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.
It can for some groups, but not for others. This is largely due to different environments; eg, there are very few fossils of jungle animals compared to plain/savannah dwellers. Classical examples of the latter are eohippus - modeern horses, and australopithecines - modern people.
Also, in cases of "rapid" evolution, Gould's hypothesis is that the speciation (ie the intermediate forms) are in a small population in a geographically-restricted area. So we should expect few transitionals in this case. However, I have read that there have been a few lucky finds of exactly this scenario, but I forget just what species were involved (IIRC it was Gould's specialty, snails).
Something that is often forgotten by anti-evos is the abundant fossil record for many higher-level transitions, such as dino-bird and reptile-mammal. Recent reseach in Precambrian and Cambrian fossils is uncovering phylum-level transitionals. The link is to an essay by Glenn Morton that shows worm-arthropod, halkeriid-brachiopod, and annelid-halkeriid-mollusc. It has some great pictures.
It'd be consistent with other things I've read about the Soviets. E.g. I once read that there was an "official" Soviet history of World War II, "The History of the Great Fatherland War" or somesuch title, which somehow significantly (shall we say) "overrepresented" the contributions of one Nikita Kruschev.
Cheers!
Bite your tongue.
Cray computers ran their own flavor of UNIX.
Cheers!
Remind me to Google some of Prigogine's stuff. If my hazy memory serves me correctly he worked on (or at least started by working on) systems "shocked" away from equilibrium and watched as they re-attained equilibrium...
Cheers!
I'm not saying theories are not important. I'm saying they can, and have been at times, disproved.
From Wikipedia:
In a standard application of the psychological principle of confirmation bias, scientific research which supports the existing scientific consensus is usually more favorably received than research which contradicts the existing consensus. In some cases, those who question the current paradigm are at times heavily criticized for their assessments. Research which questions a well supported scientific theory is usually more closely scrutinized in order to assess whether it is well researched and carefully documented. This caution and careful scrutiny is used to ensure that science is protected from a premature divergence away from ideas supported by extensive research and toward new ideas which have yet to stand the testing by extensive research. However, this often results in conflict between the supporters of new ideas and supporters of more dominant ideas, both in cases where the new idea is later accepted and in cases where it is later abandoned. Thomas Kuhn in his 1962 book The Structure of Scientific Revolutions discussed this problem in detail.
Several examples of this are present in the relatively recent history of science. For example:
- the theory of symbiogenesis presented by Lynn Margulis and initially rejected by biologists but now generally accepted.
- the theory of punctuated equilibria proposed by Stephen Jay Gould and Niles Eldredge which is still debated but becoming more accepted in evolutionary theory.
- the theory of prions -proteinaceous infectious particles causing transmissible spongiform encephalopathy diseases- proposed by Stanley B. Prusiner and at first rejected because pathogenicity was believed to depend on nucleic acids now widely accepted due to accumulating evidence.
- the theory of heliobacter pylori as the cause of stomach ulcers. This theory was first postulated in 1982 by Barry Marshall and Robin Warren however it was widely rejected by the medical community believing that no bacterium could survive for long in the acidic environment of the stomach. Marshall demonstrated his findings by drinking a brew of the bacteria and consequently developing ulcers. In 2005, Warren and Marshall were awarded the Nobel Prize in Medicine for their work on H. pylori
You wrote that great truth with such glorious simplicity! Thank you for pinging me to it!
Nobody has disputed that, or even hinted that that's wrong. My point, in turn, is that in that respect, theories are no different from laws or facts, which are also found to be wrong from time to time.
That's all very nice but the fact remains that "the peopele" never contemplated giving unelected federal judges the power to make law from the bench. There should not be any controversy about that on a conservative website. That there is causes me considerable angst but I always manage to get over it.
Oh for Pete's sake. If Eldridge's and Gould's claim that most most species experience stasis for most of their existence meshed with Darwin why was it controversial. Why would Eldridge and Gould claim Darwin to be a ""phyletic gradualist?" Why should I accept Douglas Theobald's claim that he wasn't?
Because Darwin's words are there to see. You've linked an on-line version yourself in a vain attempt to twist and shout.
From the Theobald page, which supposedly you've already read:
Contradicts PG tenet #2There he is in all his glory, saying all the things you say he never said. Will that stop you from putting the wrong words in his mouth and claiming Ann Coulter's critics are refuted? Will you finally show some class, never mind sanity and honesty? BWAHAHAHAHAHAHAHAHAHAHA!!!But I must here remark that I do not suppose that the process ever goes on so regularly as is represented in the diagram, though in itself made somewhat irregular, nor that it goes on continuously; it is far more probable that each form remains for long periods unaltered, and then again undergoes modification. (Darwin, Ch. 4, "Natural Selection," pp. 152)
Contradicts PG tenet #2
"It is a more important consideration ... that the period during which each species underwent modification, though long as measured by years, was probably short in comparison with that during which it remained without undergoing any change." (Darwin, Ch. 10, "On the imperfection of the geological record," p. 428)
Contradicts PG tenet #2, #3, and #4
"... natural selection will generally act very slowly, only at long intervals of time, and only on a few of the inhabitants of the same region. I further believe that these slow, intermittent results accord well with what geology tells us of the rate and manner at which the inhabitants of the world have changed." (Darwin, Ch. 4, "Natural Selection," pp. 140-141)
To return to Douglas Theobald, he's more a polemicist than a scientist despite his degree. Why should I accept his claims?
I notice you think Ann Coulter's crap doesn't stink. Theobald's sources are primary literature; his quotes are honest.
And Theobald isn't the answer to the question of where in the materials linked to this discussion are the examples of things clearly shown in the fossil record to have evolved a new form in one small region and migrated elsewhere, showing up as the famous "sudden appearances" of creationist cult literature. No doubt you dont' remember seeing them because you never looked, not only not this time but not any previous time.
For the first time ever in Tribune7's sheltered little life:
Speciation by Punctuated EquilibriumIs There Any Evidence For Punctuated Equilibrium?
Yes. Several examples of this exact scenario are known. For example, there's a marine microfossil, a trilobite, a brachiopod, and some dinosaurs (including a Tyrannosaurus).
The author of the above, the person you need to be attacking for undercutting Ann Coulter long before Ann Coulter wrote, is Don Lindsay, not Doug Theobald. You can console yourself that both first names start with a capital "D." I can't believe that your anti-polemicist filter somehow let Ann through. Are you trying to melt another irony-meter?
Note also that atop that page there's a nice Darwin quote not among those already given from Theobald. It looks like a summary of Punk Eek that could have been written by Gould. (I've linked a very similar description by Gould already, but that's no doubt forgotten at this late date.) By comparision with that page and Theobald's, here is Ann Coulter on what punctuated equilibrium is. The contrast should be fairly striking, not to mention the certainty that both cannot be correct in the text of their assertions.
Instead of gradual change occurring by random mutation and natural selection choosing the most "fit" to survive and reproduce--in other words, "Darwin's theory of evolution"--Gould and Eldredge hypothesized that evolution could also happen really fast and then stop happening at all for 150 million years. Basically, what happens is this: Your parents are slugs and then suddenly--but totally at random--you evolve into a gecko and your brother evolves into a shark and your sister evolves into a polar bear and the guy down the street evolves into a porpoise and so on--and then everybody relaxes by the pool for 150 million years, virtually unchanged.I'll take you through that sentence by sentence since it looks a lot like what you yourself have claimed. The lurker can probably skip this part unless he or she is an idiot.
Instead of gradual change occurring by random mutation and natural selection choosing the most "fit" to survive and reproduce--in other words, "Darwin's theory of evolution"--Gould and Eldredge hypothesized that evolution could also happen really fast and then stop happening at all for 150 million years.
Never mind what a poorly cast and cumbersome sentence that is. (Some of mine on this thread haven't been exactly winners.) There are at least two things wrong with this one sentence as more than adequately documented in the sober materials linked. A contrast has been struck between the operation of Darwinian mechanisms and the occurrence of "sudden appearances" in the fossil record as though no theory containing one can contain the other. Already in this post that idea has once again been discredited. Anyone writing about PE for publication should feel obliged to educate herself better than this. Whether or not Ann should know better, the Discovery Institute crackpots who supposedly vetted her stuff certainly should. Dembski has claimed on his blog that he takes responsibility for all errors in Ann's evolution chapters. He's carrying a heavy load these days.
The same sentence implies that evolution ceases during periods of outward morphological stasis. This too is wrong. The pressurs have become conservative rather than innovative. Even at a local fitness maximum, however, neutral drift continues, which is why molecular clocks still work. Stasis in hard fossil parts doesn't tell you if enzymes are becoming more efficient, camouflage patterns are evolving, or behavioral adaptations are changing. If all we had were fossils, we would never know that lions and tigers had become separate species.
OK, I'm going to renege here and leave the other sentences as an exercise for any student who disregared warnings and followed along thus far. As for you, you're not worth it.
Your average ain't movin' up. I'm an agnostic. I don't know if there's a God of some sort or not. It's increasingly obvious to me that the people are passionately certain on the matter are simply nuts.
But those who wonder why there aren't a myriad of transitionals along every stage of development have a fair point too, and this has caused evos to consider things like PE.
And there are problems with making things stand on the fossil record. The very nature of it leads to misassumptions and uncertainties. Did Homo sapien descend from Homo erectus or Homo ergaster? Australopithecus afarensis or Australopithecus africanus? And it's not anti-science to say none of the above.
The Glenn Morton link is a case in point. Note in his essay he says "While this is widely stated by apologists and paleontologists, it is actually an assumption not borne out by the data." IOW, the Cambrian explosion claim is accepted by the scientific establishment and it's something Morton is challenging. So you go, Glenn.
And anybody can, Vade. Anybody can.
Uh, guys
NFL is on -- 2 different games!
I think that about die-hard evolutionists
The next hurricane which hits my house is surely to cause my house to be in a higher state of greater order and complexity. You have stumbled upon the best kept secret to the real estate market.
You are right. It's after 1. Thanks.
Priorities --- Priorities ;)
Your kidding, right?
Catch me at halftime for the response.
No, he's a True Believer Troll™ with the Self-Closing Mind® option.
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