Re: Cantor's diagonal proof wrong?

From: Paul Leyland (paul_at_leyland.vispa.com)
Date: 11/16/04 

Date: 16 Nov 2004 10:17:25 +0000

Han de Bruijn <Han.deBruijn@DTO.TUDelft.NL> writes:

> fishfry wrote:
> > If all you're interested in is the physical world, then you don't
> > need infinite sets, let alone the real numbers.
>
> Huh? Would you like to argue that physics doesn't need the real numbers?

Ok, I like a challenge.

It is most certainly not yet proven, but there is (IMO) a very good
chance that physics needs integers, number theory, combinatorial
analysis, statistics, set theory, group theory and various other
branches of discrete mathematics but does not need real numbers for
anything other than computational convenience.

It is entirely possible, IMO, that spacetime is not continuous but
quantized and that the universe is an automaton (whether finite or
infinite I leave open) which evolves in discrete steps at discrete
locations. Something like a giant game of Life but with rules that
will probably turn out to be rather more complex. In this model of
physics, the universe may well be a Turing machine, with all the
limits on computability and continuity that implies.

Paul 

-- 
Hanging on in quiet desperation is the English way.
The time is gone, the song is over.
Thought I'd something more to say.

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