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.

- the theory of continental drift proposed by Alfred Wegener and supported by Alexander Du Toit and Arthur Holmes but soundly rejected by most geologists until indisputable evidence and an acceptable mechanism was presented after 50 years of rejection.

Actually continental drift is a fact and plate tectonics is an explanatory theory.

I happen to have taken geology just a few years before plate tectonics was accepted. I can assure you that continental drift was taken quite seriously. Several days of freshman geology was devoted to the supporting evidence, even though there was no known mechanism to make it possible.

Again, you have mistaken the fact that continents move for the theory that explains the movement.

There is a parallel in evolution. Successive replacement of species was widely accepted long before Darwin. What Darwin offered was not the fact of change in species, but an explanatory theory.

... The very nature of it leads to misassumptions and uncertainties. Did Homo sapien descend from Homo erectus or Homo ergaster? Australopithecus afarensis or Australopithecus africanus? And it's not anti-science to say none of the above. ...

It's anti-science to make flat-out assertions without evidence to back them up. "None of the above" is very hard to reconcile with the evidence, since, as has been pointed out before, the creationists themselves disagree whether some of these guys are in the "non-human ape baramin" or the "human baramin". If nothing else, that establishes that H. erectus, H. ergaster, et al, are neither clearly non-human nor clearly human.

"Marx, Engels, Hitler, Ugo Chavez, Mao Tse-Tung, Danny Ortega, Margaret Sanger, and (with a certain sense of imminent discovery) Fidel Castro, would certainly agree or have agreed with you."

I very much doubt the egomaniacal collection of human horrors you've assembled would agree with me about their status as first worm-food, and then later a worm substance of a different sort. If nothing else, their monumental egos would not permit them to contemplate such a fate.

Condemnation to eternal torment implies a life eternal necessary for the contemplated punishment to be inflicted. That's the problem with earthly visions of heavenly consequences; they can easily entrap us in a paradox of our own human invention. I can see that you might feel cheated at the prospect that such villians could avoid eternal torment by escaping into eternal oblivion, but I must disagree with the idea that eternal oblivion can not constitute eternal damnation.

"A firm belief in God and submission to Him: Don't leave earth without it!"

Exactly my point. That misanthropic assemblage you've concocted for our amusment won't be leaving Earth . . . ever . . . and decomposition will, finally, be turning them into something useful.

Again, you have mistaken the fact that continents move for the theory that explains the movement.

With all due respect, for scientists the reading skills as exhibited here are certainly poor. I started off saying in post 257 that scientists have set agendas, just as everyone else does. Now people would like me to explain black holes, quantum tunneling, and continental drifts. Honestly.

If one would take the time to read my post, these are NOT my example in regards to continental drifts. Rather, they are references from the research of Thomas Kuhn and detailed in his book The Structure of Scientific Revolutions on scientific consensus and minority opinion. I cannot vouch for continental drifts nor have I read Dr. Kuhn's book. However, I'm sure Dr. Kuhn could provide you with further information if you believe him to be at odds with the scientific community. I would also recommend writing Wikipedia and have the reference pulled.

Dr. Kuhn seems to support my statement and I stand by that statement until scientifically proven otherwise.

There's no usage police for words like hypothesis and theory and law, except possibly among journal editors.

Problems arise when someone tries to argue from definitions. It just doesn't work. Scientists know the categories, even if they sometimes get sloppy in informal writing.

The simplest way of thinking about this is to accept that all categories of knowledge in science progress. There are no statements in science that are not susceptible to being replaced by more comprehensive statements.

"None of the above" is very hard to reconcile with the evidence,

Oh but it's not. It's just looking at the evidence with a stricter and more skeptical set of assumptions.

You find fossils in a particular strata and if you believe in evolution you assume those fossils were the ancestor of something. If you don't believe in evolution, you might consider that those fossils belonged to something that never evolved but went extinct. Or you might think some evolution occurred but it is still basically the same creature as one still with us.

A scientist finds a fossil and he has questions for it. A creationist finds a fossil and he has dismissals for it.

Creationism has nothing to teach us.

FWIW, I've spoken to a number of scientists who've read Kuhn's book, and I don't think I ever met one who thought much of it.

OK, by your estimation, what *is* that worth? Are surveys of scientists worth more than any other poll? Or should Kuhn's assertions be vetted like any other? (OK, since Kuhn is talking about what could be called "philosophy of" or "sociology of" science, that might be harder to pull off).

But you get the point...

Cheers!

So what conclusion can be drawn from the fact that the creationists are unable to decide whether H. habilis, H. erectus, H. ergaster, et al are human or non-human?

The conclusion that I draw is that they are clearly neither one nor the other, that they are in fact intermediate.

These aren't biologists with their funky assumptions who can't fit them in one bin or the other; these are creationists, who claim it can be done, but are in fact unable to do so. (Actually, they can, it's just that they don't agree!)

A sociologist might be the top world expert on some aboriginal tribe someplace, and still not have anything useful to teach the tribesmen about what it's like to be a tribesman.

Interesting Chesterton quote in this regard, from The Noticeable Conduct of Professor Chadd (which was in his The Club of Queer Trades):

Chadd had just contributed to a magazine an article called "Zulu Interests and the New Makango Frontier', in which a precise scientific report of his study of the customs of the people of T'Chaka was reinforced by a severe protest against certain interferences with these customs both by the British and the Germans. He-was sitting with the magazine in front of him, the lamplight shining on his spectacles, a wrinkle in his forehead, not of anger, but of perplexity, as Basil Grant strode up and down the room, shaking it with his voice, with his high spirits and his heavy tread.

"It's not your opinions that I object to, my esteemed Chadd," he was saying, "it's you. You are quite right to champion the Zulus, but for all that you do not sympathize with them. No doubt you know the Zulu way of cooking tomatoes and the Zulu prayer before blowing one's nose; but for all that you don't understand them as well as I do, who don't know an assegai from an alligator. You are more learned, Chadd, but I am more Zulu. Why is it that the jolly old barbarians of this earth are always championed by people who are their antithesis? Why is it? You are sagacious, you are benevolent, you are well informed, but, Chadd, you are not savage. Live no longer under that rosy illusion. Look in the glass. Ask your sisters. Consult the librarian of the British Museum. Look at this umbrella." And he held up that sad but still respectable article. "Look at it. For ten mortal years to my certain knowledge you have carried that object under your arm, and I have no sort of doubt that you carried it at the age of eight months, and it never occurred to you to give one wild yell and hurl it like a javelin-- thus--"

And he sent the umbrella whizzing past the professor's bald head, so that it knocked over a pile of books with a crash and left a vase rocking.

Cheers!

WRT the above, to retain its preeminence, it seems Darwinism may have to adjust to the astonishing developments in physics and mathematics since its day in the sun of classical Newtonian physics. We'll have to wait and see what happens. Yockey's working on it.... :^)

Thanks for the note and thank you for thanking me, bb. Glad to poke my nose in, again, and to gain some of your wisdom.

As for Darwinism's ability to adjust, I don't think a philosophy does; it just stays where it is and people go on. And as for Darwinist Fundamentalists adjusting much, well, the impetus of their belief doesn't come from science, as we know, so why should science change them at the core?

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