tag:blogger.com,1999:blog-1500584444083499721.post1835862255457655512..comments2024-03-24T09:28:42.755+01:00Comments on CJ on Mathematics and Science: Boltzmann 175 vs 2nd Law by Finite Precision ComputationClaes Johnsonhttp://www.blogger.com/profile/07411413338950388898noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-1500584444083499721.post-35412691233095258772019-07-28T16:11:33.895+02:002019-07-28T16:11:33.895+02:00I comment here because I came to a bit similar con...I comment here because I came to a bit similar conclusion. However, from a bit different angle : the Hilbert space is big. Not Hilbert space (which is what you refer to as finite computation) is countable. Hilbert space is uncountable. <br /><br />The problem might be not in finite vs infinite but in "countable" vs "uncountable".<br /><br />The probability of picking a rational number randomly from R vs an irrational, is zero.<br /><br />Now the quesiton is : what are the equations of motions that describe our universe are "made of"?<br /><br />Is it a finite turing machine ? => rational number picked<br />Or an infinite turing machine => not rational number picked.<br /><br />If we assume that our universe is infinite (the Hilbert space really "exist"), then we assume that we are living in an universe who's laws might or might not be decideable/undecideable algorithms, if they are undecideable (turing machine never halts), then it means, that it is possible that the 2nd law of thermodynamics is "really true". <br /><br />Furthermore, if you want to pick a "universe" randomly, from all possible universes. Then that essentially means that you pick a single number from R (real numbers) and this number represents the "algorithm" that we call "physics". Now, the funny part is that the probability of living in such an universe is ZERO. <br /><br />LOL.<br /><br />Jozsef Hegedushttps://twitter.com/jozsef_hegedusnoreply@blogger.com