so i spent the last two days having a shit fit about godel's theorem
- Thread starter minxnim
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board: oh, i think i'll just go down for a few days
me: OH I THINK I'LL GET MYSELF WRAPPED INTO A NATURAL NUMBER PARADOX NIGHTMARE THANKS
me: OH I THINK I'LL GET MYSELF WRAPPED INTO A NATURAL NUMBER PARADOX NIGHTMARE THANKS
goatschool
Member
FrostGiant
Mr. Pibb > Dr. Pepper
Ok. For some reason I have no idea what these theorems are and I'm a mechanical engineer. Is that a bad thing?
frostgiant: godel basically hypothesized that any axiomatic number system that claimed it was all encompassing (always true and could express all true statements about math and natural numbers) was impossible because there would always be a true statement that was not provable within that system. thus : incompleteness.
douglas hofstadter wrote about it. its a little more complicated than what i wrote above, but his theorem seems to be provable by a contradiction of a statement like a paradox.
douglas hofstadter wrote about it. its a little more complicated than what i wrote above, but his theorem seems to be provable by a contradiction of a statement like a paradox.
VangelicSurgeon
Three Star General
FrostGiant
Mr. Pibb > Dr. Pepper
azal
love is the answer
FrostGiant
Mr. Pibb > Dr. Pepper
azal
love is the answer
FrostGiant
Mr. Pibb > Dr. Pepper
Preppy: I read the Hofstadter book a couple years back. It was good and I should revisit it.
I should also point out something about it that I think's irresponsible on Hofstadter's part: nowhere in his book does he mention that the mathematical system Godel initially proved to be incomplete, set theory, is IMMENSELY useful for musicians. That would tie in quite nicely with the musical side of the book, I think. In fact, a large part of comtemporary music theory and, as a result, composition relies heavily upon set theory and its extensions like partitioning and combinatorics. I guess the ommission of post-tonal theory and serialism in the book is an example of Godel's incompleteness theorem at work, albiet a rather trivial one.
I should also point out something about it that I think's irresponsible on Hofstadter's part: nowhere in his book does he mention that the mathematical system Godel initially proved to be incomplete, set theory, is IMMENSELY useful for musicians. That would tie in quite nicely with the musical side of the book, I think. In fact, a large part of comtemporary music theory and, as a result, composition relies heavily upon set theory and its extensions like partitioning and combinatorics. I guess the ommission of post-tonal theory and serialism in the book is an example of Godel's incompleteness theorem at work, albiet a rather trivial one.
i honestly too never really understood by hofstadter didn't go into the set theory/music idea more. i am not an expert on set theory by any means, but hofstadter is pretty obsessed with music. he must be saving up for some other bizarre and life alteringly engrossing book or something... i hope. have you read all his articles in metamagical themas? longest book, but most freakin absorbing thing ever. his strange concept of einstein's brain in book form at his time of death still makes me sit up at night and sort of geek out.
VangelicSurgeon
Three Star General
[(beer cans * pliers) + gasoline]/(Bandana * X) = 0
where X = Days Exposed to Sun * Blood Alchohol Level
where X = Days Exposed to Sun * Blood Alchohol Level
VangelicSurgeon
Three Star General
this cat epitomizes the endless mathematical loop that created consciousness via evolution of self-referential movement.......... to me... somehow....
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