**Science
in Christian Perspective**

**Letter to the Editor**

**Mathematical Impossibility**

**Kenneth P. Bube****,
Professor of Mathematics
University of Washington
Seattle, WA**

**From: ***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 F_{n}
= F_{n-1 }+ F_{n-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.