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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 justi-
fication, 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 sec-
ond part of this argument is that random design can there-
fore 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 de-
sign argument has two important problems that have gone
unrecognized. First, though presented as a finding of empir-
ical 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 em-
ploys contrastive reasoning to argue that evolutionary the-
ory 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 feath-
ers. Rogers concludes: “Different species could have differ-
ent genetic codes just as easily as different human popula-
tions speak different languages. But they don’t. Every liv-
ing 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 ge-
netic 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 con-
strained (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 logi-
cal 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 in-
terlocutor 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 de-
sign 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 com-
mitting to, and promoting, an invalid argument?

In this paper I demonstrate this is not the case. This evolu-
tionary 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 evolution-
ary premise that if the species were independently created,
then their designs would fill the design space. The poten-
tial 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 dis-



24 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 un-
der 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 ar-
gument more explicit in his Evolution textbook. After ex-
plaining 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 indepen-
dently created species. They must fill the design space.
Clearly this argument entails non empirical content. The
origins and details of the underlying metaphysics are be-
yond the scope of this paper. I will merely refer to the argu-
ment 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 de-
signs are possible. A divine design would explore the entire
range. Step 2 acknowledges that we find limitations in na-
ture’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 ar-
bitrary. 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 hy-
pothesis 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 devel-
oped 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 hy-
pothesis, 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 suffi-
ciently small. When the null hypothesis is rejected, then
the alternate hypothesis is accepted. This simple null hy-
pothesis test presents a dichotomy, and for it to function
properly it is crucial that no other explanations are possi-
ble. 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 be-
came the null hypothesis in cosmology and biology, respec-
tively, 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 ran-
dom. As we will see, the random design null hypothesis
test was, and remains today, an extremely powerful and in-
fluential argument for contingency. Today, it is a fixture
of evolutionary reasoning that is common across numerous
academic authors. Finally, Section 4 provides the conclu-
sions 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 re-
volved about the sun, and the moons about their respec-
tive 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 ori-
gin. 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 po-
sition, 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 con-
centric 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 pro-
portion 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 consis-
tency.

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 inclina-
tion.” (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 argu-
ment that the solar system patterns revealed common de-
sign could be turned on its head. For the patterns could
just as easily be seen as the result of a common mecha-
nism. 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 ran-
dom design where the planetary orbits were inclined at ran-
dom 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 coinciden-
tal 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 or-
bits, 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 de-
sign argument. Immanuel Kant used similar reasoning
twenty years later in his ambitious and expansive cosmo-
logical treatise.1 Kant’s approach was a blend of mechan-
ical principles and metaphysics. (Shea, 1986, pg. 119) Re-
garding 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 direc-
tion: of the six main planets and the ten satel-
lites, not a single one moves, either in its forward
motion or in its axial rotation, in any other di-
rection 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 necessar-
ily participates in them as precisely as possible.
(Kant, 1755, pg. 117)

Kant claimed this argument provided “proof that the collec-
tive 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 hypoth-
esis (to use modern statistical parlance). To elucidate on
the proof, Kant focused on the question of why the plan-
ets 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. There-
fore, 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 argu-
ments 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 pro-
posed 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 mate-
rial 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 Hypothe-
sis. The Nebular Hypothesis called for a cloud of material
about the sun that rotates and condenses to form the plan-
ets 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 ver-
sions 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 find-
ing 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 di-
vine 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 probabil-
ity 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 ap-
plied 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 ro-
tations 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 de-
termined 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 ran-
dom 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 under-
determined and in most cases opposing or even mutually
exclusive. But confidence was extremely high, not from the-
oretical 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 the-
ory (Brush, 1996, pg. 20) while, on the other hand, have
nothing more than an underdetermined, untested, overar-
ching notion of how the solar system actually arose. In-
deed, Laplace failed to explain new observations such as
the anomalous orbits of Uranus’ moons, discovered by Her-
schel:

Laplace was aware when he first published his the-
ory that Herschel had found the two satellites of
Uranus to have orbits in a plane nearly perpendic-
ular to the plane of the ecliptic. In 1798 Herschel
announced that the satellites of Uranus have ret-
rograde 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. In-
stead, 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 sci-
entific 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 sim-
ply 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 phe-
nomena. 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 or-
bital parameters. The direction of their revolutions
about the sun, the direction of their spin, and the in-
clination 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, ex-
planatory mechanism, but rather by the patterns found
within the solar system structure.

3. This new tradition, based on the random design ar-
gument, 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 de-
tailed 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 ex-
plain, 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 calcu-
lations. 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 de-
sign null hypothesis) which was entirely disjoint from
the derivation of the mechanism. By falsifying design,
the scientist was free to speculate about the mecha-
nism, 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 ut-
most confidence in the veracity of their respective the-
ories. Each of these theoreticians produced high-level,
phenomenological theories with theoretical shortcom-
ings. 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 com-
mon 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 sim-
ply because there has continued to be a switching in
preference between these two mutually exclusive cat-
egories. (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 convinc-
ingly 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 hy-
pothesis 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 respec-
tive theories with little or no demonstration that their
mechanisms actually could, in fact, create the solar sys-
tem. And shortcomings in their mechanisms—whether
known at the time or discovered later—were viewed
more as interesting research problems rather than evi-
dences 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 contin-
gent events, something which Newton himself called
upon to explain the variations in the inclination an-

gles 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. Ex-
planations could be fairly vague and failures could be
accommodated as research problems.

These theories of the origin of the solar system are impor-
tant 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 summa-
rized 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 in-
clude the same bones, in the same relative posi-
tions? (Darwin, 1859, pg. 434)

Darwin’s rhetorical question highlights the role of the ran-
dom 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 homol-
ogous bones in widely different animals. (Darwin,
1859, pg. 434)

Darwin found these seemingly arbitrary patterns through-
out 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 differ-
ent 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 max-
illæ. 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 or-
bits, 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 think-
ing 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 func-
tional effects. Darwin could not know that the bones of the
arm and forearm, or of the thigh and leg, could be trans-
posed 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 de-
sign 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 embry-
onic development of each species contains innu-
merable characters like the pentadactyl limb and
the genetic code: characters that are similar be-
tween 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, fash-
ioning 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 ubiqui-
tous and appears in a variety of contexts. Whales are mam-
mals 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 char-
acteristics) 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 ran-
dom design. Likewise, the fossil record should be ran-
dom 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 argu-
ment has been incorporated into biological studies in more
sophisticated and subtle ways. The remainder of this sec-
tion 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 ran-
dom design argument tradition. Penny used five proteins
(cytochrome C, hemoglobin A, hemoglobin B, fibrinopep-
tide A and fibrinopeptide B) to infer the evolutionary rela-
tionships 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 pro-
tein relationships between species are random. For exam-
ple, 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 be-
tween the human and ape.

Of course this random design null hypothesis fails spec-
tacularly. Protein differences between species tend to be
correlated. Penny et. al. expressed this failure quanti-
tatively using evolutionary trees. First, they used the five
proteins, one at a time, to construct five different evolution-
ary trees. According to the random design null hypothesis,
these trees should bear no particular similarity. The evo-
lutionary tree derived by comparing one protein across the
different species should bear no relation to the evolution-
ary 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, inde-
pendently, produced similar trees. The different evolution-
ary 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 hypoth-
esis 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 text-
book 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 ran-
dom 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 ances-
tral 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 se-
quences 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, or-
ders 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 evo-
lution:

The several subordinate groups in any class can-
not 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 cre-
ated, 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 de-
sign 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 inconsis-
tencies, 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 random-
ized 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 estab-
lish 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 nonethe-
less, 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 evi-
dence 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 ob-
served CI and the [randomized] CI predicted un-
der separate ancestry. (Baum and Smith, 2012,
pg. 21)

For example, Salamandridae is a family of salamanders con-
sisting of true salamanders and newts. Data on 40 charac-
ters from these species (Wake and Ozeti, 1969) yielded a rel-
atively low CI value of .596. When the data were random-
ized,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 inter-
preted as powerful evidence for evolution and common an-
cestry.

3.3 Evolution of primates

My final example of the influence of the random design ar-
gument 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 ances-
try as the null hypothesis. As in the previous examples,
the general approach is to construct a model of the null hy-
pothesis, compare the empirical data to the null hypothesis,
and compute the P value to determine if the null hypoth-
esis 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 ac-
cepted. 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 rear-
range the character state data so they are randomized for
each species.

3The randomization process is as follows. For each of the 40 char-
acters, 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 randomiza-
tion 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 ances-
try

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 Char-
acter

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 cos-
mological evolutionary theories discussed in Section 2, the
authors explained the essence of this approach. Even a sin-
gle character can provide strong evidence for common an-
cestry if its observed states, in different species, is a small
subset of its possible states:

in principle, a single characteristic that could ex-
ist in very many alternative states can provide ev-
idence of [common ancestry] when the states seen
in a clade, or life as a whole, occupy a smaller sub-
set 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 the-
ory of statistical history may emerge. Thus, we
hope that this article will not just stimulate fur-
ther philosophical and statistical research on evi-
dence 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 na-
ture’s designs should fill the design space, otherwise contin-
gency is implicated. Over the past three centuries the ran-
dom design argument, and in particular testing of the ran-
dom design null hypothesis, has provided for an extremely
powerful philosophy of science. It is a solution to the age-
old difficulty of how to prove a scientific theory. If a null
hypothesis can be constructed which complements the the-
ory 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 reason-
able 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 al-
ternate hypothesis. The null hypothesis and the alter-
nate 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 alter-
nate hypothesis is a fact. Contingency, both in cosmol-
ogy 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 hypothe-
sis. Variations in the planetary inclination angles, or
variations in the species hierarchical structure, are not
explained by the condensing nebula or common an-
cestry 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 fail-
ures.

The validity of the statistical reasoning behind these five
points is dependent on one special property of the null hy-
pothesis. 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 hy-
potheses. 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 pos-
sible range of values, then they must have arisen via con-
tingent 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 devel-
opment, but theory evaluation and even theory confirma-
tion. The origin and details of this theological assumption
are beyond the scope of this paper.

In the past century historians have increasingly demon-
strated 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 the-
ological 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 Zo-
ology 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 Introduc-
tion to Phylogenetic Biology. New York: W. H. Free-
man.

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 Jef-
freys. 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: Bra-
zos.

Hunter, C (2014). “Darwin’s Principle: The Use of Con-
trastive 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 the-
ory of evolution by comparing phylogenetic trees con-
structed from five different protein sequences”. In: Na-
ture 297, pp. 197–200.

Penny, D and M Hendy (1986). “Estimating the reliabil-
ity 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 Relation-
ships 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).


