Allan Harvey wrote:
"The above seemed fishy even to this non-mathematician. Whlie the poinnt 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-rigourous statement of Goedel's theorem:
>As you can see, Goedel's theorem is unlikely to have any application to the
>search for extraterrestrial life. Godel's therorem 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 thermodynamic, 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 mathematicla 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.<<
*end of quote*
OK, let me explain this. First, Goedel's theorem says that within any logical
system, there are statements that you can KNOW to be true but you can't prove
to be true. There are technical limitations on the type of logical system.
Goedel's theorem does not apply to arithmetic with only +/- operations, (See
Tipler, Physics of Immortality p 193 (I think, my book is at home and this is
from memory)).
Let's say you have recorded a signal from Alpha Centauri. That signal was
recorded from an analogue medium i.e. radiowaves. It is characterized by a
certain power level which you think is interesting. But you don't know
whether the signal is frequency or amplitude modulated. You also don't know
whether the signal is encoding digital information or analogue. You don't
know how you should display it. Should you put it out on a tape recorder and
listen? (what speed should you play the recorder?) Does the information
represent a series of matrices like our TV pictures? If you play the video
portion of the TV signal on a tape recorder it sounds like noise. If it is
matrices, what is the size of the matrix (picture)? Is the signal a military
signal from an alien civilization and the message has been encrypted?
Is the signal periodic, quasiperiodic? A quasiperiodic signal might be
mistaken for language, because language IS quasiperiodic. Look at the
repetition of the word "the" in this post. It repeats at irregular intervals.
There are natural processes which are quasiperiodic.
How do you know there is a signal at all. What I was saying about Goedel's
theorem is that you can not prove that there is a signal in this interesting
recording you have. But, and this is the part that I said yesterday, the
mathematics of information theory, will not allow you to distinguish between a
signal which is nothing but noise (randomly generated) and one with
intentional information.
I disagree with your friend.
glenn