was REFLECTION AND REFRACTION

[LUDWIK KOWALSKI <KOWALSKIL@alpha.montclair.edu>]

REPOSTING. THE FIRST MESSAGE WAS POORLY FORMATTED, WHEN RECEIVED.

> Date: Thu, 22 Jan 1998 22:00:24 -0800
> From: Leigh Palmer <palmer@sfu.ca>
> Subject: Re: REFRACTION - REFLECTION
>
> Fermat's principle doesn't explain anything. It is a valid model=
=20
> for the propagation of light, that's all. Physics doesn't explain;=
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> it can only describe. It is a good idea to keep this fact always=
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> in the front of your mind. Not doing so is the cognitive error ...

Let me try this again; we were discussing the nature of=20
explanations and understanding last year. The world consists of=20
things and events. These elements of reality can be subdivided into=
=20
two groups, those about which we know and those about which we are=
=20
ignorant. Some of the unknown elements of reality will be discovered=
=20
in the future. Yes, this is trivial but one has to start somewhere.

Events known to us (as individuals) can also be subdivided into two=
=20
groups, those that we understand, at least partially, and those=20
which we do not understand. No fuzzy logic so far. But what is=20
understanding? It is what we choose it to be, as observed by=20
Humpty-Dumpty. [=D2When I use a word, said Humpty-Dumpty, .... it=
=20
means just what I choose it to mean - neither more nor less=D3].=20
The same word means different things when we are talking about=20
poems, paintings, mathematical relations, musical symphonies,=20
medical symptoms, emotional reactions or political events. Each=20
culture, as pointed out by C.P. Snow, has its own expectations of=
=20
what is an acceptable model of understanding in its own domain.

A philosopher, whose domain is everything, would say that=20
understanding is a psychological sensation of conceptual=20
mastery; a state of satisfaction which enables us to =D2make=20
sense=D3 (another fuzzy logic term) of the world in which we=20
function. A physicist could define understanding as a pleasant=20
state of mind which enables him to make correct predictions about=
=20
material phenomena in this world. What do we mean by saying that=20
=D2A explains B=D3? Aha, another new word. If I were Humpty-Dumpty=
=20
I would say that an explanation is a process of trying to reach=20
understanding. The same process may work on some students and not=
=20
work on others. It depends on what they already know and understand.=
=20

Last night I started to read a little book called =D2Learning Perl=
=D3.=20
According to its preface, the book is "a gentle introduction=D3 to a=
=20
new programming language. Wow,it may be =D2smooth and carefully paced=
=D3=20
for some readers but I was lost in the first chapter and quickly=20
decided that =D2this stuff is not for me=D3. The first contact with P=
erl=20
turned me off. Sounds familiar? So I turned on the TV and watched a=
=20
program about - what a coincidence - understanding of music. They=
=20
said, =D2music is a way of thinking=D3, a "non-verbal communicator=
=D3 and=20
a tool =D2to move people emotionally=D3. Some are moved, others are n=
ot.

Does the Fermat Principle explain refraction? It does for me. Why?=
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For the same reason for which the energy conservation law makes me=
=20
understand why a tennis ball released from a rest position never=20
bounces to a higher elevation. (For those who are more pedantic I=
=20
may add that "the internal properties of a tennis ball do not=20
change in the process".) I have a model of explanation and my=20
understanding can be defined as a process of matching observations=
=20
to that model. My understanding may not be valuable to her or him=
=20
but that is their problem, not mine. Unless I am their teacher,=20
of course.
                                                  Ludwik Kowalski

My wife, Linda, a psychologist, tells me that all new learning is=
=20
assimilated to the student's already existing mental structures.=20
And here is a quotation about this:

"The child comes to an understanding of the world through his own=
=20
efforts. While he may accomodate his thought to the ideas of=20
others, it is only as he tries those ideas out within the context=
=20
of the ideas he has previously acquired that he makes them his own."

                                                  Jean Piaget