussed in the philosophical literature, which (a) exerted great influence on the professional literature; and (b) are likely to have a great e!ect on providing explanations in psychology. the chapter opens with a review and discussion of the three models proposed by hempel: the deductive-nomological (d-n) model, the deductive-statistical (d-s) model and the inductive-statistical (i-s) model. together these are known as the "covering-law theory" because the common idea is that a natural law, a statistical law or a statistical generalization cover explanatorily the studied phenomenon. the three models gave rise to strong criticism, and as a result other researchers proposed alternative models of explanation. the first alternative model is the statistical-relevance (sr) model proposed by salmon (1971, 1990). the important ideas behind this model are that an explanation need not necessarily rest first on a logical argument, and secondly on high probabilities close to 1, as hempel’s i-s model requires. this model experienced sharp criticism, and eventually salmon himself abandoned it for a new explanatory model based on the concept of causality. the causal-mechanical (c-m) model proposed by salmon (1984) is based on the idea that the world is a network of interactive causal processes that spread through space and time. the explanation places the studied phenomenon within this network. another causal model is the manipulationist-interventionist (m-i) model suggested by woodward (2003). its basic idea is the causal connection between x and y through a certain manipulation that changes x, hence y changes accordingly and systematically; thus the causal explanation allows seeing what is likely to happen as a result of the counterfactual operation of a certain manipulation. an additional explanatory model is the kairetic model proposed by strevens (2008). its basic idea is the application of a method of elimination to explanation: di!erent factors are removed from the list of causes potentially responsible for the studied phenomenon; the goal is to see the elimination of which factor causes the phenomenon to disappear (or be likely to disappear). the elimination is repeated until only the factors (or factor) are (is) left without which the given phenomenon would not have occurred. the chapter concludes with a discussion of two models. one is the unificationist model developed by kitcher (1989), the other is the pragmatic model proposed by van fraassen (1980). the former posits that understanding the world depends on the ability to derive from the same patterns 20 how to explain behavior: author precis of inference many phenomena that are observed in scientific research (e.g., the newtonian theory). van fraassen’s pragmatic model draws attention to the practical aspects, the background factors, of explanation as giving an answer to the questions: the subject of the question, the contrastclass (the possible alternatives for giving an answer), and the relevance-relation, a kind of relation between giving the answer and the question (e.g., “compared with the alternatives of the answer, the phenomenon occurred because...”). an important conclusion that arises from this review is that there is no single concept for scientific explanation, which is enormously complex and multi-dimensional. chapter 3 examines three additional models of explanation: rule-explanation; functional, teleological models of explanation; and the new-mechanistic model of explanation. although these models are intended to handle humans’ and animals’ behavior, they are unable to handle the most important component of this behavior, namely conscious-experience. my proposal how to deal with this appears in the last three chapters of the book. it is not possible to apply any of the models reviewed in the foregoing chapter to human behavior, for example, to the following cases: dan stopped his car when the tra"c light changed to red; or dan stood on a chair in order to take a book down from the shelf. this is because for these kinds of behavior no law, theory or appropriate empirical generalization exists. for example, stopping at a red light is not explained by an appeal to a law or empirical generalization that covers behavior of this kind, but by looking up a tra"c rule created by a human being and which a driver is obliged to obey. seven important di!erences between behavioral rules and laws are discussed: for example, laws are universal and rules are local; laws are subject to an empirical test and rules are not (rules are evaluated according to the purpose for which they were devised). although not all rules are present in consciousness (e.g., basic rules for generating language are innate), they di!er from laws of nature in that they concern information. explanation by rules is also di!erent from teleological explanation. for example, people are not always aware of the aim of the rules and they obey rules automatically. two approaches attempt to characterize functional, teleological, explanations as causal. the approach developed by nagel (1961) tries to answer the question why a certain component appears in a given system; cummins’ (1975, 1983) approach tries to answer the question how a certain component succeeds in contributing causally to the e"cient function of a given system. the chapter ends with a discussion of the new-mechanistic explanatory model. according to this model, an explanation for the given phenomenon is proposed by an appeal to a mechanism. it can be decomposed into di!erent components with di!erent functions, unique in their array and interaction, which produce the studied phenomenon. bechtel (2008a, b) draws a distinction between a newmechanistic explanatory model, which suits the sciences, and one that suits psychology, that is, a mentalistic mechanism, which processes information—the information processing (ip) mechanism. there is an important di!erence between bechtel’s (2008b, c) approach to a mentalistic mechanism and rakover’s approach. while according to bechtel processing information occurs on the non-conscious cognitive level, according to rakover mentalistic activation takes place on the conscious level. chapter 4 discusses whether an explanation model in itself can be subjected to empirical test. the chapter raises arguments against the idea that the correctness of the explanation model can be tested empirically. first, the prediction that emerges from a certain theory under certain conditions can be confirmed or refuted. in both cases the empirical result carries no implications for the explanatory model itself, but only for the theory inserted in the explanatory model. the reason is that the explanation model is just a procedure that guides the researcher on how to propose scientific explanations. an explanation model is not like a hypothesis, theory or scientific model, which may pass/fail an empirical test. a procedure is assessed by its rational course of action (e.g., it does not create situations that contradict each other) and its appropriateness for a given field. in this sense, a procedure for giving explanations is akin to an administrative procedure, such as tra"c rules that advise people how to behave in certain situations. a rule of the road is assessed as suitable or unsuitable for a certain field of behavior but it is not judged right or wrong. the chapter goes on to discuss this distinction as against the accepted distinction between descriptive, normative, theories and prescriptive ones. secondly, we may look at the argument that slight use of an explanation model mx attests to its incorrectness (i.e., mx is refuted). here the question that arises is how we may explain this finding of infrequency of mx use. clearly, it cannot be explained by mx itself (because it has already been refuted), so we must seek another model—my. however, it is reasonable to suppose (according to those who assume that an explanation model can be tested empirically) that this model too fails empirically. why? because there is very high probability that very often theories that used my proposed predictions that were disconfirmed. hence, not only is my not suitable for use as a procedure for giving explanations, no explanation model exists that can explain volume 2, issue 1 2. chapter summaries 21 the finding of slight use of mx —because all explanation models at some time have been associated with refutation of empirical results of di!erent theories. clearly then, empirical success/failure has no implications for the degree of correctness of a procedure for explanation. based on a review of the explanation models found in the literature, chapter 4 o!ers a list of several constraints, characteristics and properties for constructing an explanation model, which have been described above. these make up the infrastructure for building explanation models for psychology (see especially chapters 6 and 7). chapter 5 discusses the following question: is it possible to comprehend mentalistic concepts and explanations (based on the individual’s inner world) with the aid of mechanistic concepts and explanations (based on and accepted in the sciences)? the answer is negative, and it forges the way to the development of a new methodological approach to proposing explanations, namely the methodological dualism (md) and multi-explanation framework (mef), whose principal purpose is to propose a procedure to explain behavior that is saturated with consciousness. this methodology is based on the fact that to date no one has succeeded in developing a mind/body theory. were it possible to propose such a theory, it would be possible to forgo the dm & mef approach, because everything would obtain a mechanistic explanation. but as chapter 6 shows, this is not the situation so far. chapter 5 breaks down the above fundamental question into the following four questions: (1) can human behavior be explained mechanistically alone, without recourse to the conscious-experience concept? (2) has a theory been successfully developed that explains the connection between neurophysiological processes in the brain and conscious-experience? (3) can mentalistic explanations anchored to the concept of conscious-experience be reduced to mechanistic explanations (e.g., to a neurophysiological explanation)? (4) has a very complex and sophisticated computer proven able, like us, to behave with conscious-experience? an a"rmative answer to any of these four questions means that there is no need to develop md and mef because the standard methodology developed in the sciences can handle research in psychology. only a negative answer to all these questions will oblige one to think about the development of a new explanatory approach suited to the field of psychological research. the answers to these questions are negative. here are three popular arguments that support the negative answers. first, it seems that mentalistic theories cannot be reduced to mechanistic theories. one of the important factors that prevents this kind of reduction is multiple realizations. if a mental state or process is defined by its function, it may be realized in various ways and with various materials. hence, if reduction of a mentalistic theory to a mechanistic depends on the possibility of identifying a concept in one theory with another, this possibility is destroyed because according to multiple realizations there are many ways to realize and identify mentalistic concepts. secondly, a computer, as sophisticated as it may be, is incapable of reaching a condition similar to humans’ consciousexperience. one of the most powerful and famous arguments in support of the negative answer is searle’s (1980) "chinese room" thought experiment. according to this, activation of physical signs by means of syntactic rules (which are operated by the computer) cannot impart semantic meaning to these signs. finally, a very important obstacle blocking the development of a mind/body theory is "consciousness epiphenomenalism," which states that mental concepts and explanations are inessential. the reason is that the entire explanation of behavior falls on the shoulders of the neurophysiological process. chapter 6 describes and justifies the approach for methodological dualism (md) and multi-explanation framework (mef), which is based on chapter 5. chapter 6 is divided into several sections. the first proposes an argument justifying why md & mef should be developed. namely, if we attempt to o!er an improved explanation for behavior saturated with consciousness there is no way other than adding to a mechanistic explanation a mentalistic explanation. the second part of the chapter develops methodological dualism (md). the chapter focuses particularly on the teleological explanation that combines the individual’s will, belief and behavior. it presents a new proposition to conceive the following as a mentalistic explanation-model – a procedure for creating specific will/belief explanations: [will/belief]: if x wants g and believes that behavior b will realize his/her will, then x will perform b. this proposition immediately raises the following question: does this mentalisitic explanation-procedure satisfy the methodological requirements for explanation accepted in science? the answer is yes. 22 how to explain behavior: author precis the third section develops a theoretical framework, the multi-explanation framework (mef), by means of which it will be possible to construct a specific theory (a specific "mef-theory") for a specific research project based on two kinds of explanation: mechanistic and mentalistic. because the theory rests on multiple explanation models, a major di!erence arises between (a) the way a theory supplies an explanation in science and (b) the way an mef theory supplies an explanation in psychology. an mef-theory is based on a match between explanationprocedures (mechanistic or mentalistic) and behavior (it is called the "explanation/behavior match" for short). while there are behaviors that can be accounted for satisfactorily by an appeal to mechanistic explanations only, most behaviors and their decomposed components must be approached by both mechanistic and mentalistic explanations. the coherence of a specific mef-theory is achieved by matching appropriately the explanation-procedure to the behavior and its components by means of several guidelines based on theoretical-empirical knowledge and the principle of explanation-matching. according to the latter, the components of a mechanistic behavior (a whole behavior that has been accounted for mechanistically) cannot be explained by mentalist explanations, while the components of a mentalistic behavior (a whole behavior that has been accounted for mentalistically) can be explained mentalistically as well as mechanistically. the appropriate explanation/behavior match solves several methodological problems raised by an mef-theory. finally, the last section summarizes the main ideas of the present approach and compares it to other relevant approaches. chapter 7 presents a general explanation procedure (gep) for understanding an individual’s behavior. as can be seen from the previous chapters, psychology has used a fairly large number of explanation models or procedures: di!erent variations of hempel’s models, di!erent kinds of causal processes, mechanisms based on the computer metaphor, and di!erent kinds of procedures based on neurophysiological processes. this employment of multiplicity of explanation models raises the following question: is it possible to propose for psychology a general procedure for giving an explanation that is likely to spread its wings over other models too? the answer is a"rmative: the gep. it is based on three major theoretical ideas: (a) it is assumed that in the individual a certain real-process exists that is involved in the generation of the behavior under study; although the nature of this process is unknown, it is further assumed that it presents the real explanation for the behavior in question [this process is called the "unknown real-process" (urp)]; (b) a researcher may approximate the urp by constructing a theory (or a hypothesis, model, mechanism, etc.) that portrays the properties and operation of the urp in generating the studied behavior. if the proximity between the theory and urp is high, it may be proposed that the theory provides us with a good account of the behavior in question; (c) the degree of proximity of the theory to the urp is estimated by the development of a "proximity index.” it is based on the theory’s successful predictions. clearly, a confirmed theory is closer than a refuted theory to the urp and to the real explanation. the generality of gep is expressed in two respects. first, the urp can be approximated by diverse theories or hypotheses, models and mechanisms; secondly, the gep may handle various explanationprocedures (models) that researchers have been using in their studies. these models may be viewed as various routes for approaching the real explanation. to illustrate the gep, the chapter analyzes several explanations given for learning in animals, perception and recognition of faces, and everyday purposive behavior (will/belief accounts). finally, the chapter discusses the basic philosophical concepts and assumptions that underlie the gep. references bechtel, w. (2008a). explanation: mechanism, modularity, and situated cognition. in p. robbins & m. aydede (eds.), cambridge handbook of situated cognition. cambridge, uk: cambridge university press. bechtel, w. (2008b). mechanisms in cognitive psychology: what are the options? philosophy of science, 75, 98309994. bechtel, w. (2008c). mental mechanisms: philosophical perspectives on cognitive neuroscience. london: routledge. cummins, r. (1975). functional analysis. the journal of philosophy, 72, 741-765. cummins, r. (1983). the nature of psychological explanation. cambridge, ma: the mit press. einstein, a. & infeld, l. (1938/1950). the evolution of physics. london: the scientific book club. hempel, c. g. (1965). aspects of scientific explanation and other essays in the philosophy of science. new york: the free press. hempel, c. g. (1966). philosophy of natural science. envolume 2, issue 1 references 23 glewood cli!s, nj: prentice-hall. hempel, c. g. & oppenheim, p. (1948). studies in the logic of explanation. philosophy of science, 15, 135-175. kitcher, p. (1989). explanatory unification and the causal structure of the world. in p. kitcher & w. salmon (eds.), scientific explanation (pp. 410-505). minneapolis: university of minnesota press. lipton, p. (2009). understanding without explanation. in h. w. de regt, s. leonelli, k. eigner (eds.), scientific understanding: philosophical perspectives (pp. 43-63). pittsburgh: university of pittsburgh press. nagel, e. (1961). the structure of science: problems in the logic of explanation. london: routledge & kegan paul. popper, k. r. (1959/1995). the logic of scientific discovery. london and new york: routledge. popper, k. r. (1972). objective knowledge: an evolutionary approach. oxford: oxford university press. rakover, s. s. (2018). how to explain behavior: a critical review and new approach. new york: lexington books. rakover, s. s. & cahlon, b. (1989). to catch a thief with a recognition model: the model and some empirical results. cognitive psychology, 21, 423-468. salmon, w.c. (1971). statistical explanation. in w. salmon et al. (eds.), statistical explanation and statistical relevance (pp. 29-87). pittsburgh: university of pittsburgh press. salmon, w. c. (1984). scientific explanation and the causal structure of the world. princeton: princeton university press. salmon, w. c. (1990). four decades of scientific explanation. minneapolis: university of minnesota press. searle, j. r. (1980). minds, brains and programs. the behavioral and brain sciences, 3, 417-457. strevens, m. (2008). depth: an account of scientific explanation. cambridge, ma: harvard university press. van fraassen, b.c. (1980). the scientific image. oxford: clarendon press. woodward, j. (2003). making things happen: a theory of causal explanation. oxford: oxford university press. volume 2, issue 1 two methods of calculating axiom size jonathan bartlett doi: 10.33014/issn.2640-5652.2.1.bartlett.1 abstract 1 introduction modeling insight has been a long-standing problem for cognitive psychology. bartlett (2012) noted that humans tend to be able to infer axioms about a system in order to solve problems. however, the framework proposed there su!ers from a few theoretical problems. the first is that axioms can overlap. therefore, identifying distinct axioms is di"cult. second, the framework relies on an ordering of axioms from “small” to “large” (i.e., easy to di"cult), but fails to provide a mechanism to measure the size of axioms. here we identify two possible mechanisms for calculating the size of an axiom, and how it may help future progress of cognitive research. 2 dependent axioms bartlett (2012) di!erentiated between two kinds of axioms—independent axioms and dependent axioms. an independent axiom is one which defines the parameters of a formal axiomatic system. however, as gödel points out, any formal axiomatic system has truths which are not provable within the formal axiomatic system (raatikainen, 2018). these truths cannot be theorems within the axiomatic system, because then they would be provable within the system. however, these truths are dependent on the structure of the axiomatic system. in other words, given a particular axiomatic system a, some truth b is set for certain, but cannot be proved within a. therefore, b is not a theorem within a, but its truth value is set by the parameters of a. because of this, we identify such a truth as a dependent axiom. if b is added to a as an axiom, a becomes a!. this new system can prove b (because b is an axiom), and may also be able to prove other new truths as well. however, there are an infinite number of dependent axioms, so no finite set of dependent axioms will cover all of the truths of a. 3 the halting problem the most practical outgrowth of this line of reasoning is in turing’s halting problem. turing showed that, given a program p in a general-purpose programming language (where p includes both the program and all its input), there is no general, finite program h such that providing h with p as a parameter will tell if p will ever complete (turing, 1936). more specifically, the problem comes in the fact that, while we can tell if p does complete, we can never tell if it won’t complete. the reason is simple—if we run p a step at a time, at any given moment, p may complete. at that point, p will be known to complete. however, we won’t know if p doesn’t complete until we have waited an infinitely long time, and it hasn’t happened. therefore, while knowledge of completion takes a finite amount of time, knowledge of non-completion takes an infinite amount of time. if p will not ever complete, knowledge of that fact can be considered a dependent axiom. knowledge of whether a particular p or class of ps will not ever complete can be added to h as dependent axioms. however, because there are an infinite number of dependent axioms, we can never add all of the axioms to h and have h remain a finite program. 4 example axioms let us presume that there is a machine language such that each instruction is one byte long, and the hexadecimal code cc means “jump relative,” which looks at the next byte and modifies the program counter based on that signed value. therefore, if the byte sequence cc-00 occurs, the machine will go into an infinite loop, because it will jump relative to the current instruction, but the amount of the jump will be 0, because it doesn’t go anywhere. 26 two methods of calculating axiom size there are several ways of constructing an axiom which covers this fact. non-exhaustively, these include: 1. if the entirety of the program contains exactly the code cc-00 it will not complete. 2. if the program contains the code cc-00 within a line of code that will provably execute (i.e., contains no prior jumps or some similar criterion), then the program will not complete. 3. if the program contains the code cc-xx, where x x is a value less than or equal to zero which moves the program to a place that provably returns back to the same line of code, then the program will not complete. let us note several things about these di!erent dependent axioms. first of all, note that all of the proposed axioms include the extraordinarily simple program cc-00. thus, there is definitely overlap among the axioms. also note that while axiom 1 is specifically for a single program, axiom 2 and axiom 3 both match multiple programs. in fact, axiom 3 matches a much larger number of programs than axiom 2. also of interest, in these examples, the longer the description of the item, the more potential programs are matched. this is not necessarily true (i.e., there could be a shorter program that captures more potential programs), but it is true that more length allows for more coverage. that is, if we had a shorter program with more coverage, we could get yet even more coverage by adding bits to our program. 5 measuring the axioms i have identified two potential ways of measuring the “size” of each of these axioms, though there are probably yet others. 5.1 measuring occurrence probabilities the first way is to measure the probability of occurrence of the axiom. that is, what is the likelihood of a given arbitrary program that contains the axiom occurring? this probability could be converted into bits in order to give a size of an axiom. to see how this would work, look at axiom 1. imagine that programs were encoded as prefix-free codes.1 as a simplification, the prefix-free code will be achieved by saying first n bits are a tally of the number of bytes in the code, terminated by a single 0 bit. therefore, the prefix-free version of the program identified by axiom 1 would be 0b110 cc-00.2 the probability of this program would be 1 524288 , or 19 bits. thus, the size of axiom 1 using this metric is 19 bits. the size of the other two axioms would require significantly more investigation (and specification as to the programming system) to determine. however, for an axiom that matches a finite number of programs, the size of the axiom using this method is relatively easy to determine. 5.2 measuring the size of the axiom identifier another method for size measurement is to identify the shortest possible program which is able to identify the given axiom in code. using this method, axiom 1 could be identified by the pseudo-code, “if the size of the program is two bytes, and the first byte is cc and the second byte is 00, then return true, otherwise return false.“ obviously, we would need to spell out the rest of the language in order to determine the size of this pseudo-code, but the procedure is straightforward. 6 implications the most important result here is that dependent axioms are in fact measurable. whether these are the most important measures of axioms is only partially relevant—the idea that they can be measured has been validated. nonetheless, it seems that these measurements do have some importance. measuring the occurrence probability measures the likelihood that the axiom will come into effect in any given program, thus whether or not someone will likely be thinking about the axiom. measuring the size of the detector has even more interesting applications. it was noted in bartlett (2012) that some axioms require other axioms to be known before discovery. measuring detector size fits in well with this idea because, given an existing detector a, and a goal detector b, there may exist some mutual information between a and b which 1this is a requirement so that the individual programs can be represented as probabilities (kraft, 1949). 2note that the first part of the program is not necessarily fall on an even byte mark, so it is just given as the list of bits, while the rest of the code is given in hexadecimal. volume 2, issue 1 references 27 makes the size of b smaller given a detector for a. the proposed equation for generating axioms using insight in bartlett (2012) was a = i (q, p, i, b) (1) where i is the “insight” function of cognition, q is the decision problem you are trying to solve (i.e., the halting problem), p is the program with i as the input, and b is a set of axioms. the point of the function is to say that, given a su"ciently inclusive b, the remaining axiom(s) a needed to decide q for p and i can be found. using the detector size metric, we might posit that the critical feature is the size of a given b. that is, insight allows an amount of information of a detector to be built. given a specifically inclusive b, the amount of mutual information between b and a can reduce the number of bits required to build the detector. this provides some amount of directionality for insight problems, while still allowing for them to be found in various ways. references bartlett, j (2012). “using turing oracles in cognitive models of problem-solving”. in: engineering and the ultimate: an interdisciplinary investigation of order and design in nature and craft. ed. by j bartlett, d halsmer, and m r hall. broken arrow, ok: blyth institute press, pp. 99–122. kraft, l g (1949). “a device for quantizing, grouping, and coding amplitude-modulated pulses”. phd thesis. massachusetts institute of technology. url: http:// hdl.handle.net/1721.1/12390. raatikainen, p (2018). “gödel’s incompleteness theorems”. in: the stanford encyclopedia of philosophy. ed. by e n zalta. url: https : / / plato . stanford . edu / archives / fall2018 / entries / goedel-incompleteness/. turing, a m (1936). “on computable numbers, with application to the entscheidungsproblem”. in: proceedings of the london mathematical society 42, pp. 230–265. volume 2, issue 1 letters and notes divergent series and its assigned value in a hyperreal context bas van der reijden doi: 10.33014/issn.2640-5652.2.1.reijden.1 abstract this letter discusses the deep connection between the infinite sum of natural numbers and the value " 1 12 . aside of more widely known facts, we consider a nontrivial way in which we show the veracity of this connection; more precisely this concerns the bgn method (bartlett, gaastra, and nemati, 2020) applied on the so-called damped oscillated abel summed variant of the series. moreover, we have found a generalization of this method which ‘correctly’ assigns finite values to other divergent series. we conclude with some questions concerning whether and how we can analytically relate our hyperreal terms to frame the method in a more justifiable and applicable context. it is obvious that the sum of natural numbers 1+2+3+ · · · tends to infinity and can thus not be equal to " 1 12 . there does however exist some connection between this series and value and it is highly probable that this connection is implicitely used (i.e. ‘under the hood’) in e.g. physics (which often turns out to be perfectly justifiable, as can be shown by various experiments). the first evidence of this connection is retrieved when one considers the riemann zeta function ! (s). it is known that ! (s) is equal to " 1 12 when s = "1 and it is interesting that one retrieves the sum of natural numbers when one ‘plugs in’ s = "1 at the defining series of the riemann zeta function !# k=1 1 k s . plugging s = "1 in the above series is unfortunately not justifiable (given that ! (s) is only equal to this series when $(s) > 1) but it remains an interesting thing to mention. another evidence of the connection can be revealed when one considers the ‘smoothed version’ of the partial sums !n k=1 k, see also tao, 2010. it turns out that these smoothed partial sums have the same behaviour as the figure 1: smoothed partial sums !n k=1 k with a yintercept of " 1 12 . regular partial sums (i.e. they have the same asymptotic expansion) and thus tend to infinity when n % #. however, one probably recognizes the constant value in its asymptotic expansion, which is (according to tao (2010)) given by cn2 " 1 12 +o( 1 n ) (with c some coe"cient of little importance in this case). moreover, it is given that " 1 12 is attained when one looks at the intersection with the y-axis in figure 1. the first two evidences we mentioned are quite widely known but a more unknown fact can be observed when one considers a damped oscillating variant of the series 1 + 2 + 3 + · · · , namely #" k=1 ke"k! cos(k" ). (1) this variant was also discussed in a previous letter (bartlett and khurshudyan, 2019). in this letter it was also mentioned that, in the context of hyperreal numbers by introducing # := # (i.e. by appying the bgn method on it), (1) can be written in a closed-form expression (or at 30 letters and notes least as an approximation of it). it remained however still unclear which value/magnitude the infinitesemal quantity " must be1 in order that the bgn method applied on (1) equals the ‘appropriate’ value " 1 12 ; only numerical evidence was given. in particular, it was shown that if " = 1 " , the computing software “wolfram mathematica” will include the constant " 1 12 in its bgn expression (which is similar to the observation of the previous paragraph). at the time that bartlett and khurshudyan (2019) was written, it only seemed clear that there is a numerical evidence that (1) equals " 1 12 when we take " in a su"ciently small interval. recently, we have found that sugiyama (2014) (section 2.3) provides a more theoretical derivation of this matter. although the website and its choice of words are somewhat vague and confusing, the derivation seems correct. in this derivation there is being made use of a so-called ‘damped oscillated abel summation method’, which is a kind of generalization of the more common abel summation method used to assign finite values to divergent series. in this article, this method of ‘damped oscillated abel summation’ is consequently used on a larger class of divergent series as well; furthermore it turns out that the ‘damping’ and ’vibrating’ constant should not be necessarily equal to each other. we thus in fact have that (see also section 5.2 and section 6.1 of sugiyama (2014), we here write " instead of x) !# k=1 k i can be transformed to (letting i & 1 be an integer) "" k=1 k ie"k! cot ! 2i+2 cos(k" ) and "" k=1 k ie"k i+1 2 ! cos(k i+1 2 " ) and consequently taking the limit " % 0 yields the ‘appropriate’ assigned value; we also numerically verified this2. it remains of course interesting how this damped oscillated abel summation method can be stated in our more ‘detailed’ hyperreal context; i.e. in which we know the exact values of " (possibly in terms of #) in order that the bgn method assigns the ‘appropriate’ value to a divegent series. unless it is still untrivial which values " must have in order that the mentioned method assigns this value, we can however say from equation (5.57) in sugiyama (2014) that in general 1 ! must be a lot smaller than # (this was also shown by numerical experiments: if we set " = 0.01, # must be a lot larger than 100). in conclusion, we can thus say that the connection 1in relation to " 2by again letting ! be in a su!ciently small interval between the often assigned value of a divergent series is hidden in its asymptotic expansion. furthermore, some slight variations (performed in the context of hyperreals) of the terms in the divergent series will alterate its asymptotic expansion in such a manner that that the bgn method assigns the ‘desired value’ to it. as it is at this point still untrivial when equality holds, and how in this case " and # thus must be related, remains an interesting topic for further research. to state this in a more general and mathematically way: consider a divergent series with bgn expansion a(" (#))#2 +c +o(1/#) (here a is a value dependent of " which is in turn dependent of # and c is the ‘appropriate’ value we want to have), the question is now which variations (in terms of " (#)) we have to make in order to make a(" (#))#2 equal to zero. bartlett, j, l gaastra, and d nemati (2020). “hyperreal numbers for infinite divergent series”. in: communications of the blyth institute 2.1, pp. 7–16. bartlett, j and a khurshudyan (2019). “numberphile’s proof for the sum 1+2+3+...” in: communications of the blyth institute 1.1, pp. 54–55. sugiyama, k (2014). new proof that the sum of natural numbers is -1/12 of the zeta function. url: https : / / xseek qm . net / regularization _ e . htm # _toc524947400 (visited on 11/16/2019). tao, t (2010). the euler-maclaurin formula, bernoulli numbers, the zeta function, and real-variable analytic continuation. url: https://terrytao.wordpress. com/2010/04/10/the-euler-maclaurin-formulabernoulli numbers the zeta function and real-variable-analytic-continuation/ (visited on 01/07/2019). do mutation rates match the kelly criterion? jonathan bartlett doi: 10.33014/issn.2640-5652.2.1.bartlett.2 the kelly criterion defines an optimal betting strategy for games that have a defined risk and payo!. it was developed by john kelly, jr. at bell labs (kelly, 1956). given a bet with a probability of success p and a payout of b, the kelly volume 2, issue 1 on logic of being and wigner’s astonishment regarding the applicability of mathematics 31 criterion tells you the size of your bet compared to your overall bankroll. the kelly criterion is given as pb + p " 1 b (1) this formula can be derived from a formula for an expected total payo! of the bet given by the equation t = a(1 + b f )np (1 " f )n (1"p) (2) where t is the total winnings, a is your starting amount, n is the number of trials, and f is the bet size. optimizing for t yields equation 1. many researchers have discussed the concept of mutations in populations as “bet hedging.” (philippi and seger, 1989; bartlett, 2008; simons, 2011; grimbergen et al., 2015) since the kelly criterion allows one to at least theoretically calculate the optimum bet size for each configuration, it might be possible to calculate various optimum mutation rates at di!erent sites and compare them to their optimal size according to the kelly criterion, or an adjusted version of it. most analysis of bet hedging has merely checked to see if the hedging strategy is empirically beneficial (childs, metcalf, and rees, 2010; simons, 2011) or potentially evolvable (king and masel, 2007). applying the kelly criterion may be able to help determine how optimal organisms’ various bet hedging strategies are. one possible experimental approach would be to provide organisms with a long-term, continually-varying environment. after many generations, it would be interesting to check if the mutation rates for adaptive switching between environments had any relation to the theoretical considerations of the kelly criterion, or any other theoretical hedging system. bartlett, j l (2008). “statistical and philosophical notions of randomness in creation biology”. in: creation research society quarterly 45, pp. 91–99. childs, d z, c j e metcalf, and m rees (2010). “evolutionary bet-hedging in the real world: empirical evidence and challenges revealed by plants”. in: proceedings fo the royal society b: biological sciences 277, pp. 3055– 3064. doi: 10.1098/rspb.2010.0707. grimbergen, a j et al. (2015). “microbial bet-hedging: the power of being di!erent”. in: current opinion in microbiology 25, pp. 67–72. kelly, j l (1956). “a new interpretation of information rate”. in: the bell system technical journal 35, pp. 917–926. url: http://www.herrold.com/ brokerage/kelly.pdf. king, o d and j masel (2007). “the evolution of bethedging adaptations to rare scenarios”. in: theoretical population biology 72, pp. 560–575. doi: 10.1016/j. tpb.2007.08.006. philippi, t and j seger (1989). “hedging one’s evolutionary bets, revisited”. in: trends in ecology and evolution 4.2, pp. 41–44. simons, a m (2011). “modes of response to environmental change and the elusive empirical evidence for bet hedging”. in: proceedings of the royal society b: biological sciences 278.1712, pp. 1601–1609. doi: 10.1098/rspb. 2011.0176. url: https://royalsocietypublishing. org/doi/10.1098/rspb.2011.0176. on logic of being and wigner’s astonishment regarding the applicability of mathematics gordon e mullings doi: 10.33014/issn.2640-5652.2.1.mullings.1 the nobel prize winning physicist, eugene wigner, famously posed a powerful challenge (1960) by asking why is mathematics so e!ective, especially in the physical sciences (wigner, 1960). it is possible that the reason for the e!ectiveness of mathematics is not because mathematics is in any way causative, but instead because mathematics studies the structure of logical possibility and constraint. when plugged into a possible world, mathematics gives us the tools to analyze the logically possible outcomes. therefore, when a possible world that is expressed mathematically su"ciently aligns with reality, mathematics becomes e!ective at expressing relationships and outcomes. for example, beings (as well as possible beings and things impossible of being) can be understood in the context of possible worlds. a “possible world” is a su"ciently complete description of possible states of a!airs described through chains of propositions. we may observe that things impossible of being, such as a square circle, have in them mutually inconsistent required core attributes; they cannot be realised in any possible world. possible beings would exist in at least one possible world were it actualised. for instance, a contingent being b that depends on c might exist in a world w and not in a closely neighbouring one w ! 32 letters and notes if c is present in w but not w !; c thus being an enabling, necessary causal factor for b. by contrast, a necessary being f will exist in all possible worlds, showing itself to be a framework element for such a world. a key insight is that for any world w to be distinct from w ! it requires some factor a in w that is absent in w !. we may then partition the factors of w as w = {a|¬a}. after partitioning, we will have two distinct groups—the factor a and all of the factors which are not a. the null set corresponds to zero. each particular set in the partition can be counted as the number one, and the combination of both partitions (even in a single world where a is an empty set) is two. thus, for any particular possible world w , the quantities 0, 1, 2 are necessarily present. taking the von neumann construction, immediately we find n, thence (using additive inverses) z, so also (taking ratios) q and (summing convergent power series) r; where z provides unit-stepped mileposts in r. that is, a structured core of quantities will be present in any w , and we may regard mathematics as the study of the logic of structure and quantity. extensions to the hyperreals r' follow by construction of some h that has as reciprocal h = 1 h closer to 0 than 1 n for any n in n. therefore, relationships and linked operations across such quantities will also be present, or may be constructed as needed. illustrating, after abraham robinson (robinson, 1966), hyperreals allow calculus to be treated as extensions of algebra in r'. thus, while bare distinct identity and coherence focused on quantities will not cause things by the inherent potential or action of such entities, they instead are logical constraints on being and are tied to what can or must be or cannot be or happens not to be. so, too, we may see that the abstract logic model worlds that we may construct then lead to key entities that if necessary are framework to any possible world; thus applicable to our common world. by contrast, if certain quantities and relationships are merely part of the contingencies of some w !! that is close enough to our own, they may provide adequate analogies for modelling. as a result, we have good reason to expect that mathematical reasoning and core entities will in many cases be highly relevant to and have powerful predictive power for our common world. robinson, abraham (1966). non-standard analysis. amsterdam: north-holland publishing company. wigner, eugene (1960). “the unreasonable e!ectiveness of mathematics in the natural sciences”. in: communications in pure and applied mathematics 13.1, pp. 1–14. doi: 10.1002/cpa.3160130102. independence conservation and evolutionary algorithms eric holloway doi: 10.33014/issn.2640-5652.2.1.holloway.2 levin’s law of independence conservation leonid levin’s 1984 article (levin, 1984) is the first to this author’s knowledge to prove a fully stochastic conservation of information law. levin titled his law ’independence conservation’ which he considered fairly obvious, describing it as “torturing an uninformed witness cannot give information about the crime!” levin’s law is not well known, which is unfortunate since the more commonly known conservation laws are focused either only on the random or deterministic case. levin’s law is remarkable because it unifies both the random and deterministic cases, showing that the combination also cannot result in information increase. the second remarkable thing about his law is how easy it is to prove, given some preliminaries about algorithmic information. algorithmic information theory background first is required the notion of algorithmic information, which is defined on bitstrings. algorithmic information is the length of the shortest program that generates a particular bitstring. k (x) := min y |u (y)=x |y |. (1) the shortest program is itself known as the elegant program for that particular bitstring. each bitstring has a unique elegant program. volume 2, issue 1 independence conservation and evolutionary algorithms 33 y' := arg min y |u (y)=x |y |. (2) all programs either terminate after a fixed amount of time, or never terminate. all the programs in question are known as prefix free, which means that no terminating program begins another terminating program. algorithmic mutual information is the length of this program if we are also provided another bitstring as input, subtracted from the length if we are not provided the extra input bitstring. i (x : y) := k (y) " k (y |x). (3) unfortunately, this basic definition of algorithmic mutual information is only symmetric under a logarithmic error, because we have to mark where one bitstring starts and the other ends. this requires a number of bits logarithmic on the size of the shortest bitstring, which is x in this case. i (x : y) " i (y : x) = o(log(x)). (4) we can improve the definition of algorithmic mutual information to be completely symmetric under a constant that is independent of the bitstrings we are looking at, which in other words means we don’t have to worry about the constant and the algorithmic mutual information is symmetric as far as we are concerned. this improvement is to use the elegant program of the input bitstring instead of the bitstring itself. i'(x : y) := k (y) " k (y |x'). (5) since the elegant program halts once it has generated the input bistring, we know we can start on the next bitstring, so we avoid having to encode the bitstring length. this saves us from having to use the logarithimic term. i'(x : y) " i'(y : x) = o(1). (6) one final fascinating point on algorithmic information is that we can also use it to create a universal distribution. m(x) := 2"k (x) . (7) “universal” means is that we have a distribution that provides the highest probability for every bitstring possible, within a multiplicative constant, under the assumption that we are only dealing with computable generating sources for the bitstrings. m(x) & p(x) 'o(1). (8) the computable distribution assumption is a reasonable assumption for dealing with physical phenomena, since (as far as we know) everything physical can be modeled to theoretically perfect accuracy with enough computational resources. proving levin’s deterministic law alright, so now onto proving levin’s law. we first start with a simple lemma, that providing more information can only decrease conditional algorithmic information. in other words, the more we know about y, the less information we need to describe y. k (y |x) & k (y |x, z) +o(1). (9) we now introduce another simple lemma that with a program to generate x, namely z which we execute with turing machine u to generate x, x = u (z), (10) we can generate both x and z. thus, the joint information is the same between z and x, z. k (z) = k (x, z) +o(1). (11) this also means to generate the triple {y, x, z} we only need y and z. k (y, x, z) = k (y, z) +o(1). (12) 34 letters and notes since it is the case that k (y |x, z) = k (y, x, z) " k (x, z). (13) then performing replacements to equation 13 with equations 11 and 12, we get k (y |x, z) = k (y, z) " k (z) (14) = k (y |z). (15) combining equations 9 and 14 shows us that x can never tell us more about y than z. k (y |x) & k (y |x, z) (16) = k (y |z). (17) we can then use equation 16 to show running a program f on i does not increase mutual information with y. the notation u ( f .i) to mean we’ve run program f with input i using a universal turing machine u. first we decompose the mutual information. i'( f (i) : y) = i'(u ( f .i) : y) (18) = k (y) " k (y |u ( f .i)). (19) (20) now, we set z = f .i and x = u (z) = u ( f .i), and then apply equation 16 to equation 18. i'( f (i) : y) = i'(x : y) (21) = k (y) " k (y |x) (22) ( k (y) " k (y |x, z) (23) = k (y) " k (y |z) (24) = i'(z : y) (25) = i'( f , i : y). (26) giving the final concise result, i'( f (i) : y) ( i'( f , i : y). (27) this equation 27 states that executing function f on input i does not produce any more information about y than the function and input before they are executed. in other words, running a program doesn’t produce any information. proving levin’s random law now with the deterministic version out of the way, we can move onto the random version. the random version asks, what if we generate f randomly, could that result in an information gain? this question is based on the fact that generating f randomly will result in an f with a lot of algorithmic information, since it will be incompressible. so, even though running u ( f .i) doesn’t give us anything new, the initial selection of f may start us o! with a good amount of information about y. levin’s second step in proving the random law shows this intuition is false. to prove the second law, we will rely on the dominance property of the universal distribution in equation 8. " f p( f )i'( f , i : y) = " f p( f ) log2 m( f , i |y) m( f , i) (28) ( " f p( f ) log2 m( f , i |y) m( f )m(i) (29) ( log2 " f p( f )m( f , i |y) m( f )m(i) (30) ( log2 ! f m( f , i |y) m(i) (31) = log2 m(i |y) m(i) (32) = k (i) " k (i |y) (33) = i'(i : y) (34) which gives us the result that randomly generating an f is not expected to provide any information about y. " f p( f )i'( f , i : y) ( i'(i : y). (35) to wrap up the independency conservation law, we apply equation 27 to equation 35. " f p( f )i'( f (i) : y) ( " f p( f )i'( f , i : y) ( i'(i : y). (36) volume 2, issue 1 crowdrank: a simple ranking algorithm for crowdsourced rating systems with uneven participation 35 evolutionary algorithms what sort of impact, if any, does the law of independency conservation in equation 36 have on evolutionary algorithms? one of the simplest implications is that if there is a target area independently designated by y, then it is not possible to randomly evolve population i towards y without any fitness information. however, there are also implications even if there is fitness information provided for the evolution of i. let’s say that f represents one round of an evolutionary algorithm applied to i, which consists of the following steps: 1. crossover population 2. vary population 3. select population i is defined as a population of bitstrings selected at random. we then define y as the set of bitstrings rated at a certain level of fitness. part of f stays constant, and another part is varied randomly, such as mutation and which bitstring sections are crossed. we denote the random part as r. this gives us a surprising result. " r p(r)i'( f (i, r) : y) ( i'( f , i : y). (37) equation 37 states that each round of randomized evolution provides no further information about the fitness region y than already existed in the initial conditions of the original population i and the evolutionary algorithm f . thus, this equation proves that evolutionary algorithms cannot generate algorithmic mutual information, even in regards to regions specified according to fitness. levin, leonid a (1984). “randomness conservation inequalities; information and independence in mathematical theories”. in: information and control 61.1, pp. 15–37. crowdrank: a simple ranking algorithm for crowdsourced rating systems with uneven participation jonathan bartlett doi: 10.33014/issn.2640-5652.2.1.bartlett.3 introduction public rating systems are di"cult to score well. voting systems tend to simply favor what is already popular. averaging systems tend to have significant variance if there are not enough people scoring. for instance, let’s say that i run a songwriting contest and have 100 entries. i then put it out to a public vote on the internet to see who wins. most people are not going to listen to all 100 songs. if i do a simple “thumbs up” approach and count how many votes a song has, then whichever songwriter has the best existing following will simply tell their fans to vote for them, and it will simply devolve into a popularity contest. let’s say instead i do a rating system where you can rate a song between 0 and 100. now, songs by popular artists will actually be negatively weighted because they will have more visibility for negative ratings. it is not hard for a few votes to be all 100s, but it is hard for a thousand votes to be that way. thus, those who have fewer ratings have an advantage. the goal, then, is to come up with a fair way of handling public ratings which takes into account both the average score that people assign and the relative certainty that we have that the score is representative of the “true” score. the model this problem actually becomes rather easy once an appropriate mental model is devised. assuming a normal distribution of actual scores that come in around a “true” value for a particular score for an entry, what is the range of possible score values based on the scores that have been submitted so far? 36 letters and notes take a concrete example. let’s say that song a has 12 votes with an average score of 60. what is the range that the “real” score should lie in? the main open question when dealing with statistics is what confidence level we want to deal with. for this example, let’s say that we want to maintain a 95% confidence interval. that means that we want to know what the range is of two standard deviations from the mean. with only 12 samples, this leads to a fairly wide interval, with the real score being between 32 and 88. however, as we add more samples, this range narrows in to the average. if we have 24 samples and maintain the same average, then our range is restricted to between 40 and 80. at 144 samples, the range narrows to 52–68. so, with a few scores, the possible “real” score has a very wide range. however, as more and more scores come in, the range narrows further and further. now, even though these rankings get tighter variances with more scores, the average value for the scores remain what they were. so how do we convert this into a more legitimate ranking system than we had before? what we can do is simply rank the songs using their lowest possible scores according to the chosen confidence interval. that is, we have established statistically what the lower bound for their score is. therefore, we can definitively give them that score because we know they have earned at least that score. this minimal defensible score will be called the crowdrank score. let’s say that song a has 144 rankings that average to 60, and song b has 25 rankings that average to 70. which song should be ranked higher? as we have already noted, song a’s “real” score has a potential range of 52–68. song b, because it has fewer score submissions, has a wider potential range of 50–90. since the lowest defensible score of song a is 52, and the lowest defensible score of song b is 50, that means that song a will be ranked higher than song b. the actual ranking will be dependent on the confidence level that is chosen for the rankings. the higher confidence levels will take many more rankings for the scores to approach their averages. the calculation the calculation of each entry’s score is fairly straightforward. it is basically the inverse of standard statistical scores. p the population size n the number of samples (i.e., number of rankings on a particular entry) z the confidence level desired, expressed as a z-value (the number of standard deviations that a given confidence level uses—2.58 for 99% confidence, 1.96 for 95% confidence, etc.) e the margin of error for the confidence interval, expressed as a decimal (i.e., 0.25 for ±25%) s the average score of the samples expressed as a real number between 0 and 1. in the present example we would divide all scores by 100. m the expected value. choosing 0.5 is a “most-safe” value. typically, the number of needed samples is determined from the desired margin of error, using n = z2m(1 " m) e2 . (1) rearranging to find the margin of error from the sample size, we find e = # z2m(1 " m) n . (2) since our results are distributed as a percentage anyway (a score of zero to one), the crowdrank is just the score s " e. simplified using m = 0.5, the crowdrank calculation for a particular entry is crowdrank = s " # 0.25 z2 n . (3) if the samples are taken from a restricted population of size p (say, all the members of a club), you can get an even better measurement from the following: crowdrank = s " # 0.25 z2 n p " n p " 1 (4) di!culties there are two primary di"culties with this system. the first is that, if there are too few rankings for each entry, the confidence level will fall o! to zero. this can be mitigated by varying the desired confidence level based on the average rankings per entry. volume 2, issue 1 crowdrank: a simple ranking algorithm for crowdsourced rating systems with uneven participation 37 the other di"culty is in communicating the results to endusers. it is di"cult for them to understand why having 144 people all giving a ranking of 60 might translate to a crowdrank of 52. having scores whose origin is not transparent can lead to a lack of confidence in the system. however, because the discount to the scores is fixed for the number of entries, you can communicate this as the number of points that are discounted for a given number of entries. for instance, if you are using the 95% confidence interval, then you can post that receiving 23–25 entries will result in a 20 percentage point discount. conclusion this note introduced a system of averaging crowdsourced rankings that appropriately discounts ranking averages based on the number of submissions. this can be used in any place where a variable number of crowdsourced rankings might be received. it removes the “popularity contest” problem of simple voting, as well as the problem of having too few rankings available in a generic averaging system. volume 2, issue 1 news eric holloway publishes paper on specified complexity david nemati and blyth institute fellow eric holloway recently published a new paper in the journal biocomplexity (nemati and holloway, 2019). the paper, titled “expected algorithmic specified complexity,” explores the expected algorithmic specified complexity (asc) of a random variable, concluding that the expected asc is always less than zero. this is true both of random variables and of “processed” random variables—variables which have undergone some sort of transformation. this indicates that the existence of positive asc always counts as “surprise,” and therefore always requires explanation. new thinking on human origins this past year witnessed a plethora of new thinking on human origins. first up, new research by ola hössjer and ann gauger recently showed a unique model for looking at biodiversity (hössjer and gauger, 2019). essentially, they looked at the ways in which minor allele frequency distributions can arise, and how long di!erent distributions take to arise. new alleles essentially start out as one-o! events, arising as a mutation in a single individual and later spreading through the population or dying out (or somewhere inbetween). the frequency of these minor alleles can provide some amount of information about the history of the species in question. it takes time for an allele to spread through a population. therefore, initially, from an initially homozygous pair, the low-frequency side of the minor allele frequency spectrum will contain all of the new mutations. the mutations will take time to spread throughout the population. what hössjer and gauger discovered, though, is that a heterozygous initial pair creates an allele frequency spectrum that looks much older than it is. this is because an allele can actually start as either 25%, 50%, 75%, or 100% of the population before any mutations even occur. thus, the frequency spectrum will fill very quickly from the initial pair, and the initial heterozygosity will look equivalent to ancient mutations. using standard assumptions, hössjer and gauger calculated that the current allele frequency spectrum could be attained from an initial starting pair in 100,000–500,000 years. using other alternative assumptions about the nature of the starting pair could result in attaining the current allele frequency spectrum in an even shorter period of time. another interesting paper was done by nathaniel jeanson and ashley holland, which analyzed the human y chromosome (jeanson and holland, 2019). analyzing the human genome as a whole leads to a number of model-specific issues. if we imagine a starting pair for humanity, were the original chromosomes identical or did they house diversity? additionally, might the first human female have eggs that had additional diversity in their chromosomes? however, nearly all considerations of single-couple human origins have exactly one starting y chromosome, leading to fewer model-specific considerations. jeanson and holland aimed to improve the data available about y chromosome mutation rates by examining pedigree-based studies which used high-coverage sequencing. according to jeanson and holland, (a) a y chromosome molecular clock exists, and (b) it suggests a paternal history of the human race of about 4,500 years. finally, the year ended with the publication of joshua swamidass’s new book titled the genealogical adam and eve (swamidass, 2019). this book aims to show that the practical di!erence between popular and scientific conceptions of “adam and eve” are not too far o!. his viewpoint is that, although, according to the consensus view, there could be no single-couple origin of humans, there could be a single couple to whom all modern humans could trace their genealogies. communicating science through new venues new media becomes old media very quickly in the modern age. email was once the best technological way to communicate interpersonally. this is now often replaced with various social media platforms such as facebook, twitter, and others. likewise, youtube was once at the center of 40 news video-based media. while youtube is still the de facto destination for video content, it is useful to look at some of the newer players. first of all, some video is being distributed through apps on standard platforms. developing an app for roku, amazon fire, or apple tv is a new way to get content to users. additionally, streaming services such as twitch, and now mixer, are becoming the dominant social video platforms for the youth. science communicators should explore ways of reaching the public through these outlets. one possibility would be to play video games with scientists, discussing what they do while shooting zombies, or discussing the latest theories of the universe while racing nascar. growth opportunities are always with the latest technology. asserting a strong position while they are still unproven is the best way to establish leadership for the future. austrian society zentrum für biokomplexität & naturteleologie opens with special symposium a new austria-focused scientific society, zentrum für biokomplexität & naturteleologie, recently formed and held their first symposium. the symposium featured many european scientists and mathematicians, as well as a few from the united states as well. the organizers of the conference were günter bechly, a prominent german paleontologist who presently works as a senior scientist for the biologic institute, and siegfried scherer, a professor of microbiology and chair of microbial ecology at the technical university of munich. while the society is based in austria, the symposium itself was largely in english. many of the talks from the three day symposium are available on youtube, at https://www.youtube.com/playlist?list= plkakqujdyg2jhnqewqhnvtxz-37h0tjmb. breaking the weismann barrier and closing the loop for lamarckian evolution in multicellular organisms a recent review paper in the royal society shows that the weismann barrier is crumbling. in “the active role of spermatozoa in transgenerational inheritance,” sciamanna et al review the mounting evidence that there is a lamarckian feedback loop in dna inheritance (sciamanna et al., 2019). the paper reviews evidence that mammalian somatic tissues release rna-containing vesicles, and that these vesicles are then passed to epididymal spermatozoa. additionally, epididymal spermatozoa are known to be able to internalize foreign nucleic acids into their nuclei. this completes the communication channel between somatic cells and germ cells required for lamarckian inheritance. this communication channel was original proposed in the 1990’s. steele et al’s lamarck’s signature suggested that somatic mutations might be passed to germ line cells through an rna channel (steele, lindley, and blanden, 1999). after decades of work across multiple groups, evidence is mounting that steele’s hypothesis was largely correct. overcoming entrenched dogma about pseudogenes biologists have long known that not all non-coding dna is junk dna. however, pseudogenes have long been considered the standard bearer for the junk dna concept. since pseudogenes look like defective, non-coding copies of ordinary genes, it has been often assumed that these are evolutionary leftovers—genes which once coded for something, or a copy of a gene that once coded for something, but which some accident of mutation incapacitated its activity. while the evidence for the activity of pseudogenes has long been known, the idea that pseudogenes indicate junk dna has been ingrained in biologists. a group of researchers recently published a paper pointing out that the prejudices that biologists have about the status of pseudogenes as junk dna is impeding the progress of understanding the way that the genome functions (cheetham, faulkner, and dinger, 2019). references cheetham, s w, g j faulkner, and m e dinger (2019). “overcoming challenges and dogmas to understand the functions of pseudogenes”. in: nature reviews genetics. doi: 10.1038/s41576-019-0196-1. volume 2, issue 1 references 41 hössjer, o and a gauger (2019). “a single-couple human origin is possible”. in: 2019 (1), pp. 1–20. jeanson, n t and a d holland (2019). “evidence for a human y chromosome molecular clock”. in: answers research journal 12, pp. 393–404. nemati, d and e holloway (2019). “expected algorithmic specified complexity”. in: bio-complexity 2019 (2), pp. 1–10. sciamanna, i et al. (2019). “the active role of spermatozoa in transgenerational inheritance”. in: proceedings of the royal society b: biological sciences 286.20191263. steele, e j, r a lindley, and r v blanden (1999). lamarck’s signature: how retrogenes are changing darwin’s natural selection paradigm. basic books. swamidass, s j (2019). the genealogical adam and eve: the surprising science of universal ancestry. ivp academic. oqhmk2 jabbm2 r hbhbm; 1|q`2b+2m+2 q7 1tt�m/bm; e2`m2hb bm � 6bt2/ s2`bq/b+ �``�v, :2m2`�hbxbm; i?2 6hqr2`@p7@gb72 _q#2`i cx j�`fb aa .pa, ryxjjyr9fbbbmxke9y@8e8kxjxrxk�`fbxr �#bi`�+i *qmibmm�hhv 2tt�m/bm; t2`bq/b+�hhv i`�mbh�i2/ f2`m2hb qm i?2 irq /bk2mbbqm�h ;`b/ +�m vb2h/ bmi2`2bibm;#2�m@ ib7mh �m/ 2p2m 7�kbhb�` t�ii2`mbx 6q` 2t�kth22tt�m/@ bm; +b`+mh�` tbhh#qt b?�t2/ f2`m2hb qm � ?2t�;qm�h ;`b/�//bm; r?2m i?2`2 bb qp2`h�tvb2h/b t�ii2`mb bm+hm/@ bm; k�tbk�hhv t�+f2/ +b`+h2b �m/ � i`b[m2i`�@ivt2 i?`22 t2i�h bi`m+im`2 mb2/ iq `2t`2b2mi i?2 i`bmbiv bm *?`bb@ ib�mbivx *qmibmm2/ 2tt�mbbqm vb2h/b i?2 ~qr2`@q7@hb72 mb2/ 2ti2mbbp2hv bm �`i �m/ �`+?bi2+im`2x �//bibqm�h 2tt�mbbqm vb2h/b �m 2p2m kq`2 bmi2`2bibm; 2k2`;bm; 27@ ~q`2b+2m+2 q7 t2`bq/b+ 7mm+ibqmbx 1t�kth2 bk�;2b �`2 ;bp2m 7q` i?2 +�b2 q7 +b`+mh�` tbhh#qt �m/ +b`+mh�` +qm2 b?�t2/ f2`m2hbx lbbm; 6qm`b2` �m�hvbbb7mm/�k2mi�h t`qt2`ib2b q7 i?2b2 t�ii2`mb �`2 �m�hvx2/x �b � 7mm+@ ibqm q7 2tt�mbbqmbqk2 2|q`2b+2/ 7mm+ibqmb �bvkt@ iqib+�hhv �tt`q�+? 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p2+iq` bb q7 h2m;i? * u.m/;2qm �m/ j2`b2`2�mrn39c j�`fb aarnnrc j�`fb aakyynv� k. 2t�kth2 bb b?qrm bm 6b;m`2 rd r?2`2 k�tbk�hhv t�+f2/ +b`+h2b q7 `�/bmb ! ;2m2`�i2 t2`bq/b+biv p2+iq`b !)1 = "####$ & 2 & 2 # 3 %&&&&' ; !)2 = "####$ "& 2 & 2 # 3 %&&&&' . r?2`2 ! bb i?2 +b`+h2ƕb `�/bmbx h?2 +q``2btqm/bm; t2`bq/b+biv k�i`bt 7qhhqrb �b q = ! 2 ( 1 "1# 3 # 3 ) . ujv 6b;m`2 rd, >2t�;qm�h t2`bq/b+biv p2+iq`b bhhmbi`�i2/ 7q` k�tbk�hhv t�+f2/ +b`+h2bx � ibh2 bbqh�i2b � bbm;h2 t2`bq/ q7 i?2 t2`bq/b+ 7mm+ibqm �m/r?2m `2thb+�i2/ �++q`/bm; iq i?2 t2`bq/b+biv k�i`bt}hhb i?2 bt�+2 rbi?qmi ;�tbx 6q` ?2t�;qm�h t2`bq/b+biv� +q``2btqm/@ bm; ?2t�;qm�h ibh2 bb b?qrm bm 6b;m`2 8x 6q` � ;bp2m t2`bq/b+biv bi`m+im`2m2bi?2` q q` i?2 ibh2 b?�t2 bb mmb[m2x h?bb bb bhhmb@ i`�i2/ 6b;m`2 r3 r?2`2 ?2t�;qm �m/ � t�`�hh2hq;`�k ibh2b #qi? ?�p2 i?2 b�k2 t2`bq/b+biv p2+iq`bx � ibh2 +2mi2`2/ �i i?2 q`b;bm rbhh #2 `2thb+�i2/ qm i?2 ("1, "2) th�m2 �i i?2 p2+iq`b !)1 �m/ !)2x h?2 ibh2 rbhh �hbq #2 `2thb+�i2/ �i �mv bmi2;2` kmhibth2 q7 i?2 t2`bq/b+biv p2+iq`b7q` 2t�kth2 �i !)1 + !)2 �m/ 4!)1 " 3!)2x �mv ibh2 `2thb+�ibqm qm i?2 ("1, "2) th�m2 +�m #2 `2t`2b2mi2/ #v i?2 +qk#bm�ibqm +1 !)1 + +2 !)2 r?2`2 +1 �m/ +2 �`2 bmi2;2`bx � kq`2 +qm+bb2 2tt`2bbbqm bb +1 !)1 + +2 !)2 = q !+ r?2`2 !+ bb � irq /bk2mbbqm�h p2+iq` q7 bmi2;2`bx !+ = ( +1 +2 ) . h?2 ?2t�;qm�hhv b?�t2/ ibh2 bm 6b;m`2 8 ?�b �m �`2� q7 | det q| = # 3 !2 2 . u9v oqhmk2 jabbm2 r 9x �l�guaaa kd 6b;m`2 r3, 6q` � ;bp2m b2i q7 t2`bq/b+biv p2+iq`bi?2 +?qb+2 q7 ibh2b bb mqi mmb[m2x h?2 t2`bq/b+biv p2+iq`b bhhmbi`�i2/ �i i?2 #qiiqk q7 6b;m`2 rd +�m �hbq /2b+`b#2 i?2 t�`�hh2hq;`�k ibh2 b?qrm ?2`2x upmhv irq +qhmkmb q7 i?2 t�`�hh2hq;`�k ibh2 �`2 b?qrm ?2`2xv am #qi? +�b2bi?2 �`2� q7 i?2 ibh2| det, |bb i?2 b�k2 uj�`fb aakyynvx 6q` � ;bp2m t2`bq/b+biv bi`m+im`2 /2}m2/ #v i?2 t2`bq/b+biv k�@ i`bt q� t2`bq/b+ 7mm+ibqm rbi? � f2`m2h q7 *!" + +�m #2 r`bii2m bm � bt�+2 rbi? +qq`/bm�i2b !" �b uj�`fb aakyynv . *!" + = , !' *!" " q !+ + u8v r?2`2 i?2 bmk bb qp2` i?2 b2i q7 �hh bmi2;2` t�b`bx , !' = %, '1="% %, '2="% . lqi2 i?�i ç i?2 f2`m2h bb mqi +qmbi`�bm2/ iq #2 x2`q qmibb/2 q7 � ibh2 �m/ +�m 2p2m 2ti2m/ qp2` i?2 2mib`2 !" th�m2�m/ ç k�mv f2`m2hb +�m ;2m2`�i2 i?2 b�k2 t2`bq/b+ 7mm+ibqm. *!" +x h?2 +q``2btqm/bm; kmhib/bk2mbbqm�h 6qm`b2` b2`b2b q7 i?2 t2@ `bq/b+ 7mm+ibqm bm u8v bb i?2 6qm`b2` b2`b2b uj�`fb aakyync s�tqmhbbrnd3vn . *!" + = | det p| , !' / (p !+) exp 021!"% p !+ . uev nhq b22 i?2 t2`bq/b+biv+qmbb/2` b?b7i q7 uev 7`qk ( *!! + iq ( !! " q!) . r?2`2 !) bb �m �`#bi`�`v p2+iq` q7 bmi2;2`bx a7 ( !! " q!) . = ( *!! + 7q` �hh bm+? b?b7ibx ( *!! + bb t2`bq/b+ rbi? t2`bq/b+biv k�i`bt qx 6`qk uev( !! " q!) . = | det p | , !" * (p !') exp / "2# !! " q!) .! p !' 0 . r?2`2 p �m/ q �`2 `2h�i2/ #v �m bmp2`b2 i`�mbtqb2 p = q"% , udv h?2 2[mbp�h2m+2 q7 u8v �m/ uev bi2kb 7`qk i?2 6qm`b2` /m�h q7 i?2 sqbbbqm bmk 7q`kmh� uj�`fb aakyync s�tqmhbbrnd3c s�tqmhbb �m/ sbhh�bkyykvx , !+ $ ( !% " p!2) = | det q| , !+ # (q!2) &"2# !$! q!+ 9xr 1tt�m/bm; e2`m2hb q2 �`2 �#h2 iq mqr /2b+`b#2 i?2 2tt�m/bm; f2`m2h t2`bq/b+ 7mm+ibqm 7q` �`#bi`�`v t2`bq/b+biv k�i`bt q �m/ f2`m2h *!"+x .2}mbibqm 9xrx h?2 2tt�m/bm; f2`m2h t2`bq/b+ 7mm+ibqm#, *!" +;2m2`�i2/ #v � f2`m2h *!" + bb #, *!" + = , !' / !" " q !+ 3 0 u3v �b 3 bm+`2�b2bi?2 f2`m2h 2tt�m/x am #qi? i?2 2tt�m/bm; +b`+mh�` tbhh#qt �m/ 2tt�m/bm; +b`+mh�` +qm2 2t�kth2b3! bb i?2 `�/bmb q7 i?2 +b`+h2x 6`qk uevi?2 +q``2btqm/bm; 6qm`b2` b2`b2b q7 i?2 2tt�m/bm; f2`m2h bb #, *!" + = | det p|32 , !' / (3p !+) exp 021!"% p !+ . . unv h?2 qp2`h�ttbm; 2tt�m/bm; f2`m2hb +�m #2 /2i`2m/2/ #v 2p�h@ m�ibm; i?2 k2�m p�hm2 q7 i?2 t2`bq/b+ 7mm+ibqmx h?2 k2�m p�hm2 bm � 6qm`b2` b2`b2b 2tt�mbbqm bb i?2 x2`qi? q`/2` 6qm`b2` b2`b2b +q2{+b2mix h?bb +�m #2 2p�hm�ibm; #v bmi2;`�ibm; qp2` � bbm;h2 ibh2 7qhhqr2/ #v /bpbbbqm #v i?2 �`2� q7 i?2 ibh2x h?2 i?2q`2k iq 7qhhqr mb2b i?2 �`#bi`�`bm2bb q7 i?2 +?qb+2 q7 ibh2b r?2m bmi2;`�ibm;x am qm2 /bk2mbbqmi?2 t2`bq/ q7 � t2@ `bq/b+ 7mm+ibqmb�v ( bb �`#bi`�`vx q2 +�m +?qqb2 i?2 t2`bq/ iq #2 qm i?2 bmi2`p�h 0 & " < ( q` "(/2 & " < (/2. h?2`2 bb � h?2 2ttqm2mib�h i2`k ?2`2 #2+qk2b exp / -2# !! " q!) .! p !' 0 = exp "2#!!! p !' . exp / ""2# q!) .! p !' 0 . lbbm; udvexp ""2# !)! q! p !' .. = exp ""2# !)! !' .. = 1 bq i?�i ( !! " q!) . = ( *!! +x k3 hbhbm; 1|q`2b+2m+2 q7 1tt�m/bm; e2`m2hb bm � 6bt2/ s2`bq/b+ �``�v, :2m2`�hbxbm; i?2 6hqr2`@p7@gb72 bbkbh�` �`#bi`�`bm2bb bm i?2 +?qb+2 q7 � ibh2x hq bhhmbi`�i2+qm@ bb/2` � k. 7mm+ibqm rbi? ?2t�;qm�h `2thb+�ibqm �+`qbb � th�m2x *?qqbbm; � ibh2 bm i?bb 7mm+ibqm bb hbf2 +?qqbbm; � +qqfb2 +mii2`x �b bhhmbi`�i2/ bm 6b;m`2 r3� ?2t�;qm�h +qqfb2 +mii2` +�m #2 mb2/x "mi � ?2t�;qm bb mqi i?2 qmhv tqbbb#h2 ibh2x �b b?qrm bm i?2 };m`2� +qqfb2 +mii2` b?�t2/ hbf2 � t�`�hh2hq;`�k +�m �hbq #2 mb2/ �b +�m �mv +qqfb2 +mii2` i?�i b�ibb}2b i?2 t2`bq/b+biv +qmbi`�bmibx lqi�ibqm�hhvbmi2;`�ibm; qp2` �`2� c bm i?2 7qhhqrbm; i?2q`2k k2�mb bmi2;`�ibqm qp2` �mv bbm;h2 ibh2x 6q` �//bibqm�h /2i�bhbb22 j�`fb uj�`fb aakyynvx h?2q`2k 9xkx h?2 k2�m p�hm2 q7 i?2 2tt�m/bm; f2`m2h 7mm+@ ibqm#, *!" +bb '#,( := 1 | det q| ! !! )c #, *!" + '!" = 32 | det p| ! !! *!" + '!" uryv = 32 | det p|/ (!0) urrv h?2 `2;bqm c bb �mv `2;bqm bm i?2 !" bt�+2 +qp2`bm; � ibh2x �b 3 bm+`2�b2bi?2 /2i`2m/2/ bmk q7 i?2 2tt�m/bm; f2`m2hb bm i?2 !" th�m2 �tt`q�+?2b � rbi?qmi �mv bmi2`2bibm; bi`m+im`2x s`qq7x h?2 2tt`2bbbqm bm uryv 7q` i?2 k2�m q7 #, *!" + 7qhhqrb 7`qk i?2 !+ = !0 i2`k bm i?2 6qm`b2` b2`b2b bm unvx 1[m�ibqm urrv 7qhhqrb 7`qk i?2 bmi2;`�h t`qt2`iv ukvx ! q2 +�m mqr /2}m2 i?2 /2i`2m/2/ t2`bq/b+ 7mm+ibqmx .2}mbibqm 9xjx h?2 t2`bq/b+ 2|q`2b+2mi 7mm+ibqm4, *!" +bb i?2 /2i`2m/2/ 2tt�m/bm; f2`m2h 7mm+ibqmbx2x #, *!" + kbmmb bib k2�mx 4, *!" + = #, *!" + " '#,( . h?2 +q``2btqm/bm; 6qm`b2` b2`b2b q7 4, *!" + bb bbkthv i?2 6qm`b2` b2`b2b q7 #, *!" + bm unv rbi? i?2 x2`qi? q`/2` 6qm`b2` b2`b2b +q2{+b2mi !+ = !0 i2`k `2kqp2/xry 4, *!" + = | det p|32 , !'!!0 / (3p !+) exp 021!"% p !+ . . urkv 6`qk i?bb 2tt`2bbbqmr2 b22 i?2 6qm`b2` b2`b2b +q2{+b2mib 7q` i?2 2|q`2b+2mi 7mm+ibqm �`2 5, [ !+] = 1 | det p|32/ (3p !+) ; !+ ! !0 0 ; !+ ! !0 urjv ry"v !0r2 k2�m � p2+iq` r?qb2 qmhv 2h2k2mib �`2 x2`qx 9xk *qmp2`;2m+2 h?2 t2`bq/b+ 2|q`2b+2mi 7mm+ibqm +�m kqbi bmi2`2bibm;hv ;2m@ 2`�i2 � m2p2` `2t2�ibm; t�ii2`m q7 7�b+bm�ibm; b?�t2bx h?bb /q2b mqi ?�tt2m r?2m�b � 7mm+ibqm q7 2tt�mbbqmi?2 2|q@ `2b+2mi 7mm+ibqm `2�+?2b � hbkbi +v+h2 q` }t2/ tqbmix q2 mqr 2t�kbm2 r?2m i?bb ?�tt2mbx �bvktiqib+ *qmp2`;2m+2 q7 i?2 1|q`2b+2mi 6mm+ibqm iq w2`q q2 }`bi 2bi�#hbb? r?2m i?2 2|q`2b+2mi 7mm+ibqm 2tt�m/bm; f2`m2h �tt`q�+?2b x2`qx 6b`bi /2}m2 i?2 e`qm2+f2` /2hi� �b 6[ !+] := 1 1 ; !+ = !0 0 ; !+ ! !0 h?2q`2k 9x9x am{+b2mi +qm/bibqm 7q` +qmp2`;bm; iq i?2 k2�mx g2i * = 2xrr a7 3./ (3p !+) "* ,*% 3./ (!0)6[ !+] ur9v i?2m #, *!" + +qmp2`;2b iq bib k2�mx #, *!" + "* ,*% '#,( . �b � +qmb2[m2m+2 4, *!" + "* ,*% 0. am qi?2` rq`/b�b i?2 f2`m2hb +qmibmm2 iq 2tt�m/i?2 2|q`2b@ +2mi 7mm+ibqm �tt`q�+?2b i?2 p2`v mmbmi2`2bibm; `2bmhi q7 x2`q qp2` i?2 2mib`2 ("1, "2) th�m2x s`qq7x �b 3 * %�hh i2`kb 3./ (3p !+) bm unv i2m/ iq x2`q r?2m ur9v bb i`m2 2t+2ti r?2m !+ = !0x h?2m unv #2+qk2b #, *!" + "* ,*% 3. | det p|/ (!0) = '#,( ! � bm{+b2mi bkqqi?m2bb +`bi2`bqm *qmp2`;2m+2 q7 �m 2t@ t�m/bm; 2|q`2b+2mi 7mm+ibqm iq x2`q bb �bbm`2/ r?2m i?2 f2`m2h �/?2`2b iq bkqqi?m2bb �m/ bmi2;`�#bhbiv t`qt2`ib2bx rrh?2 i?2q`2kb ;bp2m �`2 �tthb+�#h2 bm �mv /bk2mbbqm . x q2 ?�p2 +qm+2mi`�i2/ qm k. bq rbhh b2i . = 2 iq �pqb/ +qm7mbbqmx h?bb �hbq �tthb2b iq h?2q`2k 9x8x oqhmk2 jabbm2 r 9x �l�guaaa kn h?2q`2k 9x8x *qmp2`;2m+2 iq i?2 k2�m, h?2 7qhhqrbm; i?2q`2k �tthb2b iq * /bk2mbbqmbx 6q` i?2 2t�kth2b ?2`2bm* = 2x h?2 * /bk2mbbqm�h 7mm+ibqm#, *!" ++qmp2`;2b iq bib k2�m b7 bib f2`m2h*!" +q#2vb i?2 7qhhqrbm; t`qt2`ivxrk ! !! 22222 3 .4 )=1 7"# 7""#) 5 *!" + 22222 '!" = 8 < % ur8v r?2`2 i?2 mqmm2;�ibp2 bmi2;2`b {0) |1 & 9 & *} q#2v ., )=1 0) > * urev h?2 +?qb+2 q7 !0 = [01 02 03 · · · 0. ]% bb �`#bi`�`v bq hqm; �b ur8v �m/ urev �`2 b�ibb}2/x h?2 t`qq7 bb ;bp2m bm �tt2m/bt exrx *q`qhh�`v 9xex 6q` * = 1h?2q`2k 9x8 b�vb i?2 2|q`2b+2mi 7mm+ibqm rbhh +qmp2`;2 iq x2`q b7 ! ! 2222 ' 2 '"2 -(") 2222 '" = 8 < % 1t�kth2 9xdx *qmbb/2` i?2 irq /bk2mbbqm�h f2`m2h *!" + = "("1)&"! 2 2 , r?2`2 i?2 `2+i�m;h2 7mm+ibqm bb "(") := 1 1 ; |" | & 1 2 0 ; |" | > 1 2 . urdv h?2m uqqh7`�k�ht?�x+qkkykyv ! !! 22222 73 7"32 *!" + 22222 '!" = ! % !1="% "("1)'"1 ! % !2="% 22222 '3 '"32 &"! 2 2 22222 '"2 = = 4 1 + 4&"3/2 . = 8 < % �m/ 01 + 02 = 0 + 3 > * = 2x h?2 +`bi2`b� bm h?2q`2k 9x8 �`2 k2i �m/ �bvktiqib+ +qmp2`;2m+2 q7 i?2 2|q`2b+2mi 7mm+ibqm iq x2`q bb �bbm`2/x �bvktiqib+ *qmp2`;2m+2 hq � 6bt2/ 6mm+ibqm �b i?2 7qhhqrbm; 2t�kth2 b?qrbi?2 2|q`2b+2mi 7mm+ibqm +�m +qmp2`;2 iq � }t2/ 7mm+ibqm q7 !" �b b+�hbm; bm+`2�b2bx 1t�kth2 9x3x *qmbb/2` i?2 qm2 /bk2mbbqm�h f2`m2h -(") = &"!:(") ur3v 6b;m`2 rn, lbbm; i?2 2ttqm2mib�h /2+�v f2`m2h bm ur3v `2bmhib bm i?2 4, (")ƕb b?qrmx �b 3 * %i?2 7mm+ibqm �tt`q�+?2b i?2 b�riqqi? b?qrm #v i?2 i?b+f `2/ hbm2 ;bp2m #v urnvx u6q` i?bb thqi( = 275xv r?2`2 :(") bb i?2 >2�pbbb/2 bi2t 7mm+ibqmxrj h?2m 4, *!" + +qm@ p2`;2b bm bi2�/v bi�i2 iq i?2 bqhb/ `2/ b�riqqi? r�p27q`k b?qrm bm 6b;m`2 rnx lim ,*% 4, (") = 1 2 " " ( ; 0 < " < ( urnv � t`qq7 bb ;bp2m bm �tt2m/bt exkx �bvktiqib+ gbkbi *v+h2 s2`bq/b+biv bm 3 1|q`2b+2mi 7mm+ibqmb +�m #2 �bvktiqib+�hhv t2`bq/b+ �b � 7mm+@ ibqm q7 i?2 2tt�mbbqm b+�hbm; p�`b�#h2 3x h?2q`2k 9xnx lbbm; i?2 b+�h�` t2`bq/b+biv k�i`bt q = ( i?2 qm2 /bk2mbbqm�h f2`m2h -(") = " (") `2bmhib bm � 2|q`2b+2mi 7mm+ibqm t2`bq/b+ bm 3 rbi? � t2`bq/ q7 (, = 2( x s`qq7x h?2 qm2 /bk2mbbqm�h 6qm`b2` b2`b2b 2tt`2bbbqm 7q` i?2 rk6q` . = 5 �m/ !" = [4 0 1]! 7q` 2t�kth2-3 $4 #=1 /%# /! %# # 5 0 *!! + = /5 /!4 1 /!3 0 *!! + . rj1[m�h iq qm2 7q` tqbbibp2 �`;mk2mi �m/ x2`q qi?2`rbb2x jy hbhbm; 1|q`2b+2m+2 q7 1tt�m/bm; e2`m2hb bm � 6bt2/ s2`bq/b+ �``�v, :2m2`�hbxbm; i?2 6hqr2`@p7@gb72 2|q`2b+2mi 7mm+ibqm bb 4, (") = 3 ( , '!0 sinc -3+ ( . &"2#'!/% . ukyv r?2`2 sinc(%) := sin(1%) 1% bb i?2 qm2 /bk2mbbqm�h 6qm`b2` i`�mb7q`k q7 "(")x 6q` + ! 0i?2 +i? 6qm`b2` b2`b2b +q2{+b2mi bb 5, [+] = 3/ -3+ ( . = 3 ( sinc -3+ ( . = = 1 ( sin * #', % + 1+ "2+�mb2 q7 i?2 bbm i2`k5, [+] bb t2`bq/b+ rbi? `2bt2+i iq 3 rbi? t2`bq/ 2( x 5,+2% [+] = 5, [+] abm+2 �hh q7 i?2 6qm`b2` b2`b2b +q2{+b2mib bm ukyv �`2 t2`bq/b+ rbi? t2`bq/ 2( r2 +qm+hm/2 i?�i 4,+2% (") = 4, ("). �m/ i?2 2|q`2b+2mi 7mm+ibqm qb+bhh�i2b �b � 7mm+ibqm q7 3x ! h?2 t2`bq/b+biv q7 4, (") bb bhhmbi`�i2/ bm 6b;m`2 kyx h?2 7mm+@ ibqm bb #qmm/2/ #v |4, (") | & 1 �m/ bb thqii2/ qp2` � bbm;h2 t2`bq/x h?2 6b;m`2 #2;bmb rbi? �m �hh x2`q 7mm+ibqm k�`f2/ rbi? i?2 mmk#2` 0x 3 bm+`2�b2b � #bix 6q` i?2 7mm+ibqm k�`f2/ 1i?2`2 bb mqr � b?q`i tqbbibp2 tmhb2 �m/ i?2 `2k�bm/2` q7 i?2 7mm+ibqm bb x2`qx abm+2 '4,( = 0�hh q7 i?2 7mm+ibqmb b?qrm ?�p2 x2`q �`2�x h?2 tmhb2 �i i?2 q`b;bm #2;bmb iq bt`2�/ �b 3 bm+`2�b2b �b bb b22m bm i?2 7mm+ibqmb k�`f2/ k i?`qm;? dx h?2m�i 3i?2 7mm+ibqm `2im`mb iq #2bm; b/2mib+�hhv x2`qx h?2 b2+qm/ t?�b2 bb b?qrm bm 6b;m`2 ky#x q2 #2;bm rbi? i?2 x2`q 7mm+ibqm k�`f2/ 3 bm 6b;m`2 ky� r?b+? bb �hbq k�`f2/ 3 bm 6b;@ m`2 ky#x 3 bm+`2�b2b � #bix h?2 7mm+ibqm k�`f2/ n bb � b?q`i m2;�ibp2 tmhb2x �b 3 bm+`2�b2bi?2 m2;�ibp2 tmhb2 rb/2mb �b bb b22m bm i?2 7mm+ibqmb k�`f2/ n i?`qm;? r8x 6mm+ibqm re bb b/2mib+�hhv x2`q �m/ bb i?2 b�k2 �b i?2 7mm+ibqm k�`f2/ y bm 6b;m`2 ky�x pm2 t2`bq/ bb +qkth2i2 �m/�b 3 bm+`2�b2bi?2 m2ti b/2mib+�h t2`bq/ #2;bmbx 9xj 1|q`2b+2mi 1t�kth2b h?2 kqbi bmi2`2bibm; q7 2|q`2b+2mi 7mm+ibqmb �`2 i?qb2 i?�i ?�p2 mq }t2/ �bvktiqib+ +qmp2`;2m+2 t`qt2`ib2bx am irq /b@ k2mbbqmbbm+? 2|q`2b+2mi 7mm+ibqmb +qmibmm�hhv #hqqk bm � mqm`2t2�ibm; k�mm2`x h?2 `2�/2` bb 2m+qm`�;2/ iq pb2r i?2 qmhbm2 pb/2qb ulv#�hkyr9/c lv#�hkyr9+c lv#�hkyr9#c lv@ #�hkyr9�v u2bt2+b�hhv i?2 2tt�m/bm; tbhh#qt +qm2 �m/ +b`+mh�` u�v h?2 }`bi t�`i q7 i?2 t2`bq/b+biv bm ,x u#v h?2 b2+qm/ t�`ix 6b;m`2 ky, h?2 t2`bq/b+biv bm 3 q7 4, (") 7q` 2tt�m/bm; `2+i�m;mh�` f2`m2hb bm ukyvx h?2 t2`bq/ bm 3 bb 2( x h?2 7mm+ibqm 4, (") bb �hbq t2`bq/b+ bm " rbi? t2`bq/ ( x oqhmk2 jabbm2 r 9x �l�guaaa jr +qm2 pb/2qbv iq 7mhhv �tt`2+b�i2 i?bb 2k2`;2m+2x a+`22m b?qib 7q` 2tt�m/bm; +b`+h2 �m/ +qm2 b?�t2/ f2`m2hb �`2 b?qrm bm 6b;@ m`2b jr9 �m/ r8x q2 mqr �m�hvx2 t`qt2`ib2b q7 i?2b2 irq f2`m2h ivt2bx q2 }m/ mb27mh i?2 `�/b�h k2�bm`2b ; = +!"+ �m/ < = + !%+ r?2`2 +!"+ = 6 "21 + "22 . ukrv q?2m i?2 p�`b�#h2 ; = ; ("1, "2) bb mb2/ bm � irq /bk2mbbqm�h 2tt`2bbbqmr2 �bbmk2 bi iq #2 � irq /bk2mbbqm�h 7mm+ibqm q7 "1 �m/ "2 �b 2tt`2bb2/ ?2`2x .qbm; bq �pqb/b r`bibm; qmi i?2 b[m�`2 `qqi 2tt`2bbbqm bm ukrv �i 2�+? mb�;2x h?2 p�`b�#h2 < = <(%1, %2) +�m bbkbh�`hv #2 bmi2`t`2i2/ �b � 7mm+ibqm q7 %1 �m/ %2x 1tt�m/bm; sbhh#qt *b`+h2 1t�kth2 h?2 2tt�m/bm; +b`+h2b 2t�kth2 bb � bt2+b�h +�b2 q7 u3v 7q` * = 2 /bk2mbbqmb r?2`2 i?2 f2`m2h -(!") bb qm2 bmbb/2 � +b`+h2 q7 mmbi `�/bmb �m/ bb qi?2`rbb2 x2`qxr9 -(!") = " ; 2 . . ukkv h?2m / (!0) bb bbkthv i?2 �`2� q7 � mmbi `�/bmb +b`+h2x 6`qk i?2 bb;m�h bmi2;`�h t`qt2`iv bm ukvx / (!0) = ! !! " ; 2 . '!" = 1. 6q` 2tt�m/bm; +b`+h2bi?2 2tt�m/bm; f2`m2h 7mm+ibqm bb #, *!" + = , !' " / +!" " q !++ 23 0 bq i?�i !!"q !' , . bm i?2 !+i? ibh2 bb � +b`+h2 q7 `�/bmb 3 +2mi2`2/ �i q !+x h?2 k. 6qm`b2` i`�mb7q`k q7 � mmbi `�/bmb +b`+h2 bm ukkv bb uj�`fb aakyynv / ( !%) = =1 (21<) 2< r?2`2 =1 (·) bb � }`bi q`/2` "2bb2h 7mm+ibqm q7 i?2 }`bi fbm/x �bvktiqib+�hhv u�#`�kqrbix �m/ ai2;mmrndkv =1 (21<) 2< "* 1*% <"3/2 21 cos / 21< " 3 41 0 ukjv r9at2+b}+�hhv7`qk i?2 /2}mbibqm q7 "( ·) bm urdv0 (!! ) = " (2/2) bb qm2 7q` & 2 < 1 2 x h?bb bb 2[mbp�h2mi iq 2 = +!! + = 6 !2 1 + !2 2 < 1 r?b+? /2}m2b � +b`+h2 q7 mmbi `�/bmbx bq i?�i7q` !+ ! !032/ (3p !+) = 32 =1 (213+p !++) 23+p !++ "* ,*% 1 21 7 3 +p !++3 cos / 213+p !++ " 3 41 0 h?2 bm{+b2mi +qm/bibqm q7 h?2q`2k 9x9 7q` +qmp2`;2m+2 q7 i?2 2|q`2b+2mi 7mm+ibqm iq x2`q bb i?2`27q`2 mqi k2ix sbhh#qt 1tt�mbbqm qm � >2t�;qm�h :`b/ q2 ?�p2 v2i iq bt2+b7v � t2`bq/b+biv 7q` i?2 2tt�m/bm; +b`+h2bx �bbmk2 i?2 +b`+h2 +2mi2`b �`2 bt�+2/ ?2t�;qm�hhv bm �++q`/�m+2 rbi? i?2 t2`bq/b+biv k�i`bt bm ujvx 6`qk u9v r2 b22 i?�i | det p| = 1 | det q| = 2# 3!2 . uk9v h?2 2tt�m/bm; f2`m2h 7mm+ibqmƕb k2�m7`qk uryvbb i?2`27q`2 '#,( = 32 / 2# 3!2 0 1 = 2132 # 3!2 a+`22m b?qib 7q` i?2 2|q`2b+2mi 7mm+ibqm bb b?qrm bm 6b;m`2 j 7`qk i?2 pb/2q �p�bh�#h2 qmhbm2 ulv#�hkyr9/vx 1tt�m/bm; *b`+mh�` *qm2b a2i i?2 irq /bk2mbbqm�h f2`m2h iq � +b`+mh�` +qm2 q7 mmbi ?2b;?ix *!" + = (1 " ;)" ; 2 . 6q` +b`+mh�`hv bvkk2i`b+ 7mm+ibqmbi?2 k. 6qm`b2` i`�mb7q`k #2+qk2b i?2 >�mf2h i`�mb7q`k uj�`fb aakyynv bq i?�i uqqh@ 7`�k�ht?�x+qkkykyv #2+qk2b / ( !%) = 21 ! 1 0 ; (1 " ;)=0 (21;<)'; uk8v = >0 (21<)=1 (21<) " >1 (21<)=0 (21<) 4<2 . r?2`2 >+ (·) �`2 ai`mp2 7mm+ibqmb uq2bbbi2bmkykyv �m/ =+ (·) �`2 "2bb2h 7mm+ibqmb q7 i?2 }`bi fbm/x am �tt2m/bt exjr2 b?qr i?�i 32/ (3p !+) "* ,*% " 2 12 8 33 +p !++ cos 213+p !++ " 1 4 . . ukev �b bb i?2 +�b2 rbi? i?2 2tt�m/bm; +b`+h2bi?2 +qm/bibqm q7 h?2q`2k 9x9 7q` +qmp2`;2m+2 iq i?2 k2�m 7q` i?2 2tt�m/bm; +qm2b bb i?2`27q`2 mqi k2ix 6q` �mv }t2/ p �m/ !+ ! !0i?2 hbkbi /q2b mqi �tt`q�+? x2`q �b 3 bm+`2�b2b rbi?qmi #qmm/x jk hbhbm; 1|q`2b+2m+2 q7 1tt�m/bm; e2`m2hb bm � 6bt2/ s2`bq/b+ �``�v, :2m2`�hbxbm; i?2 6hqr2`@p7@gb72 *b`+mh�` *qm2 1tt�mbbqm qm � >2t�;qm�h :`b/ �bbmk2 i?2 +qm2 +2mi2`b �`2 bt�+2/ ?2t�;qm�hhv bm �++q`/�m+2 rbi? i?2 t2`bq/b+biv k�i`bt bm ujvx h?mb r2 +�m mb2 uk9vx abm+2 =0 (0) = 1i?2 pqhmk2 q7 � +qm2 rbi? � mmbi +b`+h2 #�b2 �m/ mmbi ?2b;?i bb7`qk uk8v/ (!0) = 21 ! 1 0 ; (1 " ;)'; = 1 3 . h?2 2tt�m/bm; f2`m2h 7mm+ibqmƕb k2�m7`qk uryvbb i?2m '#,( = 32 / 2# 3!2 0 1 3 = 2 # 3132 !2 . �b r�b i?2 +�b2 7q` i?2 +b`+mh�` tbhh#qti?2 hbkbi /q2b mqi �tt`q�+? x2`q �b 3 bm+`2�b2b rbi?qmi #qmm/x a+`22m b?qib 7q` i?2 +qm2ƕb 2|q`2b+2mi 7mm+ibqm �`2 b?qrm bm 6b;m`2b r9 �m/ r8 7`qk i?2 pb/2q �p�bh�#h2 qmhbm2 ulv#�hkyr9+vx 8 *qm+hmbbqmb q2 ?�p2 bmi`q/m+2/ i?2 b/2� q7 t2`bq/b+ 2tt�m/bm; f2`m2h �m/ 2|q`2b+2mi 7mm+ibqmb �m/ ?�p2 b?qrm i?2v +�m /bbth�v rb/2hv p�`b�mi #2?�pbq`b /2t2m/2mi qm i?2 f2`m2h �m/ i?2 mm/2`hv@ bm; t2`bq/b+bivx 1t�kth2b �`2 ;bp2m q7 2|q`2b+2mi 7mm+ibqmb i?�i +qmp2`;2 iq x2`q+qmp2`;2 iq � mqm+qmbi�mi }t2/ tqbmi �m/ qb+bhh�i2x q?2m i?2 2|q`2b+2mi 7mm+ibqmb ~m+im�i2 rbi?@ qmi `2t2�ibm;t�ii2`mb `2kbmbb+2mi q7 +qmibmm�h #hqqkbm; +�m 2k2`;2x at2+b�h q++m``2m+2b 7q` � +b`+mh�` tbhh#qt f27q` q7 i?2 i?`22 t2i�h ;2qk2i`v `2t`2b2mibm; *?`bbib�mbivƕb i`bmbiv �m/ i?2 ~qr2`@q7@hb72x �hh 2k2`;2mi t�ii2`mb �`2 t2`bq/b+ �m/ +�m #2 mb2/ 7q` �`i7mh ibhbm;x e �tt2m/b+2b exr s`qq7 q7 h?2q`2k 9x8, *qmp2`;2m+2 iq i?2 k2�m h?2 /2`bp�ibp2 i?2q`2k q7 6qm`b2` �m�hvbbb bm/b+�i2b 3 .4 )=1 7"# 7""#) 5 *!" + ?�b � 6qm`b2` i`�mb7q`k q7 3 .4 )=1 ( ?21%) )"# 5 / ( !%) h?mb / ( !%) = 9 !! (/:. )=1 /%# /! %# # 0 *!" + ) &""2#!! ! !$'!" :. )=1 ( ?21%) )"# . �m/ |/ ( !%) | = 22229!! (/:. )=1 /%# /! %# # 0 *!" + ) &" -2#!!! !$'!" 2222 (21).̃ :. )=1 |% | "# ) = & 9 !! 2222 /:. )=1 /%# /! %# # 0 *!" + 2222 '!" (21).̃ :. )=1 |% | "# ) = = 8 (21).̃ :. )=1 |% | "# ) r?2`2 *̃ = ., )=1 0) . ukdv *qmibmmbm; 3. |/ (3 !%) | & 83. (213).̃ :. )=1 |% | "# ) �m/ 3. |/ (3p !+) | & 83.".̃ (21).̃ :. )=1 | (p)) !+ |"# . qbi? �hh qi?2` t�`�k2i2`b }t2/i?bb 2tt`2bbbqm i2m/b iq x2`q 7q` bm+`2�bbm; 3 r?2m * " *̃ < 0 q`mbbm; ukdv., )=1 0) > * exk s`qq7 q7 h?2q`2k 9x3, *qmp2`;2m+2 iq � }t2/ t2`bq/b+ 7mm+ibqm �tthvbm; i?2 2ttqm2mib�h f2`m2h bm ur3v iq u3v 7q` b+�h�` q = ( ;bp2b #, (") = %, '="% exp / " " " +( 3 0 :(" " +() = &"!/, %, '="% &'% /,:(" " +() oqhmk2 jabbm2 r _161_1l*1a jj pp2` i?2 t2`bq/ 0 & " < ( #, (") = &"!/, 0, '="% &'% /, . lbbm; � ;2qk2i`b+ b2`b2b #, (") = &"!/, 1 " &"% /, �m/ 4, (") = #, (") " 3 ( . 1tt`2bb i?2 2ttqm2mib�hb �b � i`mm+�i2/ h�vhq` b2`b2bx 4, (") = 1 " ! , + !2 2,2 % , " % 2 2,2 " 3 ( . �7i2` bqk2 k�mbtmh�ibqm 4, (") "* ,*% 3 * " " % 2 + + !2 2 ( * 3 " % 2 + "* ,*% 1 2 " " ( r?b+? bb i?2 /2bb`2/ `2bmhi bm urnvx exj s`qq7 q7 ukev, *qm2 +qmp2`;2m+2 h?2 ai`mp2 7mm+ibqmb mb2/ bm ukev +�m #2 /2}m2/ #v i?2b` h�vhq` b2`b2b uq2bbbi2bmkykyv >0 (.) = 2 1 %, )=0 ("1)) .2)+1 [(29 + 1)!!]2 �m/ >1 (.) = 2 1 %, )=0 ("1))+1.2) (29 " 1)!!(29 + 1)!! . h?2v ?�p2 i?2 7qhhqrbm; �bvktiqib+ #2?�pbq` uqqh7`�k _2@ b2�`+?kyky#v >0 (.) "* |( |*% 7 2 1. sin . " 1 4 . / 1 +@ / 1 .2 00 �m/ >1 (.) "* |( |*% 2 1 / 1 +@ / 1 .2 00 . gbf2rbb2i?2 "2bb2h 7mm+ibqm ?�b i?2 �bvktiqib+ #2?�pbq` uqqh7`�k _2b2�`+?kyky�v =0 (.) "* |( |*% 7 2 1. cos . " 1 4 . / 1 +@ / 1 .2 00 �m/ =1 (.) "* |( |*% 7 2 1. cos / . " 31 4 0 / 1 +@ / 1 .2 00 am hb;?i q7 i?2b2 #2?�pbq`bbmbt2+ibqm q7 ukev `2p2�hb i?2 >1 (.)=0 (.) i2`k �bvktiqib+�hhv /qkbm�i2b i?2 >0 (.)=1 (.) i2`k �m/ >1 (21<)=0 (21<) "* 1*% 2 12 < " 1 2 cos 21< " 1 4 . . h?mb 32/ (3 !%) "* ,*% " 2 12 8 33 < cos 213< " 1 4 . 7`qk r?b+? ukev 7qhhqrbx _272`2m+2b �#`�kqrbixj �m/ a � ai2;mm2/bx urndkvx >�m/#qqf q7 j�i?2k�ib+�h 6mm+ibqmb, qbi? 6q`kmh�b:`�t?b�m/ j�i?2k�ib+�h h�#h2bx oqhx 88x *qm`b2` .qp2` sm#hb+�ibqmbx �/�k�mibqb ukyrjvx �p�bh�#h2 mm/2` i?2 *`2�ibp2 *qk@ kqmb �ii`b#mibqm@a?�`2 �hbf2 jxy lmtq`i2/ hb+2mb2x m`h, ?iitb , f f +qkkqmb x rbfbk2/b� x q`; f rbfb f 6bh2 , *?bm� @ #2bdbm; @ 7q`#b//2m @ +biv @ sryyyr8d @ /2i�bhxdt;x /� obm+bg2qm�`/q ur9d3vx m`h, ?iitb , f f +qkkqmb x rbfbk2/b�xq`;frbfbf6bh2,g2qm�`/qn/�nobm+bn@ n*q/2tn�ih�mib+mbn7qhbqnjydpxdt;x .m/;2qm. 1 �m/ _ j j2`b2`2�m urn39vx jmhib/bk2mbbqm�h .b;bi�h ab;m�h s`q+2bbbm;x oqhx rx s`2mib+2@>�hh ab;m�h s`q@ +2bbbm; a2`b2bx 1m;h2rqq/ *hbzb, s`2mib+2@>�hhx 62h/f�ktg �g * .�pbb�m/ c q 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https://commons.wikimedia.org/wiki/file:floor_decoration_from_the_palace_of_king_ashurbanipal.jpg https://commons.wikimedia.org/wiki/file:floor_decoration_from_the_palace_of_king_ashurbanipal.jpg https://commons.wikimedia.org/wiki/file:flower_of_life_ephesos_square.jpg https://commons.wikimedia.org/wiki/file:flower_of_life_ephesos_square.jpg https://commons.wikimedia.org/wiki/file:flower_of_life_ephesos_square.jpg https://youtu.be/3pdmrwwphpg https://commons.wikimedia.org/wiki/file:cup_idalion_louvre_n3454.jpg https://commons.wikimedia.org/wiki/file:cup_idalion_louvre_n3454.jpg https://commons.wikimedia.org/wiki/file:cup_idalion_louvre_n3454.jpg http://youtu.be/vo-pwa1bsmg http://youtu.be/zojd8hc6d8e http://youtu.be/st3cczglmny http://youtu.be/st3cczglmny http://youtu.be/bxop5f0s33c http://robertmarks.org/reprints/1992-07_somepropertiesofthegeneralized.pdf http://robertmarks.org/reprints/1992-07_somepropertiesofthegeneralized.pdf http://robertmarks.org/reprints/1992-07_somepropertiesofthegeneralized.pdf http://robertmarks.org/reprints/1994-07_kernelsythesisforgeneralized.pdf http://robertmarks.org/reprints/1994-07_kernelsythesisforgeneralized.pdf http://mathworld.wolfram.com/struvefunction.html http://mathworld.wolfram.com/struvefunction.html https://en.wikipedia.org/wiki/heat_map https://en.wikipedia.org/wiki/heat_map https://en.wikipedia.org/wiki/penny_(united_states_coin) https://en.wikipedia.org/wiki/penny_(united_states_coin) https://en.wikipedia.org/wiki/penny_(united_states_coin) https://en.wikipedia.org/wiki/triquetra https://en.wikipedia.org/wiki/triquetra http://functions.wolfram.com/bessel-typefunctions/besselj/06/02/03/01/ http://functions.wolfram.com/bessel-typefunctions/besselj/06/02/03/01/ http://functions.wolfram.com/bessel-typefunctions/besselj/06/02/03/01/ http://robertmarks.org/reprints/1990-07_theuseofcone.pdf http://robertmarks.org/reprints/1990-07_theuseofcone.pdf about this journal the purpose of the journal paper submission policies other journal content from the editors sam s rakover and baruch cahlonsam s rakover and baruch cahlonwhen is explanation transitive? a methodological note introduction explanatory-transitivity discussion acknowledgments robert j. marks iirobert j. marks iitiling efflorescence of expanding kernels in a fixed periodic array: generalizing the flower-of-life introduction other expanding kernels properties of expanding kernels of varying periodicity analysis conclusions appendices letters and notes eric hollowaydeciding a bitstring of 1s is non-random is impossible in general jonathan bartlettproving the derivative of sin(x) using the pythagorean theorem and the unit circle j r millera response to clunn's axioms of morality jorge fernandezis information content a single, static quantity? news volume 2, issue 2 metaphor and meaning in the teleological language of biology annie crawford doi: 10.33014/issn.2640-5652.2.2.crawford.1 abstract in the early twentieth century, neo-darwinian evolutionary theory replaced traditional teleological causality as the accepted explanatory basis for biology. yet, despite this rejection of teleology, biologists continue to resort to the language of purpose and design in order to define function, explain physiological processes, and describe behavior. the legitimacy of such teleological language is currently debated among biologists and philosophers of science. many biologists and educators argue that teleological language can function as a type of convenient short-hand for describing function while some argue that such language contradicts the fundamentally ateleological nature of evolutionary theory. others, such as ernst mayr, have attempted to redefine teleology in such a way as to evade any metaphysical implications. however, most discussions regarding the legitimacy of teleological language in biology fail to consider the nature of language itself. since conceptual language is intrinsically metaphorical, teleological language can be dismissed as decorative if and only if it can be replaced with alternative metaphors without loss of essential meaning. i conclude that, since teleological concepts cannot be abstracted away from biological explanations without loss of meaning and explanatory power, life is inherently teleological. it is the teleological character of life which makes it a unique phenomenon requiring a unique discipline of study distinct from physics or chemistry. “teleology is like a mistress to the biologist; he dare not be seen with her in public but cannot live without her.” —j. b. s. haldane 1 introduction in the early twentieth century, neo-darwinian theory replaced traditional teleological causality as the accepted explanatory basis for biology. however, despite a public rejection of teleology, biologists continue to resort to the language of purpose and design in order to identify function, explain physiological processes, and describe behavior. biology textbooks, articles, and papers are indeed filled such explanations as “a flower produces perfume in order to attract pollinizers,” “the function of the heart is to pump blood,” or “felines have developed sharp protractile claws in order to hunt down prey” (galli and meinardi, 2011). to be meaningful, each of these claims depends upon reference to some kind of purpose. even on the cellular and molecular level, biologists rely liberally on the services of their intentional handmaiden, describing “insights into the ‘thought’ processes of a cell” and the “perceptual components of a cell” which are “making decisions about the appropriate use of resources” (hyduke and palsson, 2010). words that imply purpose, design, intention, and desire provide the standard language of biology, and yet both the legitimacy and the meaning of such teleological language is the subject of extended debate among both biologists and philosophers of science. some scientists and educators argue that teleological language can function as a type of convenient short-hand or heuristic device for describing biological forms while others argue that the employment of any such language contradicts the fundamentally ateleological nature of modern evolutionary theory. others, such as ernst mayr, have attempted to redefine teleology in such a way as to evade any metaphysical implications. in section 2 of this article, i will briefly consider the historical context of this debate and outline the sustained modern attempt to remove teleological concepts from biology. in section 3, i will then examine the claim that the teleological language of biology can be dismissed as superfluous heuristic metaphor and argue in response that this is true if and only if teleological metaphors can be replaced by alternative metaphors without loss of essential meaning. in section 4, i will consider whether teleological metaphors can be elimihttps://dx.doi.org/10.33014/issn.2640-5652.2.2.crawford.1 6 metaphor and meaning nated from biological discourse and demonstrate that every time teleological language is removed from biological explanations, it either jettisons important explanatory elements or still depends upon unstated teleological concepts that have been reintroduced through the backdoor. i conclude in section 5 that, since teleological concepts cannot be abstracted away from biological explanations without loss of meaning and explanatory power, life is inherently teleological. therefore, it is disingenuous to continue pretending that teleology is or can be divorced from biology. indeed, it is the teleological character of life which makes it a unique phenomenon requiring a unique discipline of study distinct from physics or chemistry. 2 the history of teleology in the biological sciences before directly entering into the contemporary debate over the role of teleological language in modern biology, it will prove helpful to understand the historical relationship between teleology and the study of life. the term ‘teleology’ derives from the greek word telos which aristotle defined as “the end, that for the sake of which a thing is done” (aristotle, physics, ii.3.). this end purpose for which something exists is also called its final cause and is one of the four fundamental causes included in aristotelian physics. teleological concepts include everything involved in the pursuit of an intrinsic, purposeful end: intentionality, purpose, design, motivation, direction, strategy, aims, goals, problems, solutions, invention, and agency. while e!cient causality, which aristotle defined as “the primary source of the change or rest,” (aristotle, physics, ii.3.) explains the source of movement, final causality explains the purpose for which the e!cient cause acted. thus, unlike e!cient causality, teleological causality implies the ability to imagine and plan for a future state of a"airs, an ability that can only exist within a mind or some other kind of non-physical or transcendent reality. while aristotelian science included the study of all four causes—material, e!cient, formal, and final—the founders of modern science began to exclude final and formal causes from their methodology. inquiries into the meaningful purpose of rocks and stars and basic elements seemed to obscure knowledge more than they aided it, for it is di!cult to ascertain with certitude the purposes for which a cosmic mind made the moon or the mountains. neither bacon nor descartes nor newton denied the existence of god or his causal activity in creating the world. however, in order to advance scientific knowledge, the founders of modern science endeavored to make a clear distinction between god as the first cause of the world and the secondary causes he set to govern the material world. in the cartesian separation of res extensa and res cogitans, e!cient causality—proper to the physical realm—was separated from the intention and purpose of mind which seemed proper only to the metaphysical realm. scientists gained reliable knowledge of the material world by isolating and determining the natural laws which function at all times and in all contexts regardless of intent or purpose. in order for empirical tests to yield such knowledge, the objects of scientific study must be reduced to the level of regular and therefore predictable laws and mechanisms. teleological causality, however, implying the personal agency and intentionality characteristic of psychic realities, is not predictable according to set and inviolable laws. this exclusive focus on e!cient causality proved incredibly successful, allowing technology to develop rapidly as scientists gained the knowledge necessary to manipulate the e!cient causes present in material entities toward our own practical ends. while the disciplines of physics and chemistry advanced through the elimination of teleological considerations, biological realities seemed inseparable from the concepts of design and purpose. even contemporary neo-darwinian materialists acknowledge that the appearance of design is what distinguishes the objects of biological study. richard dawkins famously defined biology as “the study of complicated things that give the appearance of having been designed for a purpose” (dawkins, 1996, pg. 1). jerry coyne opens his book, why evolution is true, with the observation that “if anything is true about nature, it is that plants and animals seem intricately and almost perfectly designed” (coyne, 2009, pg. 1). philosopher of science michael ruse also a!rms that “the key fact about organisms is that they are design-like, they exhibit final causes” (richards and ruse, 2016, pg. 35). until the nineteenth century, biologists generally accepted the teleological character of life at face value. life seemed designed because it was designed; life appeared purposeful because it was purposeful. immanuel kant also argued that teleology is the defining characteristic of biology which di"erentiates it from physics or chemistry. renowned twentieth century biologist ernst mayr describes kant as “a strict mechanist with respect to inanimate nature but a teleologist in the treatment of the world of life” (mayr, 1988, pg 59). according to kant, design, purpose, and intentionality are the features which distinguish life from non-life. moreover, kant did not believe that physical laws alone could ever account for the existence of these teleological qualities. in his critique of judgement kant boldly contends, it is quite certain that we can never get a su!cient knowledge of organized beings and their inner posvolume 2, issue 2 2. the history of teleology in the biological sciences 7 sibility, much less explain them, according to mere mechanical principles of nature. so certain is it, that we may confidently assert that it is absurd for men to make any such attempt, or to hope that maybe another newton will some day arrive to make intelligible to us even the production of a blade of grass according to natural laws which no design has ordered. such insight we must absolutely deny to mankind. (kant, critique of judgement, translated by james creed meredith) philosopher of science robert j. richards explains that kant believed life was irreducible to mechanical causes because for kant, “the design features of an organism cannot be explained mechanically, but must be assumed to have been the product of a plan, an idea” (richards and ruse, 2016, pgs. 160–161). since the many features of an organism function together in an intricately coordinated manner to create a purposeful whole, kant believed that life required intelligent foresight. according to kant, the idea for an integrated, purposeful whole must have existed prior to the coordinated arrangement of its parts. yet such an idea, a plan for the purposeful coordination of integrated parts, “could only be produced by an intellect. so the naturalist, in giving an account of the teleological features of organisms, must ultimately assume they have arisen because of a plan formulated by a powerful intelligence” (richards and ruse, 2016, pg. 161). since kant believed that organisms could not be fully explained by material and e!cient causality alone, he concluded that biology could not be a science in the same sense as physics. however, biologists have su"ered from what ernst mayr famously called “physics envy.” by the mid-eighteenth century, the modern scientific method had gained such philosophical, cultural, and technological power that many biologists endeavored to conform the study of life to the same methods of inquiry that served physics and chemistry so well. yet life continued to stare at her interrogators with a stubborn, purposeful intentionality and design that seemed irreducible to mere mechanism. thus, as mayr describes, “the history of the biological sciences from the seventeenth to the nineteenth centuries [was] characterized by a constant battle between extreme mechanists, who explained everything purely in terms of movements and forces, and their opponents, who often went to the opposite extreme of vitalism” (mayr, 1974, pg. 91). although kant had condemned biology to a sub-scientific status, michael ruse notes that “darwin was determined to show him wrong” (richards and ruse, 2016, pg. 34) and to raise biology to the status of a law-based science like physics and chemistry. when darwin published the origin of species, evolutionary theory was not new; his unique achievement was not to convince the world of universal common descent but to propose a plausible law-based, mechanistic explanation for the transmutation of species which then made an ateleological explanation of life possible. darwin’s theory of natural selection acting on random variations appeared to answer “the problem of final causes” (richards and ruse, 2016, pg. 37). ruse maintains that “for darwin natural selection is not just a cause, but a force in a kind of newtonian sense” (richards and ruse, 2016, pg. 44). in the “mechanism” of natural selection acting on random mutations, the teleological character of life finally appeared to be demystified and brought under the rule of physical laws and mechanical processes. while some scholars such as robert j. richards and j. scott turner argue that darwin never intended to strip biology of its vital, teleological character, his endeavor to discover the explanatory law ultimately led to the mechanistic, reductionist theory of life we know today. in retrospect, prominent biologist francisco ayala calls darwin’s “idea that the design of living organisms can be accounted for as the result of natural processes governed by natural laws” a “conceptual revolution” that “has forever changed how mankind perceives itself and its place in the universe” (ayala, 2007). although evolution itself was widely accepted, darwin’s mechanism of natural selection acting on random mutations did not become the prevailing explanatory principle in evolutionary biology until the modern synthesis of the mid-twentieth century. although biologists were not yet generally convinced that natural selection alone could fully account for the transmutation of species from a common origin, darwin had made a mechanistic explanation of life seem truly possible. the holy grail of biology, a completely mechanistic and materialistic explanation for the nature of life, now seemed inevitable. thus, according to science writer jonathan bartlett, as various theories contended for dominance, those biologists who continued to su"er acutely from physics-envy “were careful not to ascribe any purposefulness to organisms out of fear of being labelled as teleologists” (bartlett, 2017, pg. 3). in 1958, colin pittendrigh famously quipped that “biologists for a while were prepared to say a turtle came ashore and laid its eggs, but they refused to say it came ashore to lay its eggs” (pittendrigh, 1958, pg. 394). the scientific revolution had redefined science as the study of e!cient causality alone and biologists wanted to be ‘real’ scientists, so “despite the fact that it is obvious that turtles do indeed come to shore for the purpose of laying their eggs, biologists were uncomfortable with stating that plainly” (bartlett, 2017, pg. 3, emphasis mine). however, the development of a viable model for genetic in8 metaphor and meaning heritance appeared to vindicate darwin’s theory of natural selection. r. a. fisher, s. g. wright, and j. b. s. haldane devised statistical methods of analysis that reconciled the mutationism of mendelian genetics with the gradualism of darwinian evolutionism. as j. scott turner describes in his book, purpose and desire, adaptation or “fitness could now be dispassionately and precisely expressed as the tendency of an allele to replicate” (turner, 2017, pg. 150). natural selection acting on gene variation seemed able to explain the “appearance” of designed organisms apart from any real teleological, that is metaphysical, cause. this modern synthesis of darwin’s mechanism of natural selection with modern genetic theory seemed—for the moment—to solve the problem of final causes by providing a predictable, measurable, and testable mechanistic explanation for the development and functionality of life. after the triumph of neo-darwinism, teleological phraseology seemed either eliminable or able to be explained away, and biologists became freer with their language. it became safe for a biologist to say that “a turtle came ashore to lay her eggs," without worrying about implied metaphysical content. the purposiveness of organisms was reduced to a kind of epiphenomenon or secondary characteristic that could be fully explained by the law-based mechanism of natural selection acting on random mutations. according bartlett, “evolution itself cut any teleological connection between the organism and any higher organizing principle. because evolution proceeded by random or happenstance changes. . . there was no linkage between the results of evolution and any purposes within nature” (bartlett, 2017, pg. 3). random variations could account for the arrival of a new trait while natural selection accounted for the survival of the trait. this seemed to separate the creation of functionality from any kind of intentional design. since most teleological terms and phrases appeared drained of metaphysical implications, biologists felt increasingly free to indulge them. teleology seemed merely “a leftover relic that would soon go the way of alchemy” (bartlett, 2017, pg. 3). however, teleology has not died. as the discipline of biology has advanced, the mysteries of life have kept pace with our increase in knowledge, and what had for a moment seemed like a settled debate is far from over. although teleological causality has been excluded by definition from modern science, biologists continue to not only indulge but actually depend on teleological language. satisfying mechanistic explanations continue to evade biologists as life proves to be far more complex than bacon or descartes or darwin ever imagined. advances in biology have compelled scientists to increasingly reach for the language of purpose and design to explain the intricately ordered structures and dynamic systems found within even the simplest organisms. mechanistic, ateleological models have failed to provide the linguistic resources necessary to explain life. at the same time, strident materialists such as dawkins, dennett, hitchens, and many others have become more insistent on the purposeless, undesignedness of nature. thus, as biologists need teleological language more than ever to explain their new observations, the ideological pressure to reject such language is also intensifying. the debate over the role of teleology in biology has been revived. 3 teleological language is essential to biology ironically, the fact that scientists earnestly debate the legitimacy of teleological language in biology lends support to the claim that teleological language is essential to a meaningful and coherent explanation of biological phenomena. most modern biologists are so strongly committed to methodological naturalism that the use of teleological language, with all its messy metaphysical implications, would have indeed “gone the way of alchemy” and disappeared from biological discourse if it were inessential. that the language of purpose and design persists to annoy so many committed naturalists is itself evidence that the language of teleology is important to the study of life. in this section, i will first consider the common claim that teleological language functions merely as a decorative or heuristic metaphor that need not carry meaning into our theoretical understanding of life. in response to this objection, i draw from the linguistic philosophy of owen barfield, george lako", and mark johnson to argue against the possibility of “mere metaphors” in any kind of discourse. second, i will outline the arguments of those who claim that teleological language can and must be eliminated from biological discourse. using the work of ernst mayr and michael ruse, i will then demonstrate that it is impossible to remove teleological language or concepts from the discipline of biology. 3.1 teleological language as mere metaphor beginning with darwin, modern biologists commonly argue that teleological language is merely metaphor; it is a matter of words and not of concepts. many science writers and educators (especially those who work at a popular or introductory level) claim that our common sense, everyday language of intention and design has nothing to do with the real volume 2, issue 2 3. teleological language is essential to biology 9 truths of biology. teleological metaphors can be brushed aside as a “harmless figure of speech” (regenmortel, 2007, pg. 967) derived from our subjective experience as purposeful agents and thus are inessential to the objective nature of life. from this perspective, teleological language is employed decoratively for heuristic, educational, or rhetorical purposes; biologists simply use metaphors to translate between a true scientific understanding of the world and our colloquial ways of speaking about life. most who consider the language of purpose and design to be a “mere metaphor” in biology usually believe that such language could theoretically be removed from biological descriptions and explanations without altering their essential meaning. charles darwin himself dismissed his teleological language in the origin as mere metaphor. in his essay “charles darwin: rhetorician of science,” john angus campbell argues that darwin believed that his own metaphors functioned simply as non-essential rhetorical devices. according to campbell, “darwin’s public account of his metaphors creates the impression that his images could be replaced by literal statements if time were not a factor” (campbell, 1997, pg. 11). although darwin employed anthropomorphic images and intentional narratives when describing key aspects of his theory, he nonetheless “explained away his originality by insisting that his ideas were the result of ‘facts’ and his metaphors mere expressions of convenience” (campbell, 1997, pg. 6, emphasis mine). campbell claims that darwin’s concern for persuasiveness accounts for the “heavily metaphorical character of his thought” (campbell, 1997, pg. 10). darwin understood that in order to make a compelling case for the theory of natural selection, he would need to “appeal to common sense” and persuade “his peers and the wider community by using plain english words and plain english thoughts” (campbell, 1997, pg. 3). thus, darwin turned to the same rhetorical techniques of metaphor, personification, and poetic description which all persuasive writers employ. indeed, darwin’s use of metaphor in the origin enabled him to skillfully accommodate “his message to [both] the professional and lay audiences whose support was necessary for its acceptance” (campbell, 1997, pg. 3). however, darwin’s imagistic language caused confusion and was, according to campbell, “a center of controversy from the very first” (campbell, 1997, pg. 10). the “conventions of baconian induction and quasi-positivistic standards of proof,” which profoundly influenced nineteenth century understanding of science, created a tension between darwin’s imaginative language and the scientific idea he wished to defend. as campbell explains, his metaphorical images “lent his ideas popular appeal, but since they drew attention to themselves as images, explaining them away posed a distinct rhetorical challenge” (campbell, 1997, pg. 10). darwin clearly wanted to demonstrate that his theory was objectively true according to the quasi-positivist standards of modern scientific discourse, yet the progression of his argument frequently depended on imaginative speculation and metaphorical descriptions. in protest of these imaginative lines of argument, darwin’s staunch critic, the anatomist richard owen, complained that “we do not want to know what darwin believes & is convinced of, but what he can prove” (dear, 2006, pg. 102). darwin’s descriptions of the term ‘natural selection’ were especially problematic. many of the images darwin used to explain natural selection were teleological and therefore implied a goal-directed agency, yet his theory was purported to be an explanation based on the accepted scientific principles of material and e!cient causality, not old, discarded notions of final causality. in a later edition of the origin, darwin expressed surprise that “several writers have misapprehended or objected to the term natural selection.” he complained that some readers “have objected that the term selection implies conscious choice in the animals which become modified; and it has even been urged that as plants have no volition, natural selection is not applicable to them!” (darwin, 1860, pg. 81) darwin’s readers were confused, at least in part, because the term selection itself implies intentional agency, a mind that can choose one thing rather than another. if the biological realm were indeed driven by purely e!cient causes, then the language of choice—the idea that some natural force ‘chooses’ between the reproductive advantage of either organism a or organism b—should not be required. object x would simply cause y according to set, automatic laws. for example, the moon causes the earth’s oceans to move via tidal forces; there is no choice involved nor is the language of selection required to explain the phenomenon. peter dear maintains that because darwin’s “term retained the word ‘selection’. . . the old natural-theological sense of intelligent designfulness still lurked in the background” (dear, 2006, pg. 97). the term ‘natural selection’ gave darwin so much trouble that “he soon expressed the wish that he had used some other phrase that avoided the impression of conscious intent given by the word ‘selection’ ” (dear, 2006, pg. 111). however, darwin defended his metaphorical language by insisting that the meaning of a concept can be independent of the metaphors used to explain it. when criticized for his use of metaphors, darwin enigmatically responded “by pointing out that certain of his metaphors were in fact metaphors” (campbell, 1997, pg. 10). in the second edition of the origin, darwin concedes that, “in the literal sense of the word, no doubt, natural selection is a misnomer” (darwin, 1860, pg. 81). however, he protests that such metaphorical language is tolerated in chemistry and physics: “who ever objected to chemists speaking of the 10 metaphor and meaning elective a!nities of the various elements?—and yet an acid cannot strictly be said to elect the base with which it will in preference combine.” darwin implies the possibility of detaching a concept from its descriptive metaphor by complaining that “every one knows what is meant and is implied by such metaphorical expressions.” darwin justifies the use of metaphors whose meaning must be disregarded by claiming that they are “almost necessary for brevity.” while admitting that “it is di!cult to avoid personifying the word nature,” darwin suggests that given enough effort it is always possible to translate teleological language into metaphysically neutral statements. for example, he explains that by “nature” he means “only the aggregate action and product of many natural laws, and by laws the sequence of events as ascertained by us.” darwin trusts that “with a little familiarity such superficial objections” about the implied meaning of his metaphors “will be forgotten” (darwin, 1860, pg. 81). despite darwin’s protests, there remains a fundamental disconnect between what darwin claims to say about natural selection and what he actually said. campbell contends that it is “worth considering” why “the very connotations we are warned not to take seriously were instrumental in his ability to persuade both his professional peers and the general public” (campbell, 1997, pg. 10). darwin’s images and metaphors made his theory meaningful and persuasive, but they also carried implications he wanted his readers to ignore. darwin frequently personified natural selection— describing it as a power that can act, reject, economize, overmaster, disregard, succeed, seize upon, overcome, and govern—yet apparently assumed that his readers would disregard the implication of purpose and intention inherent to his verbs. the most famous passage of the origin is laden with teleological meaning; darwin imagines that “natural selection is daily and hourly scrutinising, throughout the world, every variation, even the slightest; rejecting that which is bad, preserving and adding up all that is good; silently and insensibly working, whenever and wherever opportunity o"ers, at the improvement of each organic being in relation to its organic and inorganic conditions of life” (darwin, 1859, pg. 27). it is the sense of intelligent, purposeful activity that gives this passage a compelling and coherent meaning, yet that is the very meaning we are supposed to ignore. thus, campbell concedes that “a certain disingenuousness was necessary for darwin to be persuasive” (campbell, 1997, pgs. 8–9). what campbell describes as “the distance between darwin’s public quasi-positivistic account of his metaphors and the actual use he made of figurative language”(campbell, 1997, pg. 11) is so great that modern scholars continue to vigorously debate as to whether or not darwin really intended to remove teleology from his theory of life. michael ruse and robert j. richards co-authored a book debating this very point. while ruse contends that “it was the whole purpose of his mechanism to eliminate or at least to render redundant” (richards and ruse, 2016, pg. 38) the world of teleology, richards argues that “we have mistakenly assumed that darwin banished final causes and notions of progress from biology” (richards and ruse, 2016, pg. 84). ruse seems to believe that darwin’s scientific ideas could be detached from his metaphorical language, for he weakly asserts that darwin’s anthropomorphisms were “no more essential than if we say something like ‘the eye is incredibly well designed’ ” (richards and ruse, 2016, pg. 46). while then acknowledging that “the eye is design-like in a way that the moon, for example is not,” ruse still maintains that such phraseology does not entail “an aristotelian vital force objectively out there in nature making for final causes” (richards and ruse, 2016, pg. 47). ruse dismisses the language of design as simply “our way of thinking about a mechanistic system.” however, richards objects to ruse’s suggestion that darwin’s language “was ‘merely’ metaphorical” (richards and ruse, 2016, pg. 155). richards states, “what i believe to be defective about ruse’s analysis of darwin’s theory is the assumption that metaphors are only decorative and can be safely ignored in the construction of a scientific theory. i believe they do real work” (richards and ruse, 2016, pg. 158). this continued confusion over the meaning of natural selection and the metaphysical implications of darwin’s theory demonstrate the problem with simply dismissing teleological language as “mere metaphor.” those scientists who follow darwin’s lead in considering their metaphors to be merely decorative additions that can be abstracted away from the meaning of the concept seem not to have thought very deeply about the nature of language. as the following discussion of linguistics will explain, robert j. richards rightly perceives that metaphors do real conceptual work, for the meaning of a concept is actually contained in the metaphor itself. 3.2 the meaning is in the metaphor rhetorical metaphors in biology cannot be ignored as inessential decoration because our conceptual language draws its meaning from metaphor. unless a term refers to a concrete object or activity, its meaning will be created and sustained through some kind of metaphorical reference. in poetic diction, philosopher and philologist owen barfield argues that “if we trace the meanings of a great many words. . . as far back as etymology can take us, we are at once made to realize that an overwhelming proportion, if not all of them, referred in earlier days to one of volume 2, issue 2 3. teleological language is essential to biology 11 these two things—a solid sensible object, or some animal (probably human) activity” (barfield, 1973, pgs. 63–64). all our words either directly refer to a concrete reality, such as a table or a falling leaf, or else draw their meaning from a metaphorical connection to some physical reality. as an example barfield o"ers the terms ‘abstract’ and ‘elasticity’ which “are both traceable to verbs meaning ‘draw’ or ‘drag’ ” (barfield, 1973, pg. 64).1 when we endeavor to think of what these conceptual terms mean, we may imagine something stretching like a form drawn in outline or a well-kneaded dough. admittedly, as we think or read a text, we are not normally conscious of our conceptual metaphors, yet our ability to use abstract language in meaningful ways is not a freedom from metaphor as such but rather the “power of changing the metaphors in rapid succession” (lewis, 2013, pg. 262). the metaphorical nature of human thought is why barfield’s oxford colleague c.s. lewis calls reason the organ of truth and the imagination the organ of meaning (lewis, 2013, pg. 154). while reason gives order and truth value to our thoughts, it is the imagination that gives content to our thought by mediating between our embodied experience and our thinking. abstract terms depend upon metaphors in order to have meaning, and these metaphorical meanings are not arbitrarily invented; they are rooted in our experience of the objective physical reality. the concepts to which our terms refer not only draw their meaning from metaphor, they are also metaphorically structured. in other words, we not only use metaphorical language to create meaning, we actually organize our thoughts through physically-based metaphorical models of the world. in their book metaphors we live by, george lako" and mark johnson argue that “the only reason our linguistic metaphors make sense is because our concepts are themselves metaphorically structured” (lako" and johnson, 2003, pg. 6). as embodied creatures, both our language and our ideas develop through our physical experience in the world.2 for example, we think of such ideas as 1of course, by connecting a word to our own lived experience, it is possible to correctly understand a term even when we do not know the original metaphorical meaning. for example, i may not know the ancient etymological connection between spirit and breath, yet my own observation of the same reality may lead me to independently connect breath with the word ‘spirit’. although ignorant of the original metaphor, i have not attained a meaning that is independent from all metaphor; i have given the term meaning through my own concrete experiences of the same reality. 2in the updated afterward to metaphors we live by, lako! and johnson maintain, “after twenty years of research by hundreds of investigators, vast bodies of empirical evidence for conceptual metaphor have been gathered from studies in a wide range of fields within the cognitive sciences. we initially had two primary sources of evidence— polysemy generalizations and inference generalizations. we now have at least seven other types of evidence derived from various empirical methods: (1) extensions to poetic and novel cases (lako! and turner happiness and health and power as being ‘up’ because our bodies literally droop and fall when they are tired, sick, or dead. thus, we speak of being “in top shape” or “feeling up today” or “being on top of the situation” (lako" and johnson, 2003, pg. 15). according to lako" and johnson, we are always conceptualizing “the nonphysical in terms of the physical” (lako" and johnson, 2003, pg. 59). as examples, consider the way we think of theories and arguments as buildings that can have a shaky foundation or a strong framework (lako" and johnson, 2003, pg. 46), or how we conceptualize love as a physical force that can have momentum or cause sparks (lako" and johnson, 2003, pg. 49). lako" and johnson o"er dozens of other examples as they contend that our “conceptual system, in terms of which we both think and act, is fundamentally metaphorical in nature” (lako" and johnson, 2003, pg. 3). scientific concepts and terminology are not exempt from this dependence on metaphor. biological language can be literal when describing concrete, sensible objects, which is why no one is confused over the meaning of terms such as ‘feather’ or ‘bullfrog’. however, abstract scientific concepts will depend on metaphor for meaning.3 barfield explicitly contends that all “linguistic symbols have a figurative origin; a rule from which high-sounding ‘scientific’ terms like cause, reference, organism, stimulus, etc., are not miraculously exempt!” (barfield, 1973, pg. 134, emphasis in original) lako" and johnson agree that the “so-called purely intellectual concepts, e.g. concepts in a scientific theory, are often—perhaps always—based on metaphors that have a physical and/or cultural basis” (lako" and johnson, 2003, pgs. 18–19). in his essay, “the language of nature,” stephen talbott quotes the mid-twentieth century philosopher kurt riezler as “chiding physicists with these words: “you use the word ‘force’ and, when queried, you define it by law, field, and vector; but what you really have in mind is the force you feel in commanding your muscles” (talbott, 2007, pg. 63, emphasis mine). riezler reminds scientists that they too must use metaphors in order to under1989); (2) psychological research, for example, priming studies (gibbs 1994; boroditzky 2000); (3) gesture studies (mcneill 1992); (4) historical semantic change research (sweetser 1990); (5) discourse analysis (narayanan 1997); (6) sign language analysis (taub 1997); and (7) language acquisition (c. johnson 1999). the importance of this evidence is that it comes from many di!erent methodologies and no longer rests exclusively on data from linguistic forms and inferences. these new sources have produced converging results concerning the way metaphor lies at the heart of abstract thought and symbolic expression.” (lako! and johnson, 2003, pgs. 248–249, adapted slightly for spacing). 3lako! and johnson argue that “our most fundamental ideas— not just time, but events, causation, morality, the self, and so on— were almost entirely structured by elaborate systems of conceptual metaphor. even the basic concepts of causation used in the physical and social sciences are primarily constituted by a system of nearly two dozen distinct metaphors, each with its own causal logic” (lako! and johnson, 2003, pg. 250). 12 metaphor and meaning stand what their mathematical models mean. the concept of force becomes what barfield calls “those verbal ghosts of the physical sciences” (barfield, 1973, pg. 140) unless we give it meaning by connecting the term metaphorically to our lived experience of the world. if both our language and our concepts are metaphorically structured, then there is no such thing as a ‘pure concept’. drawing from barfield’s argument, lewis concludes that we can have “either literalness, or else metaphor understood: one or other of these we must have; the third alternative is nonsense” (lewis, 2013, pg. 262). according to lewis, we never “really pass from symbol to symbolized, but only from one set of symbols to another” (lewis, 2013, pg. 261). therefore, contrary to the naïve protests of some scientists, we cannot simply disregard teleological metaphors as “nothing but linguistic expressions” or “a mere matter of words” (lewis, 2013, pg. 245). our linguistic options are to either talk about a literal entity (frog) or a metaphorically rooted concept (force). but if we attempt to make a clean break between a concept and its metaphor, we are not talking about anything. as richards argued in his debate with ruse, the meaning of a concept is in the metaphor. thus, biologists are fooling themselves when they try to construct an ateleological concept of life that is consistently expressed in terms of teleological metaphor. they are speaking nonsense. of course, the meaning of a certain metaphor may indeed be inessential to a particular concept if the concept can be adequately communicated through an alternative metaphor. according to lewis, a concept can possess meaning apart from a particular metaphor but only “in so far as these metaphors are optional: that is in so far as we are able to have the same idea without them” (lewis, 2013, pg. 258). for example, lako" and johnson discuss the metaphor “argument is war.” the metaphor of war is inessential to our concept of argument insofar as we can conceptualize an argument without reference to war. indeed, we can conceptualize an argument as more like a building or even a dance. argument does not have to be characterized by destructive conflict; it can be constructive or playful. however, if we could not fully conceptualize argument without constant recourse to the language of war, we must conclude that destructive conflict was essential to the nature of argument. lewis contends, “in so far as we cannot express the same idea apart from a given metaphor, so far it will be the unique expression, and therefore the iron limit of our thinking” (lewis, 2013, pg. 255). if we cannot talk about or conceptualize a particular idea without recourse to a specific metaphor, it is because the meaning gained by the metaphor is essential to the reality being explained. accordingly, certain metaphors can be helpful to scientists heuristically without being essential to the concepts being explained if the same concept can be conceptualized another way without the given metaphor. heuristic devices are important tools, and teleological metaphors need not always have teleological implications. as darwin rightly perceived, chemists can talk about “molecules wanting to have eight electrons in their outer shell” without students thinking electrons have actual desires. however, this is because the teleological metaphors of chemistry can be replaced by ateleological descriptions without losing any explanatory power. students can have an accurate idea of atomic structure without depending on the metaphor of desire. chemical bonding patterns are ultimately derived from mathematical equations that can be conceptualized without teleological language. we can say, for example, that “the forces present in an atom are equalized when it has eight electrons in the outer shell.” therefore, living organisms can be understood ateleologically if and only if it is possible for biological explanations to be conceptualized and communicated without teleological language. darwin could have justified his artificial selection metaphor, just as chemists can justify their heuristic “desire” metaphor, if he could have provide an adequate conception of natural selection without it. but he couldn’t. darwin depended upon the intentional model of artificial selection in order to explain how natural selection could provide an exogenic and therefore mechanistic cause of evolution that avoided the vitalism haunting endogenic explanations. in what darwin got wrong, jerry fodor and massimo piattelli-palmarini agree that “darwin was inadequately impressed by the fact that breeders have minds. . . whereas, of course, nothing of that sort [sic] is true in the case of natural selection. it would be startling, in light of this di"erence, if theories of the one could be reliable models for theories of the other” (fodor and piatellipalmarini, 2011, pg. xxi). since the meaning is in the metaphor, darwin could not make the teleological analogy of artificial selection work ateleologically just “by abstracting away the minds away” (fodor and piatelli-palmarini, 2011, pg. 116). while adaptationists continue to see artificial selection as a “harmless exegetical metaphor,” fodor and piattelli-palmarini maintain that it is “the putative analogy to artificial selection that bears the whole weight of adoptionism” (fodor and piatelli-palmarini, 2011, pg. 99). take away the mental causality and the whole ability to explain anything collapses. without teleology there is no way to construct a notion of natural selection “that isn’t just empty” (fodor and piatelli-palmarini, 2011, pg. 138), which is why what darwin got wrong opens with noam chomsky’s assessment that “it is perfectly safe to attribute [evolutionary] development to ‘natural selection’ so long as we realize that there is no substance to this assertion; it amounts to no more than a belief that there is some naturalvolume 2, issue 2 3. teleological language is essential to biology 13 istic explanation for these phenomena” (fodor and piatellipalmarini, 2011, opening page, emphasis mine). if neo-darwinists are to defend a truly ateleological theory of life, they will need to show that the language of purpose and design can be removed and replaced with ateleological metaphors that give coherent meaning to their explanatory model. if it proves impossible to eliminate teleological language from biological discourse, then we have good reasons to conclude that teleology—the realm of purpose, intention, desire, and design—is indeed essential to the nature of life. 3.3 teleology expelled: sacking biology’s mistress many scientists have intuited that metaphors do not function as harmless figures of speech and therefore actively contend for the removal of teleological metaphors from biology. uneasy with the language of purpose and design within a discipline that endeavors to explain the natural world through material causality alone, several prominent scientists argue that such language is misleading, incorrect, and the primary cause of the public’s failure to accept evolutionary theory. in his influential essay, “evolution and tinkering,” françois jacob demonstrates the way biologists expect their readers to ignore the very meaning on which their argument seems to depend. jacob describes the causal e!cacy of natural selection through language littered with intentionality and goal-directed agency. he describes natural selection as a force that “integrates mutations” and “orders them into adaptively coherent patterns” (jacob, 1977, pg. 1163). he explains that natural selection “gives direction” and “progressively produces” (jacob, 1977, pg. 1163, emphasis mine), doing “what it could with the materials at its disposal” (jacob, 1977, pg. 1164, emphasis mine). jacob explains how natural selection “adjusts” and “alters” and “arranges” an organism as it “tinkers” to create new life forms. all these verbs imply intentional, purpose-driven agency, the very qualities that neo-darwinianism is supposed to explain away. jacob’s presiding metaphor also implies teleology, although the analogy of the tinkerer was ironically conjured for the very purpose of denying purpose. jacob rejects the comparison of “the action of natural selection. . . to that of an engineer” because the latter, “in contrast to what occurs in evolution,. . . works according to a pre-conceived plan” (jacob, 1977, pg. 1163, emphasis mine). in other words, the metaphor of an engineer implies the real existence of a designing intelligence. instead, he explains the action of natural selection by comparing it to the action of a junk yard tinkerer who works with whatever random items he might find around him. although his tinkerer has “no special project in mind,” jacob’s analogy still obviously implies a process driven by intentionality and intelligence. in conclusion, after liberally employing anthropomorphic language and teleological metaphor to explain natural selection, jacob contradicts himself by claiming that “natural selection has no analogy with any aspect of human behavior” (jacob, 1977, pg. 1163, emphasis mine). jacob would have his readers ignore what his language means in their attempt to understand what he says. such passages are endemic in biological literature, which makes it no wonder that recent studies show that biology students as well as the public in general continue to interpret evolutionary processes as inherently goal-oriented. according to philosopher of science and science educators l.m. gonzález galli and e.n. meinardi, “comprehensive research in many di"erent countries has shown that students’ misconceptions are as diverse as they are abundant” (galli and meinardi, 2011, pg. 145). for example, galli and meinardi report that “many biology students believe that: acquired traits are inherited / the onset of the human species was predetermined / evolution implies progress / living organisms can change according to their needs” (galli and meinardi, 2011, pg. 146). these ideas imply a goaldirected view of the world which modern neo-darwinian theory flatly denies. in response to the public misunderstanding, dr. marc van regenmortel contends for the rejection of all “design phraseology,” which he sees as detrimental to progress in biological research. specifically, in his paper, “the rational design of biological complexity: a deceptive metaphor,” van regenmortel argues that “the design metaphor is shown to originate in human intentionality and in the anthropomorphic fallacy of interpreting objects, events, and the behavior of all living organisms in terms of goals and purposes” (regenmortel, 2007, pg. 965). while it is natural for humans to use teleological language, since purposeful action is intrinsic to our way of experiencing the world, van regenmortel maintains that the language of design wrongly projects the human experience of intentionality and foresight onto what we otherwise know—through neodarwinian theory—to be mindless physical entities. according to van regenmortel, “a biological function does not entail design for that function and functional descriptions need not be based on psychological notions of design, intention, and purpose” because functionality develops “blindly through the increased survival and reproduction of adaptive random variations” (regenmortel, 2007, pg. 967). accordingly, he argues that the language of design ought to be eliminated from biology because it can perpetuate “the un14 metaphor and meaning scientific mental habit of supposing that objects or events have a purpose” (regenmortel, 2007, pg. 967). evolutionary biologist w. j. bock of columbia university also agrees that “the concept of design is inappropriate in biology and should be eliminated from all biological explanations” (bock, 2009, pg. 7). like van regenmortel, bock contends that all biological processes are fundamentally random and therefore ateleological and un-designed. while conceding that natural selection cannot be defined as strictly accidental, since selection is indeed aimed at survival and reproduction, bock maintains that natural selection acts subsequent to the random changes making evolutionary mechanisms ultimately driven by accidental, ateleological causes. like van regenmortel, bock contends that design terminology “carries with it too many undesirable connotations, such as the existence of a creator, and should not be used in evolutionary theory” (bock, 2009, pg. 8). furthermore, he acknowledges that even when teleological language is carefully nuanced and contextualized so as to specify an ateleological source for the appearance of design, “future workers frequently overlook this restriction and use the words in a broad, general way” (bock, 2009, pg. 8). precise, technical meanings are easily lost in the more natural and enticing language of intention, purpose, and design. for this reason, biologists themselves are tempted to use teleological language because the technical language is dull, unrelated to normal human experience, and does “not readily capture the reader’s attention” (bock, 2009, pg. 8). although bock humbly admits that his proposed substitute terms, “non-accidental and non-stochastic. . . are awkward and not really informative” (bock, 2009, pgs. 8–9, emphasis mine), still he contends that it is time to “drop all usages of design from evolutionary biology” (bock, 2009, pg. 9). in an editorial from the bioessays journal, editor-in-chief andrew moore echoes these concern and argues that using teleological language is “one of the worst things we can do” as biologists. he claims that the use of intentional, purposeful language in biology is “far from being ‘excusable short-hand’ ” but is rather “an important contributor to a false impression of evolution among many non-scientists” and thus “a major reason for the lack of public acceptance of evolution” (moore, 2011, pg. 237). when biologists speak of “strategies” or biological “problems” and “solutions,” it implies some kind of aim or target which ought to be met or which the processes of evolution are striving to meet. moore claims that any goal-oriented language which implies a movement “towards” something or “in order to” is misleading. such concepts imply intentionality, purpose, and desire—the very things which neo-darwinian theory purportedly explained away. therefore, moore insists that the anthropomorphic language of purpose must be removed from the discipline of biology in order to promote an accurate understanding of the evolutionary processes which ground our modern theory of life. arguing that biologists “must find alternatives to anthropomorphic terminology,” moore suggests new ways to describe biological phenomena without recourse to “motivation, design, or strategy” (moore, 2011, pg. 237). instead of describing how “nature solved this problem,” a verb which implies intention, purpose, and forethought, moore suggests explaining “how evolution resulted in x” (moore, 2011, pg. 237, emphasis mine). rather than “organism x evolved to exploit niche y,” ecologists should state that “organism x evolved and occupied niche y.” through careful attention to meaning, moore maintains that biologists can cultivate a metaphysically neutral language that will help resolve common misunderstandings of evolutionary theory as well as help the discipline of biology progress. 3.4 the mistress vindicated van regenmortel, bock, moore, and others who call for a purge of teleological phraseology are right to take the language of biological discourse very seriously. however, they fail to take language seriously enough. these scientists have only begun to wrestle with the degree to which their language carries teleological implications. upon closer examination, it becomes clear that even those who stridently oppose teleological language still cannot help but to continue employing it themselves. as the work of mayr and ruse will show, it is impossible to eliminate teleological terms and concepts from biological discourse. despite moore’s careful attempt to articulate his ideas in metaphysically neutral verbiage—that is, using language which in no way relies on an intelligence or a vital essence as a cause of material realities—most of his suggestions are still riddled with teleological implications. moore rightly observes that the “innocent little word ‘to’ ” implies an operative will which seeks “to” work “in order to” or “with the purpose of” (moore, 2011, pg. 237). to remove the purposeful agency implied by the devilish word “to” in the claim, “to accomplish metabolic process x, enzyme y evolved a specificity for z,” moore suggests that biochemists should instead state that “in accomplishing x, y concomitantly evolved a specificity for z” (moore, 2011, pg. 237). moore has rid himself of the pesky “to” but the word “accomplish” still implies some goal which an agent desired to work toward. accomplishment is an empty, meaningless term without the implication of a goal that can be attained. again, rather than describe structure x as “perfectly adapted to perform function y,” moore suggests that biologists should say “structure x very e!ciently performs y” (moore, 2011, volume 2, issue 2 3. teleological language is essential to biology 15 pg. 237). yet terms like “e!ciently” and “performs” still imply a particular goal. how could we di"erentiate e!ciently from ine!ciently unless some targeted process were used as the standard for our evaluation? and per-forms means to accomplish through the means of form. let us go further than moore: perhaps “e!cient” could mean “maximizing power utilization on this e"ect.” this will not work either, for maximization still implies a target functionality. perhaps “accomplish” could be changed to “enzyme y eventually transformed to a sustainable equilibrium under di"erent physiological constraints.” while “sustainable equilibrium” sounds less purposeful, the “innocent little word ‘to” ” has returned, and in the context of biology equilibriums are always purposeful. a living organism is di"erent from a rock because a rock passively yields to entropy and the other forces of physics and chemistry while an organism’s activity is directed toward fighting entropy and sustaining its own unique form of equilibrium. living things are defined by their active, systematic striving toward the goal of being themselves. life is fundamentally formal. this is why, as turner argues in purpose and desire, the concept of homeostasis is necessary for any coherent definition of life and any language that accurately describes the function of a living organism will carry with it teleological implications. like moore, paul kramer of duke university also uses teleological language to argue against using teleological language. in his editorial in the journal bioscience, kramer decries terms such as ‘strategy’ and ‘tactics’ as “philosophically objectionable,” for such language “misleads readers not trained in science who often mistake the metaphor for the truth” (kramer, 1984, pg. 405). however, when attempting to describe the ateleological evolution and nature of plant life, kramer still uses such terms as “compromises” and “regulating,” both of which imply some target toward which the organism strives. he credits natural selection with the ability of “screening” random variations in a way that “minimizes deleterious e"ects and maximizes advantageous e"ects” (kramer, 1984, pg. 405). screening for what? yet again, none of these terms make any sense unless they refer to a particular goal or purpose which can provide a normative foundation for why one variation would be advantageous while another is deleterious. unless there is a goal to achieve, a final cause, one cannot meaningfully distinguish between a success or a failure. and life is intrinsically a matter of success or failure, of life or death. teleological language has proved so di!cult to eliminate that even some neo-darwinists have come to its defense.4 in the second half of the twentieth century, ernst mayr argued extensively for the necessity of purposive language in 4see, for instance, galli and meinardi (2011, pg. 140). evolutionary biology. he observed that “we find in all organisms a fitting together of inborn actions or structures so perfect that one can hardly avoid such terms as ‘design’ or ‘purposefulness’” (mayr, 1976, pg. 31). frogs and daisies demonstrate a purposeful functionality that is absent from water molecules and limestone rocks. accordingly, ruse insists that “the metaphor of design continues to be appropriate in darwinian biology in a way that is not true of physics” (richards and ruse, 2016, pg. 47). mayr also agrees that design metaphors “express something important which is lost when teleological language is eliminated from such statements” (mayr, 1988, pg. 38). teleological explanations are necessary to the science of biology not only because organisms are themselves purposeful but also because organisms are historically contingent beings. mayr explains that biological “phenomena have a history and cannot be explained directly through a strictly causal mechanical explanation, as is possible for processes in inanimate nature” (mayr, 1988, pg. 59). there is no historical component to the rules which govern hydrogen and oxygen bonding; the chemicals simply have the properties they have in all times and places. the way organisms work, however, is historically developed. thus, biological explanations cannot be reduced to merely material and e!cient causes. when biologists endeavor to explain the laws of life, they are not only looking for how an organism functions now, they are also seeking explanations for why an organism came to function in a particular way. for a chemist or a physicist, how and why have the same answers. a chemist can explain why sodium nitrate bonds in a particular way by referring to the set laws of chemistry which determine how sodium nitrate bonds. while inanimate objects act according to set laws that do not vary according to time or place, animate beings demonstrate contingencies and variability. accordingly, mayr asserts that “it is no exaggeration to claim that most of the greatest advances in biology were made possible by asking ‘why?’ questions” (mayr, 1988, pg. 55). since organisms are historically contingent phenomena, biological explanations involve a kind of contingency with which physicists and chemists need not contend.5 at every level of life, we observe behaviors and processes that are not fully reducible to set, mathematically definable laws. how 5there is some controversy over the role of contingency in biological history. while some biologists such as stephen jay gould maintain that life could have evolved in many di!erent ways, or not at all, others like simon conway morris contend that evolutionary mechanisms are more deterministic and thus certain outcomes are largely inevitable. fodor and piattelli-palmarini assume determinism a priori but believe biological causality is so complex and multilayered that a unified predictive theory will be epistemically unavailable and that biologists will therefore still depend upon apparently contingent, historical explanations. 16 metaphor and meaning an organism functions does not answer why it functions in that particular way because—as the diverse abundance of organisms demonstrates—there is no physical law that dictates how life must work in all places at all times. this is why evolutionary theory provides the theoretical basis for all modern biology. unless species were in fact created by a direct act of god, why explanations must be answered by an evolutionary history. if biologists are not to answer the question “why do fish swim?” with the unscientific answer “because god wanted fish to swim,” they must seek some evolutionary explanation for why fish developed into swimmers. since historically conditioned, biological functions cannot be exclusively understood in terms of lawful necessity, teleological concepts must drive biological inquiry if theoretical questions are to be answered at all.6 as biologists cannot ask why a fish must swim, they ask why a fish can swim. in his essay “teleology: yesterday, today, and tomorrow,” michael ruse explains that “whether or not god stands behind the design-like nature of organisms, inasmuch as one is doing biology one is simply treating organisms as if they were designed” (ruse, 2000, pg. 226). biologists must use the concept of functionality to frame their inquiries, for the functional benefit of a certain adaptation is an essential part of explaining why that particular feature of the organism exists. as stephen talbott at the new atlantis explains, without a telos, a purposeful end in view, biologists cannot o"er any kind of meaningful explanation “because no one state of a"airs would be preferable to another or mean anything di"erent from another” (talbott, 2017, pg. 65). evolutionary explanations depend upon final causes in order to describe how a particular feature contributes to the benefit of the whole organism. according to ruse it is “because, and only because, evolutionary biologists think of organisms as if they were humanly-made artifacts can they produce answers to questions about the ways in which these organisms survive and reproduce; that is to say, can they produce answers about the ways in which natural selection functions in the organic world” (ruse, 2000, pg. 230). geologists do not ask for what purpose mt. fuji towers above the japanese skyline, but in order to study any organ or plant feature, a biologist must always ask for what purpose the feature exists. ruse goes so far as to insist that 6some evolutionary biologists, such as w. j. bock, disagree with mayr and ruse, arguing instead that the contingent nature of organisms can be explained through random or stochastic processes. however, as illustrated by the inability to purge biology of teleological language and concepts, recourse to randomness is really no explanation at all. to explain something by chance is the equivalent of arguing that it simply happened because it happened. as barfield remarked, it is the task of science to explain natural phenomena through its hypotheses, but “the concept of chance is precisely what a hypothesis is devised to save us from. chance, in fact, = no hypothesis” (barfield, 1988, pg. 64). “you cannot do biology without the metaphor” of design (richards and ruse, 2016, pg. 47, emphasis mine). therefore, the removal of teleological language from biology excludes information and concepts that are essential to accurate descriptions and meaningful explanations. mayr insists that “a crucial portion of the message of a teleological sentence is invariably lost in the translation” (mayr, 1988, pg. 55). for instance, mayr considers the following sentence: “the wood thrush migrates in the fall into warmer countries in order to escape the inclemency of the weather and the food shortages of the northern climates” (mayr, 1974, pg. 106). if biologists replace the words “in order to” with “and thereby,” they jettison perhaps the most important and interesting question of why the wood thrush migrates. mayr claims that “the majority of modern philosophers are fully aware of this and agree that ‘cleaned-up’ sentences are not equivalent to the teleological sentences from which they were derived” (mayr, 1974, pg. 107). the original statement implies a “goal-directed migratory activity” (mayr, 1974, pg. 106) but the purified sentence “is greatly impoverished” in “information content” and “casual strength” (mayr, 1974, pg. 107). by removing any sense of purpose or intention, the ateleological sentence excludes the possibility of a meaningful relationship between the organism, its behaviors, and its environment. the action of the wood thrush and the resulting state of a"airs appear to be happenstance, and the appearance of disconnection is not likely to stimulate fruitful investigation. while many biologists have “maligned” teleological language “as stultifying and obscurantist,” mayr maintains that “this is simply not true” since “the nonteleological translation is invariably a meaningless platitude, while it is the [teleological] statement which leads to biologically interesting inquiries” (mayr, 1974, pg. 107). ruse also analyzes “nonteleological translations” and claims that, not only are these statements lacking in important content, they still depend indirectly upon teleological concepts. the concept of purposeful design is used to construct all biological explanations even when scientists manage to cleanse their explanations of explicitly teleological language post hoc. scientists might be able to construct a non-teleological description of an organism’s features but only because one already knows the function. consider the wood thrush example given by mayr above: a biologist can only join the clause about southern migration and the clause about escaping food shortages because he first assumed that the change in habitat had a purpose. only by assuming a purpose could a biologist make inquiries into the function of the bird’s behavior. without this teleological assumption, no biological hypothesis could be formed. therefore, ruse asserts that even if “one’s finished formal theory makes no direct reference to the metaphor of design, volume 2, issue 2 3. teleological language is essential to biology 17 and thus eliminates the teleology. . . in order to achieve the end results one has had to use the metaphor with all of the teleological implications that it carries” (ruse, 2000, pg. 230). to illustrate his point, ruse considers a typical evolutionary explanation for the development of fins on stegosauri dinosaurs. to construct a nonteleological explanation, one would say that those stegosauri with more and more diamond-like-shaped fins were those that survived and reproduced, and those which did not have such fins did not. one could even go on to say precisely why it was that the successful stegosauri survived and reproduced: the more diamond-like fins acted as e!cient heat transfers, whereas those less diamond shaped acted as less e!cient heat transfers. there was a consequent di"erential reproduction of the respective possessors. (ruse, 2000, pg. 228) however, ruse asks “how did one know in the first place that the fins would or would not be e!cient for heat transference? the answer of course is because one has been relying on the metaphor of design!” (ruse, 2000, pgs.228–229) only by understanding the fin’s function in the organism can one then in retrospect “ferret out in which ways they work” (ruse, 2000, pg. 229) and construct an explanation that employs the past-tense language of e!cient causality. after using the metaphor of design to understand the functional features of an organism, a scientist might find a way to then “drop the metaphor-like talk,” but ruse maintains that really “one is not doing without it: one is simply not acknowledging it” (ruse, 2000, pg. 229). thus, according to ruse, this attempt to eliminate teleological language from biology “is all a little bit bogus. one is using a sleight of hand. first, one uses the metaphor with all of its teleological implications. then second, when once one has achieved the ends one desires, one drops the metaphor like an unwanted spouse and one pretends that one never had anything to do with it at all” (ruse, 2000, pg. 229). if teleological metaphors are necessary to the process of answering biological questions, then teleology is an essential part of the answer itself. it is deceptive to re-word our answers so as to deny the role teleology played in providing them. fodor and piattelli-palmarini take a di"erent approach to the problem of teleological concepts in biology (what they call the “selection-for” problem) but make the same essential point as mayr and ruse: a coherent, unified theory of life requires teleological causality. based on the problem of “free-riders” developed by gould and lewontin, fodor and piattelli-palmarini argue that without recourse to mentally based final causes, natural selection cannot distinguish between coextensive traits when selecting for fitness and, therefore, natural selection cannot function as the explanatory basis for evolutionary theory. because organisms are complex functional wholes, phenotypic traits are never presented to natural selection in isolation. long necks are coextensive with long esophagi and the ability to vocalize is usually coextensive with the ability to swallow. as gould and lewontin demonstrate, some of these traits are “free-riders” that were selected along with the adaptive trait. sometimes traits increase and persist in a population not because they are advantageous but just because they were there. how can natural selection explain the di"erence between a free-rider and an adaptive trait? fodor and piattelli-palmarini argue at length that freeriders pose an insurmountable problem for neo-darwinism; natural selection cannot distinguish free-riders from traits that are “selected-for” because natural selection cannot provide grounds for distinguishing between counterfactuals. since organisms are historically contingent beings, an explanatory theory of evolution must be able to decide between the statements “if x hadn’t been selected, then y would not have been selected either” and “if y hadn’t been selected, then x would not have been selected either.” but natural selection, like all mechanistic causes, cannot take past or future events into account, which means it cannot provide grounds for deciding among these kinds of counterfactuals. as fodor and piattelli-palmarini explain, “counterfactual events cannot exert selection pressures: merely possible predators do not a"ect the evolution of a population (although, actual predators are quite likely to do so)” (fodor and piatelli-palmarini, 2011, pg. 113, emphasis mine). only a mind can imagine future scenarios and thus distinguish between counterfactuals. appeal to the mental causes in the breeder can distinguish between the selectionfor thicker wool and the free-rider of curly wool that may accompany it, but if natural selection is to provide an ateleological theory of life, it cannot likewise appeal to a mind in order to solve the “selection-for” problem presented by the coextensive traits of organisms. because it cannot account for counterfactuals, “the theory of natural selection cannot predict/explain what traits the creatures in a population are selected for” (fodor and piatelli-palmarini, 2011, pg. 110). according to fodor and piattelli-palmarini, the inability to distinguish counterfactuals is why attempts to remove teleology result in tautological explanations while purpose, desire, and intentionality are brought in the back door to provide narrative accounts of evolutionary changes. for example, hearts pump blood but they also make noise. which 18 metaphor and meaning trait is selected for fitness and which trait is a free-rider? we instinctively choose the ability to pump blood as the trait “selected-for,” but that is because, as ruse argued, we assume a purpose in order to explain “selection-for.” however, if we remove the assumption of intentionality, adaptationist explanations become question begging. if we ask why the heart pumps blood, the explanation cannot be that natural selection selected this trait for its fitness. the fitness of the heart was already at work before natural selection could select it. thus, it is the teleological concepts, the clear purpose of the heart and it’s functional design, that actually provide the explanation for the trait’s fitness; biologists only clandestinely credit the fitness to natural selection post hoc. remove the teleology, and all that remains is the same tautology that dogs all adaptationism (fodor and piatelli-palmarini, 2011, pgs 131 and 145). being “selected-for” an adaptation cannot be the cause of the adaptation that is being selected just as being a bachelor cannot be the cause of being unmarried. theoretical explanations are empty if they prove merely definitional. fodor and piattelli-palmarini conclude that a theory which cannot explain the phenomena studied is a dead, empty theory. darwinism has not dissolved traditional teleology; it is “intentionality that is the universal acid dissolving the neo-darwinian modern synthesis” (fodor and piatelli-palmarini, 2011, pg. 132). however, because they are a priori unwilling to return to a teleological explanation, fodor and piattelli-palmarini opt to conclude that there “can be no general theory of evolution” (fodor and piatelli-palmarini, 2011, pg. xxii). haldane was correct; biologists cannot live without their ill-reputed mistress. the language of purpose and design cannot be simply dismissed as harmless figures of speech nor can it be eliminated without a significant loss of explanatory power. teleological language is essential to a meaningful and coherent explanation of biological phenomena and it is impossible to conduct meaningful biological inquiry and discourse without it. to describe purposeful agents, a language of purpose will be required. despite over a century of e"ort, talbott contends that “it is no more possible than it was two hundred years ago to construct a single paragraph of proper biological description that does not draw on meaningful language of living agency considered improper in chemistry or physics” (talbott, 2010b, pg. 47). and because language is rooted either directly or metaphorically in our concrete experience of the world, language itself leads us toward truthful insight into nature.7 remarking on ruse’s argument in “teleology: 7the view of language argued in section 3 of the present essay supports a moderate form of scientific realism, that is the idea that science can give us real knowledge of the objective world. even if, as yesterday, today, and tomorrow,” galli and meinardi concede that “as long as it is not possible to explain adaptation phenomena without resorting to the metaphor of design (evidently teleological), then both the phenomenon to be explained and the explanations themselves are, in a relevant sense, teleological” (galli and meinardi, 2011, pg. 150). it now remains to determine the full meaning of this teleological language. can ‘teleological’ be conceptualized in such a way as to remove the metaphysical implications which seem so antithetical to modern biological theory? or does re-admitting the language of purpose and design pose an insurmountable problem to naturalistic explanations of life? 4 if teleological language is essential to biology, then life must be teleological in this section, i will argue that since teleological language is essential to a meaningful and coherent explanation of biological phenomena, life must be inherently teleological. biologists and philosophers of science who accept the need for teleological language object to this conclusion in two primary ways, either by attempting to redefine teleology in such a way as to remove its metaphysical implications or by arguing that the cumulative evidence in support of universal common descent is su!cient to prove that life is reducible to material and e!cient causality alone. first, i will consider how attempts to redefine teleology inevitably fail to shake the implication of an originating mind. secondly, i will briefly consider the arguments for common descent and show how the claim that life cannot be teleological since it originated from a common ancestor simply assumes the conclusion it presumes to prove. these modern attempts to deny the teleological nature of life in the classical, metaphysical sense are not based on the study of life itself but from a priori commitments to materialist philosophy. while a growing number of biologists and philosophers of science agree that the language of design is essential for a coherent explanation of life, many still argue that such language can be redefined or “naturalized” in order to elimanti-realists argue, our scientific explanations are based on metaphorical models vulnerable to underdetermination, yet those metaphorical models are not arbitrary but grounded in reality because language is itself metaphorically grounded in our embodied experience of the real world. while science may not give us perfectly objective knowledge of the mind-independent world, yet neither is scientific knowledge purely subjective. volume 2, issue 2 4. if teleological language is essential to biology, then life must be teleological 19 inate the metaphysical implications of traditional teleology. since our conceptual language is metaphorical in nature, biologists need some ateleological metaphor that can ground and structure the meaning of an inanimate, unintelligent creative power in order to reject the metaphysical intelligence and intentionality integral to the traditional concept of teleology. if the anthropomorphic metaphor of mind-based design can be replaced by a di"erent metaphorical understanding of purposeful function, then perhaps we can coherently conceive of a mindless teleology that need not threaten methodological naturalism. this is precisely the proposal which ernst mayr made in the mid-twentieth century. mayr argued that teleology can be cleansed of its metaphysical implications by uprooting the anthropomorphic metaphor of mind and replanting teleology in the metaphor of the cybernetic program. in 1958, colin pittendrigh introduced the term ‘teleonomy’ as a metaphysically neutral replacement for teleology. by changing the su!x from –ology to –onomy, pittendrigh endeavored to distinguish between goal-oriented processes that imply a metaphysical causality and goaloriented processes that emerge as a secondary characteristic of e!ciently caused material organisms. at a time when biologists were afraid to say “a turtle came ashore to lay its eggs” (pittendrigh, 1958, pg. 394), pittendrigh believed that “the biologists’ long-standing confusion would be more fully removed if all end-directed systems were described by some other term; like ‘teleonomic’ ” (pittendrigh, 1958, pg. 394). a di"erent term would “emphasize that the recognition and description of end-directedness does not carry a commitment to aristotelian teleology as an e!cient causal principle” (pittendrigh, 1958, pg. 394). perhaps by using a di"erent term, biologists would remember that purpose and intention are not ontological qualities inherent in the turtle’s nature but only observed functional attributes that emerge from the complex material laws that truly govern biological phenomena. mayr adopted pittendrigh’s term and used concepts from the new field of cybernetics to explain how teleonomic explanations could be distinguished from teleological explanations and thereby freed from any metaphysical implications. mayr conceived of dna as the biological code that formed the program of life. according to mayr, “a program is (1) something material, and (2) it exists prior to the initiation of the teleonomic process” (mayr, 1974, pg. 101). first, a program must be materialized somehow if it is to be any kind of physical cause, which a program for life certainly must be. abstractions, such as the number 5, cannot exert a causal force in the material world, but embodied data such as a braille pattern or an encoded microchip can. second, the program must exist prior to its function. we can’t read a book that hasn’t been written and we can’t use software that hasn’t first been coded. the existence of a program prior to its function, or what mayr terms its “teleonomic process,” is essential to the definition of teleonomy. mayr thus defines ‘purpose’ and ‘function’ as processes which physically result after the code exists and exerts its e"ect on the material world. if a particular code originates from purely materialistic processes, then no metaphysical reality need be implied by the secondary ‘emergent’ function. for mayr, the functional e"ect which a program produces is totally independent from the way the program was formed. this crucial gap between life’s creation and life’s purpose is how mayr proposes to prevent any metaphysical realities from intruding into the realm of biology. because the randomly created program of life, dna, always exists prior to its emergent function—that is, the genotype is created before any kind of phenotype is then tested by natural selection—the final causality attached to traditional teleology is removed from the concept of teleonomy. according to twentieth century genetics, meaningless, chance mutations in the dna create the program code independent of any purposeful functioning. sometimes these di"erent sequences have an emergent e"ect that is beneficial to the organism. when this randomly occurs, natural selection then preserves the trait within the species because of its functional advantage. as mayr explains, the action of “natural selection is strictly an a posteriori process which rewards current success but never sets up future goals” (mayr, 1974, pg. 96). the functional features of organisms are preserved teleonomically but not created teleologically. in this way, mechanical processes appear to create functionality without any intentionality. there is no teleological purpose in the creation of life’s program—which is made by random, purposeless variations—but there is a teleonomic purpose in the program’s preservation. purpose in this teleonomic sense does not refer to an ontological purpose but only to an emergent functionality. mayr insists that “teleonomic explanations are strictly causal and mechanistic,” and thus, “the acceptance of a teleonomic explanation. . . is in no way in conflict with the laws of physics and chemistry. it is neither in opposition to a causal interpretation, nor does it imply an acceptance of supernatural forces in any way whatsoever” (mayr, 1974, pg. 92). the di"erence between a teleonomic and teleological purpose is the di"erence between an apparent telos—a function which emerged as the consequence of unrelated e!cient causes— and a causally active, ontological purpose rooted in the essential nature of the being. as bartlett phrases it, mayr’s principal claim is that “organisms do have purposes, but they didn’t arrive at their purposes through a purpose” (bartlett, 2017, pg. 4). 20 metaphor and meaning mayr’s teleonomic model appeared to have resolved the tension between the teleological nature of life and its assumed material origins by explaining how “natural selection itself turns accident into design” (mayr, 1976, pg. 43). françois jacob claimed that “the concept of program has made an honest woman of teleology” (jacob, 1973, pg. 9). the program metaphor seemed to give meaning and coherence to the new concept of teleonomy as it reduced life to a mechanistic reality ultimately explainable through material and e!cient causality alone. j. scott turner describes this alluring model succinctly: “organism as algorithm. life is code. evolution is modification of code. we are all beta versions of something, with infinite updates coming” (turner, 2017, pg. 211). however, mayr’s tidy and clever solution has two fatal problems: first, the program metaphor still carries metaphysical implications, and second, advances in the last two decades of biology have shown that life does not actually function like a computer program after all. the program metaphor fails to naturalize teleonomic explanations because programs still imply a mind as the originating cause. as philosopher of science stephen meyer explains: a computer user who traces the information on a screen back to its source invariably comes to a mind—that of a software engineer or programmer. the information in a book or inscriptions ultimately derives from a writer or scribe—from a mental, rather than a strictly material, cause. our experience-based knowledge of informationflow confirms that systems with large amounts of specified complexity (especially codes and languages) invariably originate from an intelligent source from a mind or personal agent. (meyer, 2004) when attempting to distinguish the new meaning of teleonomy from traditional teleology, mayr still exclusively depends on design metaphors. he refers to blueprints, instructions, loaded dice, ‘fixed’ number wheels, computer programs, and a clock—all of which are intentionally created by intelligent agents. while many biologists hoped that the new mechanical and information metaphors derived from computer technology would help set the study of life on firmly materialistic ground, in truth it has done just the opposite. all known sources of coded information to which we may meaningfully compare dna have been created by minds. furthermore, programs do not actually exist prior to function as mayr argued; in truth, a program’s function always first exists in the mind of the programmer. as turner points out, “anyone who has done any coding appreciates that an algorithm must do something, and that something usually begins as a desire somewhere in the mind of a coder” (turner, 2017, pg. 211). this is why teleological language always carries metaphysical implications; the functional coherence of a purposeful object requires foresight. those future outcomes can only operate in the present through the imaginative activity of an intelligent mind. a computer programmer has an idea for a design, a future outcome, which he uses to guide the process of programming. if biological phenomena display evidence of design, this implies the existence of some kind of transcendent mind or intelligent world soul capable of foresight on a cosmic scale. only through the existence of a metaphysical reality—something that can transcend the temporal march of the e!cient causes that govern physical reality—can teleological causality actually exist. in their paper, “why machine-information metaphors are bad for science and science education,” massimo pigliucci and maarten boudry recognize that program metaphors, which they term “machine-information metaphors” (pigliucci and boudry, 2011, pg. 460), are inherently teleological and consequently imply an intelligent cause. as committed materialists, pigliucci and boudry therefore argue stridently for the elimination of these misleading program metaphors. they claim that machine-information metaphors have not only “been grist to the mill of id creationism” (pigliucci and boudry, 2011, pg. 469) but have also been “deleterious for science education” and hindered biological research by misdirecting “what sort of research programs biologists ought to carry out and how” (pigliucci and boudry, 2011, pg. 466). accordingly, these authors argue that it is “time to dispense with them altogether” (pigliucci and boudry, 2011, pg. 469). ironically citing the work of lako" and johnson, pigliucci and boudry admit that “metaphorical thinking seems to be a biologically entrenched functional mode of our brains” (pigliucci and boudry, 2011, pg. 469). accordingly, they reason, as i have done, that biologists will need to use alternative metaphors to counter the metaphysical implications of machine-information metaphors. however, pigliucci and boudry confess that “we certainly have not found one that we would recommend as a replacement” (pigliucci and boudry, 2011, pg. 468). they tentatively o"er only a single alternative conceptual metaphor: that dna sequences can be likened to a recipe for a cake. this bizarre analogy (which has actually been used in a high school biology textbook, mader and windelspecht (2015, pg. 258)) still implies both a set of informative instructions for a particularly designed cake as well as an intelligent source for volume 2, issue 2 4. if teleological language is essential to biology, then life must be teleological 21 both the recipe and the ‘cook’ who is able to interpret and act upon the instructions for the purpose of making something to eat. while avoiding the limits of mechanistic thinking, this metaphor actually increases the teleological implications for life as it requires more intelligent involvement than a machine, which can, once created, function mindlessly. as with all e"orts to eliminate teleological language, the pressure to find an ateleological model for biology has been great, yet still there are no feasible alternatives available. all the metaphors that help to frame our understanding of the way organisms actually work carry teleological implications. analogies to watches, machines, factories, languages, computer code, blueprints, cake recipes, and mousetraps— all of these examples depend on an intelligent source as a cause. we have no direct, concrete experience with a purposeful entity arising through an unintelligent process. every known cause of functional design is an intelligent cause. the world simply a"ords no ateleological design from which biologists can draw to give meaning to a metaphysically neutral concept of teleonomy. furthermore, not only do program metaphors fail to inoculate biology from design arguments, but recent developments have shown that life does not actually function like a program. while the cybernetic models on which mayr based his teleonomic argument have o"ered important insight into the physiological dynamics of an organism, they do not accurately predict all organism behavior. although the genetic revolution appeared to promise the tidy reduction of life to a single dna code, the subsequent epigenetic revolution has quickly dispelled the myth of life as mere program. cellular development also depends on epigenetic processes unrelated to dna transcription and translation. these include glycosylation, the transfer of spatial information stored in the cellular membranes, bioelectric codes, three-dimensional folding of proteins, and others which biologists are only beginning to discover. none of these cellular processes can be directly coded for by dna sequences which themselves only code for proteins. rather than the dna serving as the dictating, cybernetic ‘master controller’ of the cell, it has become clear that dna simply serves as the stored blueprints for protein construction which the cell references as needed according to the discernment of the organism as a whole.8 there may be one other objection that can be raised against my second claim that if teleological language is essential to a coherent explanation of biological phenomena, then life 8it is beyond the scope of the present article to discuss the inadequacies of the program metaphor factors in detail. for more information, see part one of fodor and piatelli-palmarini (2011), talbott (2010a), or wells (2017). must be inherently teleological. although i have not explicitly encountered such an argument, one might claim that, based on the strength of evidence for common ancestry, we can simply assert that teleology can and ought to be redefined as teleonomic even in the absence of any ateleological metaphor that can conceptually structure this new understanding. based on the standard cumulative argument for common ancestry which draws from multiple non-darwinian lines of evidence such as biogeography, fossils, homology, embryology, and dysteleology9 one might argue that an alternative metaphor is not necessary because life itself gives us a direct experience of design originating from a mindless, purposeless source. although darwinian mechanisms may no longer be adequate to explain exactly how design can emerge from ateleological causes, based on evidence for common descent we know that they did. however, this objection only begs the real question at hand: are living processes teleological? evidence that organisms evolved from a common ancestor does not itself prove that such a process was ateleological. as discussed above, some philosophers and scientists such as robert j. richards accept common ancestry yet still argue that darwin conceived of natural selection and evolution as teleological processes. some biologists such as j. scott turner argue that evolutionary processes are better accounted for by teleological explanations. arguments for common ancestry do not adjudicate between a teleological or ateleological explanations of those evolutionary processes. furthermore, any direct observation we have of evolution at work is not an observation of de novo design creation, but simply the adaptation of pre-existing design, which can be interpreted in and of itself as a feature of an organism’s functional design, i.e. 9a recent paper in evolution: education and outreach, “teleology’s long shadow” by a. werth and d. allchin, comes close to making this argument. like pigliucci and boudry, werth and allchin acknowledge that teleology is endemic to biological discourse and that “teleology is deeply rooted in human cognition,” but still werth and allchin argue that “historical contingency (or “chance” or “accident”) natural selection as stepwise and local, changing environments, evolutionary “reversals,” vestigial structures, pleiotropy, genetic drift, evolutionary branching, and the role of teleonomic explanations” all show that teleological causality is imposed on biological phenomenon by human understanding rather than a reality observed in organisms (werth and allchin, 2020, pg. 2). most of these points have been addressed elsewhere in this paper, but i will here add a word regarding dysteleology. dysteleological arguments use examples of supposed ‘poor design’, such as the pandas stumpy thumb or the indirect route of the recurrent laryngeal nerve in humans, to argue that organisms could not be purposefully designed because any good cosmic designer would have created only perfect designs. such arguments at most rule out the existence of a mind that only allows the creation or evolution of optimal design, but most importantly, such arguments can actually only be made within the context of a teleological world. the idea of suboptimal design is only meaningful with a world of real design. dysteleolgical concepts are parasitical on design concepts and do nothing to actually explain away the reality of design. 22 metaphor and meaning the organism was designed to be adaptable. as teleological language has proven essential to a coherent explanation of biological phenomena, there seems no way to deny that life must be inherently teleological. arguments against this conclusion are based not on scientific evidence but on materialist assumptions that are brought to, not derived from, the study of life. the endeavor to remove teleological causality from biology began and remains an a priori philosophical commitment. 5 conclusion: life all the way down teleological language and concepts are essential to the study of life, and biologists compromise the integrity of their science when they deny the meaning of the very language on which their discipline depends. life appears purposefully designed because it is purposefully designed. the endeavor to redefine or remove teleology from the study of life is an attempt to deny what an organism essentially is: an animated, integrated being full of will and intention and purpose. stephen talbott in the new atlantis contends that “the misrepresentation of this organic coherence in favor of supposed controlling mechanisms is not an innocent inattention to language; it is a fundamental misrepresentation of reality at the central point where we are challenged to understand the character of living things” (talbott, 2010b, pg. 29). whether it is the dna that ‘regulates’ or ‘controls’ the functions of the cell or whether epigenetic factors ‘inform’ and ‘regulate’ the dna, what all these cellular descriptions imply is not merely the ‘appearance’ but the reality of design and purpose and intent. something beyond mere physical mechanisms, something metaphysical is at work at every level in the origin, development, and functioning of living organisms. this ‘something’ is what di"erentiates a living organism from a dead one. both a living and a dead organism have the same component parts, but the dead organism is the one fully yielded to the inanimate processes of physics and chemistry, not the living one.10 what makes a creature alive is its teleological process: a 10considering the di!erence between a living dog and a dead one, talbott writes, “virtually the same collection of molecules exists in the canine cells during the moments immediately before and after death. but after the fateful transition no one will any longer think of genes as being regulated, nor will anyone refer to normal or proper chromosome functioning. no molecules will be said to guide other molecules to specific targets, and no molecules will be carrying signals, which is just as well because there will be no structures recognizing signals. code, information, and communication, in their biological sense, will have disappeared from the scientist’s vocabulary” (talbott, 2010b, pg. 25, emphasis in original). material form animated by the striving of a unique being to become and remain itself. biology resists transformation into a “hard” law-based mechanistic science because it studies the realm of life wherein the laws of physics and chemistry mingle with the psychic realities of will and mind. it is the purposeful desires of the organism as a whole that guide and direct its interaction with the material world of e!cient causality. we observe physics and chemistry together with cognitive intention in living organisms. where living beings exist, no physical law can ever adequately predict and account for their real ability to exercise willful activity in the world. the more our biological understanding grows, the more we are confronted with the teleological nature of life. modern biologists have peeled back the skin of life, expecting to find robotic, mechanistic realities at work beneath the living exterior. however, as talbott explains, biologists have “plunged headlong toward the micro and molecular in their drive to reduce the living to the inanimate” only to “find unapologetic life staring back at them from every chromatogram, every electron micrograph, every gene expression profile. things do not become simpler, less organic, less animate” (talbott, 2010a, pg. 24). it is “life all the way down” (turner, 2017, pg. 181) to the molecular level where biologists still perceive the dynamic, intentional, responsive activity of a cognitive being animated by purposeful striving to become and be its unique self. references ayala, f j (2007). “darwin’s greatest discovery: design without designer”. in: proceedings of the national academy of sciences 104, pp. 8567–8573. doi: 10 . 1073/pnas.0701072104. barfield, o (1973). poetic diction: a study in meaning. middletown, ct: wesleyan university press. barfield, o (1988). saving the appearances. 2nd edition. middletown, ct: wesleyan university press. bartlett, j (2017). “evolutionary teleonomy as a unifying principle for extended evolutionary synthesis”. in: bio-complexity 2017.2, pp. 1–7. doi: 10.5048/bioc.2017.2. bock, w j (2009). “design: an inappropriate concept in evolutionary theory”. in: journal of zoological systematics and evolutionary research 47.1, pp. 7–9. doi: 10.1111/j.1439-0469.2008.00505.x. campbell, j a (1997). “charles darwin: rhetorician of science”. in: landmark essays on rhetoric of science: https://doi.org/10.1073/pnas.0701072104 https://doi.org/10.1073/pnas.0701072104 https://doi.org/10.5048/bio-c.2017.2 https://doi.org/10.5048/bio-c.2017.2 https://doi.org/10.1111/j.1439-0469.2008.00505.x volume 2, issue 2 references 23 case studies. ed. by r a harris. 1st edition. mahwah, nj: hermagoras press. coyne, j (2009). why evolution is true. new york: penguin. darwin, c (1859). on the origin of species, or the preservation of favored races in the struggle for life. 1st edition. london: john murray. darwin, c (1860). on the origin of species, or the preservation of favored races in the struggle for life. 2nd british edition. london: john murray. dawkins, r (1996). the blind watchmaker. 2nd edition. w. w. norton. dear, p (2006). the intelligibility of nature: how science makes sense of the world. chicago: university of chicago press. fodor, j and m piatelli-palmarini (2011). what darwin got wrong. new york: picador. galli, l m gonzález and e n meinardi (2011). “the role of teleological thinking in learning the darwinian model of evolution”. in: evo edu outreach 4.1, pp. 142–152. doi: 10.1007/s12052-010-0272-7. hyduke, d r and b ø palsson (2010). “towards genomescale signalling-network reconstructions”. in: nature reviews genetics 11.4, pp. 297–307. doi: 10 . 1038 / nrg2750. jacob, f (1973). the logic of life: a history of heredity. trans. by b e spillmann. princeton, nj: princeton university press. jacob, f (1977). “evolution and tinkering”. in: science 196.4295, pp. 1161–1166. doi: 10 . 1126 / science . 860134. kramer, p j (1984). “misuse of the term strategy”. in: bioscience 34.7. doi: 10.2307/1309624. lako", g and m johnson (2003). metaphors we live by. chicago: university of chicago press. lewis, c s (2013). “bluspels and flalansferes: a semantic nightmare”. in: selected literary essays. new york: cambridge university press. mader, s s and m windelspecht (2015). essentials of biology. 4th edition. new york: mcgraw-hill. mayr, e (1974). “teleological and teleonomic, a new analysis”. in: methodological and historical essays in the natural and social sciences. ed. by r s cohen and m w wartofsky. boston: reidel, pp. 91–117. url: https: //philpapers.org/rec/maytat. mayr, e (1976). “accident or design: the paradox of evolution”. in: evolution and the diversity of life. ed. by e mayr. cambridge, ma: harvard university press, pp. 30–43. mayr, e (1988). toward a new philosophy of biology: observations of an evolutionist. cambridge, ma: harvard university press. meyer, s c (2004). “the origin of biological information and the higher taxonomic categories”. in: proceedings of the biological society of washington 117.2, pp. 213– 239. moore, a (2011). “we need a new language for evolution. . . everywhere”. in: bioessays 33.4, p. 237. doi: 10.1002/bies.201190011. pigliucci, m and m boudry (2011). “why machineinformation metaphors are bad for science and science education”. in: science & education 20.5–6, pp. 453– 471. doi: 10.1007/s11191-010-9267-6. pittendrigh, c s (1958). “adaptation, natural selection and behavior”. in: behavior and evolution. ed. by a roe and g g simpson. new haven, ct: yale university press, pp. 390–416. regenmortel, m h v van (2007). “the rational design of biological complexity: a deceptive metaphor”. in: proteomics 7.6, pp. 965–975. doi: 10 . 1002 / pmic . 200600407. richards, r j and m ruse (2016). “debating darwin”. in: ruse, m (2000). “teleology: yesterday, today, and tomorrow”. in: evolution: education and outreach 31.1, pp. 213–232. doi: 10.1016/s1369-8486(99)00046-1. talbott, s l (2007). “the language of nature”. in: the new atlantis 15, pp. 41–76. talbott, s l (2010a). “getting over the code delusion”. in: the new atlantis 28, pp. 3–27. talbott, s l (2010b). “the unbearable wholeness of beings”. in: the new atlantis 29, pp. 27–51. talbott, s l (2017). “evolution and the purpose of life”. in: the new atlantis 51, pp. 63–91. turner, j s (2017). purpose and desire: what makes something “alive” and why modern darwinism has failed to explain it. new york: harpercollins. wells, j (2017). “why dna mutations cannot accomplish what neo-darwinism requires”. in: theistic evolution: a scientific, philosophical, and theological critique. ed. by j p moreland et al. wheaton, il: crossway, pp. 237–256. werth, a and d allchin (2020). “teleology’s long shadow”. in: evolution: education and outreach 13.4. doi: 10. 1186/s12052-020-00118-8. https://doi.org/10.1007/s12052-010-0272-7 https://doi.org/10.1038/nrg2750 https://doi.org/10.1038/nrg2750 https://doi.org/10.1126/science.860134 https://doi.org/10.1126/science.860134 https://doi.org/10.2307/1309624 https://philpapers.org/rec/maytat https://philpapers.org/rec/maytat https://doi.org/10.1002/bies.201190011 https://doi.org/10.1007/s11191-010-9267-6 https://doi.org/10.1002/pmic.200600407 https://doi.org/10.1002/pmic.200600407 https://doi.org/10.1016/s1369-8486(99)00046-1 https://doi.org/10.1186/s12052-020-00118-8 https://doi.org/10.1186/s12052-020-00118-8 about this journal the purpose of the journal paper submission policies other journal content from the editors annie crawfordannie crawfordmetaphor and meaning in the teleological language of biology introduction the history of teleology in the biological sciences teleological language is essential to biology if teleological language is essential to biology, then life must be teleological conclusion: life all the way down salvador cordovasalvador cordovafisher's fundamental theorem of natural selection isn't fundamental after all introduction: the problem of defining fitness absolute ``darwinian'' fitness vs. relative fitness mean and variance of relative fitnesses numerical examples to illustrate fisher's theorem discussion conclusion eric hollowayeric hollowaytutorial: bioinformatics basics introduction genetic code and sequence translation sequencing and assembly accessing data finding things with blast summary letters and notes eric hollowayyou cannot get meaning from randomness jonathan bartlettactive information is a specified complexity model eric hollowayevolution in the valley of illusions jonathan bartlettis active information applicable to biology? eric hollowayempirical active information news oqhmk2 jabbm2 k *qk2ibq�i2`�m/ "b; "�m; lm+h2qbvmi?2bbb _q#2`i a?2h/qm .pa, ryxjjyr9fbbbmxke9y@8e8kxjxkxb?2h/qmxr �#bi`�+i q2 �`;m2 i?�i i?2 +qbkqhq;b+�h q`b;bm@q7@hb72 t`q#h2k bb ib;?ihv +qmm2+i2/ iq i?2 q`b;bm@q7@r�i2` t`q#h2k#2+�mb2 hb72 bb mqi tqbbb#h2 rbi?qmi �#mm/�mi r�i2`x abm+2 +qk2ib �`2 �bi`qmqkb+�hhv /�`f �m/ +qktqb2/ q7 r�i2`�b r2hh �b tqbb2bbbm; kb+`q7qbbbhbi?2v �`2 �m mm/2`2bibk�i2/ +�m/b/�i2 7q` 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a2+f#�+?ttx jejĝj3nx /qb, ryxryydfnd3@n9@yyd@kn9r@9nkrx m`h, ?iit,ffrrrx `#btxbm7qf`#bfs.6f+qh2kyrkxt/7x a?2h/qm_q#2`i ukyr8vx ǳs`bkq`/b�h *qk2ib, "b; "�m; lm+h2@ qbvmi?2bbb.�`f j�ii2` �m/ gb72ǵx am, ambi`mk2mibj2i?@ q/b�m/ jbbbbqmb 7q` �bi`q#bqhq;v soaa us`q+22/bm;b q7 asa1 neyevx 1/x #v _ " >qqp2` 2i �hxneyey_x /qb, ryxrrrdfrkxkr3drryx m`h, ?iit,ffrrrx`#btxbm7qf `#bfs.6fbtb2r8�xt/7x am#`�k�mb�me�m/�br�kv ukyrevx ǳh?2 p`b;bm1pqhmibqm �m/ ab;m�im`2b q7 s`bkq`/b�h j�;m2ib+ 6b2h/bǵx am, _2tq`ib qm s`q;`2bb bm s?vbb+b dnxdtx ydenyrx /qb, ryxry33f yyj9@9338fdnfdfydenyrx ambbfbm/g2qm�`/ ukyy3vx h?2 "h�+f >qh2 q�`, jv "�iih2 rbi? ai2t?2m >�rfbm; iq j�f2 i?2 qq`h/ a�72 7q` zm�m@ imk j2+?�mb+bx gbiih2"`qrm � *qx q�;qm2`_q#2`iqbhhb�k 6qrh2`�m/ 6`2/ >qvh2 urnedvx ǳpm i?2 avmi?2bbb q7 1h2k2mib �i o2`v >b;? h2kt2`�im`2bǵx am, h?2 �bi`qt?vbb+�h cqm`m�h r93ttx jĝ9nx m`h, ?iit,ff �/b�#bx?�`p�`/x2/mf7mhhfrned�tcxxxr93xxxxjqx q2bbbj�/2hbm2 * 2i �hx ukyrevx ǳh?2 s?vbbqhq;v �m/ >�#b@ i�i q7 i?2 g�bi lmbp2`b�h *qkkqm �m+2biq`ǵx am, l�im`2 jb+`q#bqhq;v rtx rerrex /qb, ryxryj3fmkb+`q#bqhx kyrexrrex w2hƕ/qpb+?u� " urne9vx am, aqpb2i cqm`m�h q7 �iqkb+ 1m2`;v r9tx 3jx https://doi.org/10.1086/305846 https://doi.org/10.1086/305846 https://doi.org/10.1051/0004-6361/201526234 https://doi.org/10.1051/0004-6361/201526234 https://doi.org/10.1016/j.physa.2014.06.061 https://doi.org/10.1142/s0218301317020062 https://doi.org/10.1142/s0218301317020062 https://doi.org/10.1103/physrevlett.117.201101 https://doi.org/10.1038/nature19355 https://doi.org/10.1038/nature19355 https://doi.org/10.3847/0004-637x/819/2/129 https://doi.org/10.7566/jpscp.31.011034 https://doi.org/10.7566/jpscp.31.011034 https://doi.org/10.1073/pnas.2101314118 http://adsabs.harvard.edu/full/1933achph...6..110z http://adsabs.harvard.edu/full/1933achph...6..110z https://arxiv.org/pdf/2105.13544.pdf https://arxiv.org/pdf/2105.13544.pdf https://doi.org/10.1117/12.2187138 https://doi.org/10.1117/12.624092 https://doi.org/10.1117/12.624092 http://www.rbsp.info/rbs/pdf/spie05.pdf http://www.rbsp.info/rbs/pdf/spie05.pdf https://doi.org/10.1117/12.729094 http://www.rbsp.info/rbs/pdf/spie07.pdf https://doi.org/10.1117/12.802195 http://www.rbsp.info/rbs/pdf/spie08.pdf http://www.rbsp.info/rbs/pdf/spie08.pdf https://doi.org/10.1007/978-94-007-2941-4_21 http://www.rbsp.info/rbs/pdf/cole2012.pdf http://www.rbsp.info/rbs/pdf/cole2012.pdf https://doi.org/10.1117/12.2187110 http://www.rbsp.info/rbs/pdf/spie15a.pdf http://www.rbsp.info/rbs/pdf/spie15a.pdf https://doi.org/10.1088/0034-4885/79/7/076901 https://doi.org/10.1088/0034-4885/79/7/076901 http://adsabs.harvard.edu/full/1967apj...148....3w http://adsabs.harvard.edu/full/1967apj...148....3w https://doi.org/10.1038/nmicrobiol.2016.116 https://doi.org/10.1038/nmicrobiol.2016.116 kk *qk2ibq�i2`�m/ "b; "�m; lm+h2qbvmi?2bbb wrb+fv6`bix urnjjvx ǳ.b2 _qip2`b+?b2#mm; pqm 2ti`�;�h�fibb@ +?2m l2#2hmǵx am, >2hp2ib+� s?vbb+� �+i� ettx rryĝrkdx about this journal the purpose of the journal paper submission policies other journal content from the editors eugenio darbesioeugenio darbesioa corollary of the conant-ashby theorem applied to abiogenesis robert sheldonrobert sheldoncomets, water, and big bang nucleosynthesis introduction benefits of a magnetized big bang and dark matter comets consequences of primordial comets analysis conclusions acknowledgments robert j marks iirobert j marks iisolution of the grazing goat problem: a conflict between beauty and pragmatism background grazing goat problem solution grazing goat problem inversion final thought letters and notes eric holloway2d puzzle visualizations of boolean formulae jonathan bartlettthe products of hyperreal series and the limitations of cauchy products tom and elizabeth siewertfollowing the science news v1i2 volume 1, issue 2 damned if you do and damned if you don’t the problem of god-talk in biology textbooks stephen dilley and nicholas tafacory doi: 10.33014/issn.2640-5652.1.2.dilley.1 abstract we argue that a number of biology (and evolution) textbooks face a crippling dilemma. on the one hand, significant difficulties arise if textbooks include theological claims in their case for evolution. (such claims include, for example, god would never design a suboptimal panda’s thumb, but an imperfect structure is just what we’d expect on natural selection.) on the other hand, significant difficulties arise if textbooks exclude theological claims in their case for evolution. so, whether textbooks include or exclude theological claims, they face debilitating problems. we attempt to establish this thesis by examining 32 biology (and evolution) textbooks, including the big 12—that is, the top four in each of the key undergraduate categories (biology majors, non-majors, and evolution courses). in section 2 of our article, we analyze three specific types of theology these texts use to justify evolutionary theory. we argue that all face significant objections. in section 3, we step back from concrete cases and, instead, explore broader problems created by having theology in general in biology textbooks. we argue that the presence of theology—of whatever kind— comes at a significant cost, one that some textbook authors are likely unwilling to pay. in section 4, we consider the alternative: why not simply get rid of theology? why not just ignore it? in reply, we marshal a range of arguments why avoiding god-talk raises troubles of its own. finally, in section 5, we bring together the collective arguments in sections 2–4 to argue that biology textbooks face an intractable dilemma. we underscore this difficulty by examining a common approach that some textbooks use to solve this predicament. we argue that this approach turns out to be incoherent and self-serving. the poor performance of textbooks on this point highlights just how deep the difficulty is. in the end, the overall dilemma remains: god-talk or no god-talk? 1 introduction in his groundbreaking work, the structure of scientific revolutions, thomas kuhn argued that textbooks play a crucial role in educating both scientists and non-scientists about science. “[b]oth the layman’s and the practitioner’s knowledge of science is based on textbooks and a few other types of literature derived from them,” he wrote.1 on kuhn’s view, textbooks play a regulative role: they show citizens and scientists the contours of the field, including the puzzles that remain to be solved, what counts as an acceptable solution, proper procedures for arriving at these solutions, and the like. as kuhn memorably puts it, textbooks are “pedagogic vehicles for the perpetuation of normal science.”2 that is, they give readers the correct vocabulary, values, standards, and so on—all the goods of the regnant paradigm. textbooks even show readers how to think about the history of science, its cumulative progress to the present day, and its (glowing) prospects for tomorrow. in brief, textbooks are a window to the past, a guide to the future, and a defining ideal of the present. on kuhn’s view, they show us what science is. it comes as something of a surprise, then, that quite a few biology textbooks articulate a paradigm that is beset by a theological muddle. the muddle itself centers on the presence (and absence) of theological claims in arguments for evolutionary theory. it turns out that difficulties arise either when god-talk is included or when it is excluded. in this article, we defend three primary claims. first, we argue that the presence of theology in biology textbooks is problematic. second, on the other side of the coin, we contend that the absence of theology in biology textbooks is likewise problematic. these two points lead directly to our third main claim: textbooks are thus left in a crippling dilemma—they are damned if they include theology and damned if they don’t. 1thomas kuhn, the structure of scientific revolutions, third edition (chicago: university of chicago press, 1996 [1962]), 137. 2kuhn, structure, 137. 38 damned if you do and damned if you don’t 1.1 textbooks our analysis focused on the following texts: • audesirk, teresa, gerald audesirk, and bruce e. byers. biology: life on earth, with physiology. 11th ed. boston: pearson, 2017. • barton, nicholas h., derek e.g. briggs, jonathan a. eisen, david b. goldstein, and nipam h. patel. evolution. 1st ed. cold spring harbor, ny: cold spring harbor laboratory press, 2007. • belk, colleen and virginia borden maier. biology: science for life. 5th ed. boston: pearson, 2016. • bergstrom, carl t., and lee alan dugatkin. evolution. 2nd ed. new york: w.w. norton, 2016. • brooker, robert j., eric widmaier, linda graham, and peter stiling. biology. 3rd ed. new york, ny: mcgraw-hill, 2014. • freeman, scott, kim quillin, lisabeth allison, michael black, greg podgorski, emily taylor, and jeff carmichael. biological science. 6th ed. boston: pearson, 2017. • futuyma, douglas j. and mark kirkpatrick. evolution. 4th ed. oxford, uk: oxford university press, 2017. • gunstream, stanley e. explorations in basic biology. 12th ed. san francisco: benjamin cummings, 2012. • hall, brian keith and benedikt hallgrimsson. strickberger’s evolution. 5th ed. sudbury, ma: jones and bartlett learning, 2014. • herron, jon c. and scott freeman. evolutionary analysis. 5th ed. san francisco, ca: benjamin cummings, 2014. • hillis, david m., david sadava, richard w. hill, and mary v. price. principles of life. 2nd ed. sunderland, ma: sinauer associates, 2014. • hoefnagels, marielle. biology: concepts and investigations. 4th ed. new york, ny: mcgraw-hill education, 2018. • krogh, david. biology: a guide to the natural world. 5th ed. boston: pearson, 2014. • mader, sylvia s. biology. 10th ed. new york: mcgraw-hill higher education, 2010. • mader, sylvia s. and michael windelspecht. essentials of biology. 4th ed. new york: mcgraw-hill education, 2014. • mason, kenneth a., george johnson, jonathan losos, and susan singer. understanding biology. 1st ed. new york, ny: mcgraw-hill, 2015. • miller, kenneth r. and joseph s. levine. miller & levine biology. boston: pearson, 2010. • morris, james et al. biology: how life works. 3rd ed. new york: w.h. freeman and company, 2019. • phelan, jay. what is life?: a guide to biology. 4th ed. new york: w.h. freeman and company, 2018. • raven, peter h., kenneth a. mason, jonathan b. losos, susan r. singer, and george b. johnson. biology. 10th ed. dubuque, ia: mcgraw-hill, 2014. • ridley, mark. evolution. 3rd ed. malden, ma: blackwell, 2011. • russell, peter j., paul e. hertz, and beverly mcmillan. biology: the dynamic science. 3rd ed. pacific grove, ca: brooks cole, 2013. • sadava, david, david m. hillis, h. craig heller, and sally d. hacker. life: the science of biology. 11th ed. sunderland, ma: sinauer associates, inc. 2017. • simon, eric j. biology: the core. 2nd ed. boston: pearson, 2017. • simon, eric j., jean l. dickey, and jane b. reece. campbell essential biology. 7th ed. new york: pearson, 2019. • singh-cundy, anu, michael l. cain, jennie dusheck, and richard symanski. discover biology. 5th ed. new york: w.w. norton & company, 2012. • shuster, michèle, janet vigna, matthew tontonoz, and gunjan sinha. biology for a changing world, with physiology. 2nd ed. new york: w.h. freeman and company, 2014. • solomon, eldra pearl, charles martin, diana w. martin, and linda r. berg. biology. 11th ed. australia: cengage learning, 2018. • stearns, stephen c. and rolf f. hoekstra, evolution: an introduction. 2nd ed. oxford, uk: oxford university press, 2005. • taylor, martha r., eric j. simon, jean l. dickey, kelly hogan, and jane b. reece. campbell biology: concepts and connections. 9th ed. new york: pearson, 2018. volume 1, issue 2 1. introduction 39 • urry, lisa a., michael l. cain, peter v. minorsky, steven a. wasserman, and jane b. reece. campbell biology. 11th ed. new york: pearson, 2017. • zimmer, carl, and douglas john emlen. evolution: making sense of life. 2nd ed. new york: w.h. freeman and company, 2016. while our analysis examined a variety of chapters in each textbook, we paid particular attention to two types of chapters (or sections). the first of these areas sought to articulate the historical context surrounding the advent of darwin’s theory. notably, authors invariably attempted to show the plausibility of darwin’s theory relative to other theories (or claims) available at the time. thus, these background sections function as part of textbooks’ overall justification of evolutionary theory as the correct account of biological unity and diversity. second, in a similar vein, we analyzed sections that directly presented the evidence and arguments for (contemporary) evolutionary theory. often these areas were simply labeled “the evidence for evolution.” in sum, instead of looking at one-off remarks here and there in a text, we especially focused on areas in which authors explicitly offered historical or contemporary material that they regard as firmly establishing evolutionary theory. it is in these areas that we often found theologyladen arguments and justifications.3 a critic might immediately demur, however. he might argue that the presence of theology is not really problematic. after all, any god-talk in biology textbooks is just window dressing. claims about ‘what a creator would do’ are only an historical element in the story of the rise of evolution; theological claims are not part of evolution’s epistemic justification—the real reasons why evolution is worthy of acceptance. that is, one might think that textbook authors use god-talk only for rhetorical effect, while the ‘real’ evidence for evolution lies elsewhere. on this view, ‘real’ evidence has to do with natural laws, entities, and processes, including natural selection, random mutation, homological similarities, and the like. creationism only enters the picture as a type of (historical) object lesson; it’s nothing more than an erstwhile and ersatz view that has been overcome by evolutionary theory and its explanatory success. by way of reply: there is a great deal to say on this score. in a sense, our article as a whole functions as a response to this objection. but for now, we offer a distinction that at least makes an initial step toward our broader case: there 3in addition, we are cognizant of the difference between explanations or illustrations of evolutionary theory, on the one hand, as distinct from epistemic justifications or arguments for that theory on the other. our focus is on instances of theology in the latter rather than the former. is a difference between the evidence for evolution per se versus the evidence for evolution as presented in textbooks. our goal is to examine textbooks as they portray the case for evolutionary theory. our task is not to analyze the case for evolution as it appears in some other medium or in an idealized form. rather, we focus on what textbooks actually say. whatever else might be the case, a reader can hardly be faulted for thinking that what appears in “the evidence for evolution” chapter (or section) is precisely what textbooks present as the evidence for evolution. so even if, in some proper sense, god-talk is irrelevant to the justification of evolution per se, this fact is beside the point. what matters for present purposes is the textbooks as they stand. 1.2 methodology before turning to the argument itself, however, a brief word about our methodology may be helpful. in particular, how did we decide which texts to include on our list? our primary interest is in undergraduate biological education in the united states. in this domain, there are three main categories: textbooks for biology majors, non-majors, and evolution courses, respectively. we intentionally included the top four textbooks in each of these categories in 20172018.4 thus, we directly examined the big 12. any study that purports to have robust conclusions must analyze the leading textbooks; that is precisely what we have done. yet we did not simply limit our study to the top titles in each category. in the interest of intellectual diversity, we wanted to hear more than just the most visible voices. as such, we looked at a range of books: some are recent, others are over a decade old; some are for high school, but most are for college; some are single author, others are multiple authors; some are alive and well, others are now discontinued; some are fairly basic, others much more advanced.5 and so 4while publishers tend to be cagey about releasing sales information, navstem helpfully tracks enrollment figures each year in biology courses (and their associated textbook selections) in over 350 colleges and universities across the united states. arguably, their data are the best available. see their market briefs for “biologymajors,” “biology for non-majors,” and “evolution,” respectively (www.navstem.com). according to their research, the top four titles in 2017-2018 in biology courses for majors are urry et al., campbell biology; freeman et al., biological science; morris, how life works; and sadava et al., life, respectively. the top four titles in biology courses for non-biology majors are taylor et al., campbell biology: concepts and connections; simon et al., campbell essential biology; phelan, what is life? ; and shuster, biology for a changing world, respectively. the top four titles in evolution courses are herron and freeman, evolutionary analysis; zimmer and emlen, evolution; bergstrom and dugatkin, evolution; futuyma and kirkpatrick, evolution, respectively. 5we did not exclude any book after consideration except for two 40 damned if you do and damned if you don’t on. readers familiar with the broad landscape of biology textbooks will recognize that our list nicely represents the field.6 1.3 other preliminaries a few other matters will clarify the terminology and scope of our study. first, we realize that a given textbook does not always say precisely what the author (or authors) believe. to some extent, textbooks represent combined efforts and compromises between authors, reviewers, the publisher, school boards, and so on. accordingly, when we use phrases like “textbook authors say” or “textbook authors believe,” we have in mind either the text itself or the relevant community behind it. second, by “evolutionary theory,” “darwinian evolution,” or just plain “evolution,” we mean the standard account found in biology textbooks, typically a contemporary version of darwin’s theory (i.e. an updated version of the modern synthesis). third, by “theology,” we mean propositions about any supernatural deity. these propositions need not be systematic, justified, or connected with any particular tradition. they need not approach the rigor or precision typical of professional theologians. instead, by “theology,” we simply have in mind propositions, of whatever sort, about any supernatural god. for stylistic variety, we will sometimes use the term “religious claims” (or something similar) instead of the term “theological claims.” fourth, it must be said that our argument does not imply that there is something wrong with evolutionary theory itself or with the comprehensive justification for it. simply because we contend that textbooks are caught in a debilitating dilemma does not imply that evolution cannot be defended elsewhere with greater vigor and precision. our concern is not with the theory itself nor its general grounding, but only with textbook accounts. finally, in what follows, by “the presence of theology” or “the absence of theology,” we actually have in mind the presence (or absence) of (i) theological propositions (ii) as part of the evidence for evolution—as part of a given argument or justification for evolutionary theory—in (iii) sections of biology textbooks that self-consciously provide grounds for the truth of evolution. but rather than spell out these three instances in which the books in question essentially mirrored the line of thought already found in other books we were considering. 6according to navstem, even if we consider only the big 12 textbooks, these alone comprise 64.7% of student enrollments in biology major, non-major, and evolution undergraduate courses in 2017-18. features every time, for brevity and stylistic reasons, we will abbreviate by using phrases like “the presence of theology” or “the absence of theology,” or even shorter phrases like “include theology” or “exclude theology,” and so on. the context should make matters clear in each case. 1.4 overall structure and thesis of the article having covered preliminaries, we now turn to a general map of our article, including a guide to our key claims. recall that our overall contention is that biology textbooks face an unhappy dilemma: problems arise if they include or exclude theology. we attempt to establish this claim in four parts. in section 2, we examine concrete examples of three different types of theology used to justify evolutionary theory in biology textbooks. we argue that all face significant difficulties. in section 3, we step back from concrete cases and, instead, explore broader problems created by having theology in general in biology textbooks. we argue that the presence of theology—of whatever kind—comes at a significant cost, one that some textbook authors are likely unwilling to pay.7 in section 4, we consider the alternative: why not simply get rid of theology? why not just ignore it? in reply, we contend that attempts to avoid god-talk raise difficulties of their own. for many textbooks, this option is equally unattractive. finally, in section 5, we bring together the collective arguments in sections 2–4 to argue that biology textbooks face an intractable dilemma. problems abound whether they include or exclude theology. we underscore this difficulty by examining a common approach that some biology textbooks use to try to solve this predicament. we argue that their approach is incoherent and self-serving. the poor performance of textbooks on this point shows just how deep the difficulty is. in the end, the overall dilemma remains. 7as it happens, we are not in principle opposed to the presence of god-talk in biology textbooks. we personally think that this approach has some merit. some textbook authors may agree with us on this score. but, as we will argue, others will find that this approach is deeply unwelcome. volume 1, issue 2 2. the problematic presence of theology—concrete examples 41 2 the problematic presence of theology—concrete examples in this section, we analyze three types of theology in biology textbooks. we call them: straw god theology, presumptive theology, and indeterminate theology.8 each type functions as a crucial element in various arguments that directly or indirectly support evolutionary theory. unfortunately, each type also suffers serious difficulties. these difficulties undermine the pro-evolution arguments that contain them. more generally, the failure of these arguments nicely illustrates the broader problem of incorporating god-talk into biology textbooks. two qualifications must be made at the outset. first, this section of our article is not a comprehensive analysis of all types (or instances) of theology that appear in the textbooks on our list. there is more god-talk afoot than we highlight, both here and in other biological texts.9 such cases strengthen our argument, but are beyond the present scope. second, in this section, we argue that the strong majority of textbooks on our list include theology of one kind or another. but beyond this particular segment, our overall argument in this article focuses on the dilemma of including or excluding god-talk, rather than on problems that arise from the sheer amount of theology in biology textbooks. thus, while section 2 focuses on (many) instances of theology, our broader argument emphasizes the deeper predicament surrounding the general presence or absence of theology. in this sense, our argument is qualitative rather than quantitative. 8we borrow the term “straw god” theology from jonathan wells, “darwin’s straw god argument,” journal of interdisciplinary studies 22 (2010): 67–88. however, our use of the term is not identical to his. as far as we know, the terms “presumptive theology” and “indeterminate theology” are unique to our discussion. 9the seminal work on the role of theology in the justification of evolution is paul nelson, “the role of theology in current evolutionary reasoning,” biology and philosophy 11 (1996): 493–517. see also gregory radick, “deviance, darwinian-style,” metascience 14 (2005): 453–57, esp. 455; stephen dilley, “charles darwin’s use of theology in the origin of species,” british journal for the history of science, vol. 45, no. 1 (2011): 29-58; stephen dilley, “nothing in biology makes sense except in light of theology?” studies in history and philosophy of biological and biomedical sciences 44 (2013): 774– 86; abigail lustig, “natural atheology,” darwinian heresies, ed. a. lustig et al. (cambridge: cambridge university press, 2004), 69–83; casey luskin, “zeal for darwin’s house consumes them,” liberty university law review, vol. 3, no. 2 (spring 2009): 403-89; casey luskin, “darwin’s poisoned tree,” trinity law review, vol. 21, no. 1 (fall 2015): 130-233; wells, “darwin’s straw god,” 67-88; cornelius hunter, science’s blind spot (grand rapids, mi: brazos, 2007); cornelius hunter, “darwin’s principle: the use of contrastive reasoning in the confirmation of evolution,” hopos 4 (spring 2014): 106–49; cornelius hunter, darwin’s god (grand rapids, mi: brazos, 2001); cornelius hunter, “the random design argument” communications of the blythe institute, vol. 1, issue 2: 23–36 [this issue]. 2.1 straw god theology the first type of theology we label “straw god theology” because it mischaracterizes certain rivals to evolution, making them easier to knock down. more specifically, this mischaracterization is typically part of a line of reasoning that indirectly supports evolutionary theory by attacking opponents such as special creation or young-earth creationism. eighty-four percent of the textbooks on our list deploy straw god theology.10 the classical scene while our primary interest is the contemporary scene, we begin by briefly noting two broad caricatures of nineteenthcentury special creation. first, a number of textbooks we studied characterize special creation as holding a youngearth view.11 some of these texts seem to have taken bishop ussher as the authoritative voice on the matter, while others do not mention him by name but nonetheless nod in the same direction. the authors of biological science write, for example: when darwin published his theory in 1859 in a book called on the origin of species by means of natural selection, it unleashed a firestorm of protest throughout europe. at that time, the leading explanation for the diversity of organisms was an idea called special creation. special creation held that: (1) all species are independent, in the sense of being unrelated to each other; (2) life on earth is young—perhaps just 6000 years old; and (3) species are immutable, or incapable of change. these beliefs were explained by the instantaneous and independent creation of living organisms by a supernatural being.12 in fact, the discussion of a young earth as a central matter of dispute between creationism and darwinian evolution did 10see figure 1 for a full list. 11while some textbooks explicitly claim that special creation included a young-earth view, others imply a close connection to one degree or another, often by characterizing young-earth creationism as darwin’s primary rival. for example, hoefnagels, biology: concepts and investigations, p. 238; urry et al., campbell biology, p. 467-68; mader, biology, p. 266; raven et al., biology, p. 11; belk and maier, biology, p. 207; miller and levine, miller & levine biology, p. 450, 453-54; phelan, what is life?, p. 300-304, 336-37; herron and freeman, evolutionary analysis, p. 38, 62, 66; freeman et al., biological science, p. 435, 438; mader and windelspecht, essentials of biology, p. 238; zimmer and emlen, evolution, p. 29-34, 52; simon et al., campbell essential biology, p. 247; taylor et al., campbell biology: concepts and connections, p. 260-61. 12freeman et al., biological science, p. 435. 42 damned if you do and damned if you don’t not occur until the twentieth century. early critical reviews of the origin of species by an array of prominent thinkers simply ignored this topic.13 moreover, the most prominent ‘creationist’ work of the time, william paley’s natural theology, did not advocate a young earth view.14 instead, the most notable “age of the earth” attack was from william thompson (later, lord kelvin) who contended that the earth was between 20 and 400 million years old, with the most probable time landing at 98 million.15 second, some textbooks erroneously state (or imply) that a literal reading of genesis was basically the only one available for christian creationists in the centuries (or years) leading up to the origin of species.16 consider, for example, douglas futuyma’s well-known textbook, evolution. in the opening pages, the text juxtaposes darwinian evolution with pre-darwinian views of flora and fauna. according to futuyma, these early views included plato and aristotle’s idea that “species have fixed properties.”17 after this greek notion came christian ideas: “later, christians interpreted the biblical account of genesis literally and concluded that each species had been created individually by god in the same form it has today. (this belief is known as ‘special creation.’)”18 in the rest of the narrative, futuyma gives no hint that other views were available to christian thinkers. similarly, in a passage that provides the historical backdrop to the rise of evolutionary theory, the authors of discover biology assert: “the literal interpretation of scripture, especially the book of genesis, shaped judeochristian views about the origins of life, and these were embellished by a succession of biblical scholars. james ussher, a seventeenth-century archbishop of armagh in northern ireland, claimed to know the exact date that all life was created: october 23, 4004 bc.”19 in the rest of the pas13see the fine collection in david l. hull, darwin and his critics (chicago: university of chicago press, 1973). 14william paley, natural theology, twelfth edition (london: j. faulder, 1809); adam shapiro, “william paley’s lost ‘intelligent design,” ’ history and philosophy of the life sciences, vol. 31, no. 1 (2009): 55-77; adam shapiro, “darwin’s foil: the evolving uses of william paley’s natural theology 1802-2005,” studies in history and philosophy of biological and biomedical sciences, vol. 45 (2014): 114-23. 15william thomson (lord kelvin), “of geological dynamics,” popular lectures and addresses, vol. 2 (1869): 73-131. thomson was supported by fleming jenkin, one of the critics most worrisome to darwin. fleming jenkin, “the origin of species,” [1867] in darwin and his critics, 303-44. 16for example, singh-cundy et al., discover biology, p. 386-87; belk and maier, biology, p. 207; bergstrom and dugatkin, evolution, p. 33; simon, biology, p. 152; simon et al., campbell essential biology, p. 244-48, esp. 245, 247; taylor et al., campbell biology: concepts and connections, p. 260-61, esp. 260. 17futuyma and kirkpatrick, evolution, p. 9. 18futuyma and kirkpatrick, evolution, p. 9. 19singh-cundy et al., discover biology, p. 386. as a minor detail, this quote slightly mischaracterizes ussher’s view. ussher held that god began creating the heavens and the earth on the “evening presage, the authors are silent about other christian views on the matter, which suggests to readers that a “literal interpretation of scripture, especially the book of genesis” was the only option available prior to and during darwin’s era. of course, untold numbers of christians (and special creationists) did interpret genesis in this manner in the centuries (or years) prior to the origin. and it is true, as some textbooks observe, that developments in geology during the early-to-mid nineteenth century did cause many christian thinkers to give up literalist claims about genesis, including a so-called universal flood.20 however, our concern is that futuyma and other like-minded authors do not give any indication that, by darwin’s day, non-literal interpretations of genesis were well known in christian (and creationist) circles and, more directly, a literal interpretation of genesis was not a crucial issue among most scientists who were christians. in his seminal study, charles darwin and the problem of creation, historian neal gillespie observed that during the evolution controversy, the dispute about the presence of biblicist thinking in science “was not whether literalism in biblical interpretation should survive, nor was it whether science contradicted the bible.... the point of conflict, rather, was the intellectual autonomy of science.”21 it is unsurprising, then, that an array of elite christian men of science of that era accepted views of creation that did not require a literal interpretation of genesis.22 moreover, as rev. william hayden estimated in 1851, even among the “christian public,” fully half did not believe that genesis was to be taken literally.23 none of this was without precedent, of course. the christian tradition includes a long history of non-literal interpretations, which date back to the church fathers. in the fourth century, st. augustine, who ranks as one of the most influential theologians of all time, adopted a metaphorical view of “days” in his commentary on genesis.24 other church fathers, like ceding the 23rd day of october” in 4004 b.c.; biological life did not appear until october 25. contrary to singh-cundy et al., ussher did not claim that god created “all life” on “october 23.” 20the classic study is charles coulston gillespie, genesis and geology (new york: harper & row, 1951). 21neal gillespie, charles darwin and the problem of creation (chicago: university of chicago press, 1979), 47. 22the ranks of christian (or christian-leaning) thinkers whose views of creation did not require a literal interpretation of genesis included georges cuvier, william paley, adam sedgwick, william hayden, john william dawson, arnold guyot, asa gray, william whewell, john herschel, james dwight dana, and others. 23william b. hayden, science and revelation; or, the bearing of modern scientific developments upon the interpretation of the first eleven chapters of genesis (boston: otis clapp, 1852), 77. hayden himself was disappointed that the number was not greater. see also ronald numbers, “creating creationism: meanings and uses since the age of agassiz,” evangelicals and science in historical perspective, eds. david livingston et al. (oxford, uk: oxford university press, 2014), 236. 24one must be careful about the terms ‘literal’ and ‘metaphorical’ volume 1, issue 2 2. the problematic presence of theology—concrete examples 43 clement of alexandria, origen, and st. cyprian, likewise accepted figurative interpretations of genesis.25 contrary to the claims of some textbooks, christian creationists held diverse approaches to scripture. unfortunately, other mischaracterizations of special creation surfaced as well.26 even so, our concern in pointing out these errors is not to defend special creation. on the contrary, we think the biological data run counter to this view. yet these mischaracterizations concern us. in each case above, the caricature in question is part of a larger passage (or chapter) in which textbook authors seek to show that special creation is empirically inferior to darwin’s theory. that is, these mischaracterizations play a key role in indirect arguments for evolution. the problem, of course, is that these arguments are rife with straw gods. the contemporary scene unfortunately, we also found mischaracterizations of contemporary versions of creationism. these mischaracterizations are not simply innocuous misrepresentations. they appear in sections of the text that are meant to provide support for current evolutionary theory. for example, like a number of textbooks, mark ridley’s evolution misconstrues the locus of divine activity.27 ridley juxtaposes evolutionary explanations for adaptation with creationist ones: creationism, by contrast, has no explanation for adaptation. when each species originated, it must have already been equipped with adaptations for life, because the theory holds that species are fixed in form after their origin. an unabashedly when used to delineate the exegetical methods of church fathers. in the literal meaning of genesis, augustine purported to give the proper meaning of the text rather than a metaphorical or so-called literal one (in the modern sense). using this approach, he concluded that “day” in genesis should not always be viewed as a 24-hour time period. augustine, on genesis, trans. edmund hill (hyde park, ny: new city press, 2004). 25while the church fathers overwhelmingly thought the earth was young, nonetheless they were of different minds about the so-called literal interpretation of genesis. see clement of alexandria, stromata 6.16; origen, contra celsum, book 6.50, 60; st. cyprian, treatise 11.11. 26for example, russell et al., biology, p. 440; phelan, what is life?, p. 300-304, 336-37; krogh, biology, 285; freeman et al., biological science, fifth edition, appendix a:24; shuster et al., biology for a changing world, p. 322-24. 27we found that very few textbooks recognize that modern creationism (and intelligent design) hold that god (or a designer) is not limited to creating only at the taxonomic level of species (or lower). better texts include, for example, futuyma and kirkpatrick, evolution, which sometimes avoid this error (p. 578) and sometimes does not (p. 44). and, despite some inaccuracies, ridley, evolution, includes helpful nuances, esp. p. 43-70. see also the discussion below. religious version of creationism would attribute the adaptiveness of living things to the genius of god.28 in this passage, ridley implies that, according to creationism, god created at the level of “species” (ostensibly equipping each species with necessary adaptations for their respective environments). in fact, for quite some time, many creationists, including even young-earth creationists, have explicitly rejected the claim that god created exclusively at the species taxonomic level. in 1947, young-earth creationist frank lewis marsh noted, “on every occasion creationists will continue to make the matter very clear that the modern ‘species’ is not usually the same sort of group of organisms as is the genesis kind.”29 in the genesis flood, the 1961 seminal text of modern creationism, john whitcomb and henry morris claimed that god created “kinds,” which they regard as a taxonomic level distinct from “species.”30 and in the present-day, andrew snelling’s two volume work, earth’s catastrophic past, which is perhaps the most sustained defense of young-earth creationism available, holds that genesis kinds “may be identical with the genus or even the family.”31 moreover, michael behe, the most prominent scientist in the intelligent design movement in the past two decades, argues that unaided natural processes can account for some biological phenomena at the level of species and genera. in these cases, it is unnecessary to posit an intelligent cause.32 the cases mentioned above are hardly unusual. as historian ronald numbers observes in his analysis of creationism and speciation, “by the 1970s, most of the leading special creationists had long since abandoned belief in the fixity of species and had embraced extensive—and extremely rapid—organic evolution within the originally cre28ridley, evolution, p. 67, see also p. 263-64. n.b. ridley uses the term “adaptiveness” rather than “adaptedness.” 29frank lewis marsh, evolution, creation, and science, second edition (washington, d.c.: review and herald publishing association, 1947), 199; see also 197-98. more than a decade earlier byron nelson made a similar point. byron c. nelson, “after its kind”: the first and last word on evolution, fourth edition (minneapolis, mn: augsburg publishing house, 1931), 18-25. 30john c. whitcomb and henry m. morris, the genesis flood (phillipsburg, nj: p & r publishing, 1961), 66-69, especially 69. 31andrew a. snelling, earth’s catastrophic past, 2 vols. (dallas, tx: institute for creation research, 2010), vol. 1: 215. john morris, son of creationist icon henry morris, and president emeritus of the institute for creation research, regards snelling’s 1500-page work as the sequel to the genesis flood. see morris, “foreword,” earth’s catastrophic past, vol. 1, ix-xi. 32michael j. behe, darwin devolves (new york: harperone, 2019), esp. 141-70. while intelligent design theory itself does not identify the ‘designer’ as ‘god’ per se, biology textbooks generally hold that the theory (tacitly) posits a supernatural designer. accordingly, in an effort to take these texts on their own terms, we will treat id as a theology-laden theory. 44 damned if you do and damned if you don’t ated ‘kinds’ mentioned in the first chapter of genesis.”33 he further points out: “despite the popular image of creationists being wedded to the fixity of species, no one argued for more rapid speciation by means of natural selection . . . [than] the creationists.”34 whatever else may be the case, modern creationism (and intelligent design) do not restrict the creator’s activity exclusively to the species-level. a second and related concern now surfaces. in presenting the case for evolutionary theory, a number of texts seem to assume that arguments which favor evolution over nineteenth century special creation, as they construe it, likewise favor evolution over contemporary creationism or intelligent design.35 but arguments that address a past foe are not always relevant to a present adversary. to be sure, some of the classic arguments obviously apply to the present context. for example, empirical data about the ancient age of earth are highly relevant to assessing the plausibility of current versions of young-earth creationism.36 nonetheless, many textbooks do not make clear how other arguments for the superiority of evolution over special creation also demonstrate evolution’s superiority over key contemporary rivals, notably old-earth creationism and intelligent design. textbooks need not nuance every jot and tittle of creationism, of course. yet all too often, textbook authors seem to assume that if creationists of yesteryear believed such-and-such, then creationists of today must as well. yet in his preeminent study of creationism, ronald numbers observes that, even among relatively informed individuals, a “common assumption seems to be that one creationist is pretty much like another.” but, as he says bluntly, “nothing could be further from the truth.”37 stepping back, we have noted several instances of “straw god” theology in biology textbooks. this theology mischaracterizes rivals to evolution, such as special creation or young-earth creationism, making them easier to knock down. moreover, this mischaracterization is typically part of a line of reasoning that directly or indirectly supports evolutionary theory. caricatured god-talk thus serves as 33ronald numbers, “ironic heresy: how young-earth creationists came to embrace rapid microevolution by means of natural selection,” darwinian heresies, eds. abigail lustig et al. (cambridge, uk: cambridge university press), 84-100, see esp. 87. 34numbers, “ironic heresy,” p. 100. 35fortunately, a few textbooks are better on this score. they include, for example, futuyma and kirkpatrick, evolution, 573-84, 600, although see p. 44; ridley, evolution, p. 44, 67-69; raven et al., biology, p. 432-33. curiously, the first edition of zimmer and emlen, evolution, is better on this score than the second edition (see p. 320 of the first edition). 36further discussion about the “appearance of age” and “uniformitarianism” are relevant, of course. 37ronald l. numbers, the creationists: from scientific creationism to intelligent design, expanded edition (cambridge, ma: harvard university press, 2006), 9. part of the positive case for evolution. 2.2 presumptive theology we now turn to a second type of theology, which we label “presumptive theology.” this type includes highly confident statements about god’s nature or ways. we regard these claims as “presumptive” not simply because of their level of certitude but also because they are typically asserted without any justification whatsoever. over 60% of the textbooks we analyzed deployed this theology in some of their positive arguments for evolutionary theory.38 example 1 several textbooks draw on presumptive theology as part of their positive case for common ancestry. for example, one textbook argues: an engineer would never use the same underlying structure to design a grasping tool, a digging implement, a walking device, a propeller, and a wing. instead, the structural homology exists because mammals evolved from the lungfish-like ancestor that had the same general arrangement of bones in its fins.39 a few observations are in order. first, consider how an 38notably, the content and form of presumptive theology can vary widely from case to case. sometimes it is articulated in rhetorical questions; other times it takes the form of tacit approval of darwin’s use of it in his own arguments for evolution; still other times, textbook authors appeal to what is “reasonable,” and so forth. more generally, presumptive theology typically involves one or more of the following: (i) direct claims about god, a creator, etc., (ii) claims about an engineer, designer, etc. in contexts in which the most likely referent is a divine engineer or designer, (iii) claims about what we would expect given a (particular) creationist or id view, or (iv) claims about what we would expect had the phenomenon in question arose “from scratch” (or some other phrase that, in context, has creational overtones). examples can be found in russell et al., biology, p. 440, more elliptically on p. 475; simon, biology, p. 161; bergstrom and dugatkin, evolution, p. 115; herron and freeman, evolutionary analysis, p. 56, see also 98; krogh, biology, p. 293-95; audesirk et al., biology, p. 265-66, 270-71; zimmer and emlen, evolution, p. 40; mader and windelspecht, essentials of biology, p. 248, elliptically; barton et al., evolution, p. 75, 81; futuyma and kirkpatrick, evolution, p. 45: “. . . many features that no intelligent engineer would be expected to design”; simon et al., campbell essential biology, p. 250; urry et al., campbell biology, p. 477-78, elliptically, but see p. 467-68 for context; taylor et al., campbell biology: concepts and connections, p. 264, elliptically; mason et al., understanding biology, p. 9-11, esp. 11; mader, biology, p. 277, elliptically; raven et al., biology, p. 9, 432-33, elliptically. a full list can be found in figure 1. 39freeman et al., biological science, p. 442-43. volume 1, issue 2 2. the problematic presence of theology—concrete examples 45 “engineer” is described. such an individual would “never” use the same design plan as a basis for very different tools. the assumption in play is: under no circumstances would an engineer ever modify a single structure for an array of different functions. a second observation relevant to the passage is that its broader context contends that homologous features count as evidence for common ancestry over creationism. for example, the opening paragraphs of the homology section, which frame the entire passage, state that “advocates of special creation. . . could not explain why striking similarities existed among certain organisms” whereas “common ancestry” can explain these similarities.40 likewise, the final paragraph of the section, which summarizes the overall point, says in full, “the theory of evolution by natural selection predicts that homologies will occur. if species were created independently of one another, as special creation claims, these types of similarities would not occur.”41 accordingly, in this context, the claim about an “engineer” refers to a supernatural creator. as such, the argument contains a theology-laden assumption: if god designed different species with biological structures analogous to a grasping tool, a digging implement, a walking device, a propeller, and a wing, respectively, then he would never use the same underlying structure, modifying it specially for the particular needs (and limbs) of each new species. a final observation, already implied, is that the passage makes a comparative argument. the data of “structural homology” are said to favor common ancestry over the divine engineer hypothesis. stated a bit more precisely, the argument appears to be: 1. if evolutionary theory is true, then we would very much expect to find some mammals with the “same general arrangement of bones” in their appendages (due to their descent from a “lungfish-like ancestor”). 2. if god engineered different species with biological structures analogous to a grasping tool, a digging implement, a walking device, a propeller, and a wing, respectively, then he “would never use the same underlying structure,” modifying it specially for the particular needs (and limbs) of each new species. 40freeman et al., biological science, p. 441. 41freeman et al., biological science, p. 443. 3. as a matter of fact, we have discovered that some mammals have the “same general arrangement of bones” (or “underlying structure”) in their appendages. 4. if the evidence is very much expected on one hypothesis but totally unexpected on another, then the evidence strongly supports the former over the latter. 5. thus, the fact that some mammals have the “same general arrangement of bones” (or “underlying structure”) in their appendages strongly supports evolutionary theory over the divine engineer hypothesis. premise two is crucial. it makes a claim about what a divine engineer would never do. accordingly, the argument as a whole includes a substantive theological assertion. we will examine this assertion shortly. but first another example may be helpful. example 2 some textbooks use subtler language but nonetheless marshal an argument with much the same level of confidence. what is life?, for example, states the following: among adult animals, several features of anatomy reveal the ghost of evolution in action. many related organisms show similarities that can be explained only through evolutionary relatedness. the forelimbs of mammals such as bats, porpoises, horses, and humans are used for a variety of very different functions (figure 10-39). if each had been designed for the uses necessary to that species—flying, swimming, running, grasping—we would expect dramatically different designs. and yet, all of these species possess the same bones— modified extensively—revealing that they share a common ancestor.42 this passage makes a claim about what a designer would do: “if each [mammalian forelimb] had been designed specifically for the uses necessary to that species. . . we would expect dramatically different designs.” on this view, a designer would make “dramatically different designs” rather than designs that are ‘somewhat different’ or even ‘notably different.’ given that the surrounding context of the passage clearly points to a divine designer,43 the argument rests on the following assumption: 42phelan, what is life?, p. 332-33. “figure” refers to a drawing in the original text. 43the text frames the rise and justification of darwin’s theory in contrast to key creationist claims, inter alia. see phelan, what is life?, p. 300-304, 336-37. 46 damned if you do and damned if you don’t if god had designed each mammalian forelimb specifically for the uses necessary to its particular species, then he would have made dramatically different forelimb designs. notice that the author does not qualify this key assumption about a divine designer. apparently, readers are to believe that, if god had directly designed each mammalian forelimb, he would always make dramatically different designs. at first glance, the argument seems less stalwart than our earlier example, yet closer inspection shows a familiar level of theological certitude. observations and evaluation we turn now to macro-level analysis of these cases. each of the examples above functions as a crucial premise in a positive argument for evolution. these arguments vary in particulars but nonetheless follow a basic form: 1. if evolutionary theory is true, we would expect x. 2. if god directly designed each species (or limb, etc.), then we would “never” expect x. 3. we have found x. 4. if the evidence is very much expected on one hypothesis but highly unexpected on another, then the evidence strongly supports the former over the latter. 5. thus, x strongly supports evolutionary theory over the hypothesis that god directly designed each species (or limb, etc.). premise two is of keen interest. in the examples analyzed above, premise two took various forms, depending on a given textbook’s specific language. yet the general idea in both cases is that god would not do such-and-such—in this case, the deity would not use a common template to fashion new appendages for new species. a few observations are in order. although our observations will focus on the two cases in question, these observations apply to cases of presumptive theology in other textbooks as well.44 first, in whatever form, premise two is crucial for the argument. if it is removed, the argument is logically invalid, and the conclusion no longer follows. for the proevolution argument to be successful, premise two has to be present and justified. 44as figure 1 makes clear, 20 out of 32 textbooks contain presumptive theology. second, the argument is part of the positive case for evolutionary theory. it is not simply a critique of contemporary creationism (or intelligent design). instead, as the conclusion makes clear, the whole point of the argument is to show that evolution better explains the empirical data. third, as far as we can tell, premise two is not entailed, or made probable, by young-earth creationism or intelligent design, for example. in particular, nothing in these views holds that god (or a designer) would never use a template for multiple designs. in fact this very notion has been challenged by creationists as far back as the 1930s.45 intelligent design theorists have likewise openly disputed this claim since the early years of the movement.46 the upshot is that textbook authors have not accurately represented contemporary creationist or intelligent design tenets and shown that these tenets conflict with the empirical data. instead, textbook authors have brought their own claims to the table, including their own partisan god-talk. they presuppose that god would create brand new bone structures, never drawing on a common template. as philosopher paul nelson observes in a similar context, their underlying assumption is that “[i]f the creator is free to do as he pleases, the appearance of [a] plan can become the appearance of limitation or constraint, suggesting an unimaginative or even slavish repetition of structures along some predetermined pattern.”47 these textbook authors assume that the “apparent uniformity of certain biological patterns is inconsistent with the freedom of a creator to act as he wishes.”48 on this view, the deity’s free will necessitates originality. the almighty loves novelty. but textbook authors overwhelmingly fail to provide justification for their sectarian theology. they do not cite any sources, whether secular or religious. instead, their partisan claims function as brute assertions unaccompanied by evidence, reason, or argument. just where one would ex45byron nelson actually made this a pivotal element in his challenge to evolutionary theory. see nelson, “after its kind,” 37-51, 61-68. in the 1940s, frank lewis marsh raised the matter with theodosius dobzhansky in the dobzhansky-marsh correspondence, 1944-1945, p. 42-43. 46nelson, “the role of theology,” 493–517. phillip e. johnson, defeating darwinism (downers grove, il: intervarsity press, 1997), 62-64, 73-75, 80, 114. this point has been raised in more recent publications as well: jonathan wells, icons of evolution (washington, d.c.: regnery publishing, 2000), 67-70, 281. paul nelson and jonathan wells, “homology in biology: problem for naturalistic science and prospect for intelligent design,” darwinism, design, and public education, john angus campbell and stephen c. meyer, eds. (east lansing, mi: michigan state university press, 2003), 303-22. winston ewert, “the dependency graph of life,” bio-complexity, vol. 3 (2018): 1-27, doi:10.5048/bio-c.2018.3. 47nelson, “the role of theology,” p. 511, emphasis altered. 48nelson, “the role of theology,” p. 511; cf. lustig, “natural atheology,” p. 75-76. volume 1, issue 2 2. the problematic presence of theology—concrete examples 47 pect textbooks to give good grounds—after all, arguments for evolution are central to modern biology—these texts instead offer precisely nothing. fourth, as far as we can tell, religious students in general are not rationally obligated to accept the theology in question. while we are surely not experts in world religions, these partisan theological claims do not appear to be entailed, or made probable, by any of the abrahamic traditions. moreover, they do not appear to be entailed, or made probable, by a number of other serious religious views, including process theism, henotheism, polytheism, religious pluralism, confucianism, religious taoism, theravada buddhism, mahayana buddhism, and nirguna brahman-oriented hinduism. this is not to say that a reader who adheres to one of these views cannot accept the theological claims in question. rather, it’s only to say that, as far as we can tell, a given religious reader is entirely free to reject these textbooks’ partisan theological claims, all things being equal.49 moreover, atheist or agnostic readers are not rationally obligated to accept the theology in question either. of course, a given atheist or agnostic reader could in principle accept the counterfactual ‘were a god with certain properties to exist, he would never use a common template.’ but the fact that this assertion might fit within a given atheist’s or agnostic’s worldview is beside the point. instead, the central matter is that, all things being equal, there is nothing about the content or justification of atheism or agnosticism per se that rationally mandates acceptance of this counterfactual. as with religious readers, non-believers can regard textbooks’ partisan theology as entirely optional. they can take it or leave it. * let us pause briefly to consider the ramifications of our analysis. in each case above, presumptive theology was brought to bear in an argument for evolution. while presumptive theology is not limited to any particular type of argument for evolution, the two examples given are both versions of the homology argument. this is no small matter. the homology argument is widely regarded as one of the best arguments for evolutionary theory. of course, not all versions of the homology argument draw upon god-talk. nonetheless, some clearly do. our concern 49if we consider a believer of a particular religious tradition qua believer in that particular tradition, then, all things being equal, she is epistemically justified in rejecting the presumptive theology in question either because (i) her tradition does not conceive of divine action in this manner or (ii) her tradition does not require its adherents to accept the claim that, were a monotheistic god to exist, he would “never” use a common design, or the like. is with these versions, particularly those that depend upon “presumptive” theology—strident assertions about the divine unaccompanied by any justification. they highlight, once again, problems that arise when god-talk is present in biology textbooks. 2.3 indeterminate theology is there another way forward? one possibility is to opt for statements that are more circumspect. “indeterminate theology,” as we call it, achieves this goal. this theology claims that god can create in various ways without specifying that he definitely would have created in a specific way.50 twenty-five percent of the textbooks on our list contain indeterminate theology.51 we analyze two examples below. example 1 in a section on the evidence for evolution, the authors of biology argue: an excellent example of an imperfect design is the eye of vertebrate animals, in which the photoreceptors face backward toward the wall of the eye. . . . as a result, the nerve fibers extend not backward, toward the brain, but forward into the eye chamber, where they slightly obstruct light. moreover, these fibers bundle together to form the optic nerve, which exits through a hole at the back of the eye, creating a blind spot. by contrast, the eye of mollusks [sic]—such as squid and octopuses—are more optimally de50for stylistic reasons, we sometimes employ the pronoun “he” when referring to “god.” of course, our argument does not hinge upon thinking of god in masculine terms as opposed to feminine or neuter terms. 51in total 8 textbooks include indeterminate theology, which typically involves one or more of the following: (i) direct claims about god, a creator, etc., (ii) claims about an engineer, designer, etc. in contexts in which the most likely referent is a divine engineer or designer, (iii) claims about what we might expect given a (particular) creationist or id view, or (iv) claims about what we might expect had the phenomenon in question arose “from scratch” (or some other phrase that, in context, has creational overtones). see figure 1 for a full list. note that some texts are less clearly theological than others: mason et al., understanding biology, p. 442, for context see p. 9-11, 446-47, 451; morris, how life works, 393; sadava et al., life, p. 420, 443; hillis et al., principles of life, p. 291; krogh, biology, p. 8 uses indeterminate theology, or something like it, to argue that certain appeals to an “intelligent designer” fall outside of science. in addition, a few examples surfaced in earlier editions of the textbooks on our list, notably, audesirk et al., tenth edition, biology, p. 273; futuyma, evolution, third edition, p. 639: “. . . a thoughtful designer could arrange.” 48 damned if you do and damned if you don’t signed: the photoreceptors face forward, and the nerve fibers exit at the back, neither obstructing light nor creating a blind spot. . . . such examples illustrate that natural selection is like a tinkerer, working with whatever material is available to craft a workable solution, rather than like an engineer, who can design and build the best possible structure for a given task. workable, but imperfect, structures such as the vertebrate eye are an expected outcome of evolution by natural selection.52 a few observations are in order. first, the authors write that an engineer “can” design and build the best possible structure for a given task. notice that the language of “can” does not say that it is likely an engineer would do so. instead, this passage only comments on what an engineer is capable of doing. an engineer is able to do x; he is free to do x. this is a claim about possibility, not probability. second, the broader context clearly indicates that this passage is part of the authors’ justification for evolutionary theory over and against creationism and intelligent design.53 as such, the authors’ claim about an engineer is meant to apply to a divine creator.54 so, given that the argument quoted above focuses on the eye of vertebrate animals, a key claim of this argument is: god “can design and build the best possible” eye for vertebrate animals. or, to put the matter in a conditional statement: 52raven et al., biology, p. 428-29. 53on the next page, the authors state: “it is difficult to understand vestigial structures such as these as anything other than evolutionary relicts, holdovers from the past” (raven et al., biology, p. 430). two pages later, they drive home their message: “inefficiencies of certain designs, such as the vertebrate eye and the existence of vestigial structures, do not support the idea of an intelligent designer” (p. 432-433). clearly, the authors argue that the data of inefficient or imperfect structures, like the vertebrate eye, count as evidence for evolutionary theory over intelligent design. moreover, in the opening pages of the textbook, the authors indicate that a perennial rival to evolutionary theory is creationism: “in darwin’s time, most people believed that the different kinds of organisms and their individual structures resulted from direct actions of a creator (many people still believe this)” (p. 8). the next several pages reinforce the notion that creationism is a key opponent of evolution (p. 9-12). 54presumably, their claim applies to non-divine higher intelligences as well. in fact, their claim apparently applies to any intelligent being who is capable of creating an eye and who knows the principles of engineering (at least as the authors understand these principles). so, while their claim about “an engineer” applies to more than just god, it does not apply to less. if god were to create the vertebrate eye, then he “can design and build the best possible” eye for vertebrate animals. or, equivalently: if god were to create the vertebrate eye, then perhaps he would “design and build the best possible” eye for vertebrate animals. the language of ‘perhaps’ captures the provisional nature of the statement that god “can” do such-and-such as opposed to the assertion that he would do such-and-such. god’s actions are ‘indeterminate,’ as we say, given that the statement (and argument) in question only asserts what god is able to do rather than what he would definitely do or probably do. we will explore this claim, and the argument it serves, in due course. but first we turn to another example. example 2 in a summary of “the evidence for evolution,” another textbook gives empirical arguments that common ancestry is superior to “the alternative hypothesis,” which holds “that species have been individually created by a supernatural being.”55 among these arguments is the famed homology argument, which, in this case, draws on indeterminate theology from a different angle: similarity of structure despite differences in function follows from the hypothesis that the characteristics of organisms have been modified from the characteristics of their ancestors, but it is hard to reconcile with the hypothesis of intelligent design. design does not require that the same bony elements form the frame of the hands of primates, the digging forelimbs of moles, the wings of bats, birds, and pterosaurs, and the flippers of whales and penguins.56 in this passage, the authors give a clear argument that a similar bone structure in various limbs counts as evidence in favor of common ancestry over intelligent design. that is, ‘similarity’ is a natural prediction of the common ancestry hypothesis—it “follows from” descent with modification. 55futuyma and kirkpatrick, evolution, p. 44. 56futuyma and kirkpatrick, evolution, p. 44. volume 1, issue 2 2. the problematic presence of theology—concrete examples 49 by contrast, design “does not require” similar structural elements. three elements are worthy of our attention. first, in a recent article, warren allmon and robert ross regard this argument as the “most compelling argument for interpreting homologous similarities as evidence of evolution.”57 in our view, allmon and ross’s conclusion is especially notable because it arises from a thoughtful and fair-minded analysis of various attempts to render the homology argument in its strongest and most accessible form. if they are correct, then any flaws in this version of the homology argument are particularly significant. second, this homology argument hinges upon god-talk. the reference to “intelligent design” in the main passage above is, for the authors, an implied reference to a supernatural hypothesis. in the opening paragraph of the passage, which frames how the homology argument is to be understood, the authors compare common ancestry to “the alternative hypothesis”—namely, that “species have been individually created by a supernatural being.”58 elsewhere in the text, intelligent design is likewise characterized as creationism in “camouflage.”59 so, a creationist deity is in the picture. third, the authors’ portrayal of this creationist hypothesis is quite provocative. the authors do not say that, on the god hypothesis, similarity is ‘unexpected’ or ‘improbable’ or ‘surprising.’ instead they claim that this hypothesis “does not require” similarity. in other words, god does not have to use a common design plan; he is capable of creating each species (and each concomitant limb) de novo, in which the limbs of every species have a unique underlying bone structure. that is, the almighty can create different structures each time. he is not required to reuse a similar pattern. so the argument depends upon a crucial assumption: if god created each species individually, then he was not required to use a common design pattern from which to fashion the limbs of different species. this is another way of saying: if god created each species individually, then he 57warren d. allmon and robert m. ross, “evolutionary remnants as widely accessible evidence for evolution,” evo. edu. outreach, vol. 11, no. 1 (2018), p. 9. see the discussion on p. 8 as well. (doi.org/10.1186/s12052-017-0075-1.) 58futuyma and kirkpatrick, evolution, p. 44. 59futuyma and kirkpatrick, evolution, p. 578. can create unique bone structures for limbs of different species. once again, we have the language of possibility. god is not required to do such-and-such; he is free to do the opposite. as we have seen, this idea can be expressed in the statement: if god created each species individually, then perhaps he would create unique bone structures for limbs of different species. this is indeterminate theology from another angle. observations and evaluation while each argument above has its particular focus, proevolution arguments that draw on indeterminate theology generally have the same basic structure: 1. if evolutionary theory is true, then x is highly expected (or virtually inevitable). 2. if god directly created each species (or organ, etc.), then perhaps he would create not-x. 3. x is true. 4. if x is highly expected (or virtually inevitable) on one hypothesis, but not-x is possible on another hypothesis, then x strongly supports the former over the latter. 5. thus, x strongly supports evolutionary theory over the hypothesis that god directly created each species (or organ, etc.). in our view, premise two makes a rather modest claim that it is possible for god to create not-x. both in general and in biology textbooks, the term “god” typically refers to a being who is omnipotent. even in cases in which texts mention a generic “supernatural being,” rather than the god of monotheism per se, it is generally understood that a deity of this sort has the ability to do quite a lot. one of the perks of divinity, we gather, is having a fair bit of power at hand. so, the claims that, for example, ‘god can design and build the best possible eye for vertebrate animals’ or that ‘he can create dissimilarity rather than similarity’ are trivialities. they involve nothing contrary to god’s powerful nature and they do not express or entail a logical contradiction. 50 damned if you do and damned if you don’t these statements are true, but only in the most uninformative way, like saying that a normal human is capable of blinking. unremarkably, premise two passes muster. at this point, however, a critic might worry that our assessment has been unfair. he might say that our interpretation of “can” is too literal. when textbook authors state that god “can” do such-and-such, they really mean that god “would” do such-and-such. in this sense, indeterminate theology is actually just poorly articulated presumptive theology.60 by way of reply: in our view, it is better to give textbook authors the benefit of the doubt by taking seriously what they actually say rather than to speculate about what they allegedly intend to say. competent users of the english language know the difference between “can” and “would.” they also know that the former does not imply the latter: if a free agent has the ability to do x, it simply does not follow that they will do x. (most adults in the united states have the ability to vote libertarian in every election, for example, yet that hardly means they will.) so, we plainly disagree with the objection. but even if we are wrong—that is, even if indeterminate theology collapses into presumptive theology—then the only thing that follows is that there are even more cases of presumptive theology than we had previously counted. and these cases are plagued by all the problems that accompany this type of theology. so, deep difficulties remain. thus, our broader argument about the problematic presence of theology continues unabated. in any case, for now let us suppose we are correct that indeterminate theology is a genuine means by which some textbook authors argue in favor of evolution. as noted, we analyzed premise two of this type of argument above. it passed inspection. unfortunately, premise four does not. recall the premise: if x is highly expected (or virtually inevitable) on one hypothesis, but not-x is possible on another hypothesis, then x strongly supports the former over the latter. to see why this premise is false, imagine that we have evidence e and two hypotheses, h1 and h2, which are competing accounts of e. suppose further that h1 predicts e to a very high degree, so much so that the denial of e is unthinkable. suppose also that h2 predicts e to a very high degree as well, yet the denial of e is logically possible given h2. if we discover e, this evidence barely favors h1 60alternatively, a critic might say that authors don’t necessarily have in mind what god “would” do, but perhaps only what he would “probably” do. we address this idea in section 3 below. and h2, if at all. it’s virtually a dead heat. this means that premise four is false. when applied to this scenario, premise four mandates that e would “strongly support” h1 over h2. but e does no such thing. it favors h1 by just a whisker. as a result, premise four is flawed. it articulates (or entails) an epistemic principle that falls prey to a clear counterexample. a colorful example may help illustrate this point. suppose two scientists, kopp and schoss, each champion their own new theory in physics, respectively. these theories are in competition to explain a new datum. kopp’s theory, let us say, is deterministic. and, much to kopp’s delight, it predicts the datum to a very high degree. in fact, given the deterministic nature of kopp’s theory, as well as other relevant factors, it is unthinkable that his theory would not predict the datum. so, given kopp’s theory, the datum has a probability of 1, let us say. by contrast, schoss’s theory is indeterministic in a narrow sense; it allows the slimmest possibility of indeterminate events in certain conditions on the rarest of occasions. schoss’s theory also happens to predict the datum to a very high degree, in this case to a probability of .99. so which theory does the datum favor? the answer is that it barely favors kopp’s theory over schoss’s theory.61 the former predicts the datum with certainty; the latter almost to the same degree. clearly, it would be flatly wrong to conclude that the datum “strongly supports” kopp’s theory over schoss’s theory. instead, it’s nearly a dead heat.62 the upshot is that premise four is false. and this is significant because premise four, or something like it, is required for the logical validity of the argument. if the premise (or its near equivalent) were removed, then the conclusion would no longer follow from the remaining premises. so, removal of premise four destroys the argument. on the other hand, keeping the premise saddles the argument with a false claim. this renders the argument as a whole unsound. thus, whether premise four is retained or jettisoned, the argument has fallen short.63 of course, it is possible to modify premise four in order to make it passable. an improved version would have to say something like: data strongly favor one hypothe61likelihoods, or something like them, are in play here: empirical data d favor competing hypothesis h1 over hypothesis h2 if and only if pr (d |h1) > pr (d |h2). 62in fact, this example is overly sympathetic to premise four. schoss’s theory allows the physical possibility of the denial of the datum, whereas premise four only allows the logical possibility of not-x. premise four has an even greater burden to bear. 63of course, one can salvage premise four by getting rid of the “strongly supports” language and, instead, opting for “barely supports.” however, doing so means that the biological data barely support evolution over creationism. but this runs emphatically contrary to textbook presentations of “the evidence for evolution.” volume 1, issue 2 3. the problematic presence of theology—general concerns 51 sis over another just in case the data are expected on one but not the other. that is, the data formidably support one over the other (only) if there is a clear contrast in expectations between the two hypotheses. unfortunately, this is where indeterminate theology rears its head. under its mantle, premise two neither expects nor prohibits the data. it merely states what god would perhaps do. but without a clear expectation, textbooks cannot make a contrastive claim that one hypothesis definitely expects the data more than the other does. thus, indeterminate theology in premise two undercuts precisely the requirement needed for a persuasive version of premise four. if an improved version of premise four is to succeed, textbooks must compare clear expectations of each hypothesis. but if they cannot form a clear expectation of the god hypothesis, then they cannot compare it to the expectations of an evolutionary hypothesis. as such, they cannot say that data favor the expectations of the latter over the former. as a result, they cannot claim that the evidence supports evolutionary theory over the god hypothesis. the argument as a whole fails, and indeterminate theology strikes the fatal blow. thus, even with a defensible version of premise four, the argument remains unsalvageable.64 * let us pause for a moment to summarize our argument. recall that, in the previous section, we analyzed “presumptive theology.” this approach makes unsupported assertions about what god would do or would not do—for example, god would “never” use a common design plan for different limbs in various species. claims like this are bold, especially when unaccompanied by any justification. the natural corrective to this combination of high confidence and low justification is a bit more circumspection about god’s purported actions. a humbler approach is to note that god “can” do such-and-such, rather than to assert that he must do such-and-such. yet, as we have seen, the language of “can” has problems of its own. in fact, difficulties plague both approaches. presumptive theology (coupled, as it is, with no justification) constrains a divine being’s actions too severely and so devolves into dogmatic certitude. by contrast, indeterminate theology 64for more on the testability of god hypotheses with respect to evolutionary hypotheses, see elliott sober, evidence and evolution (cambridge, uk: cambridge university press, 2008), 109-88; elliott sober, did darwin write the origin backwards? (amherst, ny: prometheus books, 2011), 121-54. replies to sober include daniel lim, “a critique of elliott sober’s goals and abilities objection to the design argument” science and religion: historical and contemporary perspectives conference, lancaster university, july 2007; dilley, “how to lose a battleship,” 621-23. see also our discussion of the contrastive nature of scientific testing in section 4 below. does not constrain god’s actions at all and so never rises above triviality. troubles abound either way. 3 the problematic presence of theology—general concerns in this section, we extend our argument by turning to general reflections, rather than concrete cases, about the presence of theology in evidence-for-evolution sections of biology textbooks. to drive home our argument, we will first address three key objections. first, a critic might point out that, even with our examples of straw god, presumptive, and indeterminate theologies, it still does not follow that god-talk in general is problematic in biology textbooks. even if there are some rotten apples in the barrel, others may still be just fine. can’t offending authors just clean up their sloppy theological language and get on with it? second, a critic might contend that authors can avoid our concerns by casting theology aside or by making more defensible theological claims. (we will address the suggestion about setting theology aside in a later section.) otherwise, the path forward is for authors to give a defense of what god would probably do, rather than on what he definitely ‘would’ do or merely ‘could’ do. the focus on god’s probable actions, coupled with solid justification, is a mean between the extremes of triviality and dogma. it allows god-talk into the discussion in a defensible way. third, an alternative way forward is for textbook authors to ask, ‘what do various versions of creationism claim that god would probably do?’ this question is even more tractable than the question of what god would probably do. to answer this question, biologists do not have to moonlight as theologians; they need not plumb the heavens, nor discern things eternal and unseen. instead, they only need to know what their creationist rivals claim about god. in sum, the objections hold that (i) the ‘problem’ of theology in biology textbooks is merely a matter of sloppy language, (ii) this sloppiness can be dispensed with by focusing on what god would probably do, or (iii), more modestly, by focusing on what various creationists say god would probably do. taken collectively, these three objections attempt to refute our overall contention that the presence of theology in biology textbooks is worrisome. by way of reply: there is much to be said on this score. an initial note, mentioned earlier, is that we are not opposed in 52 damned if you do and damned if you don’t principle to the presence of god-talk in biology textbooks. we personally think that this approach has some merit. but in what follows below, we argue that the presence of theology comes at a significant cost, one that quite a few textbook authors are likely unwilling to pay. 3.1 rhetorical and practical concerns we begin with objection three. it holds that textbook authors ought to focus on what creationists themselves say god probably would or would not do. we make two points in reply. first, a number of biologists are concerned that direct engagement with contemporary versions of creationism (or intelligent design) may give students the faulty impression that these hypotheses are legitimate contenders to evolutionary theory. students may mistakenly come to think that these views are worthy of serious consideration. by analogy, would it be okay to give astronomy students the impression that astrology is a real contender to modern astronomy? to engage in any such discussion in a detailed way would be to give astrology too much credit. as far as we can tell, some textbook authors think the same concern applies to creationism.65 second, on a more practical level, textbook authors have the laborious task of deciding just what versions of creationism (or intelligent design) they wish to engage. what complicates matters is that not all versions are the same. different versions make use of a differing array of conceptual content, explanatory resources, auxiliary hypotheses, and predictions. some accept universal common ancestry, others more limited ancestry; some accept a global deluge, others see the flood as local; some accept an old earth, others are satisfied with a young one; some place great stock in the power of selection and mutation, others accept a much more limited view of natural causation. and so on. at a minimum, wading through these differences requires a fair amount of study. this is especially true given that particular arguments for evolutionary theory conflict with some, but not all, versions of creationism. if textbook authors include god-talk (or, more modestly, if they acknowledge that some scientific facts logically imply the falsity of certain creationist claims), they should be clear on just which 65this may explain why some authors tamp down their treatment of creationism (or of related metaphysical matters) in more recent editions of their textbooks. the apparent strategy is to delegitimize creationism or id by giving them less air time. for example, see the differences between zimmer and emlen, evolution, first edition, p. 40, 42, 44, 318, 320 versus parallel passages in the second edition; miller & levine biology (2010) versus their earlier work, kenneth miller and joseph levine, biology: the living science (lexington, ma: d.c. health & co., 1994), 148-61, esp. p. 161; and, less so, futuyma, evolution, third edition, p. 631-47 versus futuyma and kirkpatrick, evolution, fourth edition, p. 573-84. arguments (or facts) impinge on which versions of creationism. yet from a practical point of view, one might protest that many textbook authors have neither the time nor interest to do so. that is precisely our point. the frequency of “straw god” theology, for example, highlights this concern in a very tangible way. practically speaking, it’s not at all clear (to us) that textbook authors are generally willing or able to carry out the task in a sufficiently nuanced manner.66 3.2 a legal concern at the high school level, court rulings about the establishment clause may add yet another layer of complexity to the issues raised in all three objections above. while our primary focus is on college instruction, it is worth mentioning that (public) high school biology textbooks must contend with legal precedents in epperson, mclean, edwards, kitzmiller, and the like. it may be that some instances of god-talk in the case for evolution run up against these legal rulings.67 if that is true, then legal barriers hamper any approach that wishes to draw on (or critique) certain theological propositions. it has been quipped that a competent lawyer armed with these cases could go a long way toward getting the origin of species banned from public high school biology classrooms. (darwin included theological claims in his “one long argument” for evolution, as noted below.) strikingly, the same might be said for parts of the evidence-for-evolution sections of current biology textbooks. perhaps organizations like the national center for science education ought to take up the cause.68 3.3 an epistemological concern shifting ground now, recall objection 2 above. it held that authors can legitimately include theology in their arguments for evolution by giving some principled grounds for what god would ‘probably’ do in organic history. this move is a solid step beyond mere assertions about what god ‘would’ or ‘could’ do. in this case, authors are not borrowing creationists’ theological tenets (as per objection 3); instead, they are bringing their own theological claims to the table. so the question is, what is the justification for 66as we noted earlier, textbook authors need not canvass every species of creationism or intelligent design. nonetheless, in general we are not optimistic that authors will have the time or interest to cover even mainstream rivals in adequate detail. 67see luskin, “zeal for darwin’s house consumes them”; luskin, “darwin’s poisoned tree.” 68for more on the ncse and various legal cases, see their website: https://ncse.com/library?f%5b0%5d=taxonomy_vocabulary_ 14%3a289. volume 1, issue 2 3. the problematic presence of theology—general concerns 53 these authors’ particular claims about god? do they have any special insight concerning what the almighty is likely to have done in organic history? these questions become more poignant for authors who do not accept that god somehow planned or guided the evolutionary processes.69 on this view, human beings are not the result of a divinely-ordained plan. more directly, humans were not created by god in order to know god (in some sense) but were produced by mindless natural forces, such as random mutation and natural selection, that simply enabled them to survive and reproduce on the african savannah. in fact, it may be the case that, given this view of evolution, it’s very difficult to say that humans have the kind of cognitive equipment that is suitable to do counterfactual theology. did we really evolve cognitive powers to know (a priori) true subjunctive theological claims about what an all-powerful, perfectly free deity would probably do at distant episodes in the ancient past? of course, it’s possible that our lineage evolved this ability. but is it probable? it’s hard to say. and that’s just the point. darwin concluded as much in his mature reflections. late in life, when trying to reason about the existence of god, he drew himself up short: “but then arises a doubt—can the mind of man, which has, as i fully believe, been developed from a mind as low as that possessed by the lowest animal, be trusted when it draws such grand conclusions?”70 elsewhere he lamented, “a dog might as well speculate on the mind of newton.”71 darwin, of course, is not alone in this sentiment.72 on an unguided view of evolution, it is likely inscrutable or improbable that human beings can do such theology. if we don’t have cognitive access to such claims, then we are not justified in using such claims in arguments for evolution. this means that, if a non-theistic version of evolutionary theory is correct, then theology-laden arguments for evolution are illegitimate. we have reached beyond our ken. so, pace objection 2, we have no legitimate grounds upon which to say, “god would probably do such-and-such” in organic history. 69see the brief arguments along these lines in dilley, “charles darwin’s use of theology”; dilley, “nothing.” 70charles darwin, the autobiography of charles darwin 18091882, ed. nora barlow (new york: w.w. norton & co., 1958), p. 92-93. 71francis darwin, the life and letters of charles darwin (london: john murray, 1887), vol. 2, p. 312. darwin does not say in this letter that his theological muddle arose because of his theory of evolution. that connection became explicit later in his autobiography. 72patricia churchland, “epistemology in the age of neuroscience,” journal of philosophy, vol. 84, no. 10 (1987): 544-53; michael ruse, “belief in god in a darwinian age,” the cambridge companion to darwin, j. hodge and g. radick, eds. (new york: cambridge university press, 2003): 368-92. see also thomas m. crisp, “on naturalistic metaphysics,” the blackwell companion to naturalism, kelly james clark, ed. (hoboken, nj: john wiley & sons, inc., 2016), 61-74. our deeper concern, of course, is not just with objection 2. instead, our epistemological worry casts doubt on an array of theology-laden arguments for evolution. whenever textbook authors bring their own partisan theology to bear—whether straw god, presumptive, or something else entirely—they run the risk of relying on unjustified premises. if unguided evolution is true, these arguments fail. (recall that over 60% of the textbooks on our list use presumptive theology. that percentage increases when we consider other types of god-talk.) even more pressing, any textbook that uses its own partisan theology falls prey to the same dynamic. in a profound way, unguided evolution erodes some of its own foundation. for those of this ilk, the presence of theology is indeed problematic. 3.4 a ‘science and religion’ concern another significant cost arises when we consider two widelyknown models of the relationship between science and religion. both models posit something of a ‘separation’ between science and religion; this creates problems for all three objections above. the first model, stephen jay gould’s “non-overlapping magisteria” (noma), posits that science and religion “do not overlap.”73 science “covers the empirical realm” whereas religion “extends over questions of ultimate meaning and moral value.”74 a second model, complementarity, holds that science and religion can overlap in the sense of studying the same phenomena, but do so at complementary levels. given that science and religion always function at different levels, they maintain a principled level of separation.75 collectively, these two models hold (or imply) that (i) the propositional content of theology cannot affect the epistemic justification of a given scientific hypothesis or theory. that is, theology can’t be used as evidence for or against scientific claims. (ii) likewise, scientific theories and evidence cannot impact the epistemic justification of any religious belief. that is, scientific claims cannot support or refute religious claims. and, (iii) theological claims cannot function as premises in a scientific argument. theology must remain separate from science. what man has cast asunder, let no one join together. yet two problems arise. first, if either of these models is correct, then all theology-laden arguments for evolution no longer belong in biology textbooks—particularly in sections that give the scientific “evidence for evolution.” claims about ‘what god would probably do’ (whether from cre73stephen jay gould, rocks of ages: science and religion in the fullness of life (new york: ballantine books, 1999). 74gould, rocks of ages, 6. 75for example, denis r. alexander’s brief, “models for relating science and religion,” faraday report no. 3 (cambridge, uk: faraday institute for science and religion), 4. 54 damned if you do and damned if you don’t ationists or others) have no relevance to scientific justifications for evolution. as such, a lot of textbooks on our list ought to eschew some of their own arguments.76 second, if either model is correct, then scientific evidence is powerless to critique creationism (given that it is a theology-laden hypothesis). it is also powerless to favor evolution over creationism. phenomena like anatomical similarities, vestigial organs, pseudogenes, and nested hierarchies, have nothing to say about the plausibility of evolution over creationism; nor do they even touch creationism. we will return to these crucial problems later. for now, the point is that, under noma or complementarity, textbooks cannot use scientific evidence against creationism nor can they use theology as evidence for evolution. the cost of separation is high: by sequestering god, one limits the reach of science. 3.5 methodological concerns one last problem remains for all three objections.77 by some lights, the presence of theological claims as part of arguments for evolution run contrary to the scientific method itself. to see why, consider that vast numbers of scientists accept “methodological naturalism” as an essential feature of science.78 methodological naturalism is roughly the idea that scientific explanation, argument, testing, research, and articulation should invoke only natural laws, processes, or 76see the “separation/hm” column of figure 1. 77the argument that follows has been developed in dilley, “how to lose a battleship.” 78for example, eugenie scott, evolution vs. creationism (berkeley, ca: university of california press, 2004), xi, 3, 50-51, 249-54; francis collins, the language of god (new york: the free press, 2006), 165–166; robert o’connor, “science on trial: exploring the rationality of methodological naturalism,” perspectives on science and christian faith 49 (march 1997): 15–30; darrel falk, coming to peace with science (downers grove, il: intervarsity press, 2004), 39; kathryn applegate, “a defense of methodological naturalism” pscf 65, no 1 (march 2013): 37–45; keith b. miller, “an evolving creation: oxymoron or fruitful insight?” perspectives on evolving creation, ed. keith b. miller (grand rapids, mi: eerdmans, 2003), 7; conor cunningham, darwin’s pious idea (grand rapids, mi: eerdmans, 2010), 265; denis alexander, creation or evolution: do we have to choose?, rev. and expanded ed. (grand rapids, mi: monarch, 2014), 216–218; holmes rolston iii, denis alexander, jeff schloss et al., “the concept of ‘intelligent design’,” the international society for science and religion, 2011, accessed march 28, 2017, http://www.issr.org.uk/issrstatements/concept-intelligent-design/; kenneth miller, finding darwin’s god (new york: harpercollins, 1999), 167–169, 218–219, 239–243; and miller, only a theory (new york, viking, 2008), 185– 187; ian barbour, “science and scientism in why religion matters,” ed. huston smith, zygon 36, no. 2 (june 2001): 207–214, esp. 209– 210; richard t. wright, biology through the eyes of faith, rev. and updated ed. (new york: harpercollins, 2003), 31–51, 74–75; karl giberson, saving darwin (new york: harpercollins, 2008), 159–160. entities rather than supernatural agents, entities, or processes.79 while religious ideas may be a source of scientific inspiration for some scientists, scientific discourse itself should not use any religious ideas or language. this directly implies that scientific arguments for evolution should not use theology-laden claims. god-talk is not permissible as a premise in any scientific argument for evolution. it is a violation of the scientific method, therefore, to use premises such as ‘god would do x’ or ‘god can do x’ or ‘god would probably do x’ or the like. theology may be legitimate in its own domain, and it may even overlap with objects or processes studied by science, but theological claims are not appropriate within scientific research and discourse proper. the problem, of course, is that, if methodological naturalism is a necessary feature of modern science (or of the modern scientific method), as many believe, then any theologyladen argument for evolution automatically falls outside the bounds of science. they are beyond the pale. this is true across the board, from ‘good’ theology to ‘bad’ theology. a given theological claim may be plausible or implausible; it may be well-defined or nebulous; it may have long-standing precedent in an ancient tradition or may be brand new from harpercollins. it doesn’t matter. any appeal to supernatural agents, entities, or processes is banned in toto. this means that all of the theology-laden arguments discussed in this paper—as well as others discussed elsewhere—have no place in scientific discourse and research. pretty clearly, if methodological naturalism is canonical, then all godtalk ought to be excluded from biology textbooks’ scientific case for evolution. otherwise, the case for evolution runs counter to the scientific method itself. and that is no small thing. just as troubling, if methodological naturalism is canonical, it also means that, within the context of science, empirical evidence cannot refute any theology-laden hypothesis or theory. given that theology is barred from scientific discourse, it cannot enter into this discourse long enough to be tested and falsified. as with noma and complementarity, methodological naturalism mandates that evidence of molecular sequences, biogeographical distribution, embryological similarity, and the like can never count as scientific evidence against any god-based claim, no matter what these data are. this, too, is problematic: science effectively loses its straightforward implications. * 79the definition given is known as intrinsic methodological naturalism. another, more mild version is so-called provisional methodological naturalism. for reasons why provisional methodological naturalism fails, see dilley, “how to lose a battleship,” 620–21. volume 1, issue 2 4. the absence of theology is also problematic 55 stepping back for a moment, it is important to note that the power and relevancy of the problems explored above vary depending upon what a given textbook says or, more generally, what a given textbook author (or authors) take to be important. for example, an author who is not committed to methodological naturalism would avoid some of problems above. as such, our list of concerns is not meant as a ‘one size fits all’ critique of every textbook on our list. instead, it is a general tour of the problems that require reckoning. and, as we observe in figure 1 and in our footnotes, a number of these problems apply in spades to many textbooks we have studied. recall now the three objections raised at the beginning of this section. they held, respectively, that (i) the ‘problem’ of theology in biology textbooks was merely a matter of sloppy language, (ii) this sloppiness can be dispensed with by focusing on what god would probably do, or (iii), more modestly, by focusing at least on what various creationists say god would probably do. yet if our argument is correct, these objections falter. instead, rhetorical, practical, legal, epistemological, demarcational, and methodological considerations all collectively ratchet up the price of including theology in textbooks’ arguments for evolution. while some textbook authors may be willing to accept these liabilities, for others they amount to a pound of biological flesh. 4 the absence of theology is also problematic having raised a number of worries about the presence of theology in arguments for evolution in biology textbooks, we now turn in the opposite direction. we argue that avoiding theology in these contexts is also problematic. this leads directly to the dilemma that we discuss further in section 5. for now, we argue that there is a high cost to the absence of god-talk in biology textbooks. some of the arguments we develop below are on the ‘other side of the coin’ to those articulated in sections 2 and 3. readers will notice that they have a parallel feel, but are developed from a different direction. to make our case, we will first raise three objections that a critic might have in mind. in the course of answering these objections, we will lay out our positive reasons why the exclusion of god-talk is undesirable for a number of textbooks. the first objection contends that theology is merely a dispensable foil. that is, a critic might think that textbook authors use god-talk only for rhetorical effect; the ‘real’ evidence for evolution centers on purely natural phenomena, like homological similarities, molecular sequences, nested hierarchies, and the like. at most, creationism (and its associated theology) is just a historical artifact that is irrelevant to the true justification of evolutionary theory, especially in the present day. second, a critic might say that theology has no place within science. on this view, science is governed by methodological naturalism, noma, complementarity, or the like. these approaches accept some version of the ‘separation’ thesis: science cannot address religious claims, or such claims are not appropriate within scientific research or discourse proper.80 third, a critic might alternatively contend that textbooks do not even need to take a principled stance on methodological naturalism, noma, complementarity, or any version of the separation thesis. each of these make some pronouncement about theology (e.g., ‘it occupies a separate magisterium than science’). instead, why not just be silent on the matter? the path forward is to make no pronouncements at all. just ignoring theology entirely.81 for brevity’s sake, we will label these as (i) the periphery objection, (ii) the separation objection, and (iii) the silence objection, respectively. 4.1 evidence and background beliefs one initial concern about all three objections is that, for many people, they do not adequately take into account the broader context of inquiry. in a narrow sense, the original inquiry is a seemingly simple question: is evolutionary theory true? to answer this question, textbooks provide various lines of evidence. (hence, the ubiquitous “evidence for evolution” sections.) yet the matter becomes immediately complicated by the fact that evidence is typically relative to a set of background beliefs. what counts as evidence for one person, given her background beliefs, may not count as evidence for another person, given his background beliefs. thus, background beliefs are in play when asking about the truth (and justification) of evolutionary theory. in the context of the western tradition and american culture, claims about god’s alleged actions in organic history form key elements of some people’s background beliefs. in80see figure 1 for a full list of textbooks that accept the separation thesis (or halfway measures, a less overt version of the separation thesis. see our discussed below). 81the best example of this on our list is gunstream, explorations in basic biology. hillis et al., principles of life apparently tries to be silent on all things theological as well, but perhaps less successfully. 56 damned if you do and damned if you don’t deed, millions have held, and continue to hold, creationist beliefs of one kind or another. moreover, many non-theists are in a similar epistemic position: some of them accept evolution in part because of theology-laden arguments.82 (we have seen some of these arguments in this article; there are more as well—for example, ‘god would never design a suboptimal panda’s thumb, but an imperfect structure is just what we’d expect on natural selection.’) more broadly, as cornelius hunter has shown, theological claims have been central to the debate on biological origins for centuries.83 in fact, the contest between natural and supernatural explanations of the physical world has been embedded in the western tradition since its inception. as cambridge classicist david sedley has observed, the matter was considered “fundamental” by ancient thinkers like socrates, plato, aristotle, anaxagoras, empedocles, democritus, the epicureans, and the stoics.84 the melee between natural and supernatural explanations continues to the present day, especially concerning matters of the origin of the universe, life, and the human mind. so, for many people, theologyladen background beliefs are crucial to evaluating the case for evolution. thus, it is simplistic to hold, as the objections do, that theology is peripheral to the discussion, or science and theology are to remain separate, or discussions of evolution can just ignore theology altogether. for many, the seemingly simple question, “is evolution true?” can only be answered by taking into account the divine. 4.2 the failure of halfway measures a parallel point concerns the ‘halfway measure problem.’ halfway measures, as we use the term, are attempts to evaluate the empirical content of a theology-laden hypothesis, but only after separating it from its theological moorings.85 the idea here is that textbooks can successfully make their case for evolution by ‘sticking to the facts’ without venturing into god-talk. this approach is very much in accord with the separation, silence, and periphery objections. consider, for example, miller & levine biology.86 in their presentation of the case for evolution, miller and levine avoid all mention of god, special creation, young-earth creation, intelligent design, and the like. indeed, even in 82as noted in dilley, “nothing,” (p. 784), some atheists and agnostics have very strong beliefs about what actions in organic history are befitting of god, were he to exist. 83hunter, “darwin’s principle”; hunter, science’s blind spot. 84david sedley, creationism and its critics in antiquity (berkeley: university of california press, 2007), xvi. 85ironically, this strategy was championed by some modern creationists themselves. see numbers, the creationists, 7, 268-85. for ridley’s halfway measure, for example, see ridley, evolution, p. esp. 43-70, esp. 44, 67-68. 86this text is one of the top high-school biology titles. their historical recounting of the origin, they state that darwin’s feat was to overthrow the view that species are fixed and the earth is young—never mentioning creationism at all!87 evidently, miller and levine are quite serious when they say, “scientific endeavors never concern, in any way, supernatural phenomena of any kind.”88 but the matter is not so easy. it turns out that ‘empirical facts’ don’t just stick to themselves; they also stick to theology. for example, miller and levine state that darwin’s “contribution to science” helped falsify claims that the earth is young and that species are fixed.89 they point out, for example, that modern geology has shown the earth to be ancient: geologists now use radioactivity to establish the age of certain rocks and fossils. this kind of data could have shown that earth is young. if that had happened, darwin’s ideas would have been refuted and abandoned. instead, radioactive dating indicates that earth is about 4.5 billion years old—plenty of time for evolution by natural selection to take place.90 so, according to miller and levine, the earth is about 4.5 billion years old. yet, if this claim is true, then any claim incompatible with it must be false. that is, let us plausibly suppose the following is true: 1. the earth originated 4.5 billion years ago. the truth of this claim entails the falsity of a competing claim—namely: 2. the earth originated 6,000 to 10,000 years ago. and, the falsity of (2) entails the falsity of third claim: 3. the earth originated 6,000 to 10,000 years ago by a direct act of god. the logic of these entailments is inescapable. if (1) is true, then (3) must be false. in effect, miller and levine have adopted a halfway measure in order to avoid the appearance 87miller and levine, miller & levine biology, p. 450-64, esp. 45354. 88miller and levine, miller & levine biology, p. 5. 89miller and levine, miller & levine biology, p. 450-53. 90miller and levine, miller & levine biology, p. 466. volume 1, issue 2 4. the absence of theology is also problematic 57 of evaluating a theology-laden claim. but this appearance is a façade. the plain reality is that the truth of evolutionary theory and its tenets logically entails the falsity of any theory that posits contrary claims. it doesn’t matter whether the theory in question includes supernatural beings or not.91 it also doesn’t matter if the theory is ‘supposed’ to be in a separate domain. a fact is a fact; any claim to the contrary is false. accordingly, it is simplistic to issue an unnuanced pronouncement, as miller and levine do, that “[s]cientific endeavors never concern, in any way, supernatural phenomena of any kind.” the direct implications of their own scientific assertions say otherwise.92 more deeply, it is likewise simplistic to claim that biology textbooks can ‘stick to the empirical facts’ and leave theological considerations aside in their case for evolution. in the end, the truth of certain empirical facts logically mandates the falsity of certain theological claims.93 combined with our discussion about background beliefs, this consideration sharpens the problems with all three objections, especially the ‘separation’ and ‘silence’ objections. for example, all versions of the ‘separation’ thesis hold that scientific claims cannot affect the plausibility of religious claims. the duo are said to occupy different domains (or complementary levels). yet in light of american culture and the western tradition, for many people, the data of an ancient earth do affect the plausibility of claims about god’s purported action 10,000 years ago. this is true not just of many evolutionists, but also for many young-earth creationists; they recognize the basic logical dichotomy in 91to be clear, our point is not that miller and levine are tacitly “doing theology” in their textbook. instead, our point is that they are doing science. like it or not, their scientific claims have undeniable implications for the truth or falsity of some other claims, including some theological claims. 92surprisingly, in another textbook, miller and levine state: “darwin knew that accepting his theory required believing in philosophical materialism, the conviction that matter is the stuff of all experience and that all mental and spiritual phenomena are its by-products.” philosophical materialism rejects the existence of god, gods, spirits, non-reductive souls, the one, atman is brahman, and the like. apparently, then, the direct implication of darwinian evolution is that virtually every major religion is false. that sounds rather unlike the claim that “[s]cientific endeavors never concern, in any way, supernatural phenomena of any kind.” see miller and joseph, biology: the living science, 148-61, esp. p. 161, original emphasis. one also wonders what kenneth miller was up to when he argued that radiometric data counters young-earth creationism in finding darwin’s god (new york: harpercollins, 1999), 57-80. 93of course, a critic can avoid this conclusion by maintaining, for example, that there are different levels (or types) of truth. (note that this is much different than the claim that there are different theories of truth.) for problems with this view, see bradley monton, seeking god in science: an atheist defends intelligent design (peterborough, ontario: broadview press, 2009), chapter 2. other attempts to avoid our conclusion also incur additional problems: cf. john worrall, “science discredits religion,” in contemporary debates in philosophy of religion, michael l. peterson and raymond j. vanarragon, eds. (malden, ma: blackwell publishing, 2004), 59-72, 87-90, esp. 59ff. play: either ancient earth data are correct or their view is correct, but not both. they simply believe that they have better grounds to accept the latter rather than the former.94 more generally, wherever one falls on the dichotomy, the point here is that many people have theology-laden background beliefs about biological origins, and they also recognize the logical incompatibility of some scientific claims with some theological claims. for this group, halfway measures are a chimera. of course, some critics disagree. they maintain an unyielding form of the separation thesis (or of the silence or periphery objections). these individuals obviously hold different background beliefs than those mentioned above; they also deny that the logical incompatibility of some empirical data and certain theological claims is of much concern. science, when rightly done, stays within its own realm; religion, when rightly interpreted, likewise minds its place. neither impinge on the plausibility of the other. by way of reply: there is, unfortunately, a high price to be paid for this approach. as we will explore more below, if science does not impinge upon theology, then scientific data cannot impinge upon the truth or falsity of any hypothesis about god’s alleged actions in organic history. textbooks cannot say, then, that scientific evidence disconfirms youngearth creationism. more generally, they cannot say that scientific evidence favors evolution over creationism. apparently, the data of embryology, biogeographical distribution, vestigial structures, and the like are of little or no use to show the empirical superiority of evolution over its supernatural rivals. scientific evidence never crosses into the religious domain with any force. instead, it is impotent. as mentioned, we will return to this point in due course. for now, we simply want to point out that maintaining any of the three objections, along with halfway measures, includes a significant cost.95 94even if one allows that philosophical ideas like the “appearance of age” and “uniformitarianism,” rather than empirical data, are highly relevant to testing young-earth creationism, the empirical data still remain vital to the discussion. after all, the “appearance of age” and “uniformitarianism” become relevant precisely because the empirical data seem to run counter to a young earth. if the data were the reverse, there would be no need to defend the “appearance of age” or to attack “uniformitarianism.” 95some critics might protest that the best form of the separation thesis allows scientific evidence to affect some, but not all, theological claims. it only informs those that are incorrect interpretations of a given religious text. so, for example, science can in principle falsify young-earth creationism given that, on this view, young earth claims are typically taken to be an incorrect interpretation of the bible. the benefit of this version of the separation thesis is that it allows science to counter incorrect theologies, but (apparently) it cannot touch correct theology (whatever it happens to be). by way of reply: we quite agree that some religious claims are beyond the purview of science (e.g., religiously-oriented ethical claims about what humans ought to do). but this insight is compatible with models of science and theol58 damned if you do and damned if you don’t stepping back, if we are correct about our general argument in this section, then it is implausible to say—at least for many people—that theology is ‘peripheral’ to the justification of evolution. it is also implausible to say that science has no epistemic implications for religious claims or that simply being silent settles the matter in a satisfactory way. for many, god-talk is simply too relevant to ignore. 4.3 mind-world affinity but the well goes deeper. evidence has emerged in the last few decades that human beings are hardwired for belief in the gods and in the design of some of the features of the natural world. for example, one oxford-led analysis involved 57 researchers who conducted 40 separate studies in 20 different countries, including countries that were traditionally theistic as well as others than were more significantly atheistic. the study concluded that humans are “predisposed” to believe in gods and an afterlife.96 other research indicates that preschool and elementary aged children naturally ascribe the origins of certain objects in terms of their function (‘this was made to do that’) and construe objects and events as intentionally caused (‘someone made this’). by 6-10 years, kids connect biological functionality in nature with “goal-directed design.”97 as alison gopnik observes, “by elementary-school age, children start to invoke an ultimate god-like designer to explain the complexity of the world around them—even children brought ogy that reject the separation thesis (e.g., the concord model). if the separation thesis is to be meaningful at all, it must claim that theological claims that touch the natural world in a significant way are, if correctly interpreted from scripture, beyond the reach of science. but we wonder whether this can really be decided prior to looking at the empirical evidence itself. it seems possible in principle, for example, for archeologists to find evidence that confirms, to one degree or another, that jesus existed (say, ancient inscriptions, ossuaries, structures, settlements, or the like that correspond to key events, people, and places in biblical accounts of the life of jesus). all things being equal, this would count as confirming, even if slightly, a major claim of the new testament: namely, that jesus lived in first-century palestine. on the other side of the coin, is seems possible in principle for archeologists to find evidence to the contrary (say, by finding a systematic pattern of error in bible accounts of first-century places, geography, people groups, events, etc. that are central to the given descriptions of the life of jesus). thus, in our view, the ‘partial’ version of the separation thesis draws arbitrary boundaries around what religious claims can or cannot be affected by science. see also note 119. 96justin barrett, cognitive science, religion, and theology (west conshohocken, pa: templeton press, 2011); justin barrett, born believers: the science of childhood religion (new york: free press, 2012); see also oxford university’s press release, “humans ‘predisposed’ to believe in gods and the afterlife,” 16 may 2011, available at: https://phys.org/news/2011-05-humanspredisposed-gods-afterlife.html. 97deborah kelemen et al., “young children can be taught basic natural selection using a picture-storybook intervention,” psychological science, vol. 25, no. 4 (2014): 894. up as atheists.”98 even veteran scientists, habitually trained to favor naturalistic explanations, cannot escape teleological thinking.99 psychology professor deborah kelemen summarizes these findings: “even though advanced scientific training can reduce acceptance of scientifically inaccurate teleological explanations, it cannot erase a tenaciously early-emerging human tendency to find purpose in nature.”100 if this is our natural way of thinking, then, at a very practical level, it will be exceedingly difficult to eradicate design-like reasoning in biology. and this will be true not just for theists, but for non-theists as well. from a cognitive point of view, the notion that theology can simply be avoided—especially in the context of biological origins—is psychologically implausible.101 it comes as little surprise, then, that even ardent evolutionary biologists wrestle with design-based thinking.102 francis crick’s admission is well known: “biologists must constantly keep in mind that what they see was not designed, but rather evolved.”103 and richard dawkins echoes this sentiment from the opposite direction: “it is almost as if the human brain were specifically designed to misunderstand darwinism, and to find it hard to believe.”104 the 98alison gopnik, “see jane evolve: picture books explain darwin,” wall street journal, 18 april 2014, available: http://www.bu.edu/cdl/files/2014/04/wsj-teaching-totsevolution-via-picture-books-wsj.com_.pdf. see also rebekah a. richert and justin l. barrett, “do you see what i see? young children’s assumptions about god’s perceptual abilities,” the international journal for the psychology of religion, vol. 15, no 4 (2005): 283-95. 99deborah kelemen, joshua rottman, and rebecca seston, “professional physical scientists display tenacious teleological tendencies: purpose-based reasoning as a cognitive default,” journal of experimental psychology: general, 15 october 2012, advance online publication: doi: 10.1037/a0030399. 100art jahnke, “the natural design default,” bostonia (winterspring 2013): 22-23, esp. 23. 101see the penetrating argument along similar lines by del ratzsch, “humanness in their hearts: where science and religion fuse,” the believing primate, eds. jeffrey schloss et al. (oxford, uk: oxford university press, 2009), 209-45. 102for example, bruce alberts, former president of nas: “why do we call the large protein assemblies that underlie cell function protein machines? precisely because, like the machines invented by humans to deal efficiently with the macroscopic world, these protein assemblies contain highly coordinated moving parts. . . [just as] a machine of our common experience.” bruce alberts, “the cell as a collection of protein machines: preparing the next generation of molecular biologists,” review issue: macromolecular machines, cell 92 (6 february 1998): 291, italics in original. see also annie crawford’s helpful analysis of the defenses of teleological language in biology by ernst mayr and michael ruse, respectively: crawford, “metaphor and meaning in the teleological language of biology,” ma thesis, houston baptist university, 13 august 2018. 103francis crick, what mad pursuit (new york: basic books 1990), 138. 104richard dawkins, the blind watchmaker (new york: w.w. norton and company, 1996), xi. volume 1, issue 2 4. the absence of theology is also problematic 59 ‘design temptation’ no doubt arises in part because of the extraordinary complexity of biological phenomena. crick and dawkins (and many other evolutionists) acknowledge that much of the world appears to be designed. of course, they think this is no actual design beneath it all. but the language of ‘appearance’ is itself significant. on their view, the mesmerizing flurry of a hummingbird’s wings and the delicate blush of an orchid look like artifacts of mind prima facie. this sentiment becomes especially significant when tied to the psychological studies on human cognition just mentioned: the biological world looks designed and the human mind naturally tends toward design-based explanations. the organic realm and the human mind fit together like jigsaw pieces—at least if one accepts the self-reports of evolutionists as well as recent research on human cognition. this apparent mind-world affinity, when applied to the present case, suggests that it is simplistic to claim, as the three objections above do, that theology is peripheral to some of the arguments for evolution, or that science and religion are separate, or that textbook authors can manage the matter by saying nothing at all. the human mind, the appearance of design, and the close connection between the two indicate otherwise. even more than the background beliefs supplied by american culture and the western tradition, this ostensible mind-world affinity shows the virtual inevitability of theology in discussions of biological origins. 4.4 arguments for evolution cast aside the absence of theology is problematic for another reason. from the origin to the present, biologists have repeatedly invoked god-talk as part of their positive case for evolutionary theory. if theology is barred (or ignored), then this array of justifications goes by the wayside. consider what this means. in the first place, the origin itself is utterly unintelligible without theological language. darwin’s primary objective was to show the superiority of evolution by natural selection over special creation.105 his repeated attacks on this view, as well as on other versions of creationism, are explicit and unmistakable.106 moreover, as scholars have shown, darwin’s conceptualization and justification of evolutionary theory itself include striking theological elements.107 105charles darwin, on the origin of species (london: john murray, 1859), p. 1-6. 106darwin, origin, 3, 6, 44, 55, 59, 95, 115, 129, 133, 138, 139, 152, 155, 159, 162, 167, 185, 186, 188, 194, 203, 244, 275, 303, 315, 352, 355, 365, 372, 389, 390, 393-94, 396, 398, 406, 413-14, 420, 434-35, 437, 453, 456, 465, 469, 470-71, 473-75, 478, 480-83, 486, and 488. 107john brooke, “the relations between darwin’s science and his religion,” darwinism and divinity, ed. john durant (new york: second, a number of prominent biologists rely on theology in their scientific case for evolution in the present day. they contend that evolution better accounts for the data in part because a respectable deity would never create a suboptimal organ, for example, or would always create new species from scratch, or the like. biologists who champion these arguments include luminaries such as theodosius dobzhansky, niles eldredge, douglas futuyma, john avise, neil shubin, jerry coyne, richard dawkins, george williams, stephen jay gould, francis collins, kenneth miller, denis alexander, and many others.108 their theology-laden oxford university press, 1985), 40–75, esp. 48–49; gillespie, charles darwin and the problem of creation; richard england, “natural selection, teleology, and the logos,” osiris 16 (2001): 270-287, esp. 274-275; dov ospovat, “god and natural selection,” journal of the history of biology 13, no. 2 (sept. 1980): 169-194; dov ospovat, “darwin’s theology,” review of neal gillespie’s charles darwin and the problem of creation,” science 207, no. 4430 (feb 1, 1980): 520; dov ospovat, the development of darwin’s theory (cambridge: cambridge university press, 1981), 223-224; momme von sydow, “charles darwin: a christian undermining christianity?” in science and beliefs: from natural philosophy to natural science, 1700-1900, eds. d. m. knight and m. d. eddy (burlington, vt: ashgate, 2005), 141-156; john cornell, “god’s magnificent law: the bad influence of theistic metaphysics on darwin’s estimation of natural selection,” journal of the history of biology vol. 20, no. 3 (fall 1987): 381412; dilley, “charles darwin’s use of theology,” 29-58; john cornell, “newton of the grassblade? darwin and the problem of organic teleology,” isis 77, no. 3 (sept. 1986): 405-421; james moore, the postdarwinian controversies (new york: cambridge university press, 1979), 318; robert j. richards, “theological foundations of darwin’s theory of evolution,” in experiencing nature, eds. p.h. theerman and k.h. parshall (dordrecht: kluwer academic pub., 1997), 61-79. 108donald prothero, evolution (new york: columbia university press, 2007), 30–49, esp. 37–39; theodosius dobzhansky, “nothing in biology makes sense except in the light of evolution,” the american biology teacher (march 1973): 125–129; stephen jay gould, ever since darwin (new york: w. w. norton, 1977), 91–96; gould, the panda’s thumb (new york: w. w. norton, 1980), 20–21, 24, 28–29, 248; gould, hen’s teeth and horse’s toes (new york: w. w. norton, 1983), 258–259, 384; gould, the structure of evolutionary theory (cambridge, ma: harvard university press, 2002), 104; gould, “evolution and the triumph of homology, or why history matters,” american scientist 74, no. 1 (1986): 60–69, esp. 63; douglas futuyma, science on trial: the case for evolution (sunderland, ma: sinauer associates, 1995), 46–50, 121–131, 197–201, 205; niles eldredge, the triumph of evolution . . . and the failure of creationism (new york: w. h. freeman, 2000), 99–100, 144–146; francisco ayala, darwin and intelligent design (minneapolis: fortress, 2006), 25–42, 85–89, esp. 34–36; francisco ayala, darwin’s gift to science and religion (washington, dc: joseph henry press, 2007), x-xi, 1–6, 22–23, 76, 88–92, 154–160; jerry a. coyne, why evolution is true (new york: penguin, 2009), 12, 13, 18, 26–58, 64, 71–72, 81– 85, 96, 101, 108, 121, 148, 161; richard dawkins, the blind watchmaker (new york: w. w. norton, 1986), 93; dawkins, river out of eden (new york: basic books, 1995), 95–133, esp. 105; dawkins, the greatest show on earth: the evidence for evolution (new york: free press, 2009), 270, 296–297, 315, 321–322, 332, 341, 351, 354, 356, 362, 364, 369, 371, 375, 388–389, 390–396 (we thank colin zwirko and caitlin maples for their fine research on coyne and dawkins); nathan h. lents, human errors (new york: houghton mifflin harcourt, 2018); r. diogo and j. molnar, “links between evolution, development, human anatomy, pathology, and medicine, with a proposition of a re-defined anatomical position and notes on constraints 60 damned if you do and damned if you don’t arguments appear in major areas of biology, including genetics, embryology, biogeography, paleontology, physiology, genomics, and the like. while we can only gesture toward this phenomenon here, we briefly note that several studies have brought to light notable features of these arguments.109 first, these studies collectively show that the biologists who make these arguments overwhelmingly view them as scientific—no doubt because they draw on scientific data, inferences, patterns of reasoning, and peer-reviewed research. second, these theological claims are typically indispensable to the arguments in which they appear.110 without god-talk, the arguments in question do not support evolutionary theory. third, these arguments are often central to a given thinker’s overall scientific case for evolution. indeed, some of these thinkers’ self-reported best arguments for evolution depend upon god-talk.111 if we adopt any of the three objections above, then this array of justifications for evolutionary theory counts for little. but this is a high price: apparently, textbooks must exclude some of the top biologists’ arguments for evolution.112 this pressing question becomes even more difficult in light of recent philosophical analysis of scientific testing. among philosophers of science, the current conventional view is and morphological ‘imperfections,” ’ journal of experimental zoology 326, no. 4 (2016): 1–10, elliptically; patrick forterre and daniele gadelle, “phylogenomics of dna topoisomerases: their origin and putative roles in the emergence of modern organisms,” nucleic acids research 37, no. 3 (2009): 679–692, esp. 679, elliptically; ulrich kutschera, “photosynthesis research on yellowtops: macroevolution in progress,” theory in biosciences 125 (2007): 81–92, esp. 90–91; émile zuckerkandl, “intelligent design and biological complexity,” gene 315 (2006): 2–18, esp. 10; george c. williams, the pony fish’s glow (new york: basic books, 1997), 2, 4, 6–10, 104, 132– 160; john c. avise, inside the human genome: a case for nonintelligent design (new york: oxford university press, 2010); neil shubin, your inner fish (new york: pantheon, 2008), 173–198; ian barbour, when science meets religion (new york: harpercollins, 2000), 111–114; denis alexander, creation or evolution, 234–251; francis collins, language of god (new york: the free press, 2006), 130, 134–137, 139, see also 176–177, 191, 193–194; karl giberson and francis collins, the language of science and faith (london: spck, 2011), 34, 38, 55, 101–108, 161; kenneth miller, finding darwin’s god, 80, 100–103, 267–269. 109dilley, “nothing”; dilley, “charles darwin’s use of theology”; nelson, “role of theology”; lustig, “natural atheology”; hunter, “darwin’s principle”; hunter, science’s blind spot ; hunter, “the random design argument.” 110see especially nelson, “role of theology”; dilley, “nothing.” 111among others, coyne, why evolution is true, 26–54, 79; dawkins, greatest show, 296–297, 315, 321–322. gould, structure, 104; dobzhansky, “nothing,” 126–128. 112it remains something of a puzzle just how biology textbooks can accurately represent their field while also ignoring the key arguments of some of their own notables. aren’t such omissions somewhat contrary to the very purpose of textbooks in the first place? (our thanks to a reviewer for bringing this point to our attention.) that scientific testing is contrastive.113 with rare exception, current models of testing require the juxtaposition of one theory against one-or-another rival. this is true of the big 3: likelihood, inference to the best explanation, and bayesian models. of course, it is possible for darwinian evolution to be tested against a non-theology-laden view (say, neo-lamarckian evolution). but the problem is that any such test only shows (at most) that darwinian evolution is empirically superior to this other non-theological theory. it does nothing to show that darwinian evolution is empirically superior to creationist rivals. justifying this latter claim requires head-to-head comparison.114 in such a comparison, god-talk is unavoidable. notably, the point here isn’t just that a number of prominent biologists happen to invoke theology in their arguments for evolution; rather, it’s that, according to recent analysis of scientific testing, any textbook author who wishes to defend evolution against all rivals cannot avoid theology. in this sense, if authors hold that darwinian evolution is the best explanation of things below, they must also contend with things above. 4.5 scientific evidence cast aside yet perhaps the most striking problem with the ‘no theology’ approach is that it undermines the very heart of biology textbooks: scientific evidence.115 if theology-laden claims are excluded, then scientific evidence is unavailable to critique creationism or to favor evolution over its supernatural rivals. regarding the first point, if science cannot address religious matters, then scientific data and arguments are impotent to falsify special creation, young-earth creationism, and the like. while some versions of creationism are not empirically testable, other versions surely are. readers even vaguely familiar with the biology textbooks on our list know that an overwhelming number claim (or imply) that radiometric dating of ancient strata run counter 113see sober, evidence and evolution, 109-88; sober, did darwin write the origin backwards?, 121-54. 114of course, some versions of creationism are not empirically testable (such as versions that invoke a deceptive deity). then again, other versions of creationism are empirically testable—at least that’s what many textbook authors seem to believe. why else would they critique creationism by reference to empirical data of, say, homologous structures, vestigial organs, pseudogenes, atavisms, the nested hierarchy, biogeographical distributions, and the like? for discussion about whether creationism, in its most defensible form, is really testable, see sober evidence and evolution, 109-88 and did darwin write the origin backwards?, 121-54. replies to sober include lim, “a critique of elliott sober’s goals and abilities objection to the design argument” and dilley, “how to lose a battleship,” 621-23. 115cf. larry laudan, “science at the bar—causes for concern,” science, technology & human values, vol. 7, no. 41 (fall 1982): 16-19; dilley, “how to lose a battleship,” 593-631. volume 1, issue 2 5. a difficult dilemma 61 to young-earth creationism, for example.116 second, if theology is ‘absent,’ then textbooks’ scientific data and arguments are also impotent to show the empirical superiority of evolutionary theory over supernatural rivals. but isn’t this a key reason why so many textbook authors promote the former over the latter? even a cursory read shows that they widely believe anatomical similarities, fossil sequences, suboptimal organs (and so on) count as empirical grounds to favor evolution over creationism. the evidence itself is supposed to have teeth. of course, a critic might counter that textbook authors can still retain all the evidence for evolution (and against creationism) without labeling this evidence as “scientific” per se. perhaps arguments that invoke theology ought to be filed under a different heading, such as “philosophical arguments” or “natural theology” or “cultural perspectives” or similar. textbooks can keep these arguments as long as they are careful to alert students to the differences between, say, scientific arguments and philosophical ones. by way of reply: this objection attempts to solve the problem by superficial relabeling. simply switching out titular headings (“philosophy” instead of “science”) hardly addresses the salient epistemological matter at hand. does empirical evidence have implications for the truth of evolutionary theory vis-à-vis creationism? do the data impinge upon creationism at all? mere labels change nothing. moreover, the arguments in question rely on scientific data, methods, inferences, articles, and patterns of thinking. they bear all the hallmarks of scientific analysis. to claim that they are not really scientific after all amounts to hollow word play. so, the point stands. the absence of theology is deeply problematic. moreover, this point transcends the analyses we have given of particular theologies in this article (presumptive theology, indeterminate theology, and so on). that is, a critic can completely disagree with our analyses of concrete cases of theology and yet still must face this problem. any scientific argument against creationism, of whatever form, requires theology (for example, ‘if god created human beings, we would expect. . . ’). and any scientific argument that claims that the data favor evolution over creationism also requires theology (for example, ‘on evolution, we’d expect similar bone structures, but if god was at work, we would not’). if theology is absent in the case for evolution, then scientific evidence is unavailable to critique creationism or to favor evolution over its supernatural rivals. the empirical evidence becomes effete. if god is gone, then so is the power of the data. 116see note 94. * we may now step back from our argument in section 4. we have contended that textbook authors must be prepared to pay the price if they wish to exclude theological considerations from their arguments for evolution. but this is not so easy, especially in the light of the failure of halfway measures, the broader influence of american culture and the western intellectual tradition, the mind-world affinity between the cognitive hardwiring of human beings and the striking appearance of design in nature, the theology-laden elements of the origin, a host of theology-laden arguments for contemporary evolutionary theory by prominent biologists, the role of comparative evaluation in scientific testing, and the centrality of empirical evidence. collectively, these factors encourage the inclusion, rather than exclusion, of god-talk in biology textbooks. 5 a difficult dilemma let us pause once again to recount our overall argument to this point. in sections 2 and 3, we contended that the presence of theology in evidence-for-evolution sections raises a whole range of problems for biology textbooks. in section 4, we argued the opposite. if our two arguments are correct, then biology textbook authors face a crippling dilemma. they are damned if they include god-talk and damned if they don’t. the difficulty of this dilemma can be further reinforced by a brief examination of a common solution offered by textbooks.117 we argue below, however, that this solution is both incoherent and self-serving. the failure of this approach underscores just how pressing the dilemma is. in a nutshell, the pressing difficulty with the ‘common solution’ is that some textbooks attempt both to incorporate theology into their scientific arguments for evolution and, at the same time, to bar theology from science itself. these texts wish to have their cake and eat it too. seventy-two percent of textbooks on our list do so.118 the problem usually begins with a demarcational claim. although these textbooks are often not as precise as they could be, in one way or another, a number of them ac117just to be clear, in our view, it’s not entirely clear that textbook authors are, in general, aware of this dilemma. so, we are careful not to say that authors are self-consciously giving a “solution” per se. rather, we will examine a typical approach among the textbooks on our list that, charitably interpreted, counts as a possible way to handle the dilemma. 118see the “separation/hm” column in figure 1. 62 damned if you do and damned if you don’t cept some version of the ‘separation’ thesis: science cannot address religious matters, or religious claims are not appropriate within a scientific context.119 this thesis is sometimes articulated in the form of noma, complementarity, or methodological naturalism. for example, in their textbook evolution, carl bergstrom and lee alan dugatkin write: the strategy of trying to explain the world based solely on natural phenomena is fundamental to the scientific method and is at the heart of modern evolutionary biology. it is sometimes called methodological naturalism. we call it naturalism because of the focus on the natural rather than the supernatural. we use the adjective methodological because this strategy provides a method or procedure for seeking scientific explanations of the world. . . . if we propose an explanation of a phenomenon based on natural processes, that is, if we develop a hypothesis, we can then test this hypothesis because we can observe and often manipulate these processes. by contrast, we have no way to observe, let alone manipulate, the supernatural, and thus we cannot test supernatural explanations.120 similarly, textbook authors colleen belk and virginia bor119for example, freeman et al., biological science, p. 9; urry et al., campbell biology, p. 16-26, esp. 18, 26; singh-cundy et al., discover biology, p. 13, 402; brooker et al., biology, p. 460, elliptically; belk and maier, biology, p. 4; solomon et al., biology, p. 16. as noted, a full list of textbooks that accept the separation thesis (or a halfway measure) can be found in figure 1. it’s worth pointing out that some textbooks accept partial versions of the separation thesis. for example, some claim that certain religious beliefs are testable by scientific methods (and so fall within the purview of science) while other religious beliefs are not testable by scientific methods (and so are isolated from science). for example, some textbooks state that scientists can test whether god created life only 6,000 years ago, but cannot test whether god exists per se. yet these textbooks virtually never provide any principled and defensible justification why “testability” applies to some religious beliefs but not others. (the oft-cited appeal to the necessity of “predictions” does not, in itself, resolve the matter; it only repackages the problem with slightly more focus.) moreover, in principle it seems possible that some scientific data, now or in the future, are relevant to the question of god’s existence. for example, depending on one’s background beliefs, a version of the problem of evil that turns on a scientific analysis of predation and animal suffering arguably has implications for the implausibility of theistic belief. or, on the other side of the coin, the existence of a fine-tuned universe may provide support for theistic belief to one degree or another—again, depending on one’s background beliefs. whatever the case, our own speculation is that textbook authors who endorse a partial version of the separation thesis either are unaware of the considerations explored here or, perhaps, are trying to placate religious students by assuring them that they are allowed a handful of generic religious beliefs (such as “god exists”), which, they are told, remain safe from the power of science. see also note 95. 120bergstrom and dugatkin, evolution, p. 32, original emphases. den maier state: for a hypothesis to be testable by science, we must be able to evaluate it through observations or measurements made within the material universe (chapter 1). because a supernatural creator is not observable or measurable, there is no way to determine the existence or predict the actions of such an entity through the scientific method. therefore, as it is stated, special creation is not a scientific hypothesis. in fact, any statement that supposes a supernatural cause—including intelligent design, which argues that while evolution is possible, some specific features of organisms must have been designed by a creator—cannot be considered science.121 as one texts simply puts it: “scientists cannot evaluate a claim about the actions of a supernatural agent, since scientific theories explain phenomena that follow natural, repeatable patterns.”122 in sum, in one way or another, many of our textbooks endorse the separation thesis.123 two concerns arise. first, if religious explanations cannot be evaluated (or are ‘not testable’), then what of the empirical tests in biology textbooks that aim to show the superiority of evolutionary theory over special creation or young-earth creationism?124 the strong majority of textbooks we examined held that, across a wide range of subdisciplines of biology, creationist hypotheses in one form or another have been vetted against the empirical data and found wanting. indeed, the whole point of comparative arguments between evolutionary theory and creationism, from the origin to the present, is to show that the data vindicate the former over the latter. unfortunately, when taken as a whole, over 70% of our textbooks offer an incoherent model of the relationship between science and religion: in the ‘nature of science’ chapters (typically), these textbooks assert that religious claims cannot be evaluated by the methods of science, for example, but in the ‘evidence for evolution’ chapters, they draw on scientific evidence to deem particular religious claims false.125 this is plainly in121belk and maier, biology, p. 207. 122zimmer and emlen, evolution, first edition, p. 320. interestingly, this quote was removed in the second edition of the text. 123in total, 21 out of 32. 124cf. laudan, “science at the bar—causes for concern,” 16-19. 125see the “incoherence” category in figure 1. examples include freeman et al., biological science, p. 9, 441-43; urry et al., campbell biology, p. 18, 26, 466-83, esp. 467-68, 477-78; mader, biology, p. 11 (elliptically), 266-79, esp. 267; singh-cundy et al., discover biology, p. 13, 386-89, 402; phelan, what is life?, p. 4-5, 24, 332-33, 336-37; audesirk et al., biology, p. 10-11, 263-66, 270-71; belk and maier, biology, p. 4, 207, 213, see also 230; bergstrom and dugatkin, volume 1, issue 2 6. final thoughts 63 coherent, like saying that a student failed an exam she was never eligible to take. a second concern surfaces as well. even if we concede that religious claims are not testable, we are still left with a problem: if the separation thesis is correct, why are theologyladen arguments present in biology textbooks in the first place? in particular, why are theological claims part of the scientific case for evolution? as we have noted, theological assertions appear in chapters (or sections) that selfconsciously present the scientific evidence for evolutionary theory. in fact, theological claims play a key role in some of these arguments. yet if god-talk remains in a separate realm from science-talk, then theological propositions have no legitimate place in this context. once again, in their opening chapters, many textbook authors prohibit the incursion of religious claims into science, then, in their ‘evidence for evolution’ chapters, they permit religious claims back into science for the purpose of bolstering evolutionary theory. theological claims are barred—except when they are not. this, too, is incoherent. even worse, it is self-serving. god-talk is only allowed when it strengthens evolution. j.b.s. haldane once quipped that “[t]eleology is like a mistress to the biologist; he dare not be seen with her in public but cannot live without her.” perhaps something similar can be said of theology: her existence is never officially acknowledged, yet her diverting benefits come in handy when desired. this underscores the difficulty that biology textbook authors face. do they include theology or do they dispense with it? the ‘solution’ so common among textbooks on our list only exacerbates the dilemma. evolution, p. 31-32, 53, 55, 115; herron and freeman, evolutionary analysis, p. 38, 43, 56, 103; hall and hallgrimsson, strickberger’s evolution, p. 56, 208, 574-75; mader and windelspecht, essentials of biology, p. 11-12 (elliptically), 237-51, esp. 248; taylor et al., campbell biology: concepts and connections, p. 6, 260-61, 264, 278. less clear, but still notable, examples include: krogh, biology, p. 8, 286-87, 293-95; simon et al., campbell essential biology, p. 4, 250; barton et al., evolution, p. 75, 81-82; sadava et al., life, p. 15, 420, 443; solomon et al., biology, p. 16, 391-405, esp. 391-95; shuster et al., biology for a changing world, p. 2-6, esp. 3, 322-24, 352-69 (in our view, the text lacks nuance about the testability of supernatural hypotheses); miller and levine, miller & levine biology, p. 5, 466 (see our discussion of miller & levine); hoefnagels, biology: concepts and investigations, p. 13, 238-43, 260-79, esp. 264; sadava et al., life, p. 15, 420, 443; zimmer and emlen’s first edition of evolution, is incoherent on this score (see p. 42, 44, 318, 320). their second edition assiduously erases any mention of the supernatural in later chapters, thus giving the appearance of avoiding the problem. but see our comments about ‘halfway measures.’ on a related note, if one is skeptical of ridley’s own halfway measure, then ridley, evolution, p. 43-70. see also futuyma and kirkpatrick, evolution, p. 44-45, 573-83, esp. 578 on testing whether “an omnipotent god. . . created anything.” 6 final thoughts in this essay, we have argued that biology textbook authors face an unwelcome predicament: there are pressing reasons both to include and to exclude theological claims in arguments for evolution. we attempted to establish this thesis in four parts. in section 2, we examined concrete examples of straw god theology, presumptive theology, and indeterminate theology. we argued that each type played an important role in some arguments for evolution and yet all three types face significant difficulties, including mischaracterizations of opponents, unsupported certitude about what god would do, and trivial expressions about what god might do. in section 3, we stepped back from concrete cases and instead explored broader problems created by generally having theology in biology textbooks’ arguments for evolution. these problems include: • the worry that direct engagement with contemporary versions of creationism (or intelligent design) may give students the mistaken impression that these hypotheses are legitimate contenders to evolutionary theory. • the practical lack of time and interest of authors to learn and nuance various versions of creationism (and id), and to tease out in their textbooks which particular arguments support evolution over which versions of creationism. • in public high schools, the legal precedents in epperson, mclean, edwards, kitzmiller, which may ban arguments for evolution that draw on (or critique) certain propositions involving a supernatural creator. • the epistemological problem that, given unguided evolution, it likely inscrutable or improbable that human beings can legitimately justify certain theological claims, including those used in arguments for evolution. • the ‘science and religion’ demarcation problem, in which the truth of either noma or complementarity renders scientific evidence powerless to critique creationism. • similarly, the truth of either noma or complementarity leaves scientific evidence impotent to favor evolution over creationism. • the ‘methodological’ problem, in which, if methodological naturalism is proper to science, then theologyladen arguments for evolution run counter to the scientific method itself. 64 damned if you do and damned if you don’t • similarly, if methodological naturalism is canonical, then, within the context of science, empirical evidence cannot refute any theology-laden hypothesis or theory. • and, finally, if methodological naturalism is correct, then, within the context of science, empirical evidence can never favor evolution over creationism. thus, the general presence of theology—of whatever kind— creates unwelcome problems for biology textbooks. while the saliency of these problems depends in part on the commitments of a given textbook (or author), nonetheless, as a collection, they pose a formidable obstacle. in section 4, we switched gears and tackled the question, “why not get rid of theology?” we argued that this is easier said than done. problems abound, including: • the broader influence of the western intellectual tradition and of american culture on the background beliefs of millions of people in the united states • the failure of halfway measures • the ‘design-oriented’ cognitive hardwiring of human beings • the striking appearance of design in nature • the mind-world affinity between this hardwiring and the appearance of design in nature • the loss of the central argument in the origin • the loss of a host of theology-laden arguments for contemporary evolutionary theory by prominent biologists • the need for comparative evaluation in scientific testing • the loss of scientific evidence to critique creationism • the loss of scientific evidence to favor evolutionary theory over creationism collectively, these factors encourage the inclusion, rather than exclusion, of god-talk. finally, in section 5, we articulated the dilemma that is now obvious. moreover, we underscored the power of this dilemma by examining a frequent ‘solution’ found in many texts. we argue that this solution is thoroughly incoherent and self-serving. the poor performance of textbooks on this point shows just how deep the difficulty is. in the end, the overall dilemma remains. it would be a mistake, of course, to say that our analysis constitutes a critique of evolutionary theory or of the comprehensive justification for it. our argument is fully compatible with the truth and justification of evolution. while we acknowledge that our worries about textbooks are not entirely disconnected from these broader topics, even so our study does not attempt an expansive analysis of the theory itself or its general grounding. we return at last to thomas kuhn’s meditation on textbooks in structure. he contends that science textbooks play a regulative ideal. they articulate to both laymen and scientists the contours, boundaries, and content of a given paradigm. they tell us what a field is, how it operates, and the way scientists are supposed to reason within that discipline. in this article, we have analyzed 32 textbooks, including the top four in each of the key undergraduate categories: biology majors, non-majors, and evolution courses. surprisingly, the paradigm that emerges from these texts includes a deep theological muddle. if our argument is correct—and if kuhn’s analysis of the role of textbooks is right—then the problems we’ve described affect more than just current undergraduates. instead, as students graduate and join the work force, they may well carry this conflicted paradigm with them to broader domains of society, from professional to lay, public to private. if so, then the problem will only deepen. darwin once said in his later years that he was in a theological muddle.126 on this point, as with so many others, darwin’s legacy will likely survive and reproduce for some time to come. acknowledgements the authors would like to thank kathryn applegate, elizabeth barnes, ashby camp, casey luskin, paul nelson, adam shapiro, jim stump, jonathan wells, and anonymous reviewers. about the authors stephen dilley, ph.d., is an associate professor of philosophy at st. edward’s university. he can be reach at stephend@stedwards.edu. nicholas tafacory, mla, is an independent scholar. he can be reached at nicholas.tafacory@gmail.com. 126charles darwin, letter to j.d. hooker. 12 july 1870. darwin correspondence project, “letter no. 7273,” accessed on 7 may 2019, http://www.darwinproject.ac.uk/dcp-lett-7273. volume 1, issue 2 god-talk table 65 figure 1: god-talk table notes: (a) an asterisk designates an elliptical statement that, in our view, can be plausibly interpreted as presumptive theology, indeterminate theology, or the like (as appropriate) when considered in the larger context of the passage. (b) “separation/hm” indicates a version of the separation thesis (e.g., noma, methodological naturalism) or a halfway measure. title straw god presumptive indeterminate separation/hm incoherence audesirk 11th p. 263 p. 265-66, 270-71 p. 10-11 p. 10-11, 263-66, 270-71 barton 1st 75 75, 81 81-82* 75, 81-82 belk 5th 205-207 4, 207 207, 213, 230* bergstrom 2nd 33 115 31-32 31-32, 53, 55, 115 brooker 3rd 460 460* freeman 6th 435-38 442-43 9, 441-43 futuyma 4th 9, 575-76 45 44-45 578 44-45, 573-83, esp. 578 gunstream 12th hall 5th 572, 575 208* 561-62, 575* 56, 208*, 561-62, 574-75* herron 5th 38, 62, 66 56, 98 38, 43, 56, 103 hillis 2nd 291* hoefnagels 4th 238 239-40 13*, 264 13*, 238-43, 260-79 krogh 5th 285 293-95 8* 8 8, 286-87, 293-95 mader 10th 266-67 277* 11* 11*, 266-79, esp. 267 mader & w 4th 238 248* 11-12* 11-12*, 237-51, esp. 248 mason 1st 9 9-11 442* miller 1st 5 5, 450-66, esp. 453-54 morris 3rd 427* 393 phelan 4th 300-304, 33637 332-33 24 4-5, 24, 332-33, 336-37 raven 10th 11 9, 432-433* 428-29 ridley 3rd 67, 263-64 281 43-70, esp. 44, 6768 44, 67-68, 263-64, 281 russell 3rd 440 440 sadava 11th 420*, 433* 15 15, 420*, 433* simon 2nd 152 161 4 simon et al. 7th 244-48, esp. 245, 247 250 4, 6 4, 6, 245, 247, 250 singh-cundy 5th 386* 13, 402 13, 402, 386-89 shuster 2nd 322-24 3 3, 322-24, 352-69 solomon 11th 16 16, 391-405, esp. 391-95 stearns 2nd taylor 9th 260-61 264* 6 6, 260-68 urry 11th 467-68 477-78* 16-19, esp. 18; 26 18, 26, 466-83, esp. 46768, 477-78 zimmer 2nd 29-34, 52 40 66 damned if you do and damned if you don’t references alberts, bruce, “the cell as a collection of protein machines: preparing the next generation of molecular biologists,” review issue: macromolecular machines, cell, vol. 92 (6 february 1998): 291-94. alexander, denis, “models for relating science and religion,” faraday report no. 3 (cambridge, uk: faraday institute for science and religion). alexander, denis. creation or evolution: do we have to choose?, rev. and expanded ed. (grand rapids, mi: monarch, 2014). allmon, warren d. and robert m. ross. “evolutionary remnants as widely accessible evidence for evolution,” evo. edu. outreach, vol. 11, no. 1 (2018). doi.org/10.1186/s12052-017-0075-1. applegate, kathryn, “a defense of methodological naturalism” pscf 65, no 1 (march 2013): 37–45. audesirk, teresa, gerald audesirk, and bruce e. byers. biology: life on earth with physiology. 11th ed. boston: pearson, 2017. augustine, on genesis, trans. edmund hill (hyde park, ny: new city press, 2004). avise, john c. inside the human genome: a case for nonintelligent design (new york: oxford university press, 2010). ayala, francisco. darwin and intelligent design (minneapolis: fortress, 2006). ayala, francisco. darwin’s gift to science and religion (washington, dc: joseph henry press, 2007). barbour, ian, “science and scientism in why religion matters,” ed. huston smith, zygon 36, no. 2 (june 2001): 207–14. barbour, ian. when science meets religion (new york: harpercollins, 2000). barrett, justin. born believers: the science of childhood religion (new york: free press, 2012). barrett, justin. cognitive science, religion, and theology (west conshohocken, pa: templeton press, 2011). barton, nicholas h., derek e.g. briggs, jonathan a. eisen, david b. goldstein, and nipam h. patel. evolution. 1st ed. cold spring harbor, ny: cold spring harbor laboratory press, 2007. behe, michael j. darwin devolves (new york: harperone, 2019). belk, colleen and virginia borden maier. biology: science for life. 5th ed. boston: pearson, 2016. bergstrom, carl t., and lee alan dugatkin. evolution. 2nd. new york: w.w. norton, 2016. brooke, john. “the relations between darwin’s science and his religion,” darwinism and divinity, ed. john durant (new york: oxford university press, 1985), 40–75. brooker, robert j., eric widmaier, linda graham, and peter stiling. biology. 3rd ed. new york, ny: mcgrawhill, 2014. churchland, patricia, “epistemology in the age of neuroscience,” journal of philosophy, vol. 84, no. 10 (1987): 544-53. clement of alexandria, stromata 6.16. collins, francis, the language of god (new york: the free press, 2006). collins, francis. language of god (new york: the free press, 2006). cornell, john. “god’s magnificent law: the bad influence of theistic metaphysics on darwin’s estimation of natural selection,” journal of the history of biology vol. 20, no. 3 (fall 1987): 381-412. cornell, john. “newton of the grassblade? darwin and the problem of organic teleology,” isis 77, no. 3 (sept. 1986): 405-421. coyne, jerry a. why evolution is true (new york: penguin, 2009). crawford, annie, “metaphor and meaning in the teleological language of biology,” ma thesis, houston baptist university, 13 august 2018. crisp, thomas m. “on naturalistic metaphysics,” the blackwell companion to naturalism, kelly james clark, ed. (hoboken, nj: john wiley & sons, inc., 2016), 61-74. cunningham, conor cunningham. darwin’s pious idea (grand rapids, mi: eerdmans, 2010). darwin, charles. on the origin of species, first edition (london: john murray, 1859). darwin, charles. origin of species, third edition (london: john murray, 1861). darwin, charles. letter to j.d. hooker. 12 july 1870. darwin correspondence project, “letter no. 7273,” accessed on 7 may 2019, http://www.darwinproject. ac.uk/dcp-lett-7273. darwin, charles. the autobiography of charles darwin 1809-1882, ed. nora barlow (new york: w.w. norton & co., 1958). darwin, francis. the life and letters of charles darwin (london: john murray, 1887), vol. 2. dawkins, richard. river out of eden (new york: basic books, 1995). dawkins, richard. the blind watchmaker (new york: w. w. norton, 1986). dawkins, richard. the blind watchmaker (new york: w.w. norton and company, 1996), xi. dawkins, richard. the greatest show on earth: the evidence for evolution (new york: free press, 2009). dilley, stephen. “charles darwin’s use of theology in the origin of species,” british journal for the history of volume 1, issue 2 references 67 science, vol. 45, no. 1 (2011): 29-58. dilley, stephen. “how to lose a battleship,” in theistic evolution, (eds.) j.p. moreland et al. (wheaton, il: crossway, 2017): 593-631. dilley, stephen. “nothing in biology makes sense except in light of theology?” studies in history and philosophy of biological and biomedical sciences 44 (2013): 774– 786. dilley, stephen. “philosophical naturalism and methodological naturalism: strange bedfellows?” philosophia christi, vol. 12, no. 1 (2010): 118-41. diogo, r. and j. molnar. “links between evolution, development, human anatomy, pathology, and medicine, with a proposition of a re-defined anatomical position and notes on constraints and morphological ‘imperfections,” ’ journal of experimental zoology 326, no. 4 (2016): 1–10. dobzhansky, theodosius. “nothing in biology makes sense except in the light of evolution,” the american biology teacher (march 1973): 125–129. eldredge, niles. the triumph of evolution . . . and the failure of creationism (new york: w. h. freeman, 2000). england, richard. “natural selection, teleology, and the logos,” osiris 16 (2001): 270-287. ewert, winston. “the dependency graph of life,” biocomplexity, vol. 3 (2018): 1-27, doi:10.5048/bioc.2018.3. falk, darrel. coming to peace with science (downers grove, il: intervarsity press, 2004). forterre, patrick and daniele gadelle. “phylogenomics of dna topoisomerases: their origin and putative roles in the emergence of modern organisms,” nucleic acids research 37, no. 3 (2009): 679–692. francis crick, what mad pursuit (new york: basic books 1990), 138. freeman, scott, kim quillin, lisabeth allison, michael black, greg podgorski, emily taylor, and jeff carmichael. biological science. 6th ed. boston: pearson, 2017. futuyma, douglas j. and mark kirkpatrick. evolution. 4th ed. oxford, uk: oxford university press, 2017. futuyma, douglas. science on trial: the case for evolution (sunderland, ma: sinauer associates, 1995). giberson, karl and francis collins. the language of science and faith (london: spck, 2011). giberson, karl. saving darwin (new york: harpercollins, 2008). gillespie, charles coulston. genesis and geology (new york: harper & row, 1951). gillespie, neal. charles darwin and the problem of creation (chicago: university of chicago press, 1979). gopnik, alison, “see jane evolve: picture books explain darwin,” wall street journal 18 april 2014, available: http://www.bu.edu/cdl/files/2014/04/wsjteaching-tots-evolution-via-picture-bookswsj.com_.pdf. gould, stephen jay. “evolution and the triumph of homology, or why history matters,” american scientist 74, no. 1 (1986): 60–69. gould, stephen jay. ever since darwin (new york: w. w. norton, 1977). gould, stephen jay. hen’s teeth and horse’s toes (new york: w. w. norton, 1983). gould, stephen jay. rocks of ages (new york: ballantine books, 1999). gould, stephen jay. the panda’s thumb (new york: w. w. norton, 1980). gould, stephen jay. the structure of evolutionary theory (cambridge, ma: harvard university press, 2002). gunstream, stanley e. explorations in basic biology. 12th ed. san francisco: benjamin cummings, 2012. hall, brian keith, and benedikt hallgrimsson. strickberger’s evolution. 5th ed. sudbury, ma: jones and bartlett learning, 2014. hayden, william b. science and revelation; or, the bearing of modern scientific developments upon the interpretation of the first eleven chapters of genesis (boston: otis clapp, 1852). herron, jon c., and scott freeman. evolutionary analysis. 5th ed. san francisco, ca: benjamin cummings, 2014. hillis, david m., david sadava, richard w. hill, and mary v. price. principles of life. 2nd ed. sunderland, ma: sinauer associates, 2014. hoefnagels, marielle. biology: concepts and investigations. 4th ed. new york, ny: mcgraw-hill education, 2018. hull david l. darwin and his critics (chicago: university of chicago press, 1973). hunter, cornelius, “darwin’s principle: the use of contrastive reasoning in the confirmation of evolution,” hopos 4 (spring 2014): 106–149. hunter, cornelius, “the random design argument,” communications of the blythe institute, vol. 1, no. 1 (this issue). hunter, cornelius. darwin’s god (grand rapids, mi: brazos, 2001). hunter, cornelius. science’s blind spot (grand rapids, mi: brazos, 2007). jahnke, art, “the natural design default,” bostonia (winter-spring 2013): 22-23, esp. 23. jenkin, fleming. “the origin of species,” [1867] in darwin and his critics, 303-44. johnson, phillip e. defeating darwinism (downers grove, il: intervarsity press, 1997). kelemen, deborah et al., “young children can be taught basic natural selection using a picture-storybook in68 damned if you do and damned if you don’t tervention,” psychological science, vol. 25, no. 4 (2014): 894. kelemen, deborah, joshua rottman, and rebecca seston, “professional physical scientists display tenacious teleological tendencies: purpose-based reasoning as a cognitive default,” journal of experimental psychology: general, 15 october 2012, advance online publication: doi: 10.1037/a0030399. krogh, david. biology: a guide to the natural world. 5th ed. boston: pearson, 2014. kuhn, thomas. the structure of scientific revolutions. 3rd ed. chicago: university of chicago press, 1996 [1962]. kutschera, ulrich. “photosynthesis research on yellowtops: macroevolution in progress,” theory in biosciences 125 (2007): 81–92. laudan, larry. “science at the bar—causes for concern,” science, technology & human values, vol. 7, no. 41 (fall 1982): 16-19. lents, nathan h. human errors (new york: houghton mifflin harcourt, 2018). lim, daniel. “a critique of elliott sober’s goals and abilities objection to the design argument” science and religion: historical and contemporary perspectives conference, lancaster university, july 2007. luskin, casey. “darwin’s poisoned tree,” trinity law review, vol. 21, no. 1 (fall 2015): 130-233. luskin, casey. “zeal for darwin’s house consumes them,” liberty university law review, vol. 3, no. 2 (spring 2009): 403-89. lustig, abigail. “natural atheology,” darwinian heresies, ed. a. lustig et al. (cambridge: cambridge university press, 2004), 69–83. mader, sylvia s. biology. 10th ed. new york: mcgraw-hill higher education, 2010. mader, sylvia s., and michael windelspecht. essentials of biology. 4th ed. new york: mcgraw-hill education, 2014. marsh, frank lewis and theodosius dobzhansky. “the dobzhansky-marsh correspondence,” 1944-1945. marsh, frank lewis. evolution, creation, and science, second edition (washington, d.c.: review and herald publishing association, 1947). mason, kenneth a., george johnson, jonathan losos, and susan singer. understanding biology. 1st ed. new york, ny: mcgraw-hill, 2014. mcdonald, patrick, “naturalism,” in a science and religion primer, eds. h. a. campbell and h. looy (grand rapids, mi: baker academic, 2009), 149-51. meyer, stephen c. “a qualified agreement response,” in science & christianity: four views, richard f. carlson, ed. (downers grove, il: intervarsity press, 2000), 111-20. miller, keith b., “an evolving creation: oxymoron or fruitful insight?” perspectives on evolving creation, ed. keith b. miller (grand rapids, mi: eerdmans, 2003), 7 miller, kenneth and joseph levine. biology: the living science (lexington, ma: d.c. health & co., 1994). miller, kenneth r., and joseph s. levine. miller & levine biology. boston: pearson, 2010. miller, kenneth, only a theory (new york, viking, 2008). miller, kenneth. finding darwin’s god (new york: harpercollins, 1999). monton, bradley. seeking god in science: an atheist defends intelligent design (peterborough, ontario: broadview press, 2009). moore, james. the post-darwinian controversies (new york: cambridge university press, 1979). morris, james et al. biology: how life works. 3rd ed. new york: w.h. freeman and company, 2019. national academy of science, teaching about evolution and the nature of science (washington, dc: national academy press, 1998). national center for science education (www.ncse.com). nelson, byron c. “after its kind”: the first and last word on evolution, fourth edition (minneapolis, mn: augsburg publishing house, 1931). nelson, paul and jonathan wells. “homology in biology: problem for naturalistic science and prospect for intelligent design,” darwinism, design, and public education, john angus campbell and stephen c. meyer, eds. (east lansing, mi: michigan state university press, 2003), 303-22. nelson, paul. “the role of theology in current evolutionary reasoning,” biology and philosophy 11 (1996): 493–517. numbers, ronald. “creating creationism: meanings and uses since the age of agassiz,” evangelicals and science in historical perspective, eds. david livingston et al. (oxford, uk: oxford university press, 2014). numbers, ronald. “ironic heresy: how young-earth creationists came to embrace rapid microevolution by means of natural selection,” darwinian heresies, eds. abigail lustig et al. (cambridge, uk: cambridge university press). numbers, ronald. the creationists: from scientific creationism to intelligent design, expanded edition (cambridge, ma: harvard university press, 2006). o’connor, robert, “science on trial: exploring the rationality of methodological naturalism,” perspectives on science and christian faith 49 (march 1997): 15–30. origen, contra celsum, book 6.50, 60. ospovat, dov. “darwin’s theology,” review of neal gillespie’s charles darwin and the problem of creation,” science 207, no. 4430 (feb 1, 1980): 520. volume 1, issue 2 references 69 ospovat, dov. “god and natural selection,” journal of the history of biology 13, no. 2 (sept. 1980): 169-194. ospovat, dov. the development of darwin’s theory (cambridge: cambridge university press, 1981). oxford university press release, “humans ‘predisposed’ to believe in gods and the afterlife,” 16 may 2011, available at: https://phys.org/news/2011-05-humanspredisposed-gods-afterlife.html. paley, william. natural theology, twelfth edition (london: j. faulder, 1809). phelan, jay. what is life?: a guide to biology. 4th ed. new york: w.h. freeman and co., 2018. prothero, donald. evolution (new york: columbia university press, 2007). radick, gregory. “deviance, darwinian-style,” metascience 14 (2005): 453–457. ratzsch, del, “humanness in their hearts: where science and religion fuse,” the believing primate, eds. jeffrey schloss et al. (oxford, uk: oxford university press, 2009), 209-45. raven, peter h., kenneth a. mason, jonathan b. losos, susan r. singer, and george b. johnson. biology. 10th ed. dubuque, ia: mcgraw-hill, 2014. richards, robert j. “theological foundations of darwin’s theory of evolution,” in experiencing nature, eds. p.h. theerman and k.h. parshall (dordrecht: kluwer academic pub., 1997), 61-79. richert, rebekah a. and justin l. barrett, “do you see what i see? young children’s assumptions about god’s perceptual abilities,” the international journal for the psychology of religion, vol. 15, no 4 (2005): 283-95. ridley, mark. evolution. 3rd ed. malden, ma: blackwell, 2011. rolston iii, holmes, denis alexander, jeff schloss et al., “the concept of ‘intelligent design’,” the international society for science and religion, 2011, accessed march 28, 2017, http://www.issr.org.uk/ issr-statements/concept-intelligent-design/. ruse, michael, “belief in god in a darwinian age,” the cambridge companion to darwin, j. hodge and g. radick, eds. (new york: cambridge university press, 2003): 368-92. russell, peter j., paul e. hertz, and beverly mcmillan. biology: the dynamic science. 3rd ed. pacific grove, ca: brooks cole, 2013. sadava, david, david m. hillis, h. craig heller, and sally d. hacker. life: the science of biology. 11th ed. sunderland, ma : sinauer associates, inc. 2017. scott, eugenie, evolution vs. creationism (berkeley, ca: university of california press, 2004). sedley, david. creationism and its critics in antiquity (berkeley: university of california press, 2007), xvi. shapiro, adam. “darwin’s foil: the evolving uses of william paley’s natural theology 1802-2005,” studies in history and philosophy of biological and biomedical sciences, vol. 45 (2014): 114-23. shapiro, adam. “william paley’s lost ‘intelligent design,” ’ history and philosophy of the life sciences, vol. 31, no. 1 (2009): 55-77. shubin, neil. your inner fish (new york: pantheon, 2008), 173–198. shuster, michèle, janet vigna, matthew tontonoz, gunjan sinha. biology for a changing world with physiology. 2nd ed. new york: w. h. freeman and company, 2014. simon, eric j. biology: the core. 2nd ed. boston: pearson, 2017. simon, eric j., jean l. dickey, jane b. reece. campbell essential biology. 7th ed. new york: pearson, 2019. singh-cundy, anu, michael l. cain, jennie dusheck, and richard symanski. discover biology. 5th ed. new york: w.w. norton & company, 2012. snelling, andrew a. earth’s catastrophic past, 2 vols. (dallas, tx: institute for creation research, 2010). sober, elliott. did darwin write the origin backwards? (amherst, ny: prometheus books, 2011). sober, elliott. evidence and evolution (cambridge, uk: cambridge university press, 2008). solomon, eldra pearl, charles martin, diana w. martin, and linda r. berg. biology. 11th ed. australia: cengage learning, 2018. st. cyprian, treatise 11.11. stearns, stephen c. and rolf f. hoekstra, evolution: an introduction. 2nd ed. oxford, uk: oxford university press, 2005. taylor, martha r., eric j. simon, jean l. dickey, kelly hogan, jane b. reece. campbell biology: concepts and connections. 9th ed. new york: pearson, 2018. thomson, william. (lord kelvin.) “of geological dynamics,” popular lectures and addresses, vol. 2 (1869): 73-131. urry, lisa a., michael l. cain, peter v. minorsky, steven a. wasserman, and jane b. reece. campbell biology. 11th ed. new york: pearson, 2017. von sydow, momme. “charles darwin: a christian undermining christianity?” in science and beliefs: from natural philosophy to natural science, 1700-1900, eds. d. m. knight and m. d. eddy (burlington, vt: ashgate, 2005), 141-156 wells, jonathan. “darwin’s straw god argument,” journal of interdisciplinary studies 22 (2010): 67–88. wells, jonathan. icons of evolution (washington, d.c.: regnery publishing, 2000). whitcomb, john and henry morris, the genesis flood (phillipsburg, nj: p & r publishing, 1961). williams, george c. the pony fish’s glow (new york: 70 damned if you do and damned if you don’t basic books, 1997). worrall, john. “science discredits religion,” in contemporary debates in philosophy of religion, michael l. peterson and raymond j. vanarragon, eds. (malden, ma: blackwell publishing, 2004), 59-72, 87-90. wright, richard t. biology through the eyes of faith, rev. and updated ed. (new york: harpercollins, 2003). zimmer, carl, and douglas john emlen. evolution: making sense of life. 2nd ed. new york: w.h. freeman and company, 2016. zimmer, carl, and douglas john emlen. evolution: making sense of life. 1st ed. new york: w.h. freeman and company, 2013. zuckerkandl, émile. “intelligent design and biological complexity,” gene 315 (2006): 2–18. 