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Re: what is understanding?




On Wed, 09 Jul 1997 15:54:51 -0500 (CDT) trappe@PHYSICS.UTEXAS.EDU (Karl
Trappe) writes:
I agree with Leigh and Hugh. I even tell my students that physics is
a
series of LIES. The question then becomes one of deciding how much of
a
lie we are willing to accept. To clarify, the most accurate
description of
nature is nature itself. I point out that in this one extreme of
accuracately identifying physics you can just "look" at the phenomena
and
marvel--kind of an "Oh, Wow!"
When you start "taking it apart", you begin to see different aspects
very
accurately, but have to tell yourself "lies" in order to understand
each
single aspect.

What I recall from freshman physics was being *told* to neglect
friction in
a certain problem. At the same time, I was learning that to accept a
false
premise would lead you to a false conclusion. So, neglecting friction
was
a LIE, and I fought that instructor like a kid learning to swim fights
water. Eventually I came to understand that you have to accept the
"lies"
in order to get some deeper understanding of the "parts". You can
then
correct the "lies" (often exchanging them for other ones) as you gain
comprehension.

My most rewarding confirmation of this came when my step-father loaned
me a
1800's encyclopedia that his parents had passed to him. In it I read
about
the luminiferous either. It was not presented as a theory. These
"scientist" were dead serious, and their (now rediculous) description
taught me that a little humility in what we call "the truth"
("understanding") might serve us more kindly in *our* old age, when
others
read our descriptions of nature, and want to laugh their heads off at
our
stupidity. Karl

I think understanding of physics is never attained. One can always
see deeper into a subject even after one feels one understands it
satisfactorily. Understanding admits of various degrees. Even the
simplest of concepts can be deeper than an expert on the concept
realizes. I have seen the understanding of the entire physics
community deepen beyond the previous understanding of even the
acknowledged world expert too many times to accept the
pronouncements of authority as final.

Leigh

It seems to me that Leigh has put his finger on an important aspect
of
understanding that has not come up in this thread (at least I haven't
noticed it). We keep thinking of understanding as a binary
quantity-either
you have it or you don't. This is clearly not true. Understanding is
a
continuum ranging from little or none to truly profound. Most physics
teachers are somewhere in the middle and the question we need to
address is
what level of understanding is appropriate for students at various
levels,
and should it be evenly spread across the spectrum of topics we deal
with
or is is acceptable if the depth varies from topic to topic, and if
so,
which topics are the most important to put our effort into to make
sure
that the understanding has passed beyond the little or none stage?

I've seen a dozen different definitions of understanding in this
thread,
some better than others, but none that satisfy me. Unfortunately, I
haven't
got any improvements to offer. It begins to seem to me that
understanding
may be one of those words like art-we may not be able to define it
but we
usually know it when we see it.


***************************************************************************
*****
Hugh Haskell

<mailto://hhaskell@mindspring.com>

The box said "Requires Windows 95 or better." So I bought a
Macintosh.
***************************************************************************
*****

Dr. Karl I. Trappe Desk Phone: (512)
471-4152
Physics Dept, Mail Stop C-1600 Demo Office: (512)
471-5411
The University of Texas at Austin Home Phone: (512)
264-1616
Austin, Texas 78712-1081



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

I am not so pessimistic. I realize that perfect understanding is
unattainable by its very nature - and ours, but we can do very well
linguistically. Also, we can draw a very useful picture - I keep
promising. See Tarski, Alfred, "The Concept of Truth in Formalized
Languages", in *Logic, Semantics,
Metamathematics*, 2cd. Ed., Ed. John Corcoran, Trans. J.H. Woodger,
Hackett, ...

This is on the right track although Tarski is quite pessimistic. I think
we need not be.

Clearly, the problem of identifying a true statement is closely related
to the question "What is understanding?". I believe we can solve our
problem once we get a little more insight into how to identify a true statement, which, by the way, cannot be done by any known method unless the
statement be in a restricted, low-order, technical language such as the
symbolism of *Principia Mathematica*; nevertheless, this does not leave
us completely helpless. The identification takes place in a
higher-order language than that in which the statement is written. But,
that may be nearly always the case in physics where a restricted
technical language is our natural medium.

I must be quiet for awhile until I am ready to present a solution.

Regards to all meta-physicians / Tom