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.

[Dimensio]

OTOH, just because scientists haven't come up with a change agent other than random genetic mutation, doesn't mean that's the answer.

Do you have evidence for a different mechanism?

[JeffAtlanta]

Wow what a mature post!

[colorado tanker]

No.

You might want to check out The Structure of Scientific Revolutions, an oldie but goodie. Today's orthodoxy will likely be tomorrow's . . . . Well, you know how kind we are to past theories like catastrophism.

[sittnick]

To pretend that we don't know anything about what large mammals were alive within the recent realm of recorded history suggests you're talking out of your ass.

I simply stated that we do not know all of the species that were around 3,000 years ago. Knowing some, knowing lots, and knowing all are different things. Lets see, "begging the question", "post hoc ergo propter hoc" and now at least the second "straw man". Trying to hit for the cycle on logical fallacies?

Huh? Peanut roots aren't edible. The edible part of the peanut is the fruit (which does grow underground).

Of course, you just answered your own earlier question about how peanuts are different from [other] legumes. The fruit grows underground! And of course peanuts are nutritionally regarded as meat.

In any event, edibility has nothing to do with the plant and everything to do with human digestion.

The reason that something is or isn't edible by humans is because there has to be something different in the object consumed. So of course it says lots about how peas and peanuts are different.

[Virginia-American]

The dispute over the point at which the collection of living cells is a 'living human' -- whether it is at the moment of conception or the moment of birth -- is a philosophical question, not a scientific one.

It's a legal question that should, IMO, be decided by legislative bodies.

[BlackElk]

D: You have yet to "demonstrate" your capacity to read. Neither Christianity nor Catholicism owes ANYTHING WHATSOEVER by way of argument to Darwinian delusion or other gummint godless religions. Western civilization is NOT based on Darwin come lately. Darwinianism is NOT the standard. It is the obviously irrational challenge to the Judaeo-Christian basis and standard of Western civilization.

One minor concession to your expressed need for evidence. If you don't believe that this Darwinian delusion is the uniform forced curriculum of gummint skewels [in spite of your citation of a pseudo-scientific apologia for Darwinism/attack on Ann Coulter which includes one of many fedcourt decisions (this time from Kansas) cramming Darwinian delusion down the throats of school kids with taxpayer dollars courtesy of the ACLU (law firm of the secular humanists and other materialists and atheists)]. As Coulter wisely observes, the public schools are the madrassas of the radical left.

If there are drivers who think they can drive safely with blood alcohol of 0.40 in urban areas on 70 MPH interstate highways that does not prove that they can. If there are "scientists" who believe in Darwinian delusion, that they are simians and that they believe in God, this proves nothing but rank confusion and that science has abandoned the search for truth in its quest for tax-subsidized hegemony over people who know better than they.

My assertions are credible: Look at Ann. No excessiely furry body. No bananas in hand or mouth. No public rib scratching. One fine looking human female with no outward appearances of apeness or chimapnzeeness or atheism or other form of liberalism. Presto: Ann is, ummmm, magnificently human and monkeys are not. "People" who think otherwise are, ummmmm, at best questionable. If y'all want to believe that y'all are really apes or baboons, hey, enjoy!!!!

The Bible is per se credible. So is the Teaching Magisterium. Darwin is not.

Simian wannabes are not worthy of respect. Their theories are not worthy of respect. The ones who want to split the difference by claiming to be "theists" while also claiming to be descended from monkeys, apes, gorillas, baboons, chimpanzees are saying that they believe in God but reject His word favoring Darwin's delusions instead. Hmmmmm....schizophrenia, anyone?????

BTW, I did not invent the term "descended from..." in this context. If Darwinian obsessives actually were "descended from" other simians as they hallucinate, the term would accurately describe their regression.

I absolutely do not care whether you believe what I say. I concede absolutely nothing to you much less that I am willfully misrepresenting anything much less falsely (wouldn't a false misrepresentation actually be a true representation????....never mind). The suggestion, rather, is that if you are a simian wannabe, you can feel free to be a simian wannabe, for all that I care. My religion is the truth whether you happen to like it or not. You are free in America and in the Catholic dogma as to free will to adopt whatever fantasies turn you on (and to take the consequences of your choices). Far be it from me to interfere with your choice of monkeys as ancestors. OTOH, don't expect me to be impressed.

The theory of evolution and its promoters need no help in thoroughly discrediting evolution. It is a self-executing discreditation and always has been. Go entertain yourself in your little laboratory. Who knows, maybe you will impress you.

I have not "admitted" anything. I have proclaimed Darwinian delusion not to rise to a level deserving respect or evidence in opposition. The burden of proof lies exclusively on the delusionists who are simian wannabes to prove their ancestry lies among the monkeys.

BTW, if you believe that man has an immortal soul, describe how it "evolved" from the mortal soul of apes. Or do you believe that apes have immortal souls????

Simian ancestors or the Truth of Christ???? Ummmmm, the Truth of Christ every time.

As to your last paragraph: "God is dead!"---Nietzsche. "Nietzsche is dead!"---God! Also: "Darwin is dead!"---God

[Coyoteman]

[Ann is...] One fine looking human female with no outward appearances of apeness or chimapnzeeness or atheism or other form of liberalism. Presto: Ann is, ummmm, magnificently human and monkeys are not. "People" who think otherwise are, ummmmm, at best questionable. If y'all want to believe that y'all are really apes or baboons, hey, enjoy!!!!

Look at the bones. Look at the genetics. You'll see how closely related primates really are. You are doing pure apologetics, not science.

(And feed that girl a milkshake and a couple of cheeseburgers!)

[BlackElk]

Thanks!

If you liked that one, you are going to love #247 and #266.

Ummmmm, maturity is not consistent with acceptance of the desperately godless Darwinian BS.

[Tax-chick]

I love your language! Although my Niceness Filter prevents me from indulging in the same sort of vehemently vivid invective, I feel good about having you do it on my behalf.

Vlad stood up this morning!

[BlackElk]

Ann's bones resemble a baboon's bones????? Her face, hair and flesh do not. I knew her much elder brother John several decades ago. Now those two resemble one another. Facial features. Height. Bright. Ability to speak (with admirable sarcasm!). Can drive cars. Would not, on a bet, push buttons in sequence for bananas or swing through the trees or scratch ribs in public or imitate apescreech. I have not met Ann's parents but I am betting that they much more resemble Ann and John than they do baboons or liberals or atheists.

Hey, just to show the kind of guy I am, I CAN AGREE that Annie needs burgers and shakes but she STILL won't look like a baboon or whatever.

I am doing truth. Darwinians are doing science fiction. They scare their apelets and keep them in line with flicks like Planet of the People.

[BlackElk]

Delighted to be of assistance to the wife of my brother Knight. Go Vlad! Go, Vlad! Wait until he hears that he is being accused of simian ancestry by the usual gang of malefactors!

[Tax-chick]

He would spit.

Well, he might do that after eating, anyway, but once in a while, he seems to be making a Statement ...

[Coyoteman]

Ann's bones resemble a baboon's bones?????

I said primate. That is a much broader class them just baboons.

Ever study bones? I have. Once you learn the human cranium you can look at a monkey cranium and all the bones are the same; somewhat different shape and size, but if you know the bones you can recognize each of them. Same for the postcranials. Genetics is even more definitive.

I am doing truth. Darwinians are doing science fiction.

I am citing verifiable data. If you don't believe it you can go to a museum or take an osteology class and see for yourself. That is the way science works.

I leave it to the lurkers to determine who is doing science fiction.

[RunningWolf]

Thanks for the ping BlackElk

You can count on at least one of the delusionals to relentlessly insist you have not substantiated any claims reject all proof you bring thereof, twist your words with each reply of his, never directly address anything you have said, and himself be so squirrelly and slippery that it is hard to determine just what if anything he has ever said or believes in except that he will somehow get to his declaration that nothing you say is worth anything and end with rejection of you as a person in as many words. That is the demented message said yet once again for most likely the thousandth time, it is so predictable.

You are accused of being belligerent dishonest and irrational by one who wears those descriptions like its painted on to him..

These is a hatred that seeps out BlackElk, and it is plain to see by all of a rational and objective mind. It comes from the rabid idolater's from the cult of darwinism, IOW the godless religion of liberals.

Well you do have a lot of powerful words there BlackElk and the Darwinists will do everything they can to make it go away.

When 'Wolf is gone for calling it as it is, hopefully BlackElk will be around to bring some balance.

Take Care,

W.

[Quark2005]

I am doing truth. Darwinians are doing science fiction.

So, exactly what is "fictional" about 'Darwinian' science? Are you capable of being more specific, or are you just going to continue to throw about haphazard libel about science (and scientifically literate people) in general (and in turn, completely play into the negative stereotype liberals have about conservatives)?

You're good at jumping up and down and making a lot of noise, here, but you haven't offered any arguments of real substance - only ad hominems and appeals to consequence.

[VadeRetro]

Dimensio hits you with specifics in 220. You "rebut" with paragraphs of unsubstantiated risible spew in 247.

For more discussion of where Ann Coulter's antievolution screed misses the mark, note this post. What will you spew in answer to that?

[Doctor Stochastic]

Coulter is not an authority ....

You're too verbose.

[betty boop]

3) Materialist presuppositions result in conclusions which are contradictory to the world. The Materialist cannot be consistent to the logic of their presuppositions, because the materialist lives in a reality which was made by something external to matter...God. This being so, Materialist is in a place of tension.

4) Materialists build up walls of protection to shield themselves from the point of tension. The materialist then erects barriers, even if completely irrational or improbable, to try to deal w/ the contradiction of how he observes the world.

Deeply perceptive insights, Freedom protector! H. von Doderer and R. Musil, et al., have given a name to this sort of thing: second reality. They are re-constructions of the world of first reality -- into which each of us is born -- by a mind that rejects vital sectors of that reality -- e.g., human nature as a given, the universality of the human condition, the order and purposefuness of nature, the existence of God, objective morality, the sanctity of life and the human person, etc. -- driving them into "oblivion." The rejection of the order of first reality is for the purpose of allowing man to construct for himself a "reality" more according to his own wishes, goals, and desires. Second realities, therefore, are ideological, not realist, in form.

Still no man can evade the essential constitution of things, no matter how hard he may try to remain blind to them. Still people will try, and the results are readily visible to us in the form of various political, social, and scientific "movements."

One of the most famous second realities was the one constructed by Karl Marx. It is completely out of whack with human nature and the natural order, and so sooner or later has failed to deliver on its promises everywhere it has been tried.

I think at the root of a whole lot of present-day sociopolitical movements you will find a second reality: e.g., gay rights, global warming, the feminist movement, secular humanism, to name a few. Furthermore I think the populist version of neoDarwinism is premised on a second reality.

Anyhoot, FWIW. Thank you so much for your excellent essay/post, FreedomProtector!

[js1138]

Dean of Discipline of the Tomas de Torquemada "Gentlemen's Club"

I have to say that the first time I encountered the phrase "Gentlemen's Club" it was attached to a building trimmed with flaming violet neon lights. We don't often get freepers who share their interest in S&M in public.

[HarleyD]

Even if this is true, an 'agenda' does not falsify scientific data.

Wouldn’t you say that is being a bit naïve? No one is necessarily accusing all scientists of falsifying data, even though some have. But how many scientists are “true” scientists, people who objectively seek out answers? I doubt that if someone was trying to prove the rainforest deforestization was leading to global warming, and they found evidence to the contrary, that they would publish the data. I’m skeptical given today’s environment that they would wish to contradiction to their agenda. There are very few people who will say, “Well, I guess I was wrong on that one.”

I was not aware that the recent increase in child obesity has been attributed to one single cause. Do you have a reference?

What constitute the “scientific community”? You say that evolution is correct based upon your scientists. I probably counter with other scientists that would say they believe in created design. Perhaps I’ve broad brushed this a bit but not unreasonably so. It really becomes who you wish to believe. It’s a matter of faith-in scientific models and premises.

The ambiguity is based upon defining when a human "life" begins, which is not a scientific question.

Nonsense. The same medical profession that goes in to operate on a fetus at 20 weeks is the same group that will think nothing of killing it. The “ambiguity” is simply a political cover. There certainly is no shortage of people looking for “scientific” funding of embryonic stem cell research money now is there? It’s simply a cop out to say no one knows when life begins. Don’t you think that would be a very important scientific question to answer before we go destroying it?

There is little dispute as to the means by which the earth came to exist, though that subject is not related to the theory of evolution.

Evolution and the earth creation are interrelated. There is no different in saying the earth was created by intelligence design than to say man was created by intelligence design. If there was “little dispute” we wouldn’t be wasting a lot of bandwidth, paper and media attention on this.

Please provide references to support this claim [about Galileo].

Why? 1) Galileo was going against hundreds of years of scientific beliefs. 2) Most scientists (if not all) were members of the Catholic Church. 3) No one came to the aid of Galileo. It reasonable to deduce that either the scientists of the day either supported the Church or they were abject cowards being afraid to advance science in the name of saving their own skins. Doesn’t this come back to our discussion about scientists being bias?

This does not falsify the extensive research and uncovered data in support of the theory of evolution.

If this is true, then man destroying us either through global warming or blowing ourselves up will be simply another step in the world's evolution. Either one must be a good thing.