The philosopher Garfinkel was fond of citing Willy Sutton on questions like
this:
REPORTER: Mr Sutton, why do you rob banks?
WILLIE: 'Cuz that's where the money is.
Without a theorem, it's impossible to to know what the question is.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University (nthomp...@clarku.edu)
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]
----- Original Message -----
From: ERIC P. CHARLES
To: Russ Abbott
Cc: The Friday Morning Applied Complexity Coffee Group
Sent: 4/25/2010 11:22:42 AM
Subject: Re: [FRIAM] Why are there theorems?
Russ,
Bypassing all the other replies, I find this question very interesting. When
faced with questions like this I usually give an answer, am told it is not
satisfactory, give another answer, am told it is not satisfactory, etc. Then at
some point I ask the questioner to give me examples of the types of answers
they would find acceptable. So.... well.... can we skip to that part? For
example, would an acceptable answer be in terms of:
Something about people who do math, explaining why they make theorems?
Something about the math people, explaining why theorems are necessary for
those activities?
Something about math itself showing theorems to be an essential part of any
math?
Something about the history of doing-math, showing why we now do math with
theorems when we otherwise might not have?
Something about the virtues of doing math different ways, showing the theorem
enhanced way to be virtuous in some respect?
Something about the limitations of human cognition, demonstrating why we need
theorems instead of simply knowing the truth?
Etc.
My hunch is that some of those types of answers would be of more interest to
you than others.
Eric
On Sun, Apr 25, 2010 12:47 AM, Russ Abbott <russ.abb...@gmail.com> wrote:
I have what probably seems like a strange question: why are there theorems? A
theorem is essentially a statement to the effect that some domain is structured
in a particular way. If the theorem is interesting, the structure characterized
by the theorem is hidden and perhaps surprising. So the question is: why do so
many structures have hidden internal structures?
Take the natural numbers: 0, 1, 2, 3, 4, ... It seems so simple: just one
thing following another. Yet we have number theory, which is about the
structures hidden within the naturals. So the naturals aren't just one thing
following another. Why not? Why should there be any hidden structure?
If something as simple as the naturals has inevitable hidden structure, is
there anything that doesn't? Is everything more complex than it seems on its
surface? If so, why is that? If not, what's a good example of something that
isn't.
-- Russ Abbott
______________________________________
Professor, Computer Science
California State University, Los Angeles
cell: 310-621-3805
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
______________________________________
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FRIAM Applied Complexity Group listserv
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Eric Charles
Professional Student and
Assistant Professor of Psychology
Penn State University
Altoona, PA 16601
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Meets Fridays 9a-11:30 at cafe at St. John's College
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