Bijan Parsia <firstname.lastname@example.org> wrote:
| >" Call a program ``elegant'' if no smaller program has the same output.
Chaitin's seems to have used "elegant" in the same way as, say, physicists
chose the names "charm" and "beauty" -- because it was cute! His work would
read equally well (perhaps better, for *this* crowd!) if he had used the word
"minimal" (or some other rough equivalent) instead of "elegant".
| That all being said, I guess I should go read the paper. Unless, of
| course, it has nothing to do with capturing the logic of the more
| problematic value predicates we use with regard to various computer
| science entities. That's what *I'm* interested in.
Chaitin's work has nothing to do with "programming language advocacy", rather,
it's about an information-theoretic approach to computability, and some
implications that arise from that approach to issues such as completeness
(or rather, incompleteness).
In particular, he shows several alternate (and probably a lot easier to
understand) derivations of Godel's first incompleteness theorem, including
some based on the Berry Paradox ("the smallest <XYZ> not describable by a
sentence/program smaller than <this one>") rather than the Liar's Paradox
("this statement is false") used by Godel. (Well, he says Godel actually
used "this statement is not provable in formal system <this one>").
His larger result is a claim that incompleteness is not a niggling artifact
of the formal system Godel chose to work in, but a much more serious universal
Personally, I found it quite fascinating! However, it has nothing at all
to do with "pretty" versus "ugly" languages.
Rob Warnock, 7L-551 email@example.com http://reality.sgi.com/rpw3/
Silicon Graphics, Inc. Phone: 650-933-1673 [New area code!]
2011 N. Shoreline Blvd. FAX: 650-933-4392
Mountain View, CA 94043 PP-ASEL-IA