Trifid Nebula NGC6514 [Courtesy NASA]

Do probability arguments refute evolution?

David H. Bailey
Updated 10 October 2021 (c) 2021

Introduction

In the past few decades, modern science has uncovered a world that is far vaster and more awe-inspiring than ever imagined before, and has uncovered a set of elegant natural laws that govern all the universe, deeply resonating with the notion of a cosmic lawgiver (and isn't it remarkable that we humans can uncover and understand these laws!). It is not just devout Judeo-Christian believers who find these results inspiring. For example, 46% of Americans (including 54% of atheists, 55% of agnostics and 43% of nones) say that they experience a "deep sense of wonder about the universe" on at least a weekly basis [Masci2016]. With regards to a harmony between science, philosophy and religion, how could one ask for more?

Nonetheless, some writers, principally of the "creationist" and "intelligent design" schools, are not content with these grand revelations, and argue instead for a worldview deeply at odds with modern science in general, and with old-earth geology and biological evolution in particular. One widely used line is that certain features of biology are so unlikely, according to simple back-of-the-envelope probability calculations, that they could never have been produced by a purely natural, "random" evolutionary process, even assuming millions of years of geologic history. Thus the entirety of evolutionary theory must be false. Why don't scientists see the light?

For example, some writers equate the hypothesis of evolution to the absurd suggestion that monkeys randomly typing at a typewriter could compose a selection from the works of Shakespeare, or that an explosion in an aerospace equipment yard could produce a working airliner [Dembski1998; Foster1991; Hoyle1981; Lennox2009]. More recent studies of this genre argue that functional biology operates on an exceedingly small subset of the space of all possible DNA sequences, and that any changes to the "computer program" of biology are, like changes to human computer programs, almost certain to make the organism non-functional [Axe2017; Marks2017].

One specific creationist-intelligent design argument addresses the human alpha-globin molecule, a component of hemoglobin that performs a key oxygen transfer function in blood. These writers argue that since alpha-globin is a protein chain based on a sequence of 141 amino acids, and since there are 20 different amino acids common in living systems, the probability of selecting human alpha-globin "at random" is one in 20141 or one in 10183 (i.e., a one followed by 183 zeroes). This probability is so tiny, so they argue, that even after millions of years of random molecular trials, no human alpha-globin protein molecule would ever appear, thus refuting the hypothesis of human evolution [Foster1991, pg. 79-83; Hoyle1981, pg. 1-20; Lennox2009, pg. 163-173].

The treacherous world of probability and statistics

Before addressing the difficulties of the creationist-intelligent design probability arguments, consider for a moment the high-level process of applied mathematical deduction:

As this chart indicates, the key initial steps in the chain of reasoning are to carefully define the physical phenomenon in question and to formulate an accurate mathematical model of this phenomenon. In the case of an application of probability theory, one must carefully address these questions: What exactly is the phenomenon being modeled? What exactly is the probability space; i.e., what exactly is the set of all possible outcomes and how exactly is probability to be measured? Is each possible event presumed to have the same probability? If so, why can this be assumed? Are the events assumed to be independent? Is so, why can this be assumed? If these and other questions are not carefully addressed, then it matters not in the slightest how good the mathematical calculations are -- the chain of inference is broken, and the argument is almost certainly invalid.

While not generally appreciated by the public at large, it is a well-known fact in the world of scientific research that arguments based on probability and statistics are fraught with numerous potential fallacies and errors. For a readable layperson's introduction to these issues, see [Hand2014] and [Pinker2021]. For these reasons, rigorous courses in probability and statistics are now required of students in virtually all fields of science, and in numerous other disciplines as well, including law [Saini2009], medicine [Banerjee2009] and finance [Bailey2014] (three specific areas that have been plagued with erroneous reckonings). One overriding lesson of probability and statistics, when rigorously applied, is that seemingly improbable "coincidences" can and do happen. For instance, a common classroom exercise is to inquire how likely it is that in a class say of 30 students, two or more of the students have the same birthday. Most students presume this is rather unlikely, but the correct probability is 70.6%; in general, it is more likely than not to happen whenever the class has 23 or more students. For numerous other examples of how seemingly "improbable" events can happen, see [Hand2014] and [Pinker2021].

The fallacies of the alpha-globin probability argument

Let us now examine how well the alpha-globin argument used by creationists and intelligent design writers measures up to these standards. To begin with, these writers seldom if ever explicitly define the underlying probability space or the probability measure. They also presume that the human alpha-globin arose by a single all-at-once random shot event among the set of all 141-long amino acid chains. But generating the alpha-globin molecule "at random" in a single shot chance assemblage of atoms is definitely not the scientific hypothesis in question -- note that this is the creationist theory, not the scientific theory, of its origin. Instead, available evidence from hundreds of published studies on the topic has demonstrated that alpha-globin arose as the end product of a long sequence of intermediate steps, each of which was biologically useful in an earlier context. See, for example, the article [Hardison2012], which cites 144 papers on the topic of hemoglobin evolution.

Secondly, these writers assume that every member of the space of 141-long amino acids is equally probable. But no justification is provided for this assumption, and given the complexity of molecular biology and its preference for certain types of structures, this assumption is clearly false. Along this line, molecular self-assembly occurs in DNA molecule duplication every time a cell divides (meiosis). If one were to compute the chances of the formation of a human DNA molecule during meiosis, using a simple-minded back-of-the-envelope probability calculation similar to that used by creationists for alpha-globin, the result would be something on the order of one in 101,000,000,000, which is far, far beyond the possibility of "random" assemblage. Yet this process occurs many times every day in the human body and in nearly every other plant and animal species.

Thirdly, the alpha-globin probability argument completely ignores the fact that a large class of alpha-globin molecules can perform the essential oxygen transfer function, so that the computation of the probability of a single instance is misleadingly remote. Indeed, almost all of the 141 amino acids in alpha-globin can be changed without altering the key oxygen transfer function, as can be seen by noting the great variety in alpha-globin molecules across the animal kingdom (see DNA). A more realistic reckoning here would change the probability figure claimed for alpha-globin by at least 150 orders of magnitude.

Finally, the alpha-globin probability argument fails to recognize that the process of natural biological evolution is not really a "random" process. Evolution certainly has some random aspects, notably mutations and genetic events during reproduction. But the all-important process of natural selection, acting under the pressure of an extremely competitive landscape, often involving thousands of other individuals of the same species and other species as well, together with numerous complicated environmental pressures such as climate change, is anything but random. This strongly directional nature of natural selection, which is the essence of evolution, by itself invalidates most anti-evolution probability arguments.

With regards to alpha-globin, it is worth noting that heme, the key oxygen-carrying component of hemoglobin, is remarkably similar to chlorophyll, the molecule behind photosynthesis. The principal difference is that heme has a central iron atom, whereas chlorophyll has a central magnesium atom; otherwise they are virtually identical. This similarity can hardly be a coincidence, and in fact researchers concluded since at least 1980, based on both functional and biochemical evidence, that these two biomolecules "have arisen in the course of evolution from a common origin" [Hendry1980]. Here is a diagram of the two molecules [from MasterOrganicChemistry.com]:

The post-hoc probability fallacy

More generally, alpha-globin argument, like virtually all other creationist-intelligent design probability arguments, is a clear instance of the classic "post-hoc" probability fallacy -- reckoning a probability after the fact and claiming that the result is remarkably improbable. Post-hoc probability arguments are well-known to be highly fallacious [Pinker2021].

As an illustration, suppose one was dealt the following 13-card hand from a standard 52-card well-shuffled deck, in order: 2C, KD, 10S, 7D, QH, 3S, 9H, 10H, JC, KS, AH, 6D, 8C (the second letter denotes clubs, diamonds, hearts and spades). One can calculate (after the fact) that the probability of this event is approximately one in 4 x 1021 (i.e., roughly one in 4 billion trillion). This probability is so tiny that even if every adult human on the planet were to repeat this experiment, it is still exceedingly unlikely (less than one in a trillion chance) that this specific hand, in order, would ever be dealt again. Allowing the specified hand to be dealt in some other order would improve these odds, but would still be very unlikely. So does this small probability constitute evidence that the original card deal event occurred outside the realm of natural law? Of course not -- any specific ordered 13-card hand dealt from a well-shuffled deck has the same probability, and some specific hand had to be dealt. Thus in reality there is nothing particularly remarkable about this specific hand at all.

In summary, the alpha-globin probability argument, which has been promoted in the creationist and intelligent design literature as a sure-fire refutation of evolution, is riddled with numerous severe errors and is clearly invalid. Such an argument would never be accepted in a rigorously peer-reviewed journal in applied probability or mathematical biology. For additional details, see [Musgrave1998; Rosenhouse2018].

Snowflakes

Some of the difficulties with probability arguments against evolution can be illustrated by considering snowflakes. Bentley and Humphrey's book Snow Crystals includes over 2000 high-resolution black-and-white photos of real snowflakes, each with intricate yet highly regular patterns that are almost perfectly six-way symmetric [Bentley1962]. A good online source with numerous high-resolution photographs has been compiled by Kenneth Libbrecht [Libbrecht2012]. Four of Bentley's photos are shown below. By employing a reckoning based on six-way symmetry, one can calculate the chances that one of these structures can form "at random" as roughly one part in 102500. So is this proof that each individual snowflake has been designed by a supernatural intelligent entity? Obviously not.

The fallacy here, once again, is presuming an all-at-once random assembly of molecules. Instead, snowflakes, like biological organisms, are formed as the product of a long series of steps acting under well-known physical laws, and the outcomes of such processes very sensitively depend on the starting conditions and numerous environmental parameters. It is thus folly to presume that one can correctly reckon the chances of a given outcome, after the fact, by means of a superficial probability calculation that ignores the processes by which it formed.

image #1 image #2 image #3 image #4

Computer programs emulating biological evolution

If there were some underlying mathematical or biological principle that forbids biological structures from evolving novel features, surely this principle should be seen in computer simulations of evolution. But quite the opposite is true -- such studies abundantly confirm that evolutionary processes really do work, not just in biology but in other arenas as well.

For example, as mentioned above, some critics have equated natural biological evolution to the absurd suggestion that some monkeys typing randomly at a keyboard could generate a passage of Shakespeare. Others have argued that any changes to a "computer program" would surely render the program unusable. But these too are fallacious arguments, since they ignore the all-important process of natural selection. As a single example, a 2009 study by the present author exhibited results of a computer program simulating natural evolution, which "evolved" segments of English text very much akin to actual passages from Charles Dickens. In many instances, a class of college students were unable to distinguish the computer-generated text segments from real text segments taken from Dickens' Great Expectations. See English-text for details.

Another example is the recent rise of "genetic algorithms" and "evolutionary computing," namely computer programs that mimic the process of biological evolution to produce novel solutions to scientific and engineering problems. As a single example, in 2017 Google researchers generated 1000 image recognition algorithms, each of which were trained using state-of-the-art deep neural networks to recognize a selected set of images. They then used an array of 250 computers, each running two algorithms, to identify an image. Only the algorithm that scored higher proceeded to the next iteration, where it was changed somewhat, mimicking mutations in biological evolution. The researchers found that their scheme could achieve accuracies as high as 94.6%, better than human efforts [Gershgorn2017]. In another Google-funded research project, a computer was programmed with only the rules of Go, together with an evolution-style "deep learning" algorithm, and then had the program play games against itself. Within a few days it had advanced to the point that it defeated an earlier Google program 100 games to zero. This earlier program, in turn, had previously defeated the world's champion human Go player [Greenmeier2017].

Improbable structures and features in nature

It is puzzling that creationist and intelligent design writers continue to attack evolution, since, by any reasonable scientific standard, the evidence for evolution today is overwhelming both in scope and in strength -- see Evolution-evidence. Along this line, numerous examples from the natural world can be cited to demonstrate the futility of trying to argue against evolution using probability -- nature can and often does produce highly improbable structures and features, by the well-understood evolutionary processes of mutation, shuffling of genes and natural selection:
  1. Lenski's 2012 E. coli experiment: In January 2012, a research team led by Richard Lenski at Michigan State University demonstrated that colonies of viruses can evolve a new trait in as little as 15 days. The researchers studied a virus, known as "lambda," which infects only the bacterium E. coli. They engineered a strain of E. coli that had almost none of the molecules that this virus normally attaches to, then released them into the virus colony. In 24 of 96 separate experimental lines, the viruses evolved a strain that enabled them to attach to E. coli, using a new molecule that they had never before been observed to utilize. All of the successful runs utilized essentially the same set of four distinct mutations. Justin Meyer, a member of the research team, noted that the chances of all four mutations arising "at random" in a given experimental line (based on a simplistic back-of-the-envelope probability calculation typical of creationist literature) are roughly one in 1027 (one thousand trillion trillion) [Zimmer2012].
  2. Synthesis of RNA nucleotides and other biomolecules: Many scientists hypothesize that RNA (a molecule similar to DNA, with four "bases" or nucleotides) was involved in the origin of life (see Origin). As recently as 1999, the appearance of RNA nucleotides on the primitive Earth was widely thought to be a "near miracle" by researchers in the field [Joyce1999]. Nonetheless, in May 2009 a team led by John Sutherland of the University of Manchester discovered a particular combination of chemicals, very likely to have been plentiful on the early Earth, that synthesized the RNA nucleotides cytosine and uracil, which are known as the pyrimidines [Wade2009]. More recently, in 2016 a team led by Thomas Carell in Munich, Germany succeeded in synthesizing in the remaining two, adenine and guanine, which are known as the purines [Service2016]. Finally, in 2018, Carell's team demonstrated a single process that created all four nucleotides [Service2018]. In short, the natural production of the four RNA nucleotides, once thought to be "impossible," is now fairly well understood.
  3. Hawaiian crickets. In the 1800s, a species of cricket was introduced to the Hawaiian Islands, where they became quite common in grassy areas. Males attract mates with their chirps, and females select males based on their songs. However, unlike their counterparts in other Pacific islands, the Hawaiian crickets have a fearsome predator -- dive-bombing flies that target chirping crickets, then implant their larvae in them. n the 1990s, researchers noted that a field in Kauai that previously was the home to many crickets now seemed silent. However, a nighttime search found that in fact there were lots of crickets there, but very few of the males now chirped -- in just five years, or roughly 20 generations, a mutation had arisen that inhibited many of the males from chirping, thus protecting the population [Zuk2013, pg. 81-82].

  4. Recent human evolution. A 2010 study found a total of 30 recently evolved genetic variants that are distinct among natives of Tibetan highlands, permitting them to live well at very high altitudes (more efficient metabolism, avoid overproducing red blood cells in thin air, etc.). They concluded that these changes constitute the fastest documented case of human evolution [Wade2010b]. Some other instances of recent human evolution include: (a) a genetic adaptation has arisen among Southern Chinese that makes them more resistant to alcohol, at the cost of turning red in the face; (b) gene changes in Eskimo populations that help them better cope with bitter cold; (c) genetic changes among certain primitive farming people that enhance vitamin B9 production, which is absent in their tuber diets; (d) two genetic mechanisms for lighter skin color, which among higher-latitude people promotes vitamin D production -- Europeans have one, while East Asians have another; (e) a gene that promotes hair with thicker shafts among East Asians, possibly as added protection against cold [Wade2010c].

  5. Evolution of the coronavirus. The Covid-19 pandemic of 2020-2021, which as of September 2021 has claimed the lives of over 650,000 Americans and 4.5 million worldwide, has underscored the reality of evolutionary novelty in a way that affects every person on the planet. The rise of the delta variant of the virus, which is roughly 40% to 60% more transmissible than the earlier alpha variant, is a particularly striking and frightening case of "evolution before our eyes" [Achenbach2021; Kupferschmidt2021; Schumaker2021]. As this is written, governments worldwide are in a race with evolution, hoping to tamp down the delta variant and others (notably the lambda and mu variants) with vaccinations and other measures, before the virus mutates further, possibly acquiring resistance to vaccines. No one "designed" these deadly virus variants.
Many other examples could be listed -- see Novelty and Origin.

Dembski's information theory arguments

Intelligent design writer William Dembski invokes both probability and information theory (the mathematical theory of information content in data) in his arguments against Darwinism [e.g., Dembski2002; Marks2017]. However, mathematicians who have examined Dembski's works have identified major flaws in his reasoning [Elsberry2011]. For a detailed discussion of Dembski's theories, see Information theory.

Does creationism provide a reasonable alternative?

Does a creationist worldview, in particular the hypothesis of independent creation of each species with no common biological ancestry, provide a reasonable alternative in terms of probability?

Here it is instructive to consider transposons or "jumping genes," namely sections of DNA that have been "copied" from one part of an organism's genome and "pasted" seemingly at random in other locations. The human genome, for example, has over four million individual transposons in over 800 families [Mills2007]. In most cases transposons do no harm, because they "land" in an unused section of DNA; and some introns have subsequently adopted biological functionality (although for the purposes of this discussion it does not matter in the least whether or not they have biological functionality). But because they are distinctive and inherited, they serve as excellent markers for genetic studies. Indeed, transposons have been used to classify a large number of vertebrate species into a family tree, with a result that is virtually identical to what biologists had earlier reckoned based only physical features and biological functions [Rogers2011, pg. 25-31, 86-92]. As just one example, consider the following table, where columns labeled ABCDE denote five blocks of transposons, and x and o denote that the block is present or absent in the genome [Rogers2011, pg. 89].

						Transposon blocks
			Species		A	B	C	D	E
        /---------	Human		o	x	x	x	x
       /----------	Bonobo		x	x	x	x	x
      / \---------	Chimp		x	x	x	x	x
     /------------	Gorilla		o	o	x	x	x
-----|------------	Orangutan	o	o	o	x	x
     \------------	Gibbon		o	o	o	o	o

It is clear from these data that our closest primate relatives are chimpanzees and bonobos. As another example, here is a classification of four cetaceans (ocean mammals) based on transposon data [Rogers2011, pg. 27]:

						Transposon blocks
		Species			A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P
    /------	Bottlenose dolphin	x  x  x  x  x  x  x  x  x  x  x  x  x  x  x  x
   /\------	Narwhal whale		x  x  x  x  x  x  x  x  x  x  x  x  x  x  x  x
---|-------	Sperm whale		x  x  x  x  x  o  o  o  o  o  o  o  o  o  o  o
   \-------	Humpback whale		x  x  o  o  o  o  o  o  o  o  o  o  o  o  o  o
Other examples could be listed, encompassing an even broader range of species [Rogers2011, pg. 25-31, 86-92].

Needless to say, these data, which all but scream "descent from common ancestors," are highly problematic for creationists and others who hold that the individual species were separately created without common biological ancestry. Transposons typically are several thousand DNA base pair letters long, but, since there are often some disagreements from species to species, let us be very conservative and say only 1000 base pair letters long. Then for two species to share even one transposon starting at the same spot, presumably only due to random mutations since creation, the probability (according to the creationist hypothesis) is one in 41000 or roughly one in 10600. For 16 such common transposons, the chances are one in 416000 or roughly one in 109600. What's more, as mentioned above, an individual species typically has at least several hundred thousand such transposons. Including even part of these in the reckoning would hugely multiply these odds.

But this is not all, because we have not yet considered the fact that in each diagram above, or in other tables of real biological transposon data, there is a clear hierarchical relationship. This is by no means assured, and in fact is quite improbable -- for almost all tables of "random" data, there is no hierarchical pattern, and no way to the rearrange the rows to be in a hierarchical pattern. For example, in a computer run programmed by the present author, each column of the above cetacean table was pseudorandomly shuffled (thus maintaining the same number of x and o in each column), and the program checked whether the rows of the resulting table could be rearranged to be in a hierarchical order. There were no successes in 10,000,000 trials. As a second experiment, a 4 x 16 table of pseudorandom data (with a 50-50 chance of x or o) was generated, and then the program attempted to rearrange the rows to be in a hierarchical pattern as before. There were only three successes in 10,000,000 trials.

These calculations are simplified and informal; more careful reckonings can be done, and one can vary the underlying assumptions. But do the fine details of the calculations really matter? One way or the other, it is clear that the creationist hypothesis of separate fiat creation of individual species does not resolve any probability paradoxes; instead it enormously magnifies them.

The only other possibility, from a strict creationist worldview, is to propose that a supreme being separately created species with hundreds of thousands of transposons already in place, essentially just as we see them today. But this merely replaces a scientific disaster (the inability of the creationist model to explain the vast phylogenetic patterns in intron data) with a theological disaster (why did a truth-loving supreme being fill the genomes of the entire biological kingdom with vast amounts of misleading DNA evidence, all pointing unambiguously to an evolutionary descent from common ancestors over the eons, if that is not the conclusion that should be drawn?). Indeed, with regards to the discomfort some have about evolution, the creationist alternative of separate creation is arguably far worse, both scientifically and theologically. See Deceiver for additional discussion.

Conclusions

It is certainly true that there are numerous complex structures in biology; alpha-globin is but one of many thousands that could be listed. How did these structures first arise, and how did they evolve to the forms we see today? For that matter, was the origin of the first self-reproducing biomolecules on the early Earth an inevitable development, or was it a fantastically improbable event unlikely to have been repeated anywhere else in Milky Way galaxy? (See Origin.) Along this line, how likely is it that intelligent, technological societies have arisen elsewhere? And why have we not yet seen clear-cut evidence of such societies? (See Fermi's paradox.) In spite of many published papers on these and similar topics, researchers in these fields would be the first to acknowledge that there is still much that is not yet fully understood. This is a large, dynamic field with many active researchers, spanning disciplines from molecular biology and DNA to astronomy and exobiology, with thousands of peer-reviewed research papers published each year.

However, the simplistic, back-of-the-envelope probability arguments that have appeared in the creationist-intelligent design literature, which typically are presented without any solid connections to current peer-reviewed empirical biology, do not help unravel these profound questions. Instead, these arguments are riddled with fallacies that would disqualify them from publication in peer-reviewed journals in applied probability and mathematical biology. These difficulties include:

  1. Failing to acknowledge that arguments based on probability and statistics are fraught with numerous potential fallacies and errors.
  2. Failing to rigorously define the mathematical model and probability measure space.
  3. Failing to acknowledge that reckoning a probability after the fact is a well-known fallacy (the "post-hoc" probability fallacy).
  4. Making empirically unjustified assumptions, such as presuming that a large class of biomolecular structures are all equally likely, or that different outcomes are independent.
  5. Presuming that a biomolecular structure came into existence "at random" via a single-shot chance assemblage of atoms. But this is not the scientific hypothesis of how they formed; instead, abundant evidence shows that they are the result of a long series of intermediate steps over the eons.
  6. Relying on sophisticated mathematical calculations, but ignoring the fact that since the underlying probability model is an invalid description of the phenomenon in question, it does not matter in the slightest how good these mathematical calculations are.
  7. Ignoring the fact that a very wide range of biomolecules could perform a similar function to the given biomolecule, so that the odds given against the formation of the given biomolecule are hugely exaggerated.
  8. Ignoring the fact that biological evolution is fundamentally not a "random" process -- mutations may be random, but natural selection, the essence of evolution, is far from random.
  9. Ignoring reams of published studies showing that evolution can and often does produce seemingly improbable structures and features.
  10. Invoking advanced mathematical concepts (e.g., information theory), but misapplying these results in ways that render the conclusions invalid in an evolutionary biology context.
  11. Failing to recognize that the creationist hypothesis of separate creation for each species does not resolve any probability paradoxes; instead it enormously magnifies them.
It is ironic that to the extent that probability-based arguments have any validity at all in analyses of evolution, it is precisely the creationist hypothesis of separate, all-at-once complete formation of individual species or features that is falsified.

Perhaps at some time in the distant future, a super-powerful computer will be able simulate with convincing fidelity the multi-billion-year biological history of the Earth, in the same way that scientists today attempt to simulate (in a much more modest scope) the Earth's weather and climate. Then, after thousands of such simulations have been performed, researchers might obtain some meaningful statistics on the chances involved in the origin of life on Earth, or in the formation of some class of biological structures such as alpha-globin. Perhaps also researchers will eventually reconstruct, in the laboratory, additional key biomolecular steps involved in the origin of life. And perhaps one day in the not-too-distant future, researchers will even discover forms of life on other planets, and eventually, after thousands of such life forms have been catalogued, may be able to empirically assess the probability of the origin of life or of specific biomolecules.

Until that time, the probability calculations that appear in creationist-intelligent design literature and elsewhere should be viewed with great skepticism, to say the least. Do these writers and others who promote these arguments really believe that the entire edifice of modern evolutionary biology can be felled with one or two back-of-the-envelope probability calculations, largely disconnected from peer-reviewed empirical biology? Do they really think that the massive bodies of empirical evidence supporting evolution can be blithely dismissed (see Evolution-evidence)? Do they further believe that if these probability arguments had any real merit, that hundreds of thousands of research biologists worldwide, most of them eager to publish groundbreaking research, would all have overlooked them?

Common sense says otherwise. As mathematician Jason Rosenhouse writes [Rosenhouse2018],

When biologists ascribe to evolution the ability to craft information-rich genomes, they are neither speculating nor guessing. The basic components of evolutionary theory are empirical facts. Genes really do mutate, sometimes leading to new functionalities. The process of gene duplication with subsequent divergence leads to the creation of information by any reasonable definition of the terms. Selection can string small variations together into directional change. On a small scale, this has all been observed. And if small increases in information are an empirical reality on human timescales, then what abstract principle of mathematics is going to rule out much larger increases on geological scales?

Then here come the ID [intelligent design] folks, full of swagger and bravado. They say the accumulated empirical evidence must yield before their back-of-the-envelope probability calculations and abstract mathematical modeling. Evolution should be abandoned in favor of the new theory of intelligent design. This theory states, in its entirety, that an intelligent agent of unspecified motives and abilities did something at some point in natural history. Not very useful.

In a larger context, one has to question whether highly technical issues such as biomolecular structures or calculations of probabilities have any place in a discussion of philosophy or religion. Surely such technical arguments can say nothing one way or the other as to whether a supreme being governed the creation of life on Earth in some sense, or for any other point of philosophy or theology. So why attempt to "prove" a theological point with probability arguments, especially when there are very serious questions as to whether any of these arguments are valid? One is reminded of a passage in the New Testament: "For if the trumpet gives an uncertain sound, who shall prepare himself for the battle?" [1 Cor. 14:8]. It makes far more sense to leave such matters to peer-reviewed scientific research.

For additional information, see Complexity, Creationism, Deceiver, Design, DNA, English text, Evolution evidence, God of the gaps, Information theory, Intelligent design, Novelty, Origin and Theory.

References

[See Bibliography].