Letter to the Editor
Mathematical Impossibility
Kenneth P. Bube
, Professor of MathematicsFrom:
PSCF 52 (March 2000): 74-75.The book, A Case against Accident and Self-Organization by Dean L. Overman, has been capably reviewed by Charles E. Chaffey in the March 1999 issue of PSCF. Perhaps the greatest weakness of the book is to claim mathematical proofs in ways that are not consistent with the nature of mathematics itself. The author puts forth a quite reasonable argument: The probability that just chance occurrences led to the universe as it is, and in particular to life itself, is very low. But he overstates what he has shown by insisting on calling any probability less than 10-50 a mathematical impossibility (even probability 0 is not the same as mathematical impossibility). It appears that the author wants the authority of mathematical proof, but by insisting on this line of argument, he weakens his case, certainly for the professional mathematician.
Overman is unfortunately not quite well enough versed in mathematics for his illustrations to work for the mathematically informed. In his appeal to the Fibonacci sequence as "a mathematical code in nature left by an intelligence," he completely misses the fact that although the Fibonacci sequence has a lot of structure, it has very little "information content": it is generated by the very simple difference equation Fn = Fn-1 + Fn-2. In fact, mathematical biologists, who have studied the formation of patterns like leopard spots and tiger stripes, have observed similar situations where the patterns are the consequence of encodings which are not as complicated as the patterns they form. In his argument that the "information content" in DNA is too high for chance, he appears to be unaware of fractals, where, like the Fibonacci numbers, simple generation schemes can provide very intricate patterns.
The author manages to fall into some of the very traps he warns his reader about at the beginning of the book. In making the statement that "the paradigm for the emergence of life contains algorithms which must have at least as much information content as the genetic messages they claim to generate" (p. 85), he makes the implicit assumption that there is some sort of "conservation of information content." This sounds plausible, but by a very similar argument it might be claimed that a person is completely determined by the gametes that first join together at conception. His argument that "DNA can function as a code only if its base sequence is not determined by physical and chemical laws" (p. 88) relies again on underlying assumptions, some of which are suspect because of the way the codes themselves physically cause the features of the living organism they encode. The author's discrediting of computer simulation misses the point because he confuses the complexity of a compiler with the simplicity of a very simple computer program (like one that generates the Fibonacci sequence).
I would agree with the author's conclusion that "Life appears to be formed only by a guided process with intelligence somehow inserting information or instructions into inert matter ... Something besides chance caused and is causing life" (p. 101). But I would state it very differently. As stated, there is the underlying assumption that there is a separation between the very existence of "inert matter" and the "inserting" of information.
The big issue concerning this book is whether or not his arguments hold water. I would say that many of them include much reasonable cause for reflecting upon the great unlikelihood that all which we see truly came from nothing (Rom. 1:19-20), but they are not mathematical proofs. To the extent that he tries to present them as such, I as a mathematician must protest. To the extent that he may have overlooked other possibilities in many of his arguments, I would say they may be flawed.
The ultimately important observation is that there is plenty of evidence for Personal design in the universe in which we live, and that those who swallow modern "chance" folklore overlook this evidence to their own peril.