A Mathematician's View of Evolution

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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*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.

To both of you and any other Darwinian delusionists, I will suggest that you take Running Wolf's #274 as my answer. The day will not dawn when tax-fed Darwinian bullies are going to move me a skinny little millimeter toward joining in their delusion that humans are "descended from" apes or whatever. Take Darwin and place him and his idjit theories where the sun shineth not.

And, Godless is, among other things, Ann Coulter's cogent explanation of the hilarious fantasy that is Darwinianism, to you, Bub.

Wanna drag race with Annie for position on the (gulp) New York Times best-seller list???? You'll lose. On such a list of National Review, Human Events or the American Spectator, you'll lose a lot worse.

BTW, right now, FR is doing a poll on whether Intelligent Design or Creationism should be taught in public skewels alongside Darwinism. I had to vote yes but only because abolition of the hideously expensive gummint brain laundries was not an option. OTOH, a very strong majority voted yes. What does Darwinian delusion or environmentalwhackoism or paleopantywaistism or other heresies have to do with CONSERVATISM????? You are aware that this is a CONSERVATIVE website and not an atheist or agnostic or liberal or "progressive" or gummint edjumakashunist or Darwinian website, right??????

To all who make of Darwinian delusion an understandably irrational pseudo-religion, science, like everything else, was created by God. Any "science" which purports to refutes the word of God is a rejection of His truth and therefore not part of a search for truth. If science is not a search for truth, then it is not science. If you want to believe that whatever passes for Nancy Pelosi's "brain" is made of Ricotta cheese, it would be an awful insult to lasagna but feel free. America, it's a free country to some extent. If you want to believe that Darwin was capable of simultaneously employing three brain cells, feel free. America, it's ..... If you believe that human beings are "descended from" apes or earthworms or pterodactyls or natural rock formations or 1929 Model A Ford 2-seaters with rumble seats or Pee Wee Herman or George McGovern or Howard the "Aaaaaaaaarrrrrrrrrgh" Dean (I think those three are "primates" and that they almost certainly are simian wannabes, or whomever or whatever, feel free but do not expect respect for such fairy tales from people who know better. If it comforts you to imagine you are "descended from" beasts of any sort, presto and abracadabra! You are a beast! Feel better????? America, it's a great country!

Now, run along and leave the people (You know, Adam and Eve's progeny and their progeny and.... NOT Bonzo's or Mighty Joe Young's progeny, if any) who have Biblical dominion over you beasts alone.

Take Darwin and place him and his idjit theories where the sun shineth not.

You have yet to demonstrate that the theory of evolution is false. Your claims are presumptious.

And, Godless is, among other things, Ann Coulter's cogent explanation of the hilarious fantasy that is Darwinianism, to you, Bub.

As has been demonstrated, Ann Coulter employs blatant falsehoods in her attacks on the theory of evolution. That you choose to ignore this fact does not negate the reality that her arguments against the theory are not valid.

Wanna drag race with Annie for position on the (gulp) New York Times best-seller list???? You'll lose. On such a list of National Review, Human Events or the American Spectator, you'll lose a lot worse.

The popularity of Ann Coulter's book does not make her invalid arguments any less invalid. You are appealing to a logical fallacy.

Any "science" which purports to refutes the word of God is a rejection of His truth and therefore not part of a search for truth.

If you have decided already that you will reject any aspect of reality that contradicts your religious beliefs, then there is no further purpose for discussion. You have already made it clear that you are arrogant enough to believe that you know God's word better than any other, thus you have demonstrated that you are wholly irrational.

I don't give a damn what Iran's homicidal maniac president (or general population) "think" (assuming that they think) about Dubya, the USA or conservatism or Catholicism or Chriostianity generally. Likewise Ugo Chavez. Likewise, Jacques "Light Fingers" Chirac. Likewise, the New York Times. Likewise, the National Education Association. Likewise, C-Span's Commies in the Morning aka Washington Journal. Likewise Noam Chomsky. Likewise Charles Darwin and his posthumous Monicas. Likewise other liberals/leftists/"progressives" whose "stereotypes" conservatives are proud to be and righfully so. OOOOOH, that Elk is just sooooooo, ummmm, ummmmm, anti-intellectual!!!!! Sooooooo politically incorrect!!!!! Liberals posing as conservatives are sooooooo embarassed!

I have no interest in worrying for my country or my conservatism about human respect (the Catholic term for what the world misthinks) and every interest in having the world become appropriately worried about what America and conservatives think. We have the weapons. They don't.

I practiced law for decades. You did not if you imagine that "science" can be libeled much less that it has been.

What is fictional about Darwinian "science?" Ummmm, everything! If you imagine yourself descended from apes or other simians to be linked later (how many centuries and government funds later???? Never mind!) or that darwinism is truth, then you are a Darwinian Church Lady.

Also "scientifically literate people" is another discredited tautology. First, you are forgetting your claim to be mere trousered apes. I am still waiting for the darwinian answer to whether there is an immortal human soul and, if so, whether it too "evolved" from whatever sould the apes had to immortal.

It only seems to you darwinians that I am jumping up and down because you are not used to being rightfully disrespected or subjected to dissent from darwinian "orthodoxy" protected as you are by federal courts which establish your false religion and force taxpayers who know better to pay for it. You are used to grandiosely setting the terms of the debate and I refuse to play along. You are used to playing establishmentarian and demanding that your critics bear the burden of proof and I refuse to play along. You are pissed. That is only natural but it does not buttress your fantasies as fact.

Go back to your laboratory and genuflect before your beakers and test tubes. I guess it's better than nuthin'.

Wouldn’t you say that is being a bit naÃ¯ve?

No. Data stands or fails as valid based upon its correspondence to reality, not because of any agenda posessed by those who report the data.
,br> 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?

If you have evidence of bias leading to false conclusions regarding the theory of evolution, then please present it. Mere speculation, however, is not evidence against a scientific theory.

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.

This would not preclude another without such an agenda of publishing 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.”

If this were true, there would be no further advances in science.

What constitute the “scientific community”?

The subset of the general population who is educated sufficiently in a scientific field to be employed in a position that requires such knowledge.

You say that evolution is correct based upon your scientists. I probably counter with other scientists that would say they believe in created design

Please cite the relevant scientific research that lends credibility to claims of "created design".

Perhaps I’ve broad brushed this a bit but not unreasonably so. It really becomes who you wish to believe.

The nature of scientific inquiry is that the methods are openly known. It is possible to investigate the research that has led to scientific conclusions to determine whether or not a claim is justified. While it is true that there exist individuals who wish to change the definition of science to one that would truly be based upon "who you wish to believe", such individuals have gained little headway outside of the state of Kansas.

It’s a matter of faith-in scientific models and premises.

Scientific models can be tested and reviewed, and in fact much face such testing and review to be accepted as valid. This is not "faith".

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.

You are speaking of medical ethics, not science. Science is not a method for defining ethics.

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.

How do you define a "human life"?

Don’t you think that would be a very important scientific question to answer before we go destroying it?

What factors would need to be observed to conclude that a collection of cells is a "human life"?

Evolution and the earth creation are interrelated.

Incorrect. The mechanisms of the process of evolution do not depend in any way on the means by which the planet on which the process occurs came to exist. If you disagree, then please explain how the mechanisms of evolution would change between a planet that formed through unguided processes and a planet that was built by interstellar contractors.

There is no different in saying the earth was created by intelligence design than to say man was created by intelligence design.

You are again incorrect. Demonstrating that the Earth were "intelligently designed" would not automatically demonstrate that humans or any other organism was initially "intelligently designed".

If there was “little dispute” we wouldn’t be wasting a lot of bandwidth, paper and media attention on this.

I should have clarified my comment. I meant to say that there is little dispute within the field of cosmology, from where the current models for planetary formation originate. (I will also note that I use the plural "models" not because there exist competing explanations, but because there are different means by which a planet can form).

Why?

You have made a specific claim. It is reasonable to expect that you will provide evidence to support it.

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?

Is it not also possible that there were not a large number of individuals who had conducted the same research that Galileo had conducted?

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.

Planets do not evolve.

Either one must be a good thing.

There is no rational basis for your conclusion.

To both of you and any other Darwinian delusionists, I will suggest that you take Running Wolf's #274 as my answer.

Good to see the two of you are teaming up. Very apt.

The day will not dawn when tax-fed Darwinian bullies are going to move me a skinny little millimeter toward joining in their delusion that humans are "descended from" apes or whatever. Take Darwin and place him and his idjit theories where the sun shineth not.

That doesn't seem to be the trend set by every recent court decision and election pertaining to this matter in recent history. (Hint: think Dover.) Rational science has the raving lunacy of theocratic fanatics in part to thank for this, as well as the fact that all modern biological and paleontological science supports evolution.

And, Godless is, among other things, Ann Coulter's cogent explanation of the hilarious fantasy that is Darwinianism, to you, Bub.

You honestly think Ann Coulter singlehandedly was able to raise 'valid' points that somehow 'eluded' the minds of scientists all over the world who dedicate their lives and educations to this research? Please. Ann Coulter is about as 'cogent' as Kent Hovind on this matter.

Irrelevant. Facts are not right or wrong based on their popularity. I think you already know that, though.

I have no problem with creationism being taught along side of evolution. Then, biology teachers could give creationism the public skewering it deserves. You do realize that this is what someone educated in biology would do in this situation, don't you? Still want them taught 'side by side'?

What does Darwinian delusion or environmentalwhackoism or paleopantywaistism or other heresies have to do with CONSERVATISM?????

What does creationism and scientific ignorance have to do with conservatism? This perceived connection is driving sensible people away from the Republican Party in droves. Statements such as yours above are typical of the scientific ignorance people (wrongly) associate with Republicans.

You are aware that this is a CONSERVATIVE website and not an atheist or agnostic or liberal or "progressive" or gummint edjumakashunist or Darwinian website, right??????

That's what I hear. That's why I support hard scientific facts, not this PC dreck called "creationism" and "intelligent design".

Rejecting any theory because it doesn't support a conclusion that you wish for is not science, it is apologetics. That's exactly what you appear to do.

If you want to believe that whatever passes for Nancy Pelosi's "brain" is made of Ricotta cheese, it would be an awful insult to lasagna but feel free. America, it's a free country to some extent.

Oookayyy...

If you want to believe that Darwin was capable of simultaneously employing three brain cells, feel free.

Darwin established a biological paradigm shift that has withstood a century and a half of scrupulous investigation, notwithstanding sultry, substanceless attacks by unqualified fundamentalist antagonists. If he did that with only three brain cells, it beckons the question of what contributions you've made to science...

If you believe that human beings are "descended from" apes or earthworms or pterodactyls or natural rock formations or 1929 Model A Ford 2-seaters with rumble seats or Pee Wee Herman or George McGovern or Howard the "Aaaaaaaaarrrrrrrrrgh" Dean (I think those three are "primates" and that they almost certainly are simian wannabes, or whomever or whatever, feel free but do not expect respect for such fairy tales from people who know better.

I think you've quite 'cogently' demonstrated through your recent posting history that you don't know better.

If it comforts you to imagine you are "descended from" beasts of any sort, presto and abracadabra! You are a beast! Feel better????? America, it's a great country!

I don't find it comforting at all. If the fact that we descended from apelike ancestors was so 'comforting', it wouldn't cause so much consternation among folk like yourself. I'm sorry science has no respect for your feelings. I prefer to learn the facts and find my way to deal with them, rather than pervert facts to fit my comfort zone. (That I leave to the leftists...)

Now, run along and leave the people (You know, Adam and Eve's progeny and their progeny and.... NOT Bonzo's or Mighty Joe Young's progeny, if any) who have Biblical dominion over you beasts alone.

Unbelievable. Ironically, you scorn the philosophy (science) that has given us dominion over much of nature, as God commanded us.

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