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
