A Mathematician's View of Evolution

The Mathematical Intelligencer ^ | Granville Sewell

[SirLinksalot]

A Mathematician's View of Evolution

Granville Sewell

Mathematics Dept.

University of Texas El Paso

The Mathematical Intelligencer 22, no. 4 (2000), pp5-7

Copyright held by Springer Verlag, NY, LLC

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."

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. 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. 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.

1. 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?"

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."

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".) 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? 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."

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. 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.)

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.

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.

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 neck*, 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.

2. 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 happen**, 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.

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? 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.

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footnotes

*Ironically, W.E.Loennig's article "The Evolution of the Long-necked Giraffe," has since convinced me that even this feature could not, and did not, arise gradually.

**An unfortunate choice of words, for which I was severely chastised. I should have said, the underlying principle behind the second law is that natural forces do not do macroscopically describable things which are extremely improbable from the microscopic point of view. See "A Second Look at the Second Law," for a more thorough treatment of this point.

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Granville Sewell completed his PhD at Purdue University. He has subsequently been employed by (in chronological order) Universidad Simon Bolivar (Caracas), Oak Ridge National Laboratory, Purdue University, IMSL (Houston), The University of Texas Center for High Performance Computing (Austin), and the University of Texas El Paso; he spent Fall 1999 at Universidad Nacional de Tucuman in Argentina on a Fulbright grant. He has written three books on numerical analysis.

[js1138]

But there is no point in figuring out the odds of a protein jumping into existence in one swoop. The question is what kind of algorithm would generate a protein.

Pi can be expressed in an infinite series of digits, or by any of several rather short algorithms.

[MHGinTN]

You offered: "Spontaneous generation is monumental problem for the evolutionist. The evolutionist has to accept it by faith, despite its incredibly low probability."

Not even remotely proper to assert ... the evolutionists need not accept or reject that which is not actually relevent to the processes they study. Abiogenesis is not the foundation upon which the processes of evolution rest. It would be just as senseless to assert that IDers must accept that at every change in life porocesses over the past 3.75 billion years, the designer poked His finger into the genome and cause the random changes thus no random changes occurred.

[Physicist]

That argument would be decisive against evolution, if evolution worked that way at all. Proteins don't "just fall together"; evolution doesn't require them to "fall together"; evolution would in fact be effectively falsified if ever they did.

All you're doing is tearing down an irrelevant strawman. Dismissed.

[Alamo-Girl]

Funny thing is the life sciences seem not to recognize formal and final causes, evidently believing instead that material and efficient causes explain everything you need to know.

So very true. The picture will remain incomplete until all four causes are considered.

Thank you so much for your outstanding essay-posts!

[YHAOS]

"In that afterlife, is there reward and punishment for what sort of life one has led prior to arriving in that afterlife?"

Why is punishment necessarily meted out in an afterlife? What if punishment were to be inflicted more directly and more immediately? By that I mean, barring accident or illness, one lives the usual three score and ten, or even four score, and then passes on, but why to an afterlife? If one believes, as a matter of positive evidence and knowledge, that life is but a brief interval here on earth, followed by eternal and utter oblivion, then why should that not be his fate? What could be more merciful and just? The one, who believes that life is finite and is followed by eternal oblivion, receives exactly what he expected; no more, no less. His free will is not even violated.

[Thalos]

A deer of comparable mental ability could do so as well.

The problem is deer wouldn't go from dumb as rocks to human intelligence in one generation. One particular deer would be a little smarter and a little slower, and he'd be the first in the belly of a wolf. Even if he weren't slower, he wouldn't have any particular advantage over other deer, since his daily routine would still be eat food, avoid wolves, and sleep.

As little as 50k years ago, a mere eyeblink of geologic time, there were giant deer, sloths, sabertoothed this and that, even sabertoothed kangaroos, but they are all gone. Did their niches change? Or did man upset the evolutionary processes by his mere existence?

Most likely man caused natural selection to speed up a bit by eating every single creature you mentioned. Whether or not that is "upset" is up to your interpretation.

[FreedomProtector]

The first idea one must accept if one presupposes that "matter is all there is" is that life arose spontaneously from non-living matter by natural random process. Either the first life came from non-life or it came from something outside of nature. Spontaneous generation is thus essential for the evolutionist. Evolution is was 'that links inorganic nature to life'.

"from the inorganic spontaneously, that is, without supernatural intervention and by the operation of material process, themselves of unknown origin, sometime during the first billion years or so of the earth's existence"

--George Gaylord Simpson

Without this concept, one will have to posulate a force outside the material world to explain the existence of the first life on earth. Any supernatural force would be in direct contradiction with the the presupposed atheistic theology and naturalistic philosophy. Therefore the evolutionist is left with the pre-scientific theory of spontaneous generation so fraught with difficulties that few scientists consider it science at all.

"Here we are, evolved though unaccounted ages from the inter-reaction of chemical and energies. Is this not the most awe-inspiring downright spine-tingling drama that can be conceived"

--Lloyd and Mary Morian


"The first living things were not anything so complex as a one celled organism, already a highly sophisticated form of life. The first stirrings wer much more humble. In early days, lightning and ultraviolet light from the Sun were breaking apart the simple hydrogen-rich molecules of the primitive atmosphere, the fragments spontaneously recombining into more and more complex molecules. The products of this early chemistry were dissolved in the oceans, forming a kind of organic soup of gradually increasing complexity, until one day, quite by accident, a molecule arose that the was able to make crude copies of itself, using building blocks other molecules in the soup."

--Carl Sagan


"Once upon a time, very long ago, perhaps two and half billion years ago, under a deadly sun, in an ammoniniated ocean topped by a poisonous atmopshere, in the midst of a soup of organic molecules, a nucleic acid molecule came accidentally into being that could somehow bring about the existence of another like itself--And from that all else would follow"

--Issac Asimov


'science' to many people has become synonymous with trying to explain the existence of the world with out God.


"It has become an accepted doctrine that life never arise except from life. So far as actual evidence goes, this is still the only possible conclusion. But since the conclusion that seems to lead back to some supernatural creative act, it is a conclusion that scientific men find very difficult of acceptance."

--J.W.N Sullivan


"It is essential for evolution to become the central core of any educational system, because it is evolution, in the broad sense, that links inorganic nature to life, and the stars with with earth, and matter and mind, and animals to man."

--Julian Huxley.


Any idea of a force outside of nature, i.e. God or supernatural does not fit into the worldview of one who presupposes that 'matter is all there is'. For this reason evolutionists start with the presupposition that evolution is a fact, and then make up atheistic fairy tales about the origin of life, and make a vain attempt to regulate the supernatural, i.e. God to the world of mythology. Either one believes in the mythology of spontaneous generation, or one believes that the first life was designed by an intelligent designer outside of nature...God.

[Sacajaweau]

I didn't read the intense article...preferring to use my own mind.

The idea that living things wouldn't contain "parts" of other living objects is an absurdity in my mind. But it doesn't follow that they are intimately connected.

ALL living things have to be connected because they are dependent. Darwin falls far short of that.

That's my blah, blah, blah for the day!! No flaming.

[Alter Kaker]

I cannot believe that you think that botanical definitions are the only way to define things.

They're not. But from an evolutionary standpoint they are. You look at similar structures in similar plants, and peanuts are very clearly legumes. I don't care about what they do in your stomach, I care what they do for the plant.

Taxonomy and other classifications are artificial constructs, made by man to help order things.

To a certain extent yes, they're artificial in that they're made up. But that doesn't mean they aren't real or meaningful.

Not the last word, but wikipedia ("evolution of horses entry") disagrees with you.

Can you read? The article you cite indicates that Equus stenonis was the first "'true' horse" in the sense that it was the first member of the genus Equus. However there have been several distinct species between Equus stenonis and Equus caballus. Your own, not-very-comprehensive article explains this, listing Equus ferus as an intermediary. In fact, Equus stenonis is likely the ancestor of all extant horse, zebra and donkey species. Since few of them can cross-reproduce succesfully or easily (newsflash: Mules aren't fertile) it seems likely that modern horses and Equus stenonis would have been reproductively isolated had they been alive at the same time. Modern horses -- Equus caballus -- only came into existence within the last 3000 years.

[Alter Kaker]

Huh? Who said anything about creating an amoral society?

I think you're projecting. I like the fact that you concede that you lack the ability, intelligence or education to articulate or defend your own position (asking a highly trained newspaper columnist to do so instead), but not the ability to insult those with whom you disagree.

[Alter Kaker]

So what is this "third way" you are implying.

Natural selection. Hares with lighter fur are less likely to be seen by hawks on a snowpack. They're more likely to survive and pass on their genes, and of their offspring sitting on snowpacks, the ones with the lightest fur are the most likely to survive in a few generations. The selection isn't random -- there's a very good reason why rabbits with lighter fur survive -- but neither is it designed.

[Alter Kaker]

Because evolution was not the mechanism by which this country was formed - actually there is no relationship at all.

Actually, there is a considerable analogy here. When two populations become reproductively isolated (much as the US and England were socially and politically isolated), they grow apart via genetic drift and may grow to occupy different niches. At some point, they grow so far apart that they cannot reproduce easily. At a further point, they will be unable to reproduce entirely. But that doesn't mean that only one descendent species can exist.

o you have any supporting evidence for this claim?

Sure! Well, for one, we share more genetic material in common with chimpanzees than chimpanzees share with other apes. That certainly suggests what I'm talking about. I'll try to find a recent paper that shows that.

[FreedomProtector]

Faith in evolution requires faith that enough molecules accidentally come together ("fall together") in a prebiotic soup to form life from non-life.

So what you are assuming is that the genetic machinery that tells the cell how to produce protein and the protein required to build that genetic machinery both originated gradually and were present and functioning in the first reproducing protocells?

But that does not fit what we observe in the laboratory...In living cells, both DNA and protein depend on each other for existence.

Even if polypeptides had formed in the primordial soup, hydrolysis would have broken them up and destroyed most amino acids. Organic compounds such as amino acids, tend to break down when dissolved in water. The higher the temperature, the faster this breakdown occurs. "…joining many amino acids together to form a protein with a useful biological activity is a much more difficult problem than forming amino acids in the first place. The major problem in hooking amino acids together is that, chemically, it involves the removal of a molecule of water for each amino acid joined to the growing protein chain. Conversely, the presence of water strongly inhibits amino acids from forming proteins….."

These probability models actually give the evolutionist the benefit of doubt when they ignore certain observable, repeatable phenomenon (facts) like hydroysis preventing of formation of polypeptides, and give the evolutionist a huge number of amino acids (even when there is no circumstantial evidence of prebiotic soup), and give the evolutionist a mechanism to put a huge number of them together over and over and over again.....

[sittnick]

They're not. But from an evolutionary standpoint they are. You look at similar structures in similar plants, and peanuts are very clearly legumes. I don't care about what they do in your stomach, I care what they do for the plant.

That is called begging the question. Modern horses -- Equus caballus -- only came into existence within the last 3000 years.

You don't know that.

[Alter Kaker]

That is called begging the question. Modern horses -- Equus caballus -- only came into existence within the last 3000 years. You don't know that.

Huh? Yes I do -- the evidence is overwhelming that Equus caballus was selectively bred out of Equus ferus populations strating about 3kya. Are you honestly suggesting that the common ancestor of all extant horse, wild ass and zebra species was... a modern horse?

[Alter Kaker]

That is called begging the question.

No it isn't. My point is that nutritional content, cooking properties and everything else you bring in is irrelevent to this discussion. Peanuts share a botanical form and function with other legumes, not with nuts. Sorry.

[betty boop]

IF evolution is geared towards survival....THEN doesn't it also follow that a brain geared for survival is not capable of doing cosmology?

Makes complete sense to me, ConservativeDude! Unless a case can be made that cosmological speculation has survival (fitness) value. You could go into the caves at Lascaux in the French Pyrrannes and find amazing paintings that suggest that the people who lived there, apparently in communities, (dated roughly 25 centuries B.C.) were already dealing with cosmological issues. But that would depend on how you chose to interpret the "evidence" -- the exact same situation that applies to the reading of the fossil record.... I.e., we tend to find what we're looking for: Our presuppositions can and do skew outcomes.

Anyhoot, to me it is senseless to say that "the brain" is "doing" cosmology. I don't think it is the brain that thinks, but the mind. It appears to me that consciousness, like life itself, cannot be reduced to purely material causes. And Darwinism has no clue about the origin of either.

Though people will speculate on such issues in ways consistent with their materialist presuppositions -- and really get no where. An excellent case in point is the abiogenetic origin of life hypothesis, that life spontaneously arises from chemistry under favorable conditions. Darwin never included such speculations in his published work; but in a personal letter to a friend that became public in 1954, he did enthuse about a "warm little pond" scenario....

But Nobelist Francis Crick basically drove a silver stake through the heart of such foolishness when he demonstrated that the progression amino acids -> proteins -> RNA -> DNA simply doesn't happen in nature. This key insight, which arose from information theory, has come to be known as the "Central Dogma" of biology.

In the end, it seems to me that focusing only on material and efficient causes puts Neo-Darwinism in a situation where it's letting the tail [of its desire] wag the dog [of its science]: its methodological materialism precludes it from recognizing that formal and final causes actually do operate in nature. I think science -- especially physics and mathematics -- is increasingly aware that an absolutist materalist reductionism may be creating a false picture of reality.

The "first scientist," Aristotle, thought you needed to consider four causes -- formal, material, efficient, final -- to explain existents in nature, not just two (material and efficient). Problem is the formal and final causes seem to be "non-corporeals." So it's difficult to say just how they operate in nature. Still, to me, this is the million-dollar question....

Thanks so much for your astute and thought-provoking essay/post, ConservativeDude!

[Quix]

Well put, as always. Thanks.

[betty boop]

Thanks for your kind words, Quix!

[hosepipe]

[ Anyhoot, to me it is senseless to say that "the brain" is "doing" cosmology. I don't think it is the brain that thinks, but the mind. It appears to me that consciousness, like life itself, cannot be reduced to purely material causes. And Darwinism has no clue about the origin of either. ]

If a human is a spirit riding a Donkey(with a brain) then who does the thinking?.. The spirit or the brain?.. Seems to me both are possibilities.. both think.. Therefore you can have a donkey riding a spirit.. or a mix...

This life is obviously a metaphorical donkey rodeo the only question is, who is the passenger?.. or is the spirit walking the donkey(on a leash) or the donkey walking the spirit(on a leash) forgoing riding.. You always taunt with such interesting questions..

The scriptural passage, "A double minded man is unstable in all his ways".. is apropos if true.. Little wonder some would walk.. instead of ride or be ridden..