On 12/15/09 12:27 PM, Robert J. Cordingley wrote:
I think this is him:
http://en.wikipedia.org/wiki/William_Thurston
The essay that Russ mentioned only mentions programming in passing.. He
doesn't say anything about it relative to `intellectual challenge', but
he does talk a lot about what is the deep value of his enterprise. The
message is in some sense that the rigor is not the end, it's the means.
Some quotes:
"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 been put into it to make it "almost"
formally correct, it is preposterous to claim that mathematics as we
practice it is anywhere near formally correct.
Mathematics as we practice it is much less formally complete and precise
than other sciences, but it is much less formally complete and precise
for its content than computer programs. The difference has to do not
just with the amount of effort: the kind of effort is qualitatively
different. In large computer programs, a tremendous proportion of
effort must be spent on myriad compatibility issues: making sure that
all of the definitions are consistent, developing "good" data structures
that have useful but not cumbersome generality, deciding on the "right"
generality for functions, etc. The proportion of effort spent on the
working part of a large program, as distinguished from the bookkeeping
part, is surprisingly small. Because of the compatibility issues that
almost inevitably escalate out of hand because the "right" definitions
changes as generality and functionality are added, computer programs
usually need to be rewritten frequently, often from scratch."
and
"The standard of correctness and completeness necessary to get a
computer program to work at all is a couple orders of magnitude higher
than the mathematical community's standard of valid proofs.
Nonetheless, large computer programs, even when they have been very
carefully written and very carefully tested, always seem to have bugs."
..and then he goes on to talk about how mathematics lacks a holistic
sort of factoring process like goes on with large [evolving] programs.
And many other interesting, reasonable remarks.
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