>Actually, as I have thought about this problem today, what we may have in
>the case of SETI is an example of Goedel's theorem. If we detect a signal
>from Betelgeuse which has exactly the format to play on my TV, and I can
>see little green men on the screen, then I know there is a signal. But
>within the mathematical realm, I can not prove that there is a signal.
>This is what Goedel's theorem is all about. There are true statements
>which can not be proven true.
The above seemed fishy even to this non-mathematician. While the point is
true, it seems to me to be just a statement of the fact that inductive
observation can never lead to 100% airtight "proof". Maybe 100% minus
epsilon with epsilon getting ridiculously small, but not rigorous proof.
This is just logic, and has nothing to do with Goedel as far as I can see.
I e-mailed a friend of mine who is a math prof and he agreed with my
assessment. He also provided this non-rigorous statement of Goedel's theorem:
>Suppose you have
>any collection of axioms that include the axioms that postulate the
>existence of the natural numbers. Then there are statements about the
>natural numbers that can be neither proved false nor true with these
>axioms.
Then my friend offered this comment:
>As you can see, Godel's theorem is unlikely to have any application to the
>search for extraterrestrial life. Godel's theorem is one those statements,
>like the 2nd law of thermodynamics and the Heisenberg uncertainty
>principle, that are forever destined to be mangled by the public.
As an occasional warrior against abuse of the 2nd law of thermodynamics, I
am especially sensitive to stuff like this. It may be OK to invoke things
like this as an analogy or metaphor (though I can't even see that connection
in the SETI example), but it creates unnecessary confusion when the metaphor
is mistaken for the real physical or mathematical result (like when the 2nd
law is mis-invoked to explain the "decay" that characterizes human sin or my
messy desk). Since we don't serve a God of confusion, I think it is
worthwhile to make the effort to not "mangle" these concepts.
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| Dr. Allan H. Harvey | aharvey@boulder.nist.gov |
| Thermophysics Division | Phone: (303)497-3555 |
| National Institute of Standards & Technology | Fax: (303)497-5224 |
| 325 Broadway, Boulder, CO 80303 | |
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| "Don't blame the government for what I say, or vice versa." |
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