On Sat, 6 Dec 2003 23:40:56 +0000 (UTC), "Kevin Aylward"
 wrote:

>Anthony Cerrato wrote:
>> "Paul P. Budnik Jr."  wrote in message
>> news:bqoo5l$9mn$1{at}darwin.ediacara.org...
>>
>> [SNIPPED]
>>
>> I don't believe Goedel has anything to do with anything
>> outside of formal math.             ...tonyC
>>
>
>But most rational models of the world *are* based on math. if we cant
>put numbers to something its difficult to say anything about it
>
>Irrespective of whether one can apply Goedel to a particular real world
>problem, what it presents is the very *idea* that there can exist true
>statements but be unprovable. This means that in it may well be
>impossible to derive everything about the world from exiting knowledge.
>Before Goedel there was no reason to hold that this might be the case.

Goedel really doesn't have anything to do with physical practicalities
in the sense that even well before Goedel there were problems known
that could not be calculated simply because our resources are bounded
by physical limitations.  For example, chess is no more difficult a
game than tic-tac-toe, mathematically.  Each is a game of complete
knowledge, no chance, and a finite number of moves.  A trivial
solution for both games is simply to enumerate all possible games.
From that point on, actually playing the games has no intellectual
value.  However, I seem to recall learning once that if every particle
in the known universe were a computer operating on a clock frequency
equivalent to the frequency of light, solving one game each clock
tick, you still couldn't work out all the games in the known lifetime
of the universe.

Whether or not that example is true, there will always be problems
that are simply too large to "solve" in the physical world even though
mathematics says they are doable -- how many zero's are there in the
decimal representation of the google'th Mersenne prime?  (Using google
in the "very-large-number sense, not the web search service sense).

Given the fact that the real universe is finite, Goedel's logic is
quite irrelevant to practical problems.  Yes, there exist problems
that are absolutely unsolvable.  There are also an enormous number of
problems that are, for all practical purposes, unsolvable.
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