Careful, here, everybody.
I don't want to be party to a misrepresentation of Thurston's point. It is not
that maths is easier that computer programming or that computer programmers are
more rigorous than mathematicians. It is that the heart of mathematical proof
is not in its rigor. Rigor often comes AFTER the proof is, to all intents and
purposes, agreed to.
Russ has kindly provided a link to the original article; don't take the word
of a former english major. Have a look at it.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]
----- Original Message -----
From: Saul Caganoff
To: [email protected];The Friday Morning Applied Complexity Coffee Group
Cc: [email protected]; The Friday Morning Applied Complexity Coffee
Group; Sean Moody
Sent: 12/14/2009 11:55:47 PM
Subject: Re: [FRIAM] Thurston: On Proof and progress
Programming is much easier because much of it is a process of trial and error.
You can generate any old crap (many programmers do) and gradually refine it by
successively throwing it at:
a) a compiler,
b) a set of unit tests (written by yourself)
c) a set of system tests
d) a set of acceptance tests.
The ultimate determinant of "correctness" is whether the customer agrees to pay
you for your deliverables. This is not necessarily related to "correctness" or
"fit for purpose".
I don't believe at all that the bar for acceptable mathematical proof is lower
than that for programming. It couldn't be!
Regards,
Saul
On 15/12/2009, at 5:19 PM, Russ Abbott <[email protected]> wrote:
Quite flattering to us programmers. (Here's the actual article.) My
experience, though, is that programming is easier. (I was a mediocre math major
as an undergraduate and then found computer science, something I could actually
do.) A similar argument might conclude that driving from New York to Los
Angeles is even harder than programming because of all the details one must get
right to arrive in the right place with crashing into anything. But that
doesn't mean it's either difficult or formally correct.
-- Russ Abbott
_____________________________________________
Professor, Computer Science
California State University, Los Angeles
Cell phone: 310-621-3805
o Check out my blog at http://russabbott.blogspot.com/
On Mon, Dec 14, 2009 at 9:43 PM, Nicholas Thompson <[email protected]>
wrote:
Dear Friammers,
We have decided to carry on from our seminar on Emergence to one on
Mathematical Thinking. Although we don't meet for a month, I found myself
reading the first assignment, Thurston's On Proof and Progress in Mathematics.
Now Thurston loves mathematics and is apparently good at it, but he is firm in
arguing that the process of proof is not as the normative account would have
it. Given our local debates about the ideal of formalism and given my
suspicion that many computer programmers suffer from math envy (the way
experimental psychologists suffer from physics envy), I was astonished by the
following paragraphs.
The standared of correctness and completeness necessary to get a computer
program to work at all is a couple of orders of magnitude higher than the
mathematical community's standard of valid proof.
Astonished, and yet, instantly convinced that it was true. Note that Thurston
is proud of how mathematicians do their work; no criticism here.
I think that mathematics is one of the most intellectually gratifying of huan
activities. Because we have a high standard for clear and convincing thinking
and because we place a high value on listening to and trying to understand each
other, we don't engage in interminable arguments and endless redoing of our
mathematics. We are prepared to be convinced by others. Intellctually,
mathematics moves very quickly. Entire mathmatical landscapes change and
change again in amazing ways during a single career.
When one considers how hard it is to write a computer program even approaching
the intellectual scope of a good mathematical paper and how much greater time
and effort have to be put into it to make it 'almost'formally correct, it is
preposterous to claim that mathematics as we practice is any where near
formally corrrect.
You would almost think that computer programming was the Queen of the Sciences.
Nick
I wonder what you all think about it.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([email protected])
http://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]
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FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
