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.

Assumption: We go swoop! from here to there without going through the middle. Not true, small changes and selection for beneficial ones allows us to get very far relatively rapidly.

The researchers set up an experiment to document how one particularly complex operation evolved. The operation, known as equals, consists of comparing pairs of binary numbers, bit by bit, and recording whether each pair of digits is the same. It's a standard operation found in software, but it's not a simple one. The shortest equals program Ofria could write is 19 lines long. The chances that random mutations alone could produce it are about one in a thousand trillion trillion.
To test Darwin's idea that complex systems evolve from simpler precursors, the Avida team set up rewards for simpler operations and bigger rewards for more complex ones. The researchers set up an experiment in which organisms replicate for 16,000generations. They then repeated the experiment 50 times.
Avida beat the odds. In 23 of the 50 trials, evolution produced organisms that could carry out the equals operation. And when the researchers took away rewards for simpler operations, the organisms never evolved an equals program. “When we looked at the 23 tests, they were all done in completely different ways,” adds Ofria. He was reminded of how Darwin pointed out that many evolutionary paths can produce the same complex organ. A fly and an octopus can both produce an image with their eyes, but their eyes are dramatically different from ours. “Darwin was right on that-there are many different ways of evolving the same function,” says Ofria.

Check out the story of Avida artificial life here.

Artificial evolution is actually a happening area in programming and circuit design because it can sample many variations very rapidly and end up constructing a system that looks really weird to us, but often works better than what we can manage through "intelligent design."

Evolution is neither random nor designed. You're presenting a false dichotomy. Natural selection is exactly what it sounds like: natural (as in natural, not designed) and selection (as in non-random).

So what is this "third way" you are implying. If something in not designed and not random - what is this third way you are talking about. If selection is not random than who or what is doing the selection? Your statement really makes no sense - are you claiming nature evolved the ability to select? How does nature perform the selection?

Like I said - if it is not random - than who or what does the selecting (please don't say nature)

Natural Selection is an observed process (in the past tense), not a force of power.

Does God exist?

Is there an afterlife?

In that afterlife, is there reward and punishment for what sort of life one has led prior to arriving in that afterlife?

Is there a set of objective and binding guidelines for one's behavior in life that determines one's eternal destiny?

If the answers to these four questions are an emphatic yes, as most Americans believe whether in response to divine revelation or to common sense observations, our society must be ordered accordingly with personal altruism being a virtue as most of us believe and not a crime as Ayn Rand and Margaret Sanger believed, a society in which there is recognition of an obligation to enforce objective right and wrong (as even our pagan Greek and Roman forebears agreed), a society structured on principle and reason and not a moral anarchy in which each individual defines morality for himself or herself and devil (dissenters should pardon the expression) take the hindmost, also a society which recognizes that neither government of whatever sort nor the unrestrained individual is or ever can be our highest authority.

Ann Coulter's latest book Goddess, whoops (I must read the title and not just look at the cover picture), that is, GODLESS has a lot of worthwhile fun to poke at those with imagination so limited as to accept Darwin.

Her analysis is far better than my usual one whereby I am willing to concede that Darwinists are descended from apes or whatever so long as they are willing to concede that the rest of us are descended from Adam and Eve via the wonders of God.

The environment selects.

How does the environment do ANYTHING - it has no means for selecting or doing anything since there is no thing that is the environment. If there is no intellegent means - its random - how can there be a third way - semi-designed semi-random - it is not possible.

The environment does nothing - it is a label for all things.

There is no selection process - it just happens - random

No force is selecting anything. Selection requires the ability to process data or impose laws to make a selection - this is something the environment can not do.

Natural Select just happens - nothing is driving it.

Natural Select is like God - it just is - you can not falsify natural selection and we cannot use natural selection to predict anything.

Like if you don't have the sense to come in out of the rain, you'll get wet, get pneumonia, and possibly die.

That would be me doing the selecting, not nature. (and I was designed by my Mother and Fathers genes I did not randomly evolve)

I can't believe you're making me argue that peanuts are not meat. My suggestion: go get a peanut plant. . . . but they're grocers, not botanists, and they're wrong.

I cannot believe that you think that botanical definitions are the only way to define things. A botanical definition is only one way to define things. Many times it is not the most practical. Grocers are not wrong when they call peanuts nuts or tomatoes vegetables. Taxonomy and other classifications are artificial constructs, made by man to help order things. They can mean different things in different contexts just as easily as a mile is different in the water than on the land or a pint in the UK rather than the US. And yes, nutritionally, peanuts, nuts and legumes are in the meat category. Perhaps you'd like to take it up with the USDA.

Wrong. Equus stenonis was not modern (modern horses are Equus caballus), but an earlier species. [ . . .]it was not a modern horse by any stretch of the imagination.

Not the last word, but wikipedia ("evolution of horses entry") disagrees with you. The fact is, all of those fossils that are put in the evolutionary chain are not necessrily related to the modern horse. You cannot scientifically say, "a is older than b, a has some resemblance to b, therefore b came from a". In any event, modern horses may well have been around 50,000 years ago. The existence of similar looking but different species tells us nothing of what might have been around that simply has not been found yet.

Do you just make up stuff on the fly?

No, as your article indicates, my statement is fairly common. The majority of incidents in your article were covered in my previous posts -- wolves having no experience with being hunted by humans, wolves in captivity, wolves attacking children or women.

Even so, the number of reported cases is fewer than the number of people killed by lightening. If wolves were commonly hunted, the number would approach zero.

But again, I made a passing remark about wolves while discussing my main point -- that humans can outrun four legged mammals over a long distance. I really didn't intend to advise chasing down large preditors. Or trying to outsprint them.

"Evolutionary algorithms" and related ( and other related algorithms Tabu search, simulated annealing, Boltzman networks etc. ) are actually an interest of mine.

x[t+1] = s( v( x[t]) )

where x[t] is the population under a representation at time t, v(.) is the variation operator(s), and s(.) is the selection operator.

Evolutionary algorithms and genetic programming are actually a subset of a more general type of stochastic method of machine learning. These algorithms are nifty but only if the selection operator and variation operator, and the termination condition are very carefully designed. Every step of the design of an evolutionary algorithm/stochastic learning algorithm requires careful planning and purposeful choices, otherwise nothing useful ever comes out of these algorithms. I know from experience that it is actually easy to write one which will never converge on the optimal set of parameters. These algorithms are often designed to discover a particular design. These algorithms also require a preexisting highly ordered/designed computational device capable of running the same set of designed instructions over and over and over again with out error.
Every "feature" in Avida “digital organism” is a mathematical abstraction of a preexisting design.

Humans discover abstractions and laws which God created in the universe. Creating observed mathematical abstractions and then running them through a stochastic method of machine learning doesn’t show that a plant or an organism is performing an optimization calculation. Avida is an intelligently contrived program from more than a more than a decade of development. One cannot prove that the world as we observed it is a by-product of chaos with an experiment centered on events inside something that owes its very existence to outside interference with nature. The fact remains that Avida and the computer itself owe their very existence to human imposition of order from outside. After more than a decade of development, because of presuppositions that ‘matter is all there is’, the fact that the artificial environment of Avida was 'intelligently designed' is ignored.

An interesting probability model that you may find interesting is calculating the probability of trying to assemble life from non-life purely by chance and natural process:

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

a) Calculations of Sir Fred Hoyle and Chandra Wickramasinghe for random generation of a simple enzyme and calculations for a single celled bacterium.
b) Calculations of Hubert Yockey for random generation of a single molecule of iso-1-cytochrome c protein.
c) Calculations of Bradley and Thaxton for random production of a single protein.
d) Calculations of Harold Morowitz for single celled bacterium developing from accidental or chance processes.

Given the incredible improbability of life arriving from non-life.....do you really believe that life as we observe it today came to be by chance and natural process, and you are willing to base your life on that belief?

No, as your article indicates, my statement is fairly common.

Common and wrong. Why not do a google before you post an attack on somebody's statement to make sure you got your facts right?

The majority of incidents in your article were covered in my previous posts -- wolves having no experience with being hunted by humans, wolves in captivity, wolves attacking children or women.

The comment was in the context of man a million or so years ago and you have absolutely no idea how wolves acted a million years ago. You really can't spin this into making sense.

Even so, the number of reported cases is fewer than the number of people killed by lightening.

Even so, it makes you "wolves don't attack humans" comment untrue - that was my only point.

The bigger point is you rarely debate - you bully and attack - often with childish name-calling. But often you are wrong - so maybe you should be a little less aggressive, a little less sarcastic, stop falling back on name-calling, and check your facts. (BTW: I am not claiming to be inocent - I am trying to follow my own advice)

I made a passing remark about wolves while discussing my main point -- that humans can outrun four legged mammals over a long distance.

Do you actually think a man can outrun a Cheetah? I did a quick google and found:

The fastest man can run about 18 MPH

A Cheetah runs at about 45 MPH

A wolf can sprint at about 40 MPH

Bears run at about 35 MPH

Lions run at about 35 MPH

While the animal speeds are sprints - Human would never get the chance for long distances because they would be caught in the first moments.

There is no way a human can outrun these animals unless there was a reality TV show where races were staged - then maybe you could have a point although making up the difference on the sprint speeds seems highly unlikely

Do you have any supporting evidence for your claim?

Given the incredible improbability of life arriving from non-life.....do you really believe that life as we observe it today came to be by chance and natural process, and you are willing to base your life on that belief?

I'm not willing to limit my definition to a couple of phrases, but basically, yes. I find Pascal's wager morally loathsome. Any deity that operated on that principle would be morally indistinguishable from Satan.

Your criticism of Avida and evolutionary algorithms is rather beside the point. Such algorithms are imperfect attempts to mimic nature. There's a lot to learn about how to make a self-sustaining self-replicating system.

Any criticism of evolution based on incredulity needs to recognize that six-sevenths of the history of life on earth is erased by geologic processes -- the first three billion years. The things we claim are descended from a common ancestor are not particularly different in degree of complexity. the cell machinery s pretty much the same in all living things, and the DNA variations are pretty much variations in parameters.

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