tag:blogger.com,1999:blog-8148573551417578681.post6529832492028036546..comments2021-09-24T12:28:25.828-07:00Comments on Dark Buzz: Aaronson says Goedel gremlins are dormantRogerhttp://www.blogger.com/profile/03474078324293158376noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8148573551417578681.post-46388361125780833532016-04-07T06:10:30.451-07:002016-04-07T06:10:30.451-07:00When people make a big deal out of undecidability,...When people make a big deal out of undecidability, I just ask them if they stop beating their wife. The law of the excluded middle was always stupid. Furthermore, why ask a system you don't trust if it's consistent? It's pure circularity! No need for a fancy proof, but for some reason books get written about it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-79341757572971972252016-04-07T05:31:59.062-07:002016-04-07T05:31:59.062-07:00In other words, you can construct nonsense linguis...In other words, you can construct nonsense linguistics AND/OR nonsense mathematics to cover over a bad premise. It doesn't matter what descriptive language you use, the language itself can not protect you from bad ideas and lies. What a tangled web we weave when we practice to deceive all the way down baby.CFTnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-62400139854848625252016-04-07T03:29:18.379-07:002016-04-07T03:29:18.379-07:00I think Motl has a real point about P vs NP, at le...I think Motl has a real point about P vs NP, at least in a theoretical sense, but the entire question is stupid because it's so open-ended and requires that proof methods condense the entire complexity of recursive algorithms to say anything either way. Are there a finite number of brute-force cases and the rest reachable by indexed pre-computation and fast heuristics? Besides threading, Turing machines don't even take into account a modern machine's constant-time jump instructions.<br /><br />The points about Godel are even more mislead than you let on. Godel is just Cantor in disguise and professional logicians and mathematicians seriously disappoint me. Very unintelligent discussions have gone on:<br /><br />Self-referential sentence proofs: Godel, Rosser, Kleene, Post, Church, Turing, Smullyan, Jech, Woodin<br />Epsilon-naught induction proofs: Kripke, Paris-Harrington, Goodstein, Hydra<br />Kolmogorov complexity proofs: Chaitin, Boolos<br /><br />Godel's result was reformulated by others in very simple terms. Given a computable axiomatic system A construct a program GODEL that does the following:<br /><br />1. Prints its own code into a variable R. (Hint: Make quining a subroutine)<br />2. Go on deducing all consequences of A, looking for a proof of the statement "R does not halt."<br />3. If it finds this statement, it halts.<br /><br />Cantor makes a more obvious appearance in the non-standard model, which requires infinite non-natural numbers after the natural numbers. Interestingly, one of the leading Godel scholars, Solomon Feferman, dispenses with Cantor but still, for some reason, entertains this incompleteness garbage. Incompleteness can be done away with using an infinitely axiomatizable system but that very fact reveals what it's really about. Poincare knew it was trivial all along.<br /><br />The same way you can't complete the infinity of reals, you can't complete the entire list of computer programs. The initial assumptions are the problem. Furthermore, the Godel sentence is basically a gibberish freak that has no provable relation to meaningful mathematical problems. The idea that all undecidability is an instance of Godel is pure garbage and imbeciles like Cohen make me embarrassed. Godel sentences are of a very strange and peculiar kind.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-1619794602884221842016-04-07T03:27:26.087-07:002016-04-07T03:27:26.087-07:00This comment has been removed by the author.Anonymousnoreply@blogger.com