Re: What is understanding?

["JACK L. URETSKY (C)1998; HEP DIVISION, ARGONNE NATIONAL LAB ARGONNE, IL 60439" <JLU@HEP.ANL.GOV>]

Hi Ludwik-
        I have just arrived at a slap the forehead kind of understanding
of a problem that I will describe at some other time.
        I think that I totally disagree with what you say, because
I think that you incorrectly perceive the role of mathematics, and
your definition of "understanding" is so circumsribed as to lack
utility.
        Mathematics is a language.  We use it to communicate ideas.
Often, the mathematics reminds us of real world experiences, and we
can communicate - often not very well - in terms of those experiences.
        The virtue of communicating through mathematics is that there
is less room for ambiguity in mathematical communications than in communications
through linguistics.  Note, in passing, that mathematicians often communicate
by drawing pictures.
        Feynman's famous statement, which, I am certain, was carefully
constructed, is not a definition of understanding.  It is, however,
a definition of not understanding. In other words, Feynman gave us
a necessary, but not a sufficient, condition to say, "I understand".
Had he known a sufficient condition, I'm sure he would have given it.
        I am currently trying to understand something that arises in
string theory.  My test for understanding, in this case, is that when
I am finished I will be able to describe the results of my investigation
in language that will be understandable to a first year graduate student.

                You write:
**************************************************
A=Understanding is an ability of a human being to generate
     syllogistic derivations from already accepted statements.
B=That definition of understanding is true only in mathematics.
*******************
        (What did you gain by putting "human being" in that
statement?)  Syllogistic logic is a branch of mathematics.  So
B is trivial or redundant.

****************************************************
Physics is not mathematics. Therefore, we should not be
focusing so much on syllogisms in this thread. That is my
personal opinion; correct me if you think that I am wrong.
*************************
        Physics is not: language, tables of numbers, cyclotrons,
bunsen burners, or Helium refrigerators.  All have their role
in doing physics, however, and we must use each as appropriate.
Same with math, especially when we want to communicate difficult
ideas.

**********************************************
Should we accept the idea that understanding means different
things in different disciplines? Or should we seek a general
definition (not necessarily formal) of that concept?
********************
        How about dropping the term.  When communication difficulties
arise, look for other ways to communicate in the particular context
that is relevant at the time.

****************************************************
Uri Ganiel wrote:
> ....: given "If not A then not B" does not lead to: "if A then B",
> since "not B" does not promise anything about A...
*************************
        Uri merely gave you some rules that, when violated, guarantee
a communications breakdown.


        Enough of this nonsense.
                                        Regards,
                                                Jack


        "I scored the next great triumph for science myself,
to wit, how the milk gets into the cow.  Both of us
had marveled over that mystery a long time.  We had
followed the cows around for years - that is, in the
daytime - but had never caught them drinking fluid of
that color."
                Mark Twain, Extract from Eve's
                Autobiography