Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?
From: Chairman of the David Hilbert Appreciation Society (mathgeekxxxxii_at_hotmail.com)
Date: 02/03/05
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Date: Thu, 03 Feb 2005 13:07:11 -0500
examachine@gmail.com wrote:
> Mitch Harris wrote:
>
>>That is probably so. The emotional reaction I do know I had was with
>>your statement "there can be no such thing as continuum in the
>>physical world", which sounded just too (baselessly) authoritarian to
>
>
>>pass up comment.
>
>
> I do not mean to be authoritative. That would be a Torkelism.
>
> I think the evidence for a discrete world far outweighs the evidence
> for a continuous world, which is basically non-existent.
I don't see why it matters, either way.
If it was proven tomorrow by physicists that space was continuous
it wouldn't invalidate discrete mathematics, would it? OTOH, if
was proven tomorrow that space was discrete it wouldn't
invalidate any mathematics based on the continuum.
I think the whole notion of getting rid of the reals
is just plain kooky.
Since you only seem to be interested in applications of mathematics,
what competing alternatives are there to the current theory of
calculus that aren't based on the existence of sets with cardinality
greater than aleph_0?
Are those theories easier for engineers and such to learn and
manipulate?
If a competing theory produces essentially the same results as
the standard theory of calculus, then why prefer the other
theory?
If any of the alternative theories of calculus are superior, then
why haven't they caught on in the last 400 years?
[...]
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