Mathematics without physics, a reality?

From: Han de Bruijn (Han.deBruijn_at_DTO.TUDelft.NL)
Date: 11/02/04 

Date: Tue, 02 Nov 2004 16:29:29 +0100

WAS: Re: physics without math, a reality?

Joe (jhelfand@umd.edu) wrote the following in that thread:

> Physics without math? What about math without physics?
>> Who's time are you wasting?

> No seriously, I think physics came before math. And math would be
> nowhere without physics.

> tsk, tsk, tsk. Can the fool (me) defend his positions?! Let me put
> it this way. Suppose you have a generation of humans, and you want to
> see how much math they can do without physics.

   [ .. rest of excellent exposure deleted .. ]

>> Right! Please name me the author who wrote this!

> Well, you can look at the name on the "From" of the message,
> it begins with Joe! It's yours, take it my friend.

A mathematics which is grounded on some basic principles from physics,
would that be a possibility which is worthwile to be considered?

Before starting a flame on me, remember what the alternatives have been.
And also remember that they all have failed miserably. The following is
a quote from 'sci.math'.

In message <ckla8b$p02$3@south.jnrs.ja.net> Robin Chapman wrote
(Re: Zenkin's paper on Cantor):

> Independence from those philosphers who attempt to impose
> normative standards on what and how mathematicians should
> or should not study has been a boon for mathematics.

So far so good. Let it be established that philosophy cannot serve as
a proper foundation of mathematics. But does it mean that mathematics
cannot have any frame of reference other than itself? Is it true that:

        Mathematics is what Mathematicians do

Is it? I severely doubt it!

As Joe has pointed out correctly, no significant part of mathematics
could have been developed without the presence of an outside world.

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.

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.

I think they are underestimating the problem.

As the title of this thread is saying: where would physics be without
mathematics? My background is in mathematical physics - computational
fluid dynamics to be precise - and I can tell you from experience that
some branches of physics can hardly be distinguished from mathematics.
Almost nothimg in fluid dynamics can be understood without mathematics.
I would even say that theoretical fluid dynamics just IS mathematics.
Very much the same holds for other branches of theoretical physics.

Now, if theoretical physics IS mathematics, and if you are developing
theories which can hardly be verified by experiments, such as a theory
of black holes. Then you have to rely entirely and exclusively on your
mathematical apparatus; there is nothing else to rely on. Now suppose
that your mathematical formalism contains elements, which are kind of
suspect from a physical point of view, such as the presence of certain
quantities which may become infinite.

Do you still think then that your conclusions will be correct? Are you
really mastering the inner workings of all the math you use? Why then
do singularities appear in the solutions of the GR equations for black
holes? While every physicist knows that NO such things can occur in a
down to earth environment! Here comes my account of the discovery of
an alike "singularity" in a chemical apparatus, called heat exchanger:

        http://hdebruijn.soo.dto.tudelft.nl/jaar2004/IHXTAK.pdf

See? I want to argue that some of you do not understand how intimately
the mathematics of physics is interwoven with physics itself. And how
misleading this can be, IFF you can't rely on something else than the
mathematics you are using.

Conclusion:

Philosophy is an Idleness in Mathematics (Wittgenstein). But ...
A little bit of Physics would be NO Idleness in Mathematics (HdB)

Han de Bruijn

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