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.

If you have evidence for the existence of God, you're either nuts or up for a Nobel.

If you have evidence of the type which will be accepted in a scientific forum...you're up for a Nobel.

If one doesn't know the difference between the types of evidence, they haven't been paying attention.

If one confuses the types of evidence, one might be nuts--or one might feel the issue to be resolved is *SO* important that a relaxation of the rules of evidence, in order to get more information on the subject, might be warranted.

And that point is usually where the flamewars and fireworks begin--argument from authority is not *logically* valid; but saying that does not mean it MUST be untrustworthy or MUST be false.

There are degrees of certainty; some warranted and some not.

Cheers!

Interesting in this regard is the following quote from Molecular Biology of the Cell, 2nd ed. (Bruce Alberts, Denis Bray, Julian Lewis, Martin Raff, Keith Roberts, and James D. Watson -- yes, *that* Watson). Chapter 1, Page 8:

"It seems likely, then, that RNA guided the primordial synthesis of proteins, perhaps in a clumsy and primitive fashion. In this way, RNA was able to create tools-in the form of proteins-for more efficient biosynthesis, and some of these could have been put to use in the replicaiton of RNA and in the process of tool production itself."

Obligatory flame bait for both sides:

From what I have read of the book so far, that remark seems awfully vague and hand-waving-ish. What is the proposed rate constant for the formation of a typical strand of RNA (suitable for doing a primitive version of amino-acid-encoding) at 25 C^o? Is stereoselection necessary at this point? *If* the RNA makes "a protein", what keeps that protein molecule around? What determines that the protein is "useful enough" to be immediately of benefit to the nascent "proto-cell" ?? And if it is not "useful enough", what is the feedback loop to change the RNA so it produces a useful protein...? (I.e. making useless protein not only wastes time and annoys the pig, as the saying goes, it also uses up the presumably limited supply of amino acids in the immediate vicinity.)

I suspect the *stock answer* would be--"but g_w, you don't understand. There isn't just *one* protocell--there are many millions, due to their small size and the available conditions in so many [tidal pools, clay substrates, whatever the current thinking is]. And by a wonderful, elegant, and convenient analogy to larger evolutionary model, by random chance all of the protocells that *did* waste their time in such a fashion just didn't survive; we happen to be the descendants of those that *did*^TM yada yada."

Point taken--except that the above merely shows a (in one sense) "plausible mechanism", which might end up being "improbable" (when you consider the *actual odds* (whatever THAT means) of generating successful, 'eating', 'self-replicating' systems from scratch.

Can you flesh out actual rates, rate constants, concentrations of likely reactants? If not, please have the grace to admit that it is not "hard science" based on experiment, empirical results, or what not; but something a couple of steps above science fiction. A hazy model, a hypothesis, a proposed mechanism -- but not yet nailed down.

Obligatory OTHER flame-bait--I'm surprised nobody has yet issued the stern chestnut that "Evolution is NOT concerned with abiogenesis, so kindly STFU." ;-)

Cheers!

The RNA world is not yet confirmed but a lot of progress has been made in the past 17 years (urg, can't believe you're referencing something that old). I've got a review article from a few months ago on the topic that I'm about halfway through.

If not, please have the grace to admit that it is not "hard science" based on experiment, empirical results, or what not

Please, why the implied slur? I never said that we know down the last detail how things occurred, I said that current thought is that the first self-replicating molecule was RNA. I would strongly encourage all creationists not to become too invested in the absolute statement "It couldn't happen, therefore God did it by miraculous intervention!" If we make progress in the next ten years that shows the RNA world is not only plausible, but likely, the creationists who've jammed God into this gap may have some difficulties with their faith. When I believed in God I had to fight this God of the gaps tendency myself. God doesn't belong in the gaps, but should be an engineer of the processes that we may eventually discover in those gaps.

And abiogenesis doesn't really have too much to do with evolution, but it's an interesting topic. :-D The theory of evolution doesn't require abiogenesis to occur on earth, it just requires an imperfectly duplicating, self-propagating organism (from abiogenesis, extraterrestrial seeding, divine intervention, etc.)

The RNA world is not yet confirmed but a lot of progress has been made in the past 17 years (urg, can't believe you're referencing something that old).

That was my point--I was attempting to *bolster* your point about current thinking. If the RNA encoding was in a book from 17 years ago, that means it isn't even "latest & greatest " anymore. :-)

Please, why the implied slur? I never said that we know down the last detail how things occurred, I said that current thought is that the first self-replicating molecule was RNA.

Not meant as a slur, implied or otherwise. Sorry to have given that impression. The gist of my point is that to hear some of the more fervent pro-evo's on this thread talk, evolution is as firmly nailed down as (say) the r² dependence of gravitational attraction, to umpteen decimal points. And virtually anyone who dares to point out possible contradictions in the mechanisms proposed (even ones put out merely carelessly as examples on this thread) is immediately lambasted as an ignorant savage. In most other fields of science I have seen, the scientists *welcome* questions, because it either gives them a chance to sharpen their intellectual claws, or because (as both Feynman *and* C.S. Lewis pointed out), if you cannot explain your subject to a layperson using mostly words of one syllable, you don't really *understand* it yourself, all the way down.

BTW, the impatience with any questions about evo on this thread might just be due to the sheer volume of trolls and people who think that Duane Gish = Stephen Jay Gould as a resource ;-0

When I believed in God I had to fight this God of the gaps tendency myself. God doesn't belong in the gaps, but should be an engineer of the processes that we may eventually discover in those gaps.

I'm not *playing* God of the gaps. I'm playing *prick the balloon* of inflated claims by people who are doing one of two things:

1) Confusing a purported mechanism, or "latest thinking" with "absolute truth"
2) Trying to point out (again, and Again, and AGAIN) that many of the cre-trolls have (at best) very little formal science training and simply DON'T KNOW THE DIFFERENCE. And so instead of flaming them, a better approach is to try to educate them.

The banned RightWingProfessor tried, but was often too irascible: and went over their heads.

Ichneumon (haven't heard from him lately) wrote elegant encyclopedias, but they took too long for a casual reader to go through.

The dictionary of scientific / philosophical terms by (I think) Coyoteman and/or CarolinaGuitarman and/or Dimensio and/or Patrick Henry is a great start.

We need more of that kind of thing on these threads.

One of the other posters suggested I start on it. It's on my to-do list and I'm seriously considering a series of bite-size threads on various beginning points.

Full Disclosure: Ironic comment only. It is odd that despite the claims that evolution isn't about disproving God, many (not all) of the most ardent evo's are at best agnostic, at worst militant atheists. As you said, "*when* you believed in God etc. etc." ;-) Cheers!

That was my point--I was attempting to *bolster* your point about current thinking. If the RNA encoding was in a book from 17 years ago, that means it isn't even "latest & greatest " anymore. :-)

It's still the best theory going, and given the amount of evidence that RNA is foundational, it's probably going to remain the forerunner. It is possible though that nucleic acids with different sugars came before RNA and then when RNA was made it took over from them and went on to catalyze the appearance of more complicated systems including DNA and protein. It will be interesting to see what comes of this research.

Duane Gish = Stephen Jay Gould

He doesn't?! ;-)

I'm not *playing* God of the gaps.

I misunderstood your post. There are a lot of posters here who seem to want to insert miraculous intervention whenever we have some uncertainty or ignorance about a process. I used to be YE creationist myself. I found to my great discouragement in (Christian, officially YEC) college that many arguments were not arguments for a young earth, but arguments against evolution based upon criticisms of dating methods, stratigraphy, phylogenetics, etc. A lot of them take the form, "Evolutionists do not understand this completely, therefore God did it." Over time I realized that many of those criticisms were invalid and things weren't as murky as others portrayed. I reached the point where I either had to acknowledge that the gaps were getting so small that God was being reduced in significance and might eventually disappear or I had to remove God from the gaps and allow the gaps to be just what they are, gaps which may eventually be filled either with natural mechanisms or supernatural, but either way should be ok with me.

At that point I had already left YEC and the removal of God from these gaps caused me to leave ID. Then I was a theistic evolutionist--God created the universe through natural means but is sovereign over it, not in the sense that he miraculously kicks it along all the time, but in the sense that he has ordained its path. I probably would have remained so indefinitely if my research into Islam had not prompted me to go back and come up with a fully integrated reason why atrocities in the OT were all right (and even laudable) but those committed by Mohommed were evil. Over a year or so I hammered away at this until I came to the conclusion that I would never resolve that without embracing an idea of God that was radically different from the one I had grown up with. I found that untenable, so right now I'm agnostic. You can read about this a bit in the post at the end of my profile. Some people use this as a gotcha--"Ah-hah! You are godless because you are evolutionist!" The reality is that acknowledging evolution occurs preceded my determination that God as I knew him does not exist, and that was based upon my analysis of morality as depicted in the Bible.

You would seem to be confused between the hawk's behavior exhibiting a pattern and the hawk knowing something about natural selection. The hawk can preferentially kill animals which are the most easy to detect without knowing or caring that his behavior matches part of a certain scientific theory widely discussed among humans.

Exactly - no pattern - just random. Natural Selection is not driving the hawk therefore Natural Selection is an observation of many points of data, not a force or structure. Natural Selection only exists in our minds.

This is the core philosophy of Evolution - the something from nothing model - a philosophy that believes extreme complexity, pattern, and design can spring forth from the complete absense of complexity, pattern, or design.

IF you think Natural Selection follows a pattern - state the pattern - although I am not too optimistic you will actually try.

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