Re:Is the universe computable?

From: David Barrett-Lennard <dbl.domain.name.hidden>
Date: Thu, 15 Jan 2004 10:43:05 +0800

Hi Eugen,

> Yeah. I'm saying that, say,
>
0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780c2ccdf0c8e100d38f20
d9
> f3064aea3fba00e723a5c7392fba0ac0c538a2c43706fdb7f7e58259
> didn't exist in this universe (with a very high probability, it being
a
> 512
> bit number, generated from physical system noise) before I've
generated
> it.
> Now it exists (currently, as a hex string (not necessarily ASCII) on
many
> systems
> around the world, rendered in diverse fonts), as soon as I remove all
> its encodings it's gone again. P00f!

I can't identity with your conception of numbers but I guess you're
entitled to it!

You admit a base 16 notation for numbers - which means you allow numbers
to be written down that aren't "physically realized" by the
corresponding number of pebbles etc. So much for talking about pebbles
in your previous emails!

In statements of the form "There exists integer x such that p(x)" do you
say this is vacuous because x hasn't been specified yet, or is it
sufficient to merely name an unspecified integer to allow it to exist?

Many proofs make these sorts of statements, and no where is the named
integer given a specific value (even though its purported existence is
crucial to the proof). Do you say these proofs are vacuous?

If I write the statement "for all integer x, x+1 > x", does this make
all the integers come into existence? Or is this another vacuous
statement?

- David
Received on Wed Jan 14 2004 - 21:48:17 PST