was REFLECTION AND REFRACTION

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

REPOSTING AGAIN. THE SECOND MESSAGE WAS ALSO POORLY FORMATTED, WHEN 
RECEIVED. I AM SORRY. TRYING TO DO THINGS DIFFERENTLY OFTEN LEADS TO 
ERRORS. FOR SOME REASON THE SAME MESSAGE SENT TO MYSELF LOOKS OK BUT
IT IS NOT OK WHEN BOUNCING FROM PHYS-L.

> 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 for the 
> propagation of light, that's all. Physics doesn't explain; it can only 
> describe. It is a good idea to keep this fact always in the front of your 
> 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. These 
elements of reality can be subdivided into two groups, those about which 
we know and those about which we are ignorant. Some of the unknown 
elements of reality will be discovered 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 groups, 
those that we understand, at least partially, and those which we do not 
understand. No fuzzy logic so far. But what is understanding? It is what 
we choose it to be, as observed by Humpty-Dumpty. ["When I use a word, 
said Humpty-Dumpty, .... it means just what I choose it to mean - neither 
more nor less"]. The same word means different things when we are talking 
about poems, paintings, mathematical relations, musical symphonies, medical 
symptoms, emotional reactions or political events. Each culture, as pointed 
out by C.P. Snow, has its own expectations of what is an acceptable model 
of understanding in its own domain.

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

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

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

                                                   Ludwik Kowalski

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

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