Gödel and the limits of logic
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Gödel and the limits of logic
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Re: Gödel and the limits of logic
#2GEB sits on my nightstand with too little time to be read. It might have to get bumped up the priority queue a bit.
Re: Gödel and the limits of logic
#3GEB sits on my nightstand with too little time to be read. It might have to get bumped up the priority queue a bit.
Likewise. I pulled it off the bookshelf last week and set it on my coffee table, but still haven't had a chance to dive in. This weekend hopefully.
Re: Gödel and the limits of logic
#4[deleted]
Re: Gödel and the limits of logic
#5In 1949 he demonstrated that universes in which time travel into the past is possible were compatible with Einstein's equations.
Wait, what?! Anyone have a ref?
Edit: Thanks to andyjohnson and vbtemp. TIA for others too.
Re: Gödel and the limits of logic
#6Its always fascinating to read about Gödel. I have not read GEB, yet reading about his findings has really changed the way I think about things.
Thanks for posting this article.
Re: Gödel and the limits of logic
#7In 1949 he demonstrated that universes in which time travel into the past is possible were compatible with Einstein's equations. Wait, what?! Anyone have a ref? Edit: Thanks to andyjohnson and vbtemp. TIA for others too.
Look at http://en.wikipedia.org/wiki/Closed_timelike_curve
I.e., "Closed timelike curves". I'm not expert in this matter, but it's a conceptual possibility that fits into general relativity.
Re: Gödel and the limits of logic
#8In 1949 he demonstrated that universes in which time travel into the past is possible were compatible with Einstein's equations. Wait, what?! Anyone have a ref? Edit: Thanks to andyjohnson and vbtemp. TIA for others too.
He discovered a solution to Einstein's field equations that permits closed timelike curves if the universe is rotating.
http://en.wikipedia.org/wiki/Godel_metric
"This solution has many strange properties, discussed below, in particular the existence of closed timelike curves which would allow for a form of time travel in the type of universe described by the solution. Its definition is somewhat artificial (the value of the cosmological constant must be carefully chosen to match the density of the dust grains), but this spacetime is regarded as an important pedagogical example"
Re: Gödel and the limits of logic
#9In 1949 he demonstrated that universes in which time travel into the past is possible were compatible with Einstein's equations. Wait, what?! Anyone have a ref? Edit: Thanks to andyjohnson and vbtemp. TIA for others too.
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Re: Gödel and the limits of logic
#10When I first became fascinated with incompleteness (following initial coursework in theory of computation), it kind of became my "religion" of sorts for a while. But as many mathematicians lament, the Incompleteness Theorem is one of the most popularly abused proofs of all time - used for non-experts to assert their own half-baked pseudo-philosophy (of course, the same goes for quantum mechanics as well).
These are a few books I recommend:
"Incompleteness - The proof and paradox of Kurt Gödel" by Rebecca Goldstein
"Gödel's Proof" by Ernst Nagel (it's a tiny book, not too technical, but technical enough for anyone with a solid CS background to appreciate and understand)