EPTBayesianism and Sleeping Beauty - Page 7
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sam!zdat
United States5559 Posts
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imallinson
United Kingdom3482 Posts
On January 05 2013 07:19 sam!zdat wrote: Ok good so the answer is one third. But suppose the arbitrarily large case. Is there a zero probability that sleeping beauty will ever see prince charming again? should she just kill herself and end this farce? Well in the limit of infinitely many mad philosophers I think the answer is a resounding yes. Also sometimes I wish I could use LaTeX to input stuff on TL would make explaining mathematical working much easier. | ||
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sam!zdat
United States5559 Posts
(sorry if I'm mixing up heads and tails I'm sure I have) | ||
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hypercube
Hungary2735 Posts
On January 05 2013 06:55 sam!zdat wrote: What information? She knows "it is now monday or tuesday, and no longer sunday." That is an indexical. But she doesn't learn anything about the coin because she has the same exact experience no matter what. She could have predicted that this would happen on Sunday, when she believed unproblematically that the answer was 1/2, so I don't see how that gains her information. edit: hypercube can you summarize your position, sorry I'm trying to figure out what you're answering but I'm confused a bit. Her opinion doesn't change between Suday and the next time she wakes up. If you asked her what she was going to answer after she wakes up she would say 1/3. What happens is that the distribution looks like (1/2 tails, 1/2 heads). Then the philosopher splits the distribution into 0.25*(1 tails, 0 heads) and 0.75*(1/3 tails, 2/3 heads). Sleeping Beauty is perfectly aware how the distribution looks before and after the split. She's aware of it on Sunday, Monday, Tuesday and however long she keeps her sanity. She doesn't change her mind. It's you who are asking her about the whole distribution on Sunday and one particular branch of the split distribution after the next time. You are getting different answers because you are asking different questions. In my view the story would look something like this: The Mad Philosopher explains the rules and throw the coin. Without showing the result he asks Sleeping Beauty what she thinks the probability of tails is. She answers 1/2. She drinks up and wakes up later. The philosopher asks her: PH: "What do you think the probability of having thown tails is now?" SB: "1/3" PH: "You changed your mind. Why?" SB: "You changed the distribution." PH: "Fair enough" The End | ||
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sam!zdat
United States5559 Posts
edit: oh and I agree that you get different answers because you ask different questions, can you formalize what the two different questions are? | ||
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imallinson
United Kingdom3482 Posts
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hypercube
Hungary2735 Posts
On January 05 2013 07:31 sam!zdat wrote: ok so what do you think about the limit case hypercube? edit: oh and I agree that you get different answers because you ask different questions, can you formalize what the two different questions are? Probability of having thrown tails goes to zero as number of days goes to infinity. I find it hard to phrase these questions in everyday langauge, that's why I phrased it in terms of probability distributions. The first one is fairly easy. You can ask on Sunday: "When I wake you up what will be the probability of having thrown tails" The second one (trying to get an answer of 1/2 on Monday or Tuesday) seems harder. You'd need to refer to events that did happen and scenarios that could have happened but didn't and then take an average over them. If there's a way to express this in everyday language I'm not aware of it. | ||
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sam!zdat
United States5559 Posts
edit: so hypercube you'd agree that there's no hope for her ever seeing prince charming again if it's the limit case? but it really feels like she has a 1/2 chance of going free | ||
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sam!zdat
United States5559 Posts
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Boblion
France8043 Posts
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imre
France9263 Posts
On January 05 2013 07:49 Boblion wrote: My head hurts now. I went from 1/3 to "you can't answer" to 1/2 to wtf is going on. Way to develop schizophrenia. Kukaracha isn't helping tho, he always puts me on tilt. my simple brain of a math ignorant screams 1/3 to me and didn't change cause i don't understand half of the stuff all of you are saying :p | ||
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Boblion
France8043 Posts
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sam!zdat
United States5559 Posts
On January 05 2013 07:49 Boblion wrote: My head hurts now. I went from 1/3 to "you can't answer" to 1/2 to wtf is going on. Way to develop schizophrenia. \ Now I know you understand the problem :D That's exactly what the experience of thinking about this is like. You say "duh, it's this." Then you go, "no wait, it's obviously this." And then you go, "agh, no, how silly, I was right the first time." And then you realize you have no idea what you're supposed to be asking in the first place. Welcome to philosophy :D :D :D | ||
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imallinson
United Kingdom3482 Posts
On January 05 2013 07:44 sam!zdat wrote: limit case: Instead of two days or one day, if the coin is heads he wakes her up in eternal groundhog day + amnesia every day until the heat death of the universe, and if it is tails he wakes her up once, asks her the question, and then lets her go. edit: so hypercube you'd agree that there's no hope for her ever seeing prince charming again if it's the limit case? but it really feels like she has a 1/2 chance of going free Now that's making me doubt the whole 1/3 thing. Probability is confusing as shit sometimes. edit: there has to be a case where it flips tails and she goes free because your original coin flip is still 50-50. | ||
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hypercube
Hungary2735 Posts
On January 05 2013 07:44 sam!zdat wrote: limit case: Instead of two days or one day, if the coin is heads he wakes her up in eternal groundhog day + amnesia every day until the heat death of the universe, and if it is tails he wakes her up once, asks her the question, and then lets her go. edit: so hypercube you'd agree that there's no hope for her ever seeing prince charming again if it's the limit case? but it really feels like she has a 1/2 chance of going free No hope is incorrect. It goes to zero as 1/(n+1), not as a constant 0 sequence. Usually you would say 0 for all practical purposes but in this case there is a practical difference between the two. For the second question, it's not just a feeling. Her total probability of going free really is 1/2. But her probability of going free at any single time goes to 0. That sounds like it's impossible but it really isn't. The first thing we notice that any time she does go free she's only asked the question once. But when she got heads she gets asked the same question over and over and over again. How should each instance contribute to the answer: 1. What's the total probability that Sleeping Beauty goes free. 2. What's the probability that Sleeping Beauty goes free on any particular occasion when she's asked the question. For number 2 each instance contributes equally. By definition when I'm asking question 2 I'm looking for the total number of SB going free over the total number of questions. It's 1/n+1. So as n+1 goes to infinity the probability in question 2 goes to zero. But for question 1 not all instances of the question are created equal. Clearly that one single case when SB actually goes free contributes much more to the total probability than the 10.000th time she gets asked the same question in the eternal groundhog day scenario. | ||
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sam!zdat
United States5559 Posts
"X" "if I utter 'X!', my utterance will express a true proposition" How the fuck can those be different? | ||
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Boblion
France8043 Posts
On January 05 2013 07:56 sam!zdat wrote: Now I know you understand the problem :D That's exactly what the experience of thinking about this is like. You say "duh, it's this." Then you go, "no wait, it's obviously this." And then you go, "agh, no, how silly, I was right the first time." And then you realize you have no idea what you're supposed to be asking in the first place. Welcome to philosophy :D :D :D It reminds me of the pictures with cubes where you don't know what is the "right" perspective. ![[image loading]](http://cdn.ateliermagique.com/uploads/thumbnails/uploads/drawing/010800/010794/cube_c160x160.jpg) It is confusing and when i get one it takes me like one or two seconds to focus and get the other "view". But this problem is more complicated and it takes more time. Oh and it is more wearying for my head lol. | ||
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hypercube
Hungary2735 Posts
On January 05 2013 08:10 sam!zdat wrote: Yeah so now we're back to the problem of there being different probabilities for the beliefs: "X" "if I utter 'X!', my utterance will express a true proposition" How the fuck can those be different? It's not the same X. Don't know how to explain it differently but it really isn't. | ||
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sam!zdat
United States5559 Posts
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hypercube
Hungary2735 Posts
On January 05 2013 08:10 sam!zdat wrote: Yeah so now we're back to the problem of there being different probabilities for the beliefs: "X" "if I utter 'X!', my utterance will express a true proposition" How the fuck can those be different? Actually this can happen even if X really is the same thing in both cases: "There's no duct-tape over my mouth" "if I utter "There's no duct-tape over my mouth", my utterance will express a true proposition". Do these beliefs have the same probabilities? If not, is that really a paradox? | ||
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