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Re: Tom's essay


On Sun, 13 Jul 97 20:51:05 EDT LUDWIK KOWALSKI
<kowalskil@alpha.montclair.edu> writes:
On Sun, 13 Jul 1997 twayburn@juno.com (Thomas L Wayburn) wrote:

Perhaps someone will read my diagrammatic approach to understanding?

I have improved the picture, lately, with a model that incorporates
four categories: (1) W, the world, (2) M, mental images, (3) P,
perceptions, and (4) W*, the "reader's" conception of the world in
which he imagines phenomena occurring.

I did try to penetrate your message, Tom, twice, but not "with a
pencil
in my hand". This was not enough for me to grasp its usefulness (sorry

for being so direct). You said you have a mathematical model of
understanding.
To me "a mathematical thing" would be somthing that quantifies a
concept,
does numerical calculations or proves and disproves other things. I do
not
know how the object you created can be used for such purposes.

If I were you I would try to present the essey to mathematical
logicians
who are familiar with the vocabulary and symbolism of your essay, and
with
the references you give. Showing it to people like me may not provide
you
with valid criticism. Your ideas may be brilliant but people like me
may
not be able to recognize this.

Keep in mind that my background in mathematical logic is only two bits

above zero. I am still waiting for somebody more knowledgable to
comment
here on your message. Perhaps then I will see how it can help us to
"map
ideas from one mind to another". Please do not be discouraged; your
efforts
to help us understand udnersatnding were probably appreciated by many,
even
by those who did not understand you.
Ludwik Kowalski

Hi Lufwik, Unfortunately, I could not present the diagrams. The point is that, if the diagram commutes, the statement is successful and
understanding has been achieved.
Nowadays, mathematicians "speak" more so in diagrams (of triangles and
squares, etc.) than was done in the nineteenth century. What one can
do with them is define when an understanding has occurred.
Occasionally, actual computational results are achieved, but this is not
the main idea. I was afraid it would not be understood. Of course,
*you* must draw the diagrams with your pencil to have a fighting chance.
What prompted a not inconsiderable effort is the wonderful vagueness of
every attempt by a physicist to define (or even describe)
understanding. You all seemed so helpless. Believe me, I meant well.
And, oh yes, it goes into a chapter of a book, but with actual pictures
and slicker notation. Regards / Tom

P.S. Thanks for taking the trouble to answer.