Originally shared by Event Horizon
"No matter how far mathematics progresses and no matter how many problems are solved, there will always be, thanks to Gödel, fresh questions to ask and fresh ideas to discover. It is my hope that we may be able to prove the world of physics as inexhaustible as the world of mathematics... If it should turn out that the whole of physical reality can be described by a finite set of equations, I would feel disappointed."
- F. J. Dyson. Infinite in all Directions. London: Penguin Books, 1990, p. 53.
The idea that Gödel's logical insights might reflect deeply upon physics is fascinating. I am still working hard to wrap my cortex fully around the logic and the theorems but, as I understand it, applied in this context of physical laws this suggests that there would always be further and deeper iterations and recombinatory organisational constellations of physical models and theory. This strikes me as absolutely and utterly beautiful.
It is even more fun! For certain amount of people it is sexy to say that reality has only finite number of states. But in such circumstances, theorem of Gödel about Logic completeness is no longer valid, so in fact you cannot expect for theorems with proofs to have a models and vice versa...
ReplyDeleteTake a look here: https://en.m.wikipedia.org/wiki/Trakhtenbrot%27s_theorem
en.m.wikipedia.org - Trakhtenbrot's theorem - Wikipedia
I got through an about 50 page overview of Gödel's proof. I think it's fair to say I got the gist of it. It's certainly tempting to think that it somehow applies to physics or any other study.
ReplyDeleteI love Gödel. What an inspiration.
ReplyDeleteBTW: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
ReplyDeleteA nice watch about similar topics:
ReplyDeleteDangerous Knowledge (Spanish Subtitles) 1/2 - on Vimeo:
vimeo.com - Dangerous Knowledge (Spanish Subtitles) 1/2