tag:blogger.com,1999:blog-8666091.post321152055582112475..comments2021-02-05T18:38:25.974+01:00Comments on The Reference Frame: Sleeping beauty in Guantánamo BayLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-8666091.post-87386220780682623152014-08-02T20:54:26.604+02:002014-08-02T20:54:26.604+02:00Right, but the unit of your profit is one dollar s...Right, but the unit of your profit is one dollar so it clearly means that you can't interpret the profit from a particular bet as a probability.<br /><br />If you write the formulae correctly, you will be able to derive from the profits that the probability is 1/2, even if you buy 2 shares in the "heads" weeks. See e.g. this particular DISQUS comment<br /><br />Search for "The expectation value of the benefits is" at<br /><br />http://motls.blogspot.cz/2014/07/the-sleeping-beauty-problem.html?m=1#comment-1509340449Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-2148430089136527822014-08-02T19:30:19.555+02:002014-08-02T19:30:19.555+02:00Dear Lubos,
let's say the beauty is offered 10...Dear Lubos,<br />let's say the beauty is offered 100 Euros for each time she is woken up and guessing right. If she says Tails always she has a 50% chance of winning 100 Euros. If the says Heads always she has a 50% chance of winning 200 Euros. I think this is what Prof. Polchinski meant by defining probabilities with betting. I think the CIA example works very similar. If you bet on the CIA you most likely don't win anything. But you have a small chance of winning a huge amount of money. You can adjust the number so that betting on the CIA gives you a higher expectation value for the money you win. It is just that the expectation value is not what you care about here.Mikaelnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-72638303336055804692014-08-02T17:25:13.827+02:002014-08-02T17:25:13.827+02:00Dear Uncle Al, I would agree that the problems are...Dear Uncle Al, I would agree that the problems aren't equivalent. But there is a factor of chance in the Monty Hall paradox, too. The door where the prize is hidden has also been randomly chosen, wasn't it?Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-4071749264930819722014-08-02T17:23:20.613+02:002014-08-02T17:23:20.613+02:00True, Gordon.
If I decorate your statement, some...True, Gordon.<br /><br /><br />If I decorate your statement, some possibilities may fail to eventuate *even* if they contain two creatures that are identical to us, electron by electron. If these observers are there and the same as us, it doesn't mean that the possibility is equally likely as the possibility we know to be true. ;-)<br /><br /><br />I actually forgot to mention the "many worlds". A key mistake in the many worlds is to think that the "two worlds" are equally likely just because the two options look equally real. They may look equally real as options but the whole point of the concept of probability is that the probabilities don't have to be equal to each other and to 1/2 or 1/N each.<br /><br /><br />The Monty Hall problem has some other subtleties, about the behavior of the host and assumptions about that, and so on. These complications are avoided in the Sleeping Beauty Problem. On the other hand, the "exactly repeated experience" is avoided in the Monty Hall Problem so I wouldn't agree that the problems are equivalent in any way.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-59939428414035404492014-08-02T17:18:04.479+02:002014-08-02T17:18:04.479+02:00The Monty Hall Paradox is contingent upon knowing ...The Monty Hall Paradox is contingent upon knowing one of the outcomes. The coin flip has all unknown outcomes. The coin flip is not the Monty Hall Paradox.<br /><br /><br />If one of your postulates is empirically defective, your rigorously derived axiomatic system is no better when it is contingent upon that postulate.Uncle Alhttp://www.mazepath.com/uncleal/qz4.htmnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-14370038110471821632014-08-02T17:11:15.346+02:002014-08-02T17:11:15.346+02:00Good analysis IMO, but I can see the dummer pobel ...Good analysis IMO, but I can see the dummer pobel saying they interpret the problem and its framing differently. They<br />are wrong. It is not the Monty Hall problem.<br />Also, changing horses for a moment, not only are we not Boltzmann brains, but they most likely don't exist as well.<br />In an infinite universe or multiverse, not every possibility has<br />to eventuate---some "possibilities" could have 0% probability of occurring. There are "smart" thought experiments of the Einstein variety, and there are "dumb" thought experiments of the XXXX (fill in name) variety.Gordonnoreply@blogger.com