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echo: quik_bas
to: BILL WHITE
from: DAVID WILLIAMS
date: 1998-03-23 10:00:00
subject: Old Folks

->    This seems impossible and I don't think everyone
-> actually believed the test results completely.  This
-> same thing _could_ happen in software.  Having a
-> "supervisor" excise a section that's never been used in
-> 1000000 runs, does not mean it won't be called on the
-> 1000001st run!
There's a theorem in logic called Goedel's Theorem. As I understand it
(maybe not very well!), what it says is that, in any fairly complex
logical system, such as mathematics, there are statements that are
universally true - i.e. can never be demonstrated false - but which
cannot be proved from the fundamental axioms of the system. So it is
always possible that someone may come up with a mathematical theorem
that is always true, but which is absolutely unprovable. The four-colour
theorem of maps, and Fermat's last theorem about powers of numbers have
both been suspected of being cases of this, but I believe proofs of both
of them have now been found. But something else may yet turn out to be a
Goedel case.
I suppose Goedel's Theorem might apply to physical logical systems, such
as computers, too. It is conceivable that a particular electrical pin
might *never* be addressed, even though the thinking on which the system
was designed may not give any reason to suspect that this would be the
case. The particular pin that you discovered was clearly one that was
addressed only extremely rarely. Maybe one of the ones that *were*
properly connected was never addressed at all!
Biological evolution, of course, does not heed your caveat about
supervisors. If a biological feature is useful only exceedingly rarely,
evolution is likely to let it decay. The odd chicken that gets killed
because it can't fly well is just evolutionary cannon-fodder. Tough!
                           dow
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