tag:blogger.com,1999:blog-8666091.post6549343198568618029..comments2021-06-11T20:12:08.082+02:00Comments on The Reference Frame: Joe's weird objections against state dependenceLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger14125tag:blogger.com,1999:blog-8666091.post-77505510943646114422014-08-15T08:31:26.985+02:002014-08-15T08:31:26.985+02:00What you wrote was meant to be
P(tails) = P(tol...What you wrote was meant to be<br /><br /><br /><br />P(tails) = P(toldTT) P(tails|toldTT) + P(notToldTT) P(tails|notToldTT)<br /><br /><br />wasn't it? But this formula makes no sense because it doesn't express her subjective probability of "tails" at any single well-defined moment, neither by objective time nor by subjective time.<br /><br /><br />You're summing probabilities at "a" moment when she's told something with "a" moment when she's not told something, and these are not mutually exclusive because assuming "tails", she is both told (on Tuesday) and not told (on Monday).Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-36234346080859282932014-08-15T07:57:33.409+02:002014-08-15T07:57:33.409+02:00Dear Lubos, Thank you for your answer. Now suppo...Dear Lubos, Thank you for your answer. Now suppose that instead of being put back to sleep, after a minute she is simply told, `it's T/t'. So in the other three cases, it is exactly the same as the previous modified protocol, she gains the same information after one minute. <br /><br />So, if she is told (which is 1/4 of the time), then it's 100% that it is T/t. If she is not told (3/4) then it's 50% that it is M/t and 25% each that it is M/h and T/h. This seems to give a total probability of .25*1 + .75*.5 = .625 that she is in one of the tails cases. The thirder calculation would give .25*1 + .75*.333 = .5.Ramanujannoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-69915026888355778512014-08-15T06:13:48.045+02:002014-08-15T06:13:48.045+02:00Of course that I disagree with the result 1/3 here...Of course that I disagree with the result 1/3 here. After the "demo minute" or "demo second", her knowledge is exactly the same as in the original problem, so your problem becomes the original problem! And it's a way to formulate the right solution "by parts" which may be even clearer than all the solutions so far.<br /><br /><br />Before she may be put to sleep, there are 2 possible coin states, heads and tails, and 2 possible days, Monday and Tuesday. By two Z2 symmetries, the probability of each of the 4 possibilities is 1/4. Would you really disagree with that?<br /><br /><br />Now, after the second or minute for the short awakening, the situation changes because she's getting a new information in general.<br /><br /><br />How much information she is getting by staying up depends on the coin state. If the coin shows "heads", she is getting no information because in the "heads" case, staying up is predicted for both days.<br /><br /><br />If one assumes that the coin is showing "tails", then she is definitely getting information by staying up. Before the momentum of "possible putting back to sleep", the probabilities of Monday-tails and Tuesday-tails were 25% each. That means that the conditional probabilities of Monday and Tuesday, assuming tails, were both 50%.<br /><br /><br />After the moment when she can be put back to sleep, the probabilities change. The "fluid" of the "Tuesday tails" just flows to "Monday tails" because Tuesday tails is getting riuled out. So the conditional probabilities of Monday and Tuesday, assuming tails, become 100% and 0%. They still share the same initial probability reserved for "tails" so this 100-0 translates to 50% - 0% in absolute probabilities.<br /><br /><br />The probabilities of heads-Monday and heads-Tuesday stay at 25% because if one/she assumes heads, one/she is learning nothing about the day of the week! <br /><br /><br />The result, after the minute/second expires, is of course the same 50-25-25 as before.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-47100570907225800372014-08-15T05:35:30.335+02:002014-08-15T05:35:30.335+02:00Suppose that we change the SB puzzle, but only in ...Suppose that we change the SB puzzle, but only in the protocol for Tuesday after tails (T/t). The new protocol is that she is awakened, and, after a pause of a minute, is put back to sleep (but only on T/t). Again, she knows the full protocol in advance. In the first minute after awakening, she assigns equal probabilities for M/h, T/h, M/t, T/t. After a minute, if she is still awake, she excludes T/t and is left with equal probabilities for M/h, M/t, T/h. So in this case the 1/3 is correct. Do you agree with this result for the modified problem? If so, how can the changed protocol for T/t affect her relative weightings of the other three cases? What if she's only awake for a second?Ramanujannoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-54280237319454760082014-08-14T17:53:10.201+02:002014-08-14T17:53:10.201+02:00Actually, Lubos, not everyone behaves like you, in...Actually, Lubos, not everyone behaves like you, insulting those who disagree with them, and banning them. There is ample discussion of state-dependence in the scientific community.lojyknoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-27276452187090062592014-08-14T17:49:32.511+02:002014-08-14T17:49:32.511+02:00Remember, anyone who disagrees with Lubos, or actu...Remember, anyone who disagrees with Lubos, or actually understands probability, like DN, is banned from the forum. So only Lubos's sycophants remain. So this comment has no chance of being accepted.lojyknoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-80008366364159297482014-08-14T17:39:58.610+02:002014-08-14T17:39:58.610+02:00Remember that anyone who might disagree with Lubos...Remember that anyone who might disagree with Lubos, like DN, has been banned, so only his sycophants remain.lojyknoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-67082169419524463622014-08-14T12:32:06.220+02:002014-08-14T12:32:06.220+02:00Oh my God, even though I had not yet time to read ...Oh my God, even though I had not yet time to read all of the sleeping-beuty articles in detail, agree that it seems that Joe P. has same bad misunderstandings abou basic probability theory (being a thirder).<br /><br />Also from teading about different methods to qualtise ST for example, it always seemed to me that as soon as one has defined everything, results of measurements can just be calculated and there is no need to continuously change the starting point of quantization.Dilatonnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-81650843370762785572014-08-14T11:09:35.287+02:002014-08-14T11:09:35.287+02:00No, I know, but maybe it wasn't enough for Jua...No, I know, but maybe it wasn't enough for Juan to buy an AdS/CFT-10,000 T-shirt. ;-)Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-37702540211427088672014-08-14T10:54:16.265+02:002014-08-14T10:54:16.265+02:00it seems to me that milner already gave him someth...it seems to me that milner already gave him something like that a couple of years ago, some kind of coupon if i remember well.mmanu_Fnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-17061638200861919152014-08-14T08:49:57.891+02:002014-08-14T08:49:57.891+02:00Thanks, Michael, but you exaggerate. The silence o...Thanks, Michael, but you exaggerate. The silence on the blog is because the blog readers are either non-experts or shy workers who are working on their research. I think that those that know (including Kyriakos and Suvrat) aren't really too afraid to disagree with Joe even though such fear does exist, too.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-78469034016895076242014-08-14T08:43:12.143+02:002014-08-14T08:43:12.143+02:00Wow, the silence here is deafening. Apparently nob...Wow, the silence here is deafening. Apparently nobody competent enough to recognize your arguments for what they are -- obviously correct -- dares to speak out and mess with the Big Polchinski. Politics trumps science in academia, I guess.Michaelnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-56660891414940220042014-08-14T07:39:38.673+02:002014-08-14T07:39:38.673+02:00A cool milestone - I hope that Milner or someone w...A cool milestone - I hope that Milner or someone will also send him a T-shirt or hoodie like Stack Exchange is sending me for crossing 100,000. ;-)Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-11219019911828612282014-08-13T22:10:04.688+02:002014-08-13T22:10:04.688+02:00(not so) off topic : maldacena's conjecture ar...(not so) off topic : maldacena's conjecture article has reached 10.000 citations today!mmanu_Fnoreply@blogger.com