----- Original Message -----
From: "Stephen Paul King" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Cc: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Wednesday, January 21, 2004 5:39 PM
Subject: Re: Is the universe computable
You are confussing the postential existence
of a computation with its "meaningfulness". But in the last time you are
getting close to my thesis. We should not take the a priori existence of,
for example, answers to NP-Complete problems to have more "ontological
weight" than those that enter into what it takes for "creatures like us" to
"view" the answers. This is more the realm of theology than mathematics. ;-)
..This is rather like an argument I like to put forward when I'm feeling
outrageous, and one which I've eventually come to believe: That the real
number line 'does not exist.' There are only countably many numbers you
could give a finite description of, even with a universal computer (which
the human mathematical community probably constitutes, assuming we don't die
out), and in the end the rest of the real numbers result from randomly
choosing binary digits to be zero or one (see eg. anything by G. Chaitin).
So while the natural numbers and the integers have a rich internal structure
(rich enough to contain the whole universe and more, according to most
subscribers on this list, I suspect), the reals can be encoded in the single
'program' of tossing a coin. By this I mean that the only 'use' or 'meaning'
you could extract from some part of the binary representation would be of
the form 'is this list of 0s and 1s the same as some pre-chosen lis of 0s
and 1s?', which just takes you back to the random number choosing program
you used to create the reals in the first place.
-- Chris Collins
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