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There's a Hole at the Bottom of Math

Posted: Wed May 26, 2021 3:12 am
by Philo Sofee
https://www.youtube.com/watch?v=HeQX2HjkcNo

One of the most spectacularly informative, mysterious, and incredible videos I have ever watched. It has it all, math, science, infinity, Godel, Hilbert, Russell, logic, Turing, computers, knowledge, and our place in the world of knowing. MUST SEE, I promise it's the singular most spectacular 1/2 you will spend in the next 6 months... Just flippin WOW. The graphics are absolutely outta sight!!! The concept is deeply, viscerally, VERY disturbing...

Re: There's a Hole at the Bottom of Math

Posted: Wed May 26, 2021 8:14 am
by Chap
So this is basically about Godel's (1931) proofs that any consistent formal system will contain true statements that cannot be proved within the system, and that the system cannot prove its own consistency?

Re: There's a Hole at the Bottom of Math

Posted: Wed May 26, 2021 9:41 pm
by Gunnar
I highly recommend the Pulitzer Prize winning book, Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter on this and related subjects. It is one of the most interesting and profound books I ever read!

Re: There's a Hole at the Bottom of Math

Posted: Thu May 27, 2021 11:37 pm
by Philo Sofee
Gunnar wrote:
Wed May 26, 2021 9:41 pm
I highly recommend the Pulitzer Prize winning book, Gödel, Escher, Bach: An Eternal Golden Braid, by Douglas Hofstadter on this and related subjects. It is one of the most interesting and profound books I ever read!
Yes it is! It's been quite a while since I have read it. I also really enjoyed his magnus tome Metamagical Themas...

And, honestly, one of my favorites on the subject is Rudy Rucker's Infinity and the Mind. That was one of my first full book exposures to infinity, and I am still sputtering... :D

Re: There's a Hole at the Bottom of Math

Posted: Fri May 28, 2021 9:16 am
by Chap
Yup - I remember that as a good book, though I read it a l o o o o o ng time ago!