Fermat's last theorem, Godel's theorem, intelligent design

ken.w.smith@cmich.edu
Tue, 19 Mar 1996 10:42:42 -0500

Hi all,
I think there are several mathematical topics that have been
intermingled in a number of posts on Intelligent Design. There is Godel's
incompleteness theorem and the general unsolvability of diophantine
equations (the solution to Hilbert's tenth problem). Both of these
essentially make negative statements about the extent of mathematical
reasoning: "No matter how good you get, there will still be problems which
are unsolvable!"
Someday when I'm not busy, I will see if I can work out a readable
explanation of these things. (I will have to understand it better myself
first...)
Fermat's theorem got mixed up in all of this, I think, because
people wondered if it might be an example of a diophantine equation which
was algorithmically unsolvable and where the existence of a solution was
undecidable. So Yockey uses Fermat's diophantine equation as his example.
However, Wiles' recent proof shows that Fermat's Last Theorem is indeed
decidable.

About Yockey and intelligent design: Glenn Morton sent me Yockey's
statements on attempting to mathematically model information theory in such
a way as to separate noise from intelligent information. My reactions,
after reading Yockey are:
(1) Yes, it would indeed be difficult to mathematically model the
statement that "intelligent information is encoded in a signal". Glenn is
right in challenging those attempts.
(2) Godel-like arguments and the unsolvability of diophantine
equations *suggest* that it would be *impossible* to do this. I don't,
however, believe one can get Godel's theorem to *prove* that it is
undecidable as to whether a signal is "random" or "organized".

An aside: the goal of modern cryptology is to take organized,
intelligent sequences and, via a deterministic process, make them *appear*
to be merely random bits. Naturally, if one reverses the process (in
decryption) one attempts to examine random sequences and recover organized
sequences from them. This is very hard and usually relies on some
underlying assumptions about the method of encryption.

In Christ,
Ken

PS. Welcome to the ASA list, Jim Turner!
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Ken W. Smith, Professor of Mathematics
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Central Michigan University, Mt. Pleasant, MI 48859 computers may weigh
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