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.

I know because I've had to relearn some theories since I taught this class 25 years ago, but the facts are the same. For example, the universe has doubled in age since I was a boy,which gives you an idea of just how old I am.

That's a really strange quote, and a fairly worthless one. I wouldn't repeat it. It starts off OK, but then when the author goes to give an example of a theory that has changed, he says, "the age of the universe has doubled".

"The age of the universe" is not a theory. It is a fact: it is a physical property of the universe that we measure. It may be possible to derive a prediction of the age of the universe from a theory, but that's not what is done: we calculate it from a series of physical measurements.

"But in order to calculate, you need a theory!" you say. Perhaps, but those aspects of the theory (e.g. how light propagates through the universe, and how stars and supernovae work) haven't changed very much, while the measurements and measurement techniques have. The age of the universe is no more a theory than the length of your foot is a theory.

If anything, his example stands as a counterexample of his assertion that facts remain the same.

Now, you may argue that the "fact" is the true age of the universe, and that that hasn't changed (much), even if our measurement has changed. But when it comes to physical properties, measurements are all science ever has to work with. And yes, they change.

And PE would be the same as phyletic gradualism, except that evolution does not occur at a constant rate. As Gould explains it:

Faced with these facts of evolution and the philosophical bankruptcy of their own position, creationists rely upon distortion and innuendo to buttress their rhetorical claim. If I sound sharp or bitter, indeed I am—for I have become a major target of these practices.
I count myself among the evolutionists who argue for a jerky, or episodic, rather than a smoothly gradual, pace of change. In 1972 my colleague Niles Eldredge and I developed the theory of punctuated equilibrium. We argued that two outstanding facts of the fossil record—geologically "sudden" origin of new species and failure to change thereafter (stasis)—reflect the predictions of evolutionary theory, not the imperfections of the fossil record. In most theories, small isolated populations are the source of new species, and the process of speciation takes thousands or tens of thousands of years. This amount of time, so long when measured against our lives, is a geological microsecond. It represents much less than 1 per cent of the average life-span for a fossil invertebrate species—more than ten million years. Large, widespread, and well established species, on the other hand, are not expected to change very much. We believe that the inertia of large populations explains the stasis of most fossil species over millions of years.
We proposed the theory of punctuated equilibrium largely to provide a different explanation for pervasive trends in the fossil record. Trends, we argued, cannot be attributed to gradual transformation within lineages, but must arise from the different success of certain kinds of species. A trend, we argued, is more like climbing a flight of stairs (punctuated and stasis) than rolling up an inclined plane.
Since we proposed punctuated equilibria to explain trends, it is infuriating to be quoted again and again by creationists—whether through design or stupidity, I do not know—as admitting that the fossil record includes no transitional forms. Transitional forms are generally lacking at the species level, but they are abundant between larger groups.

Of course, Darwin had actually beat Gould and Eldredge to a lot of that, including being dishonestly quote-mined to death.

All you need to know about Punctuated Equilibrium (almost)

There are two common uses of "gradualism," one of which is more traditional and correct, the other of which is equivalent to Eldredge and Gould's "phyletic gradualism."
Darwin was not a "phyletic gradualist," contrary to the claims of Eldredge and Gould.
PE is not anti-Darwinian; in fact, the scientific basis and conclusions of PE originated with Charles Darwin.
PE does not require any unique explanatory mechanism (e.g. macromutation or saltation).
Eldredge and Gould's PE is founded on positive evidence, and does not "explain away" negative evidence (e.g. a purported lack of transitional fossils).

Each item above is expanded and factually supported in detail on the web page.

Not that this will stop you from LOLing back next time with the same pig-ignorant unfactual talking points you're clinging to against all evidence here.

IOW, the fossil record does not support Darwn's gradualism as Miss Coulter has been saying.

Absolutely false and already refuted by the post to which you purportedly reply here. You ignore what Darwin said, what PE is, and what the fossil record is, all of which has been presented to you. Read the materials before "rebutting," please.

What Coulter has been saying is full of untruths and fallacies, as richly documented. So are your own statements.

So here you are in LOLing repetition, refuted but still playing the broken record. Not much more to be said. Your brain on creationism--grownups misbehaving in public. You're one of the poster boys (but so are all the rest of you) for why I don't want to "teach the controversy." "The controversy" exists outside of science and was invented by ineducable LOLing snotheads.

"The age of the universe is no more a theory than the length of your foot is a theory."

When you observe a car driving down the road at speed of 30 mph for and 1/8 of a mile, of coarse you know exactly how long the car has been driving for because:

You can know for sure exactly where that car started. It surely started in a town 30 miles away. That is of coarse not an assumption.

You certainly know for sure that the car has been traveling a constant speed for its entire life, nothing could change that. (and absolutely sure constant for 4 billion years)

So you know for sure that that the car trip, after observing the car for 1/8 of a mile has, has been traveling exactly 1 hour to 5 significant digits. Of coarse there are no assumptions in this. This is a measurement and "this is no more a theory than the length of your foot is a theory".

Of coarse you know with absolute certainty how much radioactive or daughter substance was present at the start, or where x started. Your invention of the very first time machine for going backwards in time to observe x is quite remarkable, the first of its kind, you should patent it.

Of coarse you know that the rate of decomposition, or the speed x, the always remained constant, and has certainly remained absolutely constant to 5 significant digits for exactly 4 billion years to 10 significant digits, this is
"this is no more a theory than the length of your foot is a theory".

Pardon the sarcasm, but you are making assumptions and calling it "no more a theory than the length of your foot is a theory".

Time is the escape hatch of your chance + enough time worldview, and given enough you time you believe that the absurdly improbable can certainly happen....just give it enough time. Be careful that you don't drown in your all- knowing assumptions, as your escape hatch may not be as open as you believe.

I can't argue astronomy. I'm not an astronomer. But I do know words and words mean things. This college professor, who has been teaching for a number of years, quote about theories is accurate. Theories can, and do, change. However, there are many scientists today who would like you to believe that theories are laws. They are not.

I take it you are not an astronomer yourself so your astronomical opinions are about like mine-next to meaningless. (Since you've labeled yourself "Physicist" you actually may have more knowledge about astronomy than my two semesters in it. But I digress.) I would suggest what you find wrong with this author is his statement that theories can change-not his views on astronomy. Astronomers better than anyone knows how frequently theories changes and, at least, are up front about that.

When did I claim that the theory of evolution is "established fact"?

Thus far, however, there exists absolutely no reason to believe that "intelligent design" is a credible explanation.

I wouldn't dismiss things that have no credible explanation. That is often the way science advances.

I did not state that science does not attempt to define "life". I stated that science does not define whether a collection of living cells is "a human being" or "a collection of living cells". You are attempting to exchange definitions of a term. That is a logical fallacy.

Before you can move to a "human being" you have to know what is life? If you have a definition what is it? Don't you think it would be good to know if pulling a fetus out of the womb and crushing it's scull constitute life?

This is a conservative website. Atheist or agnostic or other liberal dimwits who believe that they are beasts are not going to own the podium on a conservative website. They are gorilla noises braying in the wilderness and nothing more. Some have even resorted to fedcourt decisions to "prove" that they are trousered apes. That suggests that when our lawless and Lawless SCOTUS decided Roe vs. Wade that it must have been truth as well as homicidal idiocy crammed down our throats as "constitutional law." Ditto lavender "rights." Coming to courts near others: Faggot "marriage." Only a matter of time before the rights of consenting "beasts" of all sorts are recognized by SCOTUS so long as we are one judge short as we are.

The leftist smears on behalf of the argument that there are no people only trousered apes has no effect if you recognize the source and ignore such "arguments" accordingly.

I'm Catholic but I can certainly see the Biblical wisdom in: "God said it. I believe it. That settles it."

One final time. God said it. I believe it. That settles it.

Any "science" that claims that men are trousered apes is BS and no more worthy of considered response than is the notion that the moon is made of green cheese. By definition, God CANNOT be wrong. The same cannot be said of "science."

If simple faith is unsatisfying to you, ask me if I care.

Conservative websites should serve to unite conserevatives in matters political for action to translate ideals into reality and not as advertising forums for the propagation of ridiculous nonsense like evolution.

Since you want to do question and answer: Just what are YOUR personal credentials as a conservative activist since you plainly propagandize for the secular humanist enemies of conservatism when you claim that men are apes or descended from apes or whatever the Darwinian falsehood du jour may be?

How is that Free Republic poll on teaching creationism and intelligent design coming????

Marx's book of his observations north and south is/was (in bad condition as early as 1968) in the reserve stacks of the New Haven Public Library. AND, of course, you are still wrong as to Lincoln and virtually all things relating to the Second War for Independence.

If I were going to invent on this subject, on a conservative website, it would have made more sense to suggest that Lincoln was the apple of Marx's eye. The actual fact was that even Marx had no use for Lincoln.

Revise your sentence to insert "a London Times correspondent" for "the London Times correspondent."

If the correspondent to whom you refer was surnamed Russell, he was probably the son of Lord Russell and therefore an unlikely press agent for Lincoln as well. Either Lord Russell or, more likely, Lord Palmerston then owned the London Times. Neither Lord Russell nor Lord Palmerston (Tory MPs who took turns as PM and Foreign Secretary during the Second War for Independence) were particular fans of Abraham Lincoln. It took Prince Albert of Coburg, Victoria's hubby, on his death bed to dissuade Palmerston and Russell of recognizing the Confederacy solely on the question of slavery, but not before the British laird Shipyards built and launched the magnificent Confederate rams Alabama and Tennessee.

What were your credentials as a conservative, if any??????

So now your saying Darwin was a gradualist?

I've told you what I'm telling you. I've given you detailed supporting materials for what I'm telling you. The best you can do is feign confusion (as quoted above) and then proceed as quoted below.

I do read your materials, generally. They don't rebut anything. Your post don't rebut anything. You are putting your fingers in your ear, closing your eyes and shouting "Lalalalalala, I can't hear you. Everything was an accident."

Not good. Not good at all. The worst part is that you are doing creation/ID that much worse than most of its proponents, including its leading lights Sarfati, Gish, Dembski, and now Coulter, etc.

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