3 ms·
This theorem seems to be like monads: Someone posts about it on the internet, someone doesn't understand and asks for help, someone comes along and writes a sim
by bulatb 7y ago
This theorem seems to be like monads: Someone posts about it on the internet, someone doesn't understand and asks for help, someone comes along and writes a simple explanation that seems to make sense, then someone says that explanation is completely wrong (but here's this totally inscrutable "correct" one... which someone comes along and says is even worse.)
And everyone is left confused.
- anaphor 7y agoJust read this book, IMO https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814758371 https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081... It's only 160 pages and gives what seems to be a good explanation of the basics.
- novalis78 7y agoCurrently reading Morris Kline’s “Loss of certainty” - a beautiful very readable work that elucidates the relationship of Mathematics with concepts of ‘truth’ and ‘reality’ throughout mathematical history. https://www.amazon.com/dp/0195030850/ref=cm_sw_r_cp_api_i_aJ.BDb2XFHVCA https://www.amazon.com/dp/0195030850/ref=cm_sw_r_cp_api_i_aJ...
- theWheez 7y agoLike monads, I think the issue comes from "frames" of thinking. You cannot understand monads in terms of functions as is understood in most languages. You also can't understand it in terms of its common uses like I/O. Yes, it can be applied in those domains, but it is like explaining the internet with electricity.
- adamnemecek 7y agoFunny that you mention this, you can construct monads with this in some sense. GCT talks about adjointness (it's analogous to William Levwere's work "adjointness in foundations"). One can build monads from adjoint functors. http://www.stephendiehl.com/posts/adjunctions.html http://www.stephendiehl.com/posts/adjunctions.html
- bulatb 7y agoI was mistakenly thinking of the incompleteness theorems when I wrote this, but I guess it kind of works for this one too. https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...