RE: The significance of mathematics - and why it can prove its own incompleteness
Hey everyone! This is my very first post/comment on steemit, excited to have joined the community :)
I'm glad I found your article on Godel in one of the first scrolls through new posts (I bookmarked the post and am just commenting now which probably isn't ideal), I've become kind of obsessed with figuring out what the incompleteness theorems are saying to their fullest extent... they're mind-boggling. I won't give any of my own half-baked interpretations but thought I'd throw out the stuff I've been reading or have watched that have helped.
I watched Rebecca Goldstein and Gregory Chaitin talk about it in this video, it's an awesome introduction and had me hooked.
That led me to Goldstein's book Incompleteness: The Proof and Paradox of Kurt Gödel which is terrific and nontechnical for the layperson (me).
Godel's Proof by Ernest Nagel is probably a good step #2 into the quagmire.
And then there's stuff like Douglas Hofstadter's Godel, Escher, Bach: An Eternal Golden Braid which was a huge bestseller at the time apparently. The guy is a genius, and actually makes reading about these technical things fun. His use of language is incredible, and the whole book is sort of half-puzzle half-narrative, I've only made stabs at it because it's such heady stuff. (I also found out David Chalmers, of "the hard problem of consciousness" fame, if anyone else is into philosophy of mind here, was a student of Hofstadter's which I think is a cool tidbit.)
There's obviously a ton out there but these were good starts for me. I'm not entirely sure how to go about commenting and Steeming, being a newbie, so I hope this wasn't overkill!
Thanks for posting, I really enjoyed it! (And a little peeved I missed out on the convo...)
Those are very thoughtful recommendations. I've read 'Gödel, Escher, Bach' myself and have to agree that it offers some clever insight although it can get a bit lengthy at times.
Glad to have you here ;)