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Re: Teaching of math Was: Re: Engineering or Math?
Posted:
Nov 24, 1997 10:32 AM
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Herman is correct, in almost all respects. I offer one
exception, as listed below:
On 24 Nov 1997, Herman Rubin wrote:
> In article <657aq2$cqu$2@news.ccit.arizona.edu>,
> Elvis Presley <michaels@bigdog.engr.arizona.edu> wrote:
> >Herman Rubin (hrubin@mean.stat.purdue.edu) wrote:
> >: In article <64u3nj$jto$1@news.ccit.arizona.edu>,
> >: Elvis Presley <michaels@bigdog.engr.arizona.edu> wrote:
> >: >Herman Rubin (hrubin@mean.stat.purdue.edu) wrote:
>
> >: Philosophy classes will not affect the mathematics side of the
> >: problem, nor do I think it will help the physics side. You are
> >: expecting from mathematics what it cannot deliver, and failing
> >: to realize what it can, and does, deliver.
>
> >this sounds existentialist to me! but, consider Quantum physics.
> >is light a particle or a wave? surely mathematics and engineering
> >have formulated and used both viewpoints. has either been able
> >to bring us any close to understanding the nature of the universe?
>
> I have no problem with the physical model which states that
> particles have no position or momentum, and that their behavior
> is described mathematically by a wave function. Nor do I have
> any problem with the intuition for this. Physicists have used
> mathematical constructs as explanations. These mathematical
> constructs exist, whether or not the physical model is reasonably
> approximated by it.
>
> >the guys who started HP saw that the Wein Bridge could be used
> >to create an oscillator. today, the vision is trivialized in
> >mathematical concept. yesterday, it wasn't.
>
> The mathematical concept existed yesterday. The use of that
> description to state the approximate physical situation apparently
> did not. The only thing which changed was the use of this specific
> formulation by the physicists.
>
> >: No matter what mathematical model is used for physics, mathematics
> >: is still the same. The use of limits and continuity is needed
> >: even in discrete models. These come in in says which appear at
> >: first to be totally unreasonable.
>
> >: Mathematics is applied to physics, engineering, biology, linguistics,
> >: or anything else by having the people in those areas who understand
> >: the mathematical constants formulate models. Mathematics then gets
> >: additional results. If the results are a bad fit, the model is not
> >: a good approximation to the real world, and the physicist has to go
> >: back to the drawing board.
>
> >i'm sure that some would say that mathematics "is" applied physics
> >because mathematics hasn't created any "new" physics. mathematics
mathematics has not created any 'new' or 'old' physics.
> >only describes physics. a model is limited by the mathematics that
> >describe its physics. perhaps engineers study the prevailing
> >mathematical theory and find where it falls short? then, mathematicians
> >try to "engineer/invent" better mathematics.
>
> Mathematics can be used to describe anything if the practitioners of
> that are able to find the appropriate formulation. If the mathematics
> exists, it may still be a matter of someone finding the connection.
> If the mathematics does not exist, the formulation cannot be made
> until it is invented. I have a reasonable idea of the intuition
> behind the Feynman path integral, but the mathematics is, as far as
> I know, still unclear. It is clear enough that Feynman's claimed
> mathematical formulation is not mathematics.
>
> Not all mathematics "comes from" physics. Mathematics cannot create
> physics or biology or anything else of that type. It can be used to
> model those, if the mathematics is there and the scientist has a
> model covered by the known mathematics.
>
> Newton used the known mathematics to create new physics. Mathematics
> is a completely abstract subject; it exists independently of the "real
> world",
>
Newton did not first come up with the mathematics associated with
his physics. The physics came first, the math model second, as
you cited several times, yet for some reason exempted Newton
from this well know process.
I hope that you agree with this order of thinking, or provide
a clear explanation.
> >the experimentalist and the theorist seem to need each other.
>
>
> --
> This address is for information only. I do not claim that these views
> are those of the Statistics Department or of Purdue University.
> Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
> hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
>
>
Regards,
Milo Gardner
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