Re: Mathematics without physics, a reality?

From: John T Lowry (jlowry100_at_earthlink.net)
Date: 11/02/04 

Date: Tue, 02 Nov 2004 16:02:56 GMT

"Han de Bruijn" <Han.deBruijn@DTO.TUDelft.NL> wrote in message
news:cm894p$fo8$1@news.tudelft.nl...
> WAS: Re: physics without math, a reality?
>
> Joe (jhelfand@umd.edu) wrote the following in that thread:
>
> > Physics without math? What about math without physics?
> >> Who's time are you wasting?
>
> > No seriously, I think physics came before math. And math would be
> > nowhere without physics.
>
> > tsk, tsk, tsk. Can the fool (me) defend his positions?! Let me put
> > it this way. Suppose you have a generation of humans, and you want
> > to
> > see how much math they can do without physics.
>
> [ .. rest of excellent exposure deleted .. ]
>
> >> Right! Please name me the author who wrote this!
>
> > Well, you can look at the name on the "From" of the message,
> > it begins with Joe! It's yours, take it my friend.
>
> A mathematics which is grounded on some basic principles from physics,
> would that be a possibility which is worthwile to be considered?
>
> Before starting a flame on me, remember what the alternatives have
> been.
> And also remember that they all have failed miserably. The following
> is
> a quote from 'sci.math'.
>
> In message <ckla8b$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

I vote for Engineering Before Language!

John Lowry
Flight Physics

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