Re: Calculus XOR Probability

On Thu, 16 Mar 2006 20:28:30 +0000 (UTC), stephen@xxxxxxxxxx wrote:

Han.deBruijn@xxxxxxxxxxxxxx wrote:
stephen@xxxxxxxxxx wrote:

Why should anyone hesitate to recognize that 'infinite' and 'finite'
are very different things?

If it comes to non-mathematics, physics for example, then the 'finite'
_becomes_ 'infinite' only by increasing the former. Meaning that there
is _no_ essential difference between the two.

But that is not what it means to mathematicians. If you
are going to discuss things with mathematicians, you should
either use mathematical definitions, or make it clear that
you are using a different definition.

In mathematics there is an essential difference between finite
and infinite, which is why mathematicians are not all hesitant
to recognize that finite and infinite are very different things.

'Infinite' in physics is
a way of expressing that something is finite, but very large.

But that is not what 'infinite' means in mathematics.

I don't think it's really the way it's actually used
in physics either. For example when people talk about
a spacetime of infinite extent they mean _infinite_.

Han is just confused by the fact that in various
situations an infinite mathematical object can be
a useful mathematical model for the local behavior
of a very large object. Like if we're studying the
way heat propagates in a huge piece of metal we
simplify the math and still get quite accurate
results by studying brownian motion in R^2. It
doesn't follow that anyone but him actually
thinks that "infinite" and "very large" actually
mean the same thing in physics.

Why you stubbornly refuse to recognize that fact is
quite puzzling. It seems rather childish to insist
everyone use the physicists definition of 'infinite',
assuming of course that is actually the physicists definition.
I seem to recall the last time you provided a quote
to support your position, the quote actually contradicted
your position.

This is amusing. I wrote the paragraph above just speculating
on how things must be - this would seem to confirm my conclusion
that yes, it's just Han not reading things carefully enough.

So large
that it doesn't matter anymore how large. The other way around: finite
though very large means: that physicists still _are_ interested in the
size of such a quantity. Therefore the same quantity can be finite in
one theory and infinite in another. And physics is a prototype for any
other science, if we're talking about these matters.

Who was talking about physics? Was your question about
probability theory supposed to by a physics question?

Anyway, if you want to use "infinite" which literally means
"not finite" to mean "finite, but very large", then go ahead.
Just do not be so foolish to assume that is what everyone
else means by the word, or that is what everyone else should
mean by the word.

Stephen


************************

David C. Ullrich
.

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