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 suppose if repeating arguments I've already conceded or excluded could be called pedantry

You need to read a little closer - I was addressing the argument you conceded.

No would you like to consider the situation where the human is chasing the prey, and the prey is not a carnivore, or not chasing the human?

what kind of non-carnivore are you talking about - an Impala? a Gazelle? a rat?

None of us know all of the creatures that were around three or four or thirty thousand years ago. We certainly don't know what similar looking specimens could mate with others and produce fertile offspring. (If an archeologist in the year 20000 AD came upon a poodle and rottweiler skeleton, not knowing of the existence of either because they died out, he would likely conclude they were different species) Heck, we STILL don't know all the species that are in the world right now. A good scientist doesn't just throw out raw assertions as facts. There is so much we don't know, and a large number of things we THOUGHT we know that have since been disproven or brought into question. ---- No it isn't. My point is that nutritional content, cooking properties and everything else you bring in is irrelevent to this discussion.

It is absolutely relevant. Peanuts are different from legumes in all sorts of ways. Just because a botanist happens to classify them based on how they grow does not mean that peanuts come from some other legume. It is just a handy way to categorize, nothing more. I am glad to see that you no longer pretend that the grocer is "wrong" to put the peanuts in with the other nuts in the supermarket.

Hares with lighter fur are less likely to be seen by hawks on a snowpack.

So are you claiming something made this happen (design)?

You are reviewing historic data and applying a rule to it - nothing selected these animals - it just happened. Natural Selection is random because Natural Selection is an observation - not a force or power that can do anything. While black rabbits on the snow would not have a chance - still nothing is doing the selecting - it is random mutation with random success. In the past tense we can apply structures but nothing selected the rabbits.

Read Darwin - if it is not random, it is not evolution.

The selection isn't random -- there's a very good reason why rabbits with lighter fur survive -- but neither is it designed.

Answer the question please - if Natural Selection is not random - what force/god/designer is doing the selecting? What makes the selection?

Nothing designates a creatures ability to survive - it happens randomly.

None of us know all of the creatures that were around three or four or thirty thousand years ago.

Of course we do. We have intact humans from longer ago than that. 3000 years ago was well within the realm of recorded history, in many places.

We certainly don't know what similar looking specimens could mate with others and produce fertile offspring.

No, and without DNA from early Equines, we will likely never know. But we can make a very educated guess, judging from the fact that extant equines (like horses, zebras and asses) cannot normally produce fertile offspring.

Peanuts are different from legumes in all sorts of ways.

Name one.

I am glad to see that you no longer pretend that the grocer is "wrong" to put the peanuts in with the other nuts in the supermarket.

Should grocers pack Swedish Fish in the seafood section too?

Actually, there is a considerable analogy here.

An analogy is not a relationship

At some point, they grow so far apart that they cannot reproduce easily

The country cannot reproduce easily? How does a country reproduce?

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

That does not even address your statement "Not only have apes evolved, they have evolved at least as much as humans have evolved."

Can you show that other apes evolved at least as much as humans have evolved? What do you use to measure evolution?

You are reviewing historic data and applying a rule to it - nothing selected these animals - it just happened.

No, in this isntance, the hawks are doing the selecting. Some hares will have alleles leaving them darker, others will have alleles leaving them lighter, and that distribution will be somewhat random. But the fact that the hawks will eat more of the dark ones is anything but random, and it's the hawks that lead to a gradual shift in allele frequencies (aka evolution). Dark hares would have a chance and white hares wouldn't be invulnerable, but over time, lighter hares will clearly be more reproductively succesful than darker hares.

Answer the question please - if Natural Selection is not random - what force/god/designer is doing the selecting?

You're still not getting it. Here, the environment is doing the selecting. In this case, the active selector are the hawks. You either survive to pass on your genes or you don't, and if you don't, you're selected out of the game.

Nothing designates a creatures ability to survive - it happens randomly.

If that were the case, then it wouldn't matter what pigment a hare's fur is -- surival rates would be roughly the same for all populations. Faster rabbits would have no edge over slower rabbits. Smarter rabbits wouldn't be better at foraging for food than dumber rabbits.

Can you show that other apes evolved at least as much as humans have evolved? What do you use to measure evolution?

Yes you can. You compare DNA. Humand DNA and Chimpanzee DNA share more in common than Chimp and Gorilla DNA. That says something abot how much other apes have evolved relative to one another.

Excellent post. Thank you. Two things I am quite certain of: 1) materialism is false (ie, it doesn't tell the whole story), 2) the presuppositions of evolutionary scientists color everything they do, and many / most are incapable of even acknowledging that they have presuppositions, let alone are they able to rationally discuss them, and this is a problem.

ps - I stole my very truncated version of that point about naturalism being self-defeating from Alvin Plantinga (you probably know that, already though).

Actually, Conservative Dude, this is THE problem (i.e., the lack of acknowledgement of presuppositions, and so the inability to rationally discuss them).

I'm not familiar with Alvin Plantinga, but would like to be. Please may I have the source for his point about naturalism being self-defeating? I so agree with that assessment!

Thanks so much for your kind words!

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

If the brain has been programmed only by chance, by random nature, why trust it?

Materialist reduction of ones consciousness to purely a host of biochemical reactions is an problem the evolutionist struggles with....

there are examples of this in evolutionary articles....hold on...providing evidence via quoting what evolutionists write....is defined as quote-mining by definition

Two things I am quite certain of: 1) materialism is false (ie, it doesn't tell the whole story), 2) the presuppositions of evolutionary scientists color everything they do, and many / most are incapable of even acknowledging that they have presuppositions, let alone are they able to rationally discuss them, and this is a problem.

perhaps worth adding to that....

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.

5) We must lovingly and with true tears help to remove the shelter/roof and allow the truth of the created world to beat upon the materialist. Removing the irrational and improbable walls of protection is an important first step in communicating with people brainwashed by the materialism of the twentieth century.

materialism is false (ie, it doesn't tell the whole story)

You have no evidence that this is true, which makes sense as such evidence is outside the realm of the observable.

the presuppositions of evolutionary scientists color everything they do

Everyone's presuppositions color everything they do, as your post illustrates. The important thing is to be able to identify and evaluate one's presuppositions.

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.

Once again, no evidence of this, it's outside the realm of the observable. You assume something does exist "out there," and you're taking it on faith that it is God as you think of him and not something or someone else.

Yet you call other people "brainwashed."

AK:

Insulto, ergo sum.

Actually, how does one go about insulting someone who sincerely believe that he/she is descended from apes?

If I were to articulate my position, it would be a very long post. Out of consideration, I referenced the the best conservative book of the year which also demolishes the Darwinian fantasy and pretenses quite effectively but has an economy of prose which I find hard to match. Not only that but Ann is quite obviously not related to apes in any way and, besides, I knew her elder brother John about 35 years ago. He's no ape either. Nor am I but I will certainly let you speak for yourself on your own ancestry.

Of course, I never attended a gummint skewel until I attended law school and so I was brought up Catholic and not brought up to believe that I was a trousered ape. I also missed the Marxism, the eugenics, the birth controlism, the abortionism, the environmental whackoism, and other gummint skewel heresies.

Finally, those who argue for the fantasy of a godless universe, with life being strictly temporal and ending in oblivion at death regardless of moral or immoral behavior in life may well not see "pragmatism" (Lenin: You have to break eggs to make omelettes) as amoral or immoral but merely the greatest good for the greatest number and devil take the hindmost in the name of "progress." You have a right to be wrong but you do not have a right to be taken seriously.

"Yes you can. You compare DNA. Humand DNA and Chimpanzee DNA share more in common than Chimp and Gorilla DNA. That says something abot how much other apes have evolved relative to one another."

That will not demonstrate what you claim unless you also have the DNA from chimps millions of years ago. Similar DNA is merely an observation that in and of itself proves nothing - chimps being different than Gorillas is irrelevant. To claim this proves chimps evolved as much as humans is merely an assumption.

No, in this isntance, the hawks are doing the selecting.

Somewhat. Hawks eat what they can - they are not selecting. The end of the process is called natural selection. The animals eat what they can but it is still random - based on random mutation some animals don't get eaten - no matter how you slice it. it is still random and no "force" is controlling it.

You're still not getting it.

I say the same thing to you. You are not getting it. Nothing is directing the selection. Random mutations mean randomly things will survive or not survive. The changes start with a random mutation and the environmental response to this mutation is random (not directed)

Here, the environment is doing the selecting.

Yes but it is still random (not directed)

Let's review:

Random - proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of numbers.

If you are claiming Natural Selection is is not random than it most has an aim, reason, or pattern - it does not.

If that were the case, then it wouldn't matter what pigment a hare's fur is -- surival rates would be roughly the same for all populations.

I think you are confused as to the meaning of the word "random"

OK, lets sum this up into one question

You claim Natural Selection is not random

This is the definition of random:

Random - proceeding, made, or occurring without definite aim, reason, or pattern: the random selection of numbers.

So if Natural Selection is not random, as you claim, what is the aim, reason, or pattern of Natural Selection?

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