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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 already-
solved problems, and try to trivialize them, to make them
obvious. In other words, the theorizer’s goal is to shed con-
ceptual 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 diffi-
cult 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 recog-
nized 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 pay-
ments 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 learn-
ing, 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 ma-
chine learning who, essentially, clarify things that we for-
mally know but don’t intuitively understand, or for refram-
ing problems in a much easier-to-understand way. Nomina-

tions 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 re-
search 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, Demb-
ski, and Marks II, 2014), Algorithmic Mutual Information
(Milosavljevi, 1995), and other models all use fundamen-
tally 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 uni-
formly positive), and r is a scaling factor where r ≥ v(Ω) to
normalize the distribution. The − log2() is applied to con-
vert 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 specifica-
tion 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 mathe-
matics of Specified Complexity (focusing on Algorithmic
Specified Complexity), available at https://youtu.be/
5CWu_8CTdDY. This obviously does not include the gener-
alization found in the presently-discussed paper, but might



86 News

provide a decent background for understanding the con-
cepts 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 dif-
ferentials (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 spe-
cial 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 consis-
tent and correct results.

This surprising fact is generally left unexplained in stan-
dard 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 ma-
nipulate 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 alge-
braic 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 Tech-
nologies.” 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 re-
cently published papers “Extending the Algebraic Manipu-
lability 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 par-
ticipated 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, med-
ical researchers, and technologists, have been meeting to-
gether 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 un-
derway or in development, including a survey of engineering
in the biology literature, detailed engineering models of the
bacterial flagellum (and developing requisite reusable mod-



Volume 1, Issue 2

87

eling tools), a survey of repeatable and reversable adaptive
mechanisms in biology, developing coherence metrics for en-
gineered 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). Controlla-
bility of Dynamic Systems: The Green’s Function Ap-
proach. Newcastle: Cambridge Scholars Publishing.

Bartlett, J L and A Zh Khurshudyan (2019a). “Extending
the Algebraic Manipulability of Differentials”. In: Dy-
namics of Continuous, Discrete and Impulsive Systems,
Series A: Mathematical Analysis 26.3, pp. 217–230.

Bartlett, J L and A Zh Khurshudyan (2019b). “Number-
phile’s Proof for the Sum 1 + 2 + 3 + . . . ” In: Com-
munications of the Blyth Institute 1.1, pp. 54–55.

Durston, K K et al. (2007). “Measuring the functional se-
quence complexity of proteins”. In: Theoretical Biology
and Medical Modelling 4.47. doi: 10.1186/1742-4682-
4-47.

Ewert, W, W A Dembski, and R J Marks II (2014). “Algo-
rithmic 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 al-
gorithmic mutual information”. In: Machine Learning,
pp. 35–50.

Montañez, G D (2018). “A Unified Model of Complex Spec-
ified 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.


