tag:blogger.com,1999:blog-3722233.post7535440237536455199..comments2024-04-20T13:30:48.050-05:00Comments on Computational Complexity: The Rubik's Cube Conjecture PROVEN! (Do we care?)Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger18125tag:blogger.com,1999:blog-3722233.post-23601950952006869252010-10-20T05:22:24.417-05:002010-10-20T05:22:24.417-05:00Could someone please tell me what the 20 moves are...Could someone please tell me what the 20 moves are so I can solve mine?<br /><br />You can find these yourself. Feed them into the incredible Cube Explorer program (http://kociemba.org/cube.htm) and you get the solution in 20 moves.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-91129705858702610182010-09-10T17:55:00.271-05:002010-09-10T17:55:00.271-05:00Yaaaay......
Could someone please tell me what th...Yaaaay......<br /><br />Could someone please tell me what the 20 moves are so I can solve mine?99tacoloverhttps://www.blogger.com/profile/00412973346006716566noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-77460360427543210442010-09-10T06:42:34.041-05:002010-09-10T06:42:34.041-05:00The proof must be interesting (hmmm- then we need ...<i>The proof must be interesting (hmmm- then we need to define interesting).</i><br /><br />Yes, yes, please, please <i>define</i> "interesting" (or beautiful) in maths.<br />You probably cannot do that using only mathematical statements, then what?Kevembuanggahttp://www.kevembuangga.com/blog/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-43852358037993082912010-09-10T06:26:48.398-05:002010-09-10T06:26:48.398-05:00@5
"needed" means "required",...@5<br /><br />"needed" means "required", so the "minimum needed" is 0, not 20.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-83107837643351238182010-09-10T02:20:49.357-05:002010-09-10T02:20:49.357-05:00This is epic result, much more important than 99.9...This is epic result, much more important than 99.9% of the trash published in the so called TCS. That you are unable to understand that only highlights how overrated TCS people are.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-32600342831100214952010-09-09T15:42:41.228-05:002010-09-09T15:42:41.228-05:00Here's a question: does the Rubik's Cube c...Here's a question: does the Rubik's Cube count as "real world phenomena"? Somehow because it's a toy it seems the answer should be no, or at least this justification is much less strong than if, for instance, the conjecture was related to curing cancer.<br /><br />On the other hand, I think popular interest in this problem is actually more than for say the Poincare Conjecture.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-23260545959484074782010-09-08T20:12:10.964-05:002010-09-08T20:12:10.964-05:00In a sense not even Wiles believed FLT to be a pro...In a sense not even Wiles believed FLT to be a problem important on its own. Only when a way to prove FLT that had connections to deep maths became apparent did he devote his complete attention to it.<br /><br />Many other mathematicians have commented on the utter irrelevance of the FLT question. <br /><br />The Rubik cube has connections to some really deep group theory, and when this is eventually re-proven for the n-sided cube it will likely be as relevant as FLT was.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-70817609218077859152010-09-08T20:11:25.106-05:002010-09-08T20:11:25.106-05:00Carroll's Riddle:
Why is God's Chess Numb...<b>Carroll's Riddle:</b> <br />Why is <a href="http://www.youtube.com/watch?v=wxIaMcO2amE" rel="nofollow">God's Chess Number</a> like a writing desk? <br /><br /><b>Answer:</b> <br />Because both Turing and Shannon wrote upon it.<br /><br />------------<br />Note: white has 61 "only" moves.John Sidleshttp://www.mrfm.orgnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-88304505574219806752010-09-08T18:19:07.989-05:002010-09-08T18:19:07.989-05:00As a counterpoint to David: 4 color theorem by a f...As a counterpoint to David: 4 color theorem by a finite calculation.<br /><br />I suppose there is a question of how "obvious" it is that a finite calculation can solve the problem.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-30875300799762949042010-09-08T16:34:15.670-05:002010-09-08T16:34:15.670-05:00As an utter layman, I'd suggest that "int...As an utter layman, I'd suggest that "interesting" be defined as "holding the attention of provers long enough to prove it" when the amount of time it takes to prove something is not trivial. Rubik's cube is therefore surprisingly interesting, as this proof about essentially a toy took many person-years of effort to emerge, and yet the effort was made.<br /><br />At least, that's why it interests me!Tedhttps://www.blogger.com/profile/06056113743661875113noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-90063466895846722722010-09-08T16:21:13.277-05:002010-09-08T16:21:13.277-05:00I agree with David. In this case the "proof&q...I agree with David. In this case the "proof" is some sort of (clever, but still quite-brute-force) calculation.<br /><br />We can admire the nice exploitation of symmetries and the expertise in coding a lot of programming tricks in order to speed up the computation, but if the proof had been "on paper" probably it would have been more interesting.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-3077470817736073822010-09-08T14:57:30.315-05:002010-09-08T14:57:30.315-05:00I think there's also a certain finiteness prin...I think there's also a certain finiteness principle here: if a question can in principle be reduced to a finite calculation (even though in practice we can't do that calculation) then it's less likely to be interesting than a problem where any solution would have to be more conceptual.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-90970831953765293982010-09-08T13:37:46.707-05:002010-09-08T13:37:46.707-05:00This result can really show the power of math to a...This result can really show the power of math to a foreign world. Not many people know of the theoretical side of math, but lots know how much of a headache solving a Rubik's cube can be. Even if the proof is hard for a novice to understand, such a result can inspire conversation about how to prove similar things for simpler puzzles. And if this conversation helps more people to see the beauty of mathematics, then this is indeed an important result.Blakehttps://www.blogger.com/profile/16116043731993061151noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-32501574464875042222010-09-08T13:14:42.618-05:002010-09-08T13:14:42.618-05:00@1 and @2
Minimum is correct.
For example, if I ...@1 and @2<br /><br />Minimum is correct.<br /><br />For example, if I gave you 21 moves, you could still always solve the cube. However, if I only gave you 19 moves, you could not always solve the cube. Thus, "the minimum number of moves needed to solve Rubik's Cube is 20".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-58215021558993333702010-09-08T13:05:02.694-05:002010-09-08T13:05:02.694-05:00"Why are numbers beautiful? It's like ask..."Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is."<br /> - Paul ErdÅ‘sBlakehttps://www.blogger.com/profile/16116043731993061151noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-27016668426845691262010-09-08T12:31:02.804-05:002010-09-08T12:31:02.804-05:00Objectively, FLT isn't that much more natural ...Objectively, FLT isn't that much more natural than Rubik's Cube. It's got the fact that it's a generalization of Pythagorean triples, but that's about it. That it's received so much attention seems like a sort of fluke of math history. It's created interesting math and even provided some applications, but only through a kind of sheer force-of-will. It wouldn't be that surprising if the Martians HADN'T studied it.Xamuelhttp://www.xamuel.comnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-57676770701407457552010-09-08T12:17:06.500-05:002010-09-08T12:17:06.500-05:00That is, it was shown that the minimum number of m...<i>That is, it was shown that the minimum number of moves needed to solve Rubik's Cube is 20 (it was known that there are starting configurations that require 20).</i><br /><br />You probably mean "maximum number of moves".Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-32244991687688488942010-09-08T12:16:34.410-05:002010-09-08T12:16:34.410-05:00minimum -> maximum?minimum -> maximum?Anonymousnoreply@blogger.com