A Mathematician’s (Highly Flawed) View of Evolution

By Jack Scanlan

03
Feb. 10

I recently mentioned, on my blog, Dr. Granville Sewell, Professor of Mathematics at the University of Texas, El Paso, in relation to a new book of his, filled with essays about intelligent design and evolution, that was recently published by the Discovery Institute. Sewell is an intelligent design proponent/​advocate, and due to his status as a professor at a legitimate university, he gets put up on a pedestal by pro-​​ID organisations (such as the Discovery Institute) as one of the supposedly “many” scientists who reject evolutionary theory in favour of intelligent design.

This treatment also extends to any publications Sewell happens to write on the subject of evolution, and two of these appear in the Discovery Institute’s Peer-​​Reviewed & Peer-​​Edited Scientific Publications Supporting the Theory of Intelligent Design (Annotated). Of course, they aren’t true academic papers but articles published in journals — hence they don’t really have any scientific weight — but intelligent design proponents will use anything they can get their hands on and hold it up as legitimate science, so long as it can be professionally cited and looks all fancy to the layperson.

One of these articles written by Sewell is called “A Mathematician’s View of Evolution” [The Mathematical Intelligencer 22, no. 4 (2000), pp5-​​7], and it will be the focus of this blog post to analyse and look at the arguments he puts forward in it. Hopefully it will demonstrate to you that scientists and academics outside their fields of expertise cannot be believed as quickly as creationists and ID proponents would have you think.

In 1996, Lehigh University biochemist Michael Behe published a book entitled “Darwin’s Black Box” [Free Press], whose central theme is that every living cell is loaded with features and biochemical processes which are “irreducibly complex” – that is, they require the existence of numerous complex components, each essential for function. Thus, these features and processes cannot be explained by gradual Darwinian improvements, because until all the components are in place, these assemblages are completely useless, and thus provide no selective advantage. Behe spends over 100 pages describing some of these irreducibly complex biochemical systems in detail, then summarizes the results of an exhaustive search of the biochemical literature for Darwinian explanations. He concludes that while biochemistry texts often pay lip-​​service to the idea that natural selection of random mutations can explain everything in the cell, such claims are pure “bluster”, because “there is no publication in the scientific literature that describes how molecular evolution of any real, complex, biochemical system either did occur or even might have occurred.”

While Sewell can be given some leeway for citing Behe in 2000, before the major backlash his book received later in the decade, it’s still an unacceptable argument to refer to and draw upon for support. The argument from irreducible complexity, as used by Behe, is essentially an argument from ignorance, which states that simply because evolutionary biologists do not have an answer yet as to how a certain biological feature evolved, it must have been designed. Behe conflates a lack of current knowledge with the lack of any possible explanation, especially when he ignores things like biological scaffolding and exaptation that offer plausible mechanisms by which supposedly “irreducibly complex” systems can easily evolve.

From this first paragraph of Sewell’s article, it wouldn’t be a stretch to assume that the rest of the article will not contain original thoughts by Sewell himself, but rehashed arguments of other ID proponents. I mean, if he’s citing Behe as the first thing he says… it’s probably not too far off the mark.

When Dr. Behe was at the University of Texas El Paso in May of 1997 to give an invited talk, I told him that I thought he would find more support for his ideas in mathematics, physics and computer science departments than in his own field.

Wait, Behe would find more support for intelligent design in non-​​biological fields such as physics than in biology, where it’s supposed to be applied? That’s like saying that there could be more evidence for the existence of dark matter in chemistry than in cosmology and astronomy — total nonsense. Or is Sewell talking about the people in those fields? Does he mean that non-​​biologists are going to accept a biologically-​​applied, yet unscientific, idea more readily than biologists who actually know what they’re talking about in the field of evolution? That I can totally understand, yet it doesn’t help Behe’s (or Sewell’s) ideas very much — you shouldn’t gloat about academic support from irrelevant disciplines.

I know a good many mathematicians, physicists and computer scientists who, like me, are appalled that Darwin’s explanation for the development of life is so widely accepted in the life sciences. Few of them ever speak out or write on this issue, however – perhaps because they feel the question is simply out of their domain.

And rightly so — nobody should take them seriously in a scientific context. It is out of their domain. Why does Sewell feel he needs to mention this? It’s not going to convince any serious scientist.

However, I believe there are two central arguments against Darwinism, and both seem to be most readily appreciated by those in the more mathematical sciences.

He then begins with an explanation of the first argument:

The cornerstone of Darwinism is the idea that major (complex) improvements can be built up through many minor improvements; that the new organs and new systems of organs which gave rise to new orders, classes and phyla developed gradually, through many very minor improvements. We should first note that the fossil record does not support this idea, for example, Harvard paleontologist George Gaylord Simpson [“The History of Life,” in Volume I of “Evolution after Darwin,” University of Chicago Press, 1960] writes:

“It is a feature of the known fossil record that most taxa appear abruptly. They are not, as a rule, led up to by a sequence of almost imperceptibly changing forerunners such as Darwin believed should be usual in evolution…This phenomenon becomes more universal and more intense as the hierarchy of categories is ascended. Gaps among known species are sporadic and often small. Gaps among known orders, classes and phyla are systematic and almost always large. These peculiarities of the record pose one of the most important theoretical problems in the whole history of life: Is the sudden appearance of higher categories a phenomenon of evolution or of the record only, due to sampling bias and other inadequacies?”

Wow, one quote by a paleontologist in the 1960s! Convincing stuff. But in what context was this written? It seems unlikely that Simpson, one of the most important paleontologists of the twentieth century and an expert in evolutionary theory, would be talking about the notion that the fossil record does not support evolution. And if it seems unlikely, it’s because Simpson was not talking about that, but instead the evidence that lead him to postulate the multi-​​tempoed theory of evolutionary change: something that could explain the differences between species gaps and gaps in the higher taxons. Sorry Sewell, not a quote that supports your idea that the fossil record doesn’t underlie evolutionary theory.

An April, 1982, Life Magazine article (excerpted from Francis Hitching’s book, “The Neck of the Giraffe: Where Darwin Went Wrong”) contains the following report:

“When you look for links between major groups of animals, they simply aren’t there…‘Instead of finding the gradual unfolding of life’, writes David M. Raup, a curator of Chicago’s Field Museum of Natural History, ‘what geologists of Darwin’s time and geologists of the present day actually find is a highly uneven or jerky record; that is, species appear in the fossil sequence very suddenly, show little or no change during their existence, then abruptly disappear.’ These are not negligible gaps. They are periods, in all the major evolutionary transitions, when immense physiological changes had to take place.”

This is, again, not a problem with evolution, but a consequence of both the multi-​​tempoed nature of evolutionary change (as proposed by George Gaylord Simpson, and later, in a different way, validated by Stephen Jay Gould) and the sporadic nature of the fossil record. Combined together, these two things create a fossil record that looks as Raup describes — although as more time progresses gaps are slowly filled in by new fossil discoveries, such as Tiktaalik roseae and other “transitional forms”, meaning that the fossil record is not a useless tool in investigating past evolutionary change.

Even among biologists, the idea that new organs, and thus higher categories, could develop gradually through tiny improvements has often been challenged. How could the “survival of the fittest” guide the development of new organs through their initial useless stages, during which they obviously present no selective advantage? (This is often referred to as the “problem of novelties”.)

Sewell, in 2000, obviously had never heard of, or seriously thought about, exaptation — the process by which a feature with a certain function can be altered to have a different function. This means that any “primitive” previous versions of a system might not have necessarily had no function at all, they could have had a different function that drew on the help of natural selection to evolve. This ties back to Behe’s irreducible complexity argument of course, which, through demonstrations of obvious exaptation by evolutionary biologists, has been shown to be rather invalid. But you already knew that.

Or guide the development of entire new systems, such as nervous, circulatory, digestive, respiratory and reproductive systems, which would require the simultaneous development of several new interdependent organs, none of which is useful, or provides any selective advantage, by itself?

This argument rests on the assumption that none of the current systems in the bodies of organisms could function at all with modified versions of all the other systems. This is what would happen with true evolutionary change — entire systems don’t pop out of nowhere, they gradually evolve alongside other systems, eventually becoming so intertwined with each other that they have become interdependent. And how does Sewell know that the various organs couldn’t function by themselves, either with their current function or a to-​​be-​​exapted function? Some examples would have been nice here.

The creationist’s strawman of a sequential evolution of physiological systems is common, yet utterly indefensible. Sewell should know better — even more so if he were actually a biologist instead of a mathematician.

French biologist Jean Rostand, for example, wrote [“A Biologist’s View,” Wm. Heinemann Ltd. 1956]:

“It does not seem strictly impossible that mutations should have introduced into the animal kingdom the differences which exist between one species and the next…hence it is very tempting to lay also at their door the differences between classes, families and orders, and, in short, the whole of evolution. But it is obvious that such an extrapolation involves the gratuitous attribution to the mutations of the past of a magnitude and power of innovation much greater than is shown by those of today.”

Really, Rostand? I wouldn’t think so. Note that the quote is from the 1950s, when less was known about genetics than is today. I suppose that could explain this statement, an incomplete understanding of genetic mutations… but quote-​​mining by Sewell could still be a possibility.

Behe’s book is primarily a challenge to this cornerstone of Darwinism at the microscopic level. Although we may not be familiar with the complex biochemical systems discussed in this book, I believe mathematicians are well qualified to appreciate the general ideas involved.

Hrm. Perhaps. Perhaps not.

And although an analogy is only an analogy, perhaps the best way to understand Behe’s argument is by comparing the development of the genetic code of life with the development of a computer program. Suppose an engineer attempts to design a structural analysis computer program, writing it in a machine language that is totally unknown to him. He simply types out random characters at his keyboard, and periodically runs tests on the program to recognize and select out chance improvements when they occur. The improvements are permanently incorporated into the program while the other changes are discarded. If our engineer continues this process of random changes and testing for a long enough time, could he eventually develop a sophisticated structural analysis program? (Of course, when intelligent humans decide what constitutes an “improvement”, this is really artificial selection, so the analogy is far too generous.)

He might be able to… but then again, think about the analogy one more time. On the one hand you have this computer programmer, who is selecting advantageous mutations in computer code towards a specified goal, while in evolution’s case you have a blind process, selecting mutations in the genetic code towards a momentary advantageous position in the gene pool. Sewell recognised this, of course, but he didn’t recognise its important implications for his argument.

The computer analogy, by working towards a specified goal, does not allow for exaptation and the gradual evolution of seemingly irreducibly complex systems within the program, which would obviously have to exist for the program to function as a structural analyser. Biological evolution does not have this “single goal” problem. Sewell’s analogy is deeply flawed.

If a billion engineers were to type at the rate of one random character per second, there is virtually no chance that any one of them would, given the 4.5 billion year age of the Earth to work on it, accidentally duplicate a given 20-​​character improvement. Thus our engineer cannot count on making any major improvements through chance alone. But could he not perhaps make progress through the accumulation of very small improvements? The Darwinist would presumably say, yes, but to anyone who has had minimal programming experience this idea is equally implausible. Major improvements to a computer program often require the addition or modification of hundreds of interdependent lines, no one of which makes any sense, or results in any improvement, when added by itself. Even the smallest improvements usually require adding several new lines. It is conceivable that a programmer unable to look ahead more than 5 or 6 characters at a time might be able to make some very slight improvements to a computer program, but it is inconceivable that he could design anything sophisticated without the ability to plan far ahead and to guide his changes toward that plan.

I could have explained the analogy’s flaws after this and other subsequent paragraphs, but I put it above it all just so you could see how little Sewell thought about the differences between his analogy and the real thing. The answer to his questions about evolution, if he were a biologist, would be screaming at him, so much so that he would have to realise it somewhere along the track and correct his errors. Not so for Sewell, the mathematics professsor.

If archeologists of some future society were to unearth the many versions of my PDE solver, PDE2D , which I have produced over the last 20 years, they would certainly note a steady increase in complexity over time, and they would see many obvious similarities between each new version and the previous one. In the beginning it was only able to solve a single linear, steady-​​state, 2D equation in a polygonal region. Since then, PDE2D has developed many new abilities: it now solves nonlinear problems, time-​​dependent and eigenvalue problems, systems of simultaneous equations, and it now handles general curved 2D regions. Over the years, many new types of graphical output capabilities have evolved, and in 1991 it developed an interactive preprocessor, and more recently PDE2D has adapted to 3D and 1D problems. An archeologist attempting to explain the evolution of this computer program in terms of many tiny improvements might be puzzled to find that each of these major advances (new classes or phyla??) appeared suddenly in new versions; for example, the ability to solve 3D problems first appeared in version 4.0. Less major improvements (new families or orders??) appeared suddenly in new subversions, for example, the ability to solve 3D problems with periodic boundary conditions first appeared in version 5.6. In fact, the record of PDE2D’s development would be similar to the fossil record, with large gaps where major new features appeared, and smaller gaps where minor ones appeared. That is because the multitude of intermediate programs between versions or subversions which the archeologist might expect to find never existed, because– for example – none of the changes I made for edition 4.0 made any sense, or provided PDE2D any advantage whatever in solving 3D problems (or anything else) until hundreds of lines had been added.

The argument here is a variation of Paley’s Watchmaker Argument — that complex things must be designed, aka. life was designed. Sewell puts it a little differently here, but the concept is very much the same and it falls for the same reason — both Paley’s watch and Sewell’s PDE2D do not have the reproductive capabilities and environmental pressures that are necessary to evolve under the powers of natural selection. Life, on the other hand, does, so evolution is a great explanation for its diversity. Human/​intelligent intervention is needed for the creation of some complex inanimate objects, especially those which we already know are/​were designed and created.

Whether at the microscopic or macroscopic level, major, complex, evolutionary advances, involving new features (as opposed to minor, quantitative changes such as an increase in the length of the giraffe’s neck1, or the darkening of the wings of a moth, which clearly could occur gradually) also involve the addition of many interrelated and interdependent pieces. These complex advances, like those made to computer programs, are not always “irreducibly complex” – sometimes there are intermediate useful stages. But just as major improvements to a computer program cannot be made 5 or 6 characters at a time, certainly no major evolutionary advance is reducible to a chain of tiny improvements, each small enough to be bridged by a single random mutation.

I think we all know, at this stage, why this doesn’t make sense. Sewell doesn’t understand various evolutionary mechanisms, and it shows very, very clearly in his arguments.

What follows next is Sewell’s second argument against evolution. Hold onto your hats, people, he’s going to talk about thermodynamics!

The other point is very simple, but also seems to be appreciated only by more mathematically-​​oriented people. It is that to attribute the development of life on Earth to natural selection is to assign to it – and to it alone, of all known natural “forces” – the ability to violate the second law of thermodynamics and to cause order to arise from disorder. It is often argued that since the Earth is not a closed system – it receives energy from the Sun, for example– the second law is not applicable in this case. It is true that order can increase locally, if the local increase is compensated by a decrease elsewhere, ie, an open system can be taken to a less probable state by importing order from outside. For example, we could transport a truckload of encyclopedias and computers to the moon, thereby increasing the order on the moon, without violating the second law. But the second law of thermodynamics – at least the underlying principle behind this law – simply says that natural forces do not cause extremely improbable things to happen2, and it is absurd to argue that because the Earth receives energy from the Sun, this principle was not violated here when the original rearrangement of atoms into encyclopedias and computers occurred.

Oh come on. There’s so much wrong with this…

Okay, the best way to show how wrong he is is to come up with something else that must be impossible within Sewell’s misunderstanding of thermodynamics, yet clearly are not. This is, of course, the development of life via reproduction. Or the continuous state of being alive that all living creatures are currently in. Both of these are open systems that increase total entropy in favour of a local decrease in entropy in the form of new cells, new proteins, new DNA strands etc. Clearly, Sewell is majorly wrong when it comes to thermodynamics.

Since evolution is a natural consequence of the existence of living things, it cannot violate the second law of thermodynamics if the existence of life itself does not. The mutations necessary for evolutionary change come about through decreases in entropy (or no change, depending on the mutation) in the DNA of the germ cells that are well within the entropy changes allowed by the regular consumption of food (and therefore energy) by the organism. The decrease in entropy is so low in fact, when compared to all the other thermodynamic processes going on in a living organism, it really does seem laughable that anyone with any grasp of the topic could think that it is impossible under the second law to occur.

The biologist studies the details of natural history, and when he looks at the similarities between two species of butterflies, he is understandably reluctant to attribute the small differences to the supernatural. But the mathematician or physicist is likely to take the broader view. I imagine visiting the Earth when it was young and returning now to find highways with automobiles on them, airports with jet airplanes, and tall buildings full of complicated equipment, such as televisions, telephones and computers. Then I imagine the construction of a gigantic computer model which starts with the initial conditions on Earth 4 billion years ago and tries to simulate the effects that the four known forces of physics (the gravitational, electromagnetic and strong and weak nuclear forces) would have on every atom and every subatomic particle on our planet (perhaps using random number generators to model quantum uncertainties!). If we ran such a simulation out to the present day, would it predict that the basic forces of Nature would reorganize the basic particles of Nature into libraries full of encyclopedias, science texts and novels, nuclear power plants, aircraft carriers with supersonic jets parked on deck, and computers connected to laser printers, CRTs and keyboards? If we graphically displayed the positions of the atoms at the end of the simulation, would we find that cars and trucks had formed, or that supercomputers had arisen?

Err, probably not, simply due to chance factors that occurred along the way to our current time? But such arguments from personal incredulity won’t work on the educated masses, Sewell. Your understanding of the processes involved is not needed for the scientific community’s understanding.

Certainly we would not, and I do not believe that adding sunlight to the model would help much. Clearly something extremely improbable has happened here on our planet, with the origin and development of life, and especially with the development of human consciousness and creativity.

Mmm, that’s a satisfying argument — “I can’t understand it, so some supernatural force, that I won’t name because I know I’ll get in trouble, must have been involved! Wow, I’m doing science!” Nice one, Sewell.

So, do you now understand why expertise in a scientific field is usually necessary to make much sense in that field, especially when you have an agenda like promoting intelligent design creationism? The Discovery Institute really shouldn’t promote this as a scientific publication that supports intelligent design —  because it just doesn’t. All it supports is my hypothesis that Dr. Granville Sewell doesn’t know the first thing about evolutionary biology.

Tags: Evolution, Homologous Legs, Intelligent Design, Mathematics, Thermodynamics

6 Responses to “A Mathematician’s (Highly Flawed) View of Evolution”

  1. 1
    Mark Z says:

    Great post Jack.
    I love how the DIers have completely heterogenous opinions on evolution. There are a few young earthers, some which accept “microevolution” and some who base all arguments on the improbability of abiogenesis. Seems their only common thread is their faith and the hatred of Darwin. If only they could take out some time and read a good population genetics book *sigh*.

  2. 2
    Richard Hughes says:

    Holy sensitivity to initial conditions, Batman!

    As a mathematician, one assumes that the man has to have at least a passing acquaintance with continuous dynamical systems; enough, at least to know that attempting to run a simulation accurate enough to replicate abiogenesis and natural selection using only the four fundamental forces of physics and a set of initial conditions is doomed to failure due primarily to the insane number of initial conditions required, and secondarily because of the mind-​​blowing amount of computational power required to run the simulation.

    In other words, you can’t get the information you need to start, and even if you could, your computer would crash and burn.

  3. 3
    Shockstrut says:

    It’s always worth pointing out to mathematicians who come out with “hey, I’ve shown that evolution is mathematically impossible” that “sorry, evolution is actually happening, we can see it. It’s your model that’s wrong.”

  4. 4
    Sam Brentnall says:

    Brilliant — SIC em Rex — careful they are IDCists are rich and dangerous. Great good luck to you for your looming career path — sorry I did not get to see you — my best to you  — UncSam

  5. 5
    Dennis says:

    Careful … your arrogance is showing.

  6. 6
    Jack Scanlan says:

    @Dennis: Would you be so kind as to point out where that is?

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