Posted on 09/20/2006 9:51:34 AM PDT by SirLinksalot
A Mathematician's View of Evolution
Granville Sewell
Mathematics Dept.
University of Texas El Paso
The Mathematical Intelligencer 22, no. 4 (2000), pp5-7
Copyright held by Springer Verlag, NY, LLC
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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footnotes
*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.
LOL! That statement illustrates the foundation of all your arguments. It is man made definitions and doctrines.
"The same cannot be said of "science."
Science is rational and recognizes reality. It is not founded on such arbitrary definitions and doctrines.
Sure. God personally told you all the secrets of the universe. Shut down all brain cells & full steam ahead.
Any "science" that claims that men are trousered apes is BS and no more worthy of considered response than is the notion that the moon is made of green cheese.
Good to see you have an open mind.
By definition, God CANNOT be wrong.
But you can. You don't speak for God.
The same cannot be said of "science."
Science has an infinitely better track record than any religion at describing the natural world. That includes your religion.
Since you want to do question and answer: Just what are YOUR personal credentials as a conservative activist since you plainly propagandize for the secular humanist enemies of conservatism when you claim that men are apes or descended from apes or whatever the Darwinian falsehood du jour may be?
What 'credentials' does one need? As far as propaganda for secular humanists goes, your comments are their stereotypical dream come true. You do a good job helping them out.
How is that Free Republic poll on teaching creationism and intelligent design coming????
Again irrelevant. The discoveries of science will march on, with or without those who choose to remain ignorant. All available evidence points to the evolution & common descent of life on earth, including the descent of all humans from apelike ancestors - that includes me, you, your mother, your father, your children, conservatives and liberals alike. This is what qualified science teachers teach, and what they will continue to teach, with more and more confidence as more evidence comes in to support this claim. You'd best leave science to the pros who actually know what they're talking about when it comes to such matters.
So many of them do that. Science is outperforming religion at the job of understanding the universe. That won't do. Science delenda est, even if only by dragging it down with the vile and nasty accusation that it's A RELIGION! (Eeeeewwwww!!!)
To clarify, meant to say that you are NOT doing that much worse than the list that follows. (Especially the delightful Ms. Coulter.)
Fingers in the ears going "La la la?" Do I need to blast all that inline to make it clear how ridiculous the game on this thread really is?
But keep those eyes closed.
Yes, of course they were. Linnaeus and later scientists used the morphologies, biodistribution, behavior, etc, to construct the classes, orders, families, and other taxa. Lamarck, Buffon, Comte, et al, and later Darwin and Wallace interpreted these taxonomies as phylogenetic trees.
But, as one of the earlier posts on the thread pointed out, the eye in the fruit fly, and in the octopus, have very different structures though a common purpose...they are both "eyes". Similarly, since whales came from land animals, the fins [nitpick - whales have flukes] developed independently from those of fish.
Eyes have developed independently many times, I've seen estimates as high as 40. Being able to tell light from dark, or to better resolve images, has obvious survival value in many different environments.
Whale flukes are a specialization of the tetrapod limb: one bone close to the body, two further out, then five groups. So are the flippers of ichthyosaurs, mesosaurs, pinnipeds, and sirenians.
So what methods or safeguards are put in place to prevent misclassification based upon structural similarities which may turn out to be of completely independent origin?
A good question. Convergent evolution is the fact that natural selection will tend to select the same features to adapt to the same niche. A famous case is the saber tooth "tiger" and its marsupial look-alike. Another one is the way fish, cetaceans, and ichthyosaurs have very similar fins (or flukes or whatever the right term is for the ichthyosaurs) and streamlining.
The answer is by studying the details of anatomy. The saber-toothed cat and the marsupial one are both extinct, so you can't just compare wombs and pouches. However, marsupial skeletons can be differentiated from placental ones, though you'll have to ask someone other than me about the details.
(Or is it a moot point since that type of thing happens so seldom...?)
It has happened, but not that often. Basilosaurus was given a reptilian name, even though it's a mammal. It's more of a problem, obviously, with fossils, but you still hear discussion as to how the giant panda, the red panda, bears, and raccoons should be classified. DNA analysis can provide conclusive answers.
You are right and, the good Lord willing and the creek don't rise, I am taking your wise advice and I am oughtta here. Those guys are worth nothing.
Whoops! outta here NOT oughtta here.
The mistake your are making is equating your worldview with "science". It's not. It's a faith based on emotion not objective reason.
The Bill of Rights applies and is of fundamental importance to conservatives. The 1st Amend. provides a Constitutional reason for keeping religion and it's nonscientific creationist and ID claims out of the science class. No religion is to be established by the state. IOWs no one is to corrupt science with nonscientific religious claims and nonscientific claims based on religious motivations.
Both creationism and ID are nonscientific. Both claim the laws of physics are insufficient to govern the world. That is not what is found scientifically. If you want to teach that to your kids, enroll them in a parochial school, or homeschool them. The first Amend. forbids forcing religion though the public school system, especially by attempting to forcefully inject the fraud into the science class where it has no place at all.
BWAAAAAAAAAAAAAAAAAAAAAHAHA!
Your "reality" has repeatedly failed under examination during this exchange.
Hiya, Balrog
Why not? Its purpose is to accommodate the feelings of anti-evolutionists by pretending that their beliefs are actually a nonstandard form of science. That's as PC as Ebonics.
The tactic the anti-evolution activists are employing is basically to call for affirmative action for ID. Again, that's pretty PC.
IMO, the ID lobbyists might get further with the Dhimms than with the GOP; after all, it wasn't that long ago that they were part of the Dhimm coalition (think of W.J. Bryan), since their arguments for "fairness", "inclusiveness", "teach the controversy", etc, are usually employed by the left. Not to mention that there already are a large number of liberal ID-ists and creationists, such as Jesse Jackson and Al Sharpton. Creationism is quite common in the black church-going community.
Bottom line: PC exists on the right as much as on the left. The mascots may be different, but the feelings-based, affirmative action stuff is the same.
And you are so much smarter and more in touch with reality that all the tens of thousands of biologists, geologists, chemists, physicists, astronomers, archaeologists and such that have lived in the last two hundred years? In your wet dreams.
Hiya JS
Darwin wrote extensively about both gradualism and saltation. Without radiometric dating and ERVs, and with the rather skimpy fossil record at his disposal, he had no way of settling the issue.
The fact is he understod the problem thoroughly.
Well, I have a college degree in it...does that count?
But in any case, you don't have to be an astronomer to know that "the age of the universe" falls into the category of "fact" and not "theory". And you don't have to be a scientist to know that facts, as far as they pertain to science, can be wrong.
As for whether theories change, often they do, but that doesn't in any way address the point that you were attempting to refute.
However, there are many scientists today who would like you to believe that theories are laws. They are not.
Codswallop. Scientists know the difference, even if you don't. The fact that theories can change and laws can't makes theories stronger than laws, and far more important to science. Theories are conceptual models; laws are empirical rules of thumb. If a theory is wrong, it is either discarded or modified; if a law is wrong (e.g. Ampere's Law), it remains wrong.
I would suggest what you find wrong with this author is his statement that theories can change-not his views on astronomy.
Your theory is wrong. Change it.
Jist a quick question. Is dismissing evolution as a "religion" name calling or not? Is it intended as an admission that evolution is the ultimate TRUTH, or is it placing evolution in the sewer?
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