Re: Mathematics without physics, a reality?
From: Mark Fergerson (nunya_at_biz.ness)
Date: 11/10/04
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Date: Wed, 10 Nov 2004 10:14:42 -0700
Han de Bruijn wrote:
<snip>
> As Joe has pointed out correctly, no significant part of
mathematics
> could have been developed without the presence of an
outside world.
Well, without something to analyze mathematically, what's
the point?
> I have to say such things more carefully in the
'sci.math' newsgroup,
> but in 'sci.physics'? How about a mathematics which is
founded upon
> some basic principles in physics ? I mean, taking into
account such
> phenomena as the - empirical - non-existence of
infinities? Because
> there is no physical device in the universe which can
ever detect a
> thing which is infinite. Infinities are not observable
empirically.
>
> Am I right?
>
> Oh, don't come up now with stories about singularities &
black holes.
What's the measurable charge/volume of an electron?
> I was talking about *basic* principles in physics. You
shouldn't mix
> up a bunch of advanced mathematics, interwoven with some
speculative
> physical hypotheses, with the far more down-to-earth
principles I have
> in mind here. Any physics that needs that highly advanced
mathematics
> can not serve as a foundation for mathematics anyway.
That would imply
> a vicious circle, obviously.
>
> No, what I mean are simple things, such as the denial of
infinities.
>
> Now I know that some of you will argue that far fetched
mathematical
> theories like those about transfinite cardinals and
ordinals "can do
> no harm" to physics. Because physicists know what they
are doing and
> they would not allow the mathematics to take over their
experiments.
How about the far-fetched domain of trigonometry? You
know, where the simple tangent function sticks to nice,
measurable ratios until you get to 90 degrees?
<snip>
Mark L. Fergerson
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