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.
No problem.
OK, Vade. The fossil record supports gradualism. Close your eyes real hard and keep telling yourself that over and over. It won't make it any truer but you should manage to protect your world view.
Do you understand that human beings are defined as the species homo sapiens. Do you understand how specious the claim is that they are not human beings but they do belong to the species homo sapiens is? This is science and those hewing to killing embryos for science want to argue philosophy and law because the science is agianst them.
It is pathetic.
Your arguments suck. You are under the impression that artificially setting a nervous system as the point where the embryo/foetus acquires homo sapienhood is somehow supported by science. It is nonsensical and pathetic.
The honest adherer to scientism simply ackowledges the fact that the embryo is a living human being (which is by the way a scientific term meaning modern member of the species homo sapiens) and proclaims that killing them for research is for the "greater good".
Thanks for the chuckle.
I suggest you make it a bit more personal so he can understand it at the baby level. Ask him if undifferentiated cells with his mother's DNA are somehow his mother...
I do not understand. How did you find my recognition of your claims about me as false to be amusing?
Not according to Merriam-Webster, unless you have your own special evo List-O-Definitions definiton for that, too.
Main Entry: em·bryo
1 a archaic : a vertebrate at any stage of development prior to birth or hatching b : an animal in the early stages of growth and differentiation that are characterized by cleavage, the laying down of fundamental tissues, and the formation of primitive organs and organ systems; especially : the developing human individual from the time of implantation to the end of the eighth week after conception
Note the last part: especially : the developing human individual from the time of implantation to the end of the eighth week after conception
Now here's some links to embroyonic development up until that 8 week stage.
http://en.wikipedia.org/wiki/Embryo
http://www.nrlc.org/abortion/facts/fetusdevelopment.html
http://www.nlm.nih.gov/medlineplus/ency/article/002398.htm
You are correct, I presented an incorrect definition. I should not have so hastily skimmed the Wikipedia article, as I misread key elements of the entry.
Fine. Just pointing it out for the lurkers. Real science versus LOL science.
If you do have the time, FreedomProtector, I'd be very glad if you were to ping me. :^) Thank you!
Now with self-pitying note, "Why am I always late to all the good threads?"
Cheers!
Thanks for writing, dear dude!
Here's what your Mr. Lindsay says about these snail shells concerning "A Pliocene Snail": If there had been gaps in the fossil sequence, we would have thought that these were fossils from several different species. If we look at snails alive today, we can find separate species which differ by less than the difference shown in the picture.
Quick quiz: what's another, more reasonable, more rational explanation for the difference in those snail shells other than evolution into different species?
It shouldn't be a wonder that science is bringing about the end of the Darwinist era.
Meanwhile, age of boop will go on and on....
You have some severe problems with "theory," "fact," and the place of intelligent design in science.
Take a look at these definitions (from a google search, with additions from this thread). I think they might help you frame your arguments:
Theory: a well-substantiated explanation of some aspect of the natural world; an organized system of accepted knowledge that applies in a variety of circumstances to explain a specific set of phenomena; "theories can incorporate facts and laws and tested hypotheses." Addendum: "Theories do not grow up to be laws. Theories explain laws." (Courtesy of VadeRetro.)
Theory: A scientifically testable general principle or body of principles offered to explain observed phenomena. In scientific usage, a theory is distinct from a hypothesis (or conjecture) that is proposed to explain previously observed phenomena. For a hypothesis to rise to the level of theory, it must predict the existence of new phenomena that are subsequently observed. A theory can be overturned if new phenomena are observed that directly contradict the theory. [Source]
When a scientific theory has a long history of being supported by verifiable evidence, it is appropriate to speak about "acceptance" of (not "belief" in) the theory; or we can say that we have "confidence" (not "faith") in the theory. It is the dependence on verifiable data and the capability of testing that distinguish scientific theories from matters of faith.
Hypothesis: a tentative theory about the natural world; a concept that is not yet verified but that if true would explain certain facts or phenomena; "a scientific hypothesis that survives experimental testing becomes a scientific theory"; "he proposed a fresh theory of alkalis that later was accepted in chemical practices."
Proof: Except for math and geometry, there is little that is actually proved. Even well-established scientific theories can't be conclusively proved, because--at least in principle--a counter-example might be discovered. Scientific theories are always accepted provisionally, and are regarded as reliable only because they are supported (not proved) by the verifiable facts they purport to explain and by the predictions which they successfully make. All scientific theories are subject to revision (or even rejection) if new data are discovered which necessitates this.
Law: a generalization that describes recurring facts or events in nature; "the laws of thermodynamics."
Model: a simplified representation designed to illuminate complex processes; a hypothetical description of a complex entity or process; a physical or mathematical representation of a process that can be used to predict some aspect of the process; a representation such that knowledge concerning the model offers insight about the entity modelled.
Speculation: a hypothesis that has been formed by speculating or conjecturing (usually with little hard evidence). When a scientist speculates he is drawing on experience, patterns and somewhat unrelated things that are known or appear to be likely. This becomes a very informed guess.
Guess: an opinion or estimate based on incomplete evidence, or on little or no information.
Assumption: premise: a statement that is assumed to be true and from which a conclusion can be drawn; "on the assumption that he has been injured we can infer that he will not to play"
Impression: a vague or subjective idea in which some confidence is placed; "his impression of her was favorable"; "what are your feelings about the crisis?"; "it strengthened my belief in his sincerity"; "I had a feeling that she was lying."
Opinion: a personal belief or judgment that is not founded on proof or certainty.
Observation: any information collected with the senses.
Data: Individual measurements; facts, figures, pieces of information, statistics, either historical or derived by calculation, experimentation, surveys, etc.; evidence from which conclusions can be inferred.
Fact: when an observation is confirmed repeatedly and by many independent and competent observers, it can become a fact.
Truth: This is a word best avoided entirely in physics [and science] except when placed in quotes, or with careful qualification. Its colloquial use has so many shades of meaning from ‘it seems to be correct’ to the absolute truths claimed by religion, that it’s use causes nothing but misunderstanding. Someone once said "Science seeks proximate (approximate) truths." Others speak of provisional or tentative truths. Certainly science claims no final or absolute truths. Source.
Science: a method of learning about the world by applying the principles of the scientific method, which includes making empirical observations, proposing hypotheses to explain those observations, and testing those hypotheses in valid and reliable ways; also refers to the organized body of knowledge that results from scientific study.
Religion: Theistic: 1. the belief in a superhuman controlling power, esp. in a personal God or gods entitled to obedience and worship. 2. the expression of this in worship. 3. a particular system of faith and worship.
Religion: Non-Theistic: The word religion has many definitions, all of which can embrace sacred lore and wisdom and knowledge of God or gods, souls and spirits. Religion deals with the spirit in relation to itself, the universe and other life. Essentially, religion is belief in spiritual beings. As it relates to the world, religion is a system of beliefs and practices by means of which a group of people struggles with the ultimate problems of human life.
Belief: any cognitive content (perception) held as true; religious faith.
Faith: the belief in something for which there is no material evidence or empirical proof; acceptance of ideals, beliefs, etc., which are not necessarily demonstrable through experimentation or observation. A strong belief in a supernatural power or powers that control human destiny.
Dogma: a religious doctrine that is proclaimed as true without evidence.
Some good definitions, as used in physics, can be found: Here.
Based on these, evolution is a theory. CS and ID are beliefs.
[Last revised 8/27/06]
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