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.

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

Questions are fine but declaring conclusions as unquestionable is not fine.

Creationism has nothing to teach us.

I think you are placing many, many different world-view philosophies under that rubric, and the word should be restricted to the belief that Genesis and the calculations based on Biblical genealogies should be unquestioned.

If you use the world broadly, however, as in "we are endowed by our Creator" creationism can teach us much.

You say you are an agnostic. What's more important to know -- the existence of God or the age of the Earth?

Questions are fine but declaring conclusions as unquestionable is not fine.

Science is a systematic investigation of nature. You aren't investigating if you refuse to realize when you're getting someplace.

You say you are an agnostic. What's more important to know -- the existence of God or the age of the Earth?

If you have evidence for the age of the Earth, you've been paying attention. If you have evidence for the existence of God, you're either nuts or up for a Nobel.

Science is a systematic investigation of nature.

Right. And, almost by definition, you will be unable to prove the source of that nature through nature -- I almost feel like invoking Godel here. Further, when investigating it is critical that one keeps in mind the difference between investigating and solving.

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

And you are looking for material evidence, which sort of makes my point. The true nature of the universe including the answer to the critical question as to what is our purpose may not be able to be revealed via material evidence. In fact, I think it is impossible for material investigation to address this.

And the existence of God must be addressed whether one has material evidence for it or not.

"Natural forces, such as corrosion, erosion, fire and explosions, do not create order, they destroy it.”

We observe many things happening on earth that result in a local lowering of entropy, many of these things are triggered by "natural forces" such as heat and light. When the foundation of a person's argument is the denial of these readily observable phenomenon, the rest of their argument fails, being built upon sand.

Science doesn't have the ultimate answers and maybe never will, but it converges upon an increasingly accurate description of nature. It has done so particularly rapidly over the last two centuries, the very period of progress Witch Doctor Luddites tend to reject as some kind of bizarre wrong turn.

And the existence of God must be addressed whether one has material evidence for it or not.

Not in science class.

Ah, yet another case of the shrinking angel phenomenon, an unexpected side effect of the "God of the Gaps" SOP. As we cram God into the gaps in order to prove he exists, God must grow smaller to fit the gaps as the gaps grow smaller, and the angels sadly shrink simultaneously. Perhaps the angels originally teased the atoms into place with incredibly fine angel hairs, but now it takes a minuaturized angel to do the same job.

perhaps you should read the rest of the quote from article which you quoted...

"...The second law is all about probability. The reason natural forces may turn a spaceship into a pile of rubble but not vice-versa is probability: of all the possible arrangements atoms could take, only a very small percentage could fly to the moon and back."

When you can spontaneously generate silicon chips from your pile of sand via chance and natural process "Natural forces, such as corrosion, erosion, fire and explosions" or heat and sunlight, you will certainly be rich.

While we observe process happening on earth that result in a local lowering of entropy, we never observe any of those process put things together in an orderly way as a result of random changes, whether they be the building blocks to life---amino acids do not combine in moving water to form proteins--- or metal parts do not combine in tornados to form bicycles.

from Tim M. Berra, "Evolution and the Myth of Creationism"

"For example, an unassembled bicycle that arrives at your house in a shipping carton is in a state of disorder. You supply the energy of your muscles (which you get from food that came ultimately from sunlight) to assemble the bike. You have got order from disorder by supplying energy. The Sun is the source of energy input to the earth's living systems and allows them to evolve."

This is funny in a couple of ways:

1) there is intelligence putting the bike together

2) It is so improbable that it is funny that someone could believe that sunlight+some ridiculous amount to time+chance and natural processes could arrive at life as we observe it today.

While it is true that the Sun's energy ultimately supplying the energy to put the bike together, it is ridiculous to say that the sun is supplying the intelligence to put the bike together, or that there was no intelligence involved. Maybe the evolutionist is a closet worshiper of the Sun. Or perhaps it is rational and probable that the world was intelligently designed by the Son.

The rest of the quote was irrelevant nonsense, as I've pointed out that the premise is wrong.

While we observe process happening on earth that result in a local lowering of entropy, we never observe any of those process put things together in an orderly way as a result of random changes, whether they be the building blocks to life---amino acids do not combine in moving water to form proteins--- or metal parts do not combine in tornados to form bicycles.

Yes we do observe such changes, ignoring the fallacious idea that the first proteins were made from amino acids combining all on their lonesome. I too used to think that entropy forbade processes leading to the origin of life, but I've come to realize that reality disagrees. In actuality in chemistry and biochemistry many organizing processes are entropy driven. These processes include some coupling reactions, cyclizations, and folding of macromolecules. And indeed they are the result of randomness. In a chemical reaction or conformational change the randomness comes from random molecular movement, from intramolecular changes by atoms turning, twisting, or stretching, or from intermolecular interactions from molecules bashing into each other as they move about randomly. These movements are often reversible--two molecules may collide and merge, spitting out a water molecule, and then a moment later be struck by another water molecule and split apart, with the water molecule merging with one of the resultant molecules. A peptide may sample multiple conformations before finding the lowest energy one, again driven by entropy as the folding excludes water molecules that raise local entropy. The result is a statistical sampling where a large percentage of the population is in a thermodynamic energy well, with the option of reversing if enough energy is attained and the right partners are present.

That's it. You have unlocked the secret to creating life from non-life. Claim your million dollar prize here:

http://www.us.net/life/index.htm

Evolutionists have a $1,000,000 reward for anyone who can explain spontaneous generation by chance and natural processes...The Orgin-of-Life prize.

One part that is particularly funny....

"Other than announcements in scientific journals, The Prize will not be publicly advertised in lay media. The Origin-of-Life Foundation, Inc. wishes to keep the project as quiet as possible within the scientific community. No media interviews will be granted until after the Prize is won."

One tiny little problem though.... it violates a scientific law--that of abiogenesis, but I'm sure that your vitamin pill is smart and clever (I dare not say intelligence here) enough to find a way around that.

"ignoring the fallacious idea that the first proteins were made from amino acids combining all on their lonesome."

Oh, so there had to have been something else present for life to form....good point....the genetic machinery that tells the cell how to produce protein...the DNA. The problem is that both both DNA and protein depend on each other for existence, and you are assuming that "The genetic machinery that tells the cell how to produce protein and the protein required to build that genetic machinery both originated gradually" So not only do proteins need to be generated by the clever and smart (don't say intelligence that is a bad word) chance machine, DNA needs to be generated at the same time by the same clever and smart chance machine at the same time.

Even if polypeptides had formed in the primordial soup, hydrolysis would have broken them up and destroyed most amino acids. Organic compounds such as amino acids, tend to break down when dissolved in water. The higher the temperature, the faster this breakdown occurs. …joining many amino acids together to form a protein with a useful biological activity is a much more difficult problem than forming amino acids in the first place. The major problem in hooking amino acids together is that, chemically, it involves the removal of a molecule of water for each amino acid joined to the growing protein chain. Conversely, the presence of water strongly inhibits amino acids from forming proteins…..

This and other problems w/ spontaneous generation posted here:

http://www.freerepublic.com/focus/f-news/1689062/posts?page=185#185

There could be a interesting section or two added on the probability of designed enzymes as part of a discussion of some of the types of reactions you mentioned (enzymes are often required).... typical bacterium, which is the simplest of cells, is made up of 2000 enzymes...And of course, the formation of enzymes is but one improbable step in the formation of life....I will try to add that if I can find time.....

Thanks for the ping. I appreciate your effort to add material to the discussion. I wish I had a copy. While it is tempting to remark on improbability of randomly appearing RNA, it would be arrogant and against my principles to comment on something I haven't read at least excerpts of...

...you never know the alter ego of FreedomProtector may not be a science laymen....who is that masked man?

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