was REFLECTION REFRACTION

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

Date: Thu, 22 Jan 1998 22:00:24 -0800
=46rom: Leigh Palmer <palmer@sfu.ca>
Subject: Re: REFRACTION - REFLECTION

> Fermat's principle doesn't explain anything. It is a valid model fo=
r the=20
> propagation of light, that's all. Physics doesn't explain; it can o=
nly=20
> describe. It is a good idea to keep this fact always in the front o=
f your=20
> mind. Not doing so is the cognitive error ....

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

Events known to us (as individuals) can also be subdivided into two g=
roups,=20
those that we understand, at least partially, and those which we do n=
ot=20
understand. No fuzzy logic so far. But what is understanding? It is w=
hat=20
we choose it to be, as observed by Humpty-Dumpty. [=D2When I use a wo=
rd,=20
said Humpty-Dumpty, .... it means just what I choose it to mean - nei=
ther=20
more nor less=D3]. The same word means different things when we are t=
alking=20
about poems, paintings, mathematical relations, musical symphonies, m=
edical=20
symptoms, emotional reactions or political events. Each culture, as p=
ointed=20
out by C.P. Snow, has its own expectations of what is an acceptable m=
odel=20
of understanding in its own domain.

A philosopher, whose domain is everything, would say that understandi=
ng is=20
a psychological sensation of conceptual mastery; a state of satisfact=
ion=20
which enables us to =D2make sense=D3 (another fuzzy logic term) of th=
e world=20
in which we function. A physicist could define understanding as a ple=
asant=20
state of mind which enables him to make correct predictions about mat=
erial=20
phenomena in this world. What do we mean by saying that =D2A explains=
 B=D3?=20
Aha, another new word. If I were Humpty-Dumpty I would say that an=
=20
explanation is a process of trying to reach understanding. The same=
=20
process may work on some students and not work on others. It depends =
on=20
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 =
new=20
programming language. Wow,it may be =D2smooth and carefully paced=
=D3 for some=20
readers but I was lost in the first chapter and quickly decided that =
=D2this=20
stuff is not for me=D3. The first contact with Perl turned me off. So=
unds=20
familiar? So I turned on the TV and watched a program about - what a=
=20
coincidence - understanding of music. They said, =D2music is a way of=
=20
thinking=D3, a "non-verbal communicator=D3 and a tool =D2to move peop=
le=20
emotionally=D3. Some are moved, others are not.

Does the Fermat Principle explain refraction? It does for me. Why?=
=20
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 may=
=20
add that "the internal properties of a tennis ball do not change in t=
he=20
process".) I have a model of explanation and my understanding can be=
=20
defined as a process of matching observations to that model. My=20
understanding may not be valuable to her or him but that is their=
=20
problem, not mine. Unless I am their teacher, 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 eff=
orts.
While he may accomodate his thought to the ideas of others, it is onl=
y as=20
he tries those ideas out within the context of the ideas he has previ=
ously
acquired that he makes them his own."
                                                  Jean Piaget