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 author of this piece is an idiot, with a diploma from a degree mill, who is such a fool, he probably couldn't even get a job teaching at Bob Jones."

Let's cut that avenue of the critics' attack early:

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.

Okay, then why did humans continue to evolve if there was no impetus to do so?.......

Humans continue to evolve and cockroaches continue to evolve. As long as allele frequencies change, evolution is taking place. There are a number of factors currently driving evolution in both humans and cockroaches: DNA mutation, the fact that not all individuals reproduce succesfully (aka natural selection), gene flow, and genetic drift.

But it's only teleological in the Pee-wee Herman sense: "I meant to do that!"

Dembski is definitely the Pee-Wee Herman of mathematics. It's fun to watch his web site, wondering what Nigerian email scam he'll fall for next.

Man cannot outrun a wolf, but used his brain to devise methods to counteract the danger of the wolf or other creatures. A deer of comparable mental ability could do so as well. As little as 50k years ago, a mere eyeblink of geologic time, there were giant deer, sloths, sabertoothed this and that, even sabertoothed kangaroos, but they are all gone. Did their niches change? Or did man upset the evolutionary processes by his mere existence?..............

And if early humans evolved from apes, why are there still apes?

If the United States is descended from England (via the colonies) then why does England still exist?

Why did they not evolve even slightly over the millions of years it supposedly took humans to evolve?

Not only have apes evolved, they have evolved at least as much as humans have evolved.

The mathematical improbability of arriving at life (and a world so perfectly suited for life) as we observe it today solely by chance and natural processes even given any ridiculous amount of time suggested so far is incredibly very low--essentially null.

....a central point in the creation/design vs. world arriving by chance debate/discussion

article/thread well suited for mass ping :)

Okay, then why did humans continue to evolve if there was no impetus to do so?.......

Evolutionists would say that there WAS one or more (changing weather, changing food sources, new predators to outflank, etc.) For the record, I am on your side, I believe Darwinian macro-evolution to be ridiculous. I was just pointing out that this particular argument is easily dealt with by them.

It's easy to postulate things happening in prehistoric times, because, as Chesterton points out, it's prehistoric. We really don't know what happened. The scientifically honest approach would be to say that we DON'T know where everything came from (from a scientific point of view) and leave it at that. The whole question does not lend itself to study by the scientific method. There are limitations to what scientific method can reveal or prove.

Is this supposed to surprise creos? No, but I bet the evos go into attack mode.

Don't really have a dog in this fight but one thing that bothers me about evolution - evolution operates on years to million years time frames but survival is a second by second proposition. I can't quite reconcile the different time scales.

"And if early humans evolved from apes, why are there still apes? Why did they not evolve even slightly over the millions of years it supposedly took humans to evolve? "

A news species that evolves does not mean that other species cease to exist. It is not a zero-sum game. In reality, today's apes and humans have evolved to the state they are in from a common ancestor species.

The apes evolved in one direction, and humans evolved in another. We did not evolve from any existing ape species. We are on separate evolutionary tracks, although we come from a common prior species.

By many definitions, human beings are just another ape, anyhow. Chimps, Gorillas, Humans, Orangutans...we're all in the same family. We do different things, and are adapted for a different environment. Otherwise, we're all pretty darned similar, as a trip to any primate house in any zoo will demonstrate rather quickly.

We're not better than the other apes...just different.

Humans continue to evolve and cockroaches continue to evolve.

Says who? The Darwinian approach does not require further evolution. How do you define evolution? Are you saying that a revived 50,000 year old cockroach would not be able to mate and produce fertile offspring with present day cockroach? Do you consider minor variations within a species evolution?

"evolution operates on years to million years time frames but survival is a second by second proposition. I can't quite reconcile the different time scales.
"

Evolution is not a matter of individual animals, but species. If one monkey dies, it does not affect evolution. The species continues and reproduces.

Evolution does not address the survival of individual critters, just species.

"If evolution is an ongoing process, and all living things start at the same point, then by now there should be not only sentient humans, but fish, birds and reptiles, etc. Why would just one of the myriad species evolve to a superior position, and not the others......"

I will try to explain the conventional knowlege through a hypothetical.

If you take 1 species (Population A) and put half of that species in a different environment (with a lot of time) the population in a new environment (population B) will either die out or change. If this change is to such a degree that population A can not make viable offspring with population B, you now have two different species.

The two primary conditions are isolation between the populations, and a different environment for each population. Both of which occur on earth.

Man cannot outrun a wolf, but used his brain to devise methods to counteract the danger of the wolf or other creatures.

Intelligence works in some places, speed works in others, and strength in yet others. Species have evolved to find a happy medium between the three that yields optimum survival for them.

Did their niches change? Or did man upset the evolutionary processes by his mere existence?..............

Yes to both. Hunman evolution has upset many niches, although the same is true for the evolution of other predators. Species either evolve to find new niches or they go extinct. I think humans are somewhat unusual because they have had unique evolutionary pressures over the last few hundred thousand years pushing ever-greater intelligence. But there are costs and limites to increased human intelligence as well -- brain size is limited by the width of the female pelvis. If the brain is too large, humans can't be born vaginally. If female pelvises were wider, women wouldn't be able to walk bipedally.

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