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Sleeping Beauty is kidnapped by a mad philosopher.
The philosopher explains to her the following:
Sleeping Beauty, my dear, I've brought you here for a special purpose. You are honored to the subject of...
A PHILOSOPHICAL EXPERIMENT
Today is Saturday. Tomorrow will be Sunday, the Day After That will be Monday, and the Following Day will be Tuesday. Just so we're clear.
Tomorrow I will give you a magic potion that will put you to sleep. After that, I will flip a Coin.
The Coin is fair, scout's honor.
If the COIN IS HEADS:
I will wake you up on Monday, and we will have tea. Then I will give you a second potion which will put you to sleep and erase all memory of Monday. Then I will wake you up on Tuesday and we will have tea.
If the COIN IS TAILS:
I will not wake you up on Monday. You will sleep through Monday, looking beautiful. Then I will wake you up on Tuesday and we will have tea.
OK SO:
Sleeping Beauty drinks the potion on Sunday. She's asleep, and then the mad philosopher wakes her up. They have tea. Then the philosopher asks:
Sleeping Beauty, my ravishing somnolent darling, what credence do you ascribe to the proposition that "the Coin was tails"
 
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So its supposed to be a 1/3 chance the coin was tails?
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that's one possible answer
but there's a new thought experiment you can propose that makes that seem like a bad belief. can you find it?
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I'm assuming it's perfectly valid that at the moment of the question, it is Monday, since Sleeping Beauty doesn't forget all that shit until after Monday is over with?
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yeah it could be monday, no way to tell, they seem the same
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Eh then it would seem to be 1/2. Really you gain no useful information from waking up and having tea because it was bound to happen anyways. And we have no reason to believe the random choice of heads or tails was biased.
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From Sleeping Beauty's subjective perspective, Pr(tails) should be 1/2. As far as she knows, the priors are equal (fair coin), and the conditionals are equal (being woken up at some point occurs regardless of the flip, and she doesn't know on what day she's awoken), so the posteriors should also be equal. What am I missing here?
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And actually this instantly reminded me of an analogue with entangled quantum bits. Say we have (1/sqrt(2))|01> and (1/sqrt(2))|10>, and then one dude measures 0. Well, obviously the other dude's is 1, but fuck if we know which guy measured first, since we didn't actually gain any information. So it's 50/50 who measured first, until we go and ask the other guy when they measured.
Same thing seems to apply to this, cause knowing that I'm awake and drinking tea didn't give me any useful information.
The only thing I can imagine that might be a possible source of information is the fact that if it were heads, we have 2 days on which to wake up, so the day we are being asked could be either Monday or Tuesday, whereas for tails it is Tuesday. But still, either way we only remember it once, so to Sleeping Beauty they are one and the same.
And if we consider the Pr(tea) = 1, and Pr(tea | tails)=1 as well, then we are left only with Pr(tails), so yea definitely looks smells and reads like a case of absolutely 0 information gain... so 1/2.
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Just looked at the wikipedia article, nothing new there, but it says it would make sense that because being woken up gives sleeping beauty no new information, the probability may be one half, as well as giving an explanation for the one third answer. I still think the one third answer makes more sense, because from sleeping beauties perspective, she will be right twice if she chooses heads every time and it is heads, but right only once if she chooses tails and it is tails.
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On January 04 2013 15:27 32 wrote:
Just looked at the wikipedia article, nothing new there, but it says it would make sense that because being woken up gives sleeping beauty no new information, the probability may be one half, as well as giving an explanation for the one third answer. I still think the one third answer makes more sense, because from sleeping beauties perspective, she will be right twice if she chooses heads every time and it is heads, but right only once if she chooses tails and it is tails.
Lol I just wiki'd it. I think I'll go with the religious argument and appeal to divine solution.
+ Show Spoiler +
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If she says 1/2 and then makes book on it she'll have terrible EV
edit: I'm not going to say what I think, I wrote a paper about it in college and argued about it for hours in seminar so that'll take the fun out of it. but people should argue because it's a fun problem and it's an issue for bayesians
edit: 32 is on a right track, if it's heads you get sampled twice and that's a big part of the issue. But how do express a credence in the proposition then?
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On January 04 2013 15:34 EtherealDeath wrote:Show nested quote +On January 04 2013 15:27 32 wrote:
Just looked at the wikipedia article, nothing new there, but it says it would make sense that because being woken up gives sleeping beauty no new information, the probability may be one half, as well as giving an explanation for the one third answer. I still think the one third answer makes more sense, because from sleeping beauties perspective, she will be right twice if she chooses heads every time and it is heads, but right only once if she chooses tails and it is tails. Lol I just wiki'd it. I think I'll go with the religious argument and appeal to divine solution. + Show Spoiler +
What if we applied a platonic solution, that really the tea and day were imperfect and that somewhere there is a perfect tea and day and therefore none of this really happened. I might be putting Descarte before the horse here though HUEHUEHUE.
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On January 04 2013 15:39 sam!zdat wrote:
If she says 1/2 and then makes book on it she'll have terrible EV
edit: I'm not going to say what I think, I wrote a paper about it in college and argued about it for hours in seminar so that'll take the fun out of it. but people should argue because it's a fun problem and it's an issue for bayesians
Um, I demand you upload paper and argue.
Also yea, at first I was going to say 1/3, which is why I asked about Monday and memory, but then I looked at it in a Bayesian sense and was like nahhhhh 1/2.
But then, it's godawful EV. Meh.
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I don't have the paper anymore.
But what happens if instead of 2 days on heads, it is arbitrarily large?
The point is we were talking about bayesianism in another thread and I wonder how bayesian solves the EV problem
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On January 04 2013 15:42 docvoc wrote:Show nested quote +On January 04 2013 15:34 EtherealDeath wrote:On January 04 2013 15:27 32 wrote:
Just looked at the wikipedia article, nothing new there, but it says it would make sense that because being woken up gives sleeping beauty no new information, the probability may be one half, as well as giving an explanation for the one third answer. I still think the one third answer makes more sense, because from sleeping beauties perspective, she will be right twice if she chooses heads every time and it is heads, but right only once if she chooses tails and it is tails. Lol I just wiki'd it. I think I'll go with the religious argument and appeal to divine solution. + Show Spoiler + What if we applied a platonic solution, that really the tea and day were imperfect and that somewhere there is a perfect tea and day and therefore none of this really happened. I might be putting Descarte before the horse here though HUEHUEHUE.
Actually here is a simple, simple solution.
Monday didn't exist. Scummy bastard could scam us out of our betting money anyways if we bet on it hue hue hue hue hue (not like we would ever remember being scammed zzzzzz).
But then since we are apparently a she in this case, good and potent use of puppy eyes could counter that. Mmmm the possibilities. You'd never remember all the awfully loose stuff you did the previous day to guarantee you weren't scammed! I mean, even pregnancy would have to reverse itself, else we'd realize we were up to something on Monday, and thus the assumptions of the problem broken!
Yes, it is it!
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Man, this is pretty dang messed up.
Moral implications aside, I unfortunately can't see any argument that the chance is not 1/2. So, to answer the question, moderate credence.
I made a probability tree to show my thinking: + Show Spoiler +
Edit: Does EV mean expected value?
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I think you are forced to accept that one can have two separate modalities of credence, or something.
because "objectively" it's definitely 1/2. but "subjectively" it feels like it must be1/3. of course you get sampled twice in one instance, so the payoff is like leveraged or something? god idk
@above yes EV=expected value
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i end up thinking it's 75%. :<
edit: no i don't. i read question wrong.
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On January 04 2013 15:46 sam!zdat wrote:
I think you are forced to accept that one can have two separate modalities of credence, or something.
because "objectively" it's definitely 1/2. but "subjectively" it feels like it must be1/3. of course you get sampled twice in one instance, so the payoff is like leveraged or something? god idk
@above yes EV=expected value
Man, but when one mode ends up losing you money, it's hard to view it as valid (even if you were using it before).
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you can also ask the question, which I originally had and edited out because I'm dumb, "what is the probability that it is Monday?"
but that involves an indexical so it's harder
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On January 04 2013 15:49 sam!zdat wrote:
you can also ask the question, which I originally had and edited out because I'm dumb, "what is the probability that it is Monday?"
but that involves an indexical so it's harder
Well, from a Bayesian sense it would seem to be 1/4, but from a betting standpoint I suppose I'd bet 1/3.
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ah, maybe that was what happened.
i was thinking it was 75% that it was tuesday. if it's tuesday it's 50% of tails.
25% that it's monday. 0% tails.
i'd always put my money on heads.
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so part of the problem is that Heads(monday) and Heads (tuesday) are in the same possible world, but at different times.
I mean, what bayesian credence can you give to claim "it's 5:00"? idk man. either you know, or you have no fucking idea. at which point as Double Reed tells me you give equal credence to all possible things, but what are all the possible times??? my head explode
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I love threads like these. Thanks for making it, I still like one third though. I think wikipedia says that if you run this on a computer with many trials it comes out to one third, so while expressing the probability as one third may not represent the problem fully, I like this answer because its consistent over time.
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running it over many trials is what we mean when we talk about EV
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The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant).
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On January 04 2013 15:53 sam!zdat wrote:
how do you get 1/4?
Hopefully I didnt fuck something up in my head.
Ok so we want Pr(Monday | tea), so
Pr(tea | Monday) * Pr(Monday) / Pr(Tea).
Pr(tea | Monday) = Pr(Heads) = 1/2 if we do it Bayesian.
Pr(Monday) = 1/2 (pick a day at random, unbiased manner)
Pr(tea) = 3/4
fuck it never mind lololol I inserted a 1 randomly in my head.
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assume the philosopher explains the whole thing to sleeping beauty. she knows as much as we know.
but say, if you think 1/3, it's arbitrarily many number of days. either sleeping beauty escapes, or she is trapped forever in groundhog day + amnesia. is there an arbitrarily small possibility she will see prince chamring again??
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On January 04 2013 15:54 sam!zdat wrote:
so part of the problem is that Heads(monday) and Heads (tuesday) are in the same possible world, but at different times.
I mean, what bayesian credence can you give to claim "it's 5:00"? idk man. either you know, or you have no fucking idea. at which point as Double Reed tells me you give equal credence to all possible things, but what are all the possible times??? my head explode
The possible times are whatever you design them to be. If you limit your resolution to a minute, then Pr(5:00) = 1/1440 :D
Yeah, I'm not really sure how to approach this, either.
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On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant).
Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis.
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three possible states of waking up.
after the cointoss is head -> 50%
you can either be on monday or tuesday, it seems fair to assume that there is an equal probability of both, since nothing 'happens' in between, and the events are already determined at this point. hence 25% on each (half of 50%).
after the cointoss is tails -> 50%
it is 100% that it is tuesday.
so when you wake up in one of these three states there's no point in going for tails.
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Monty Hall is not problematic like this is, it's much more simple because it doesn't involve memory loss.
I should say that the reason I make this is I wish to defend claim:
"It is not the case that Bayesian reasoning can be applied to all types of beliefs"
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On January 04 2013 16:02 sam!zdat wrote:
Monty Hall is not problematic like this is, it's much more simple because it doesn't involve memory loss.
I should say that the reason I make this is I wish to defend claim:
"It is not the case that Bayesian reasoning can be applied to all types of beliefs"
Lol that's a fun way of putting it. A problematic result from Bayesian reasoning when amnesia is applied.
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On January 04 2013 16:01 nunez wrote:
three possible states of waking up.
after the cointoss is head -> 50%
you can either be on monday or tuesday, it seems fair to assume that there is an equal probability of both, since nothing 'happens' in between, and the events are already determined at this point. hence 25% on each (half of 50%).
after the cointoss is tails -> 50%
it is 100% that it is tuesday.
so when you wake up in one of these three states there's no point in going for tails.
but the point is you're asked to say what odds you want to bet on that it's tails. the payoff doesn't have to be equal; YOU set the payoff
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On January 04 2013 16:04 sam!zdat wrote:Show nested quote +On January 04 2013 16:01 nunez wrote:
three possible states of waking up.
after the cointoss is head -> 50%
you can either be on monday or tuesday, it seems fair to assume that there is an equal probability of both, since nothing 'happens' in between, and the events are already determined at this point. hence 25% on each (half of 50%).
after the cointoss is tails -> 50%
it is 100% that it is tuesday.
so when you wake up in one of these three states there's no point in going for tails. but the point is you're asked to say what odds you want to bet on that it's tails. the payoff doesn't have to be equal; YOU set the payoff
a valid point.
i can't think of a way to set an odds, i can only get so far as to saying p(heads) > p(tails) when you wake up.
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On January 04 2013 16:00 EtherealDeath wrote:Show nested quote +On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis.
Can you rephrase that, I don't understand what you mean.
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On January 04 2013 15:59 sam!zdat wrote:
assume the philosopher explains the whole thing to sleeping beauty. she knows as much as we know.
but say, if you think 1/3, it's arbitrarily many number of days. either sleeping beauty escapes, or she is trapped forever in groundhog day + amnesia. is there an arbitrarily small possibility she will see prince chamring again??
Yea that is curious. If we changed the Heads condition instead to some arbitrarily large number of days, each day being woken for tea, and say that after Tuesday (the last day), she's free to go home, what we are actually saying is that upon being woken up, there is a 1/2 chance we are good to go after tea.
Which sure as fuck is not the case. What a pain.
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Would it be a cop-out to claim that agents with amnesia don't qualify as rational any more?
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On January 04 2013 16:06 hypercube wrote:Show nested quote +On January 04 2013 16:00 EtherealDeath wrote:On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis. Can you rephrase that, I don't understand what you mean.
From a Bayesian standpoint, you repick. So, no apparently false conclusion. This however makes the Bayesian answer look stupid as fuck.
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On January 04 2013 16:06 MidnightGladius wrote:
Would it be a cop-out to claim that agents with amnesia don't qualify as rational any more?
a clever response. but I don't think anybody's rational so therefore Bayesianism is action philosophy for robots, which is a conclusion I'm ok with
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On January 04 2013 16:06 MidnightGladius wrote:
Would it be a cop-out to claim that agents with amnesia don't qualify as rational any more?
Uh, that wouldn't really change anything because we know it could be Monday when we do the analysis, we are just not sure that it is. Would beg the question of what types of random variables cannot be involved in a problem if we want a reasonable answer by Bayesian methods.
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idk I mean I think sleeping beauty is exactly as rational as you
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this was all just a ruse to make tl bayesians look silly?
tl bayesians... what are the odds of that?
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On January 04 2013 16:07 EtherealDeath wrote:Show nested quote +On January 04 2013 16:06 hypercube wrote:On January 04 2013 16:00 EtherealDeath wrote:On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis. Can you rephrase that, I don't understand what you mean. From a Bayesian standpoint, you repick. So, no apparently false conclusion. This however makes the Bayesian answer look stupid as fuck.
Repick what? Are talking about the modified Monty Hall problem or the mad philosopher? I'm still not following.
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On January 04 2013 16:11 hypercube wrote:Show nested quote +On January 04 2013 16:07 EtherealDeath wrote:On January 04 2013 16:06 hypercube wrote:On January 04 2013 16:00 EtherealDeath wrote:On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis. Can you rephrase that, I don't understand what you mean. From a Bayesian standpoint, you repick. So, no apparently false conclusion. This however makes the Bayesian answer look stupid as fuck. Repick what? Are talking about the modified Monty Hall problem or the mad philosopher? I'm still not following.
Monty Hall.
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I don't want to broaden this into a discussion on what it means to be rational, but in practical terms, if I find myself suffering from amnesia, and if someone asks me what time it is when I have no way of independently verifying the time, I'm just going to tell them that I have no idea :3
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well, I suppose if you were an orthodox bayesianism you would say that you figured out how many minutes were in a day and divided the credence by that, since you would express the time in a discreet number ways in natural language.
and then you would gather evidence about how it was or wasn't more likely to be different times
Or when your girlfriend says "I love you" you would consider the probability of your belief that she was actually sincere in this utterance.
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On January 04 2013 16:18 sam!zdat wrote:
well, I suppose if you were an orthodox bayesianism you would say that you figured out how many minutes were in a day and divided the credence by that, since you would express the time in a discreet number ways in natural language.
and then you would gather evidence about how it was or wasn't more likely to be different times
Yea but then you'd calculate the odds and say the probability of being X day was 1/7, which is just as expected and you wouldn't be bleeding money if you bet on it, so amnesia in that sense doesn't fuck you over like it does here.
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Sorry, I lost track of the topic and was just making fun of bayesian. sorry I'll stop.
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On January 04 2013 16:22 sam!zdat wrote:
Sorry, I lost track of the topic and was just making fun of bayesian. sorry I'll stop.
No don't stop, it's like someone just gave me an e-Bayesian. So do you have a hidden trap somewhere that will put my Bayesian addiction back on track?
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On January 04 2013 16:12 EtherealDeath wrote:Show nested quote +On January 04 2013 16:11 hypercube wrote:On January 04 2013 16:07 EtherealDeath wrote:On January 04 2013 16:06 hypercube wrote:On January 04 2013 16:00 EtherealDeath wrote:On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis. Can you rephrase that, I don't understand what you mean. From a Bayesian standpoint, you repick. So, no apparently false conclusion. This however makes the Bayesian answer look stupid as fuck. Repick what? Are talking about the modified Monty Hall problem or the mad philosopher? I'm still not following. Monty Hall.
In that situation you need a probability distribution of what kind of strategy the other agent follows.
This is actually what strong poker players do when they meet a new opponent. They make assumptions based on prior experience as well as any information they can get their hands on. It's very much a Bayesian approach but it's hard to quantify because of the number of different variables that goes into it.
I mean, I guess you could say that when you have an intelligent agent the Bayesian approach gives no sensible answer if you have no information whatsoever on his strategy. I guess that's true, but that's true for any other view too.
In this case the position of the prize is just a distraction. The question is really about the strategy of the host. Specifying that we know nothing about the strategy and then asking for a number that directly depends on it seems disingenuous.
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On January 04 2013 16:37 hypercube wrote:Show nested quote +On January 04 2013 16:12 EtherealDeath wrote:On January 04 2013 16:11 hypercube wrote:On January 04 2013 16:07 EtherealDeath wrote:On January 04 2013 16:06 hypercube wrote:On January 04 2013 16:00 EtherealDeath wrote:On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis. Can you rephrase that, I don't understand what you mean. From a Bayesian standpoint, you repick. So, no apparently false conclusion. This however makes the Bayesian answer look stupid as fuck. Repick what? Are talking about the modified Monty Hall problem or the mad philosopher? I'm still not following. Monty Hall. In that situation you need a probability distribution of what kind of strategy the other agent follows. This is actually what strong poker players do when they meet a new opponent. They make assumptions based on prior experience as well as any information they can get their hands on. It's very much a Bayesian approach but it's hard to quantify because of the number of different variables that goes into it. I mean, I guess you could say that when you have an intelligent agent the Bayesian approach gives no sensible answer if you have no information whatsoever on his strategy. I guess that's true, but that's true for any other view too. In this case the position of the prize is just a distraction. The question is really about the strategy of the host. Specifying that we know nothing about the strategy and then asking for a number that directly depends on it seems disingenuous.
What does that have to do with Bayesian analysis giving a straight up illogical answer in this case?
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On January 04 2013 16:44 EtherealDeath wrote:Show nested quote +On January 04 2013 16:37 hypercube wrote:On January 04 2013 16:12 EtherealDeath wrote:On January 04 2013 16:11 hypercube wrote:On January 04 2013 16:07 EtherealDeath wrote:On January 04 2013 16:06 hypercube wrote:On January 04 2013 16:00 EtherealDeath wrote:On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis. Can you rephrase that, I don't understand what you mean. From a Bayesian standpoint, you repick. So, no apparently false conclusion. This however makes the Bayesian answer look stupid as fuck. Repick what? Are talking about the modified Monty Hall problem or the mad philosopher? I'm still not following. Monty Hall. In that situation you need a probability distribution of what kind of strategy the other agent follows. This is actually what strong poker players do when they meet a new opponent. They make assumptions based on prior experience as well as any information they can get their hands on. It's very much a Bayesian approach but it's hard to quantify because of the number of different variables that goes into it. I mean, I guess you could say that when you have an intelligent agent the Bayesian approach gives no sensible answer if you have no information whatsoever on his strategy. I guess that's true, but that's true for any other view too. In this case the position of the prize is just a distraction. The question is really about the strategy of the host. Specifying that we know nothing about the strategy and then asking for a number that directly depends on it seems disingenuous. What does that have to do with Bayesian analysis giving a straight up illogical answer in this case?
What's the answer of the Bayesian analysis in your opinion?
+ Show Spoiler +Have you made an assumption on the host's strategy? Explicitly or implicitly?
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On January 04 2013 16:49 hypercube wrote:Show nested quote +On January 04 2013 16:44 EtherealDeath wrote:On January 04 2013 16:37 hypercube wrote:On January 04 2013 16:12 EtherealDeath wrote:On January 04 2013 16:11 hypercube wrote:On January 04 2013 16:07 EtherealDeath wrote:On January 04 2013 16:06 hypercube wrote:On January 04 2013 16:00 EtherealDeath wrote:On January 04 2013 15:58 hypercube wrote:
The answer is 1/3 if we know the philosopher will ask the question. Otherwise the philosopher can manipulate the probability to be any amount he wishes.
There's an analogous situation in the Monty Hall problem. If the game show host has the choice of offering or not offering the switch he can manipulate probabilities to the point where switching offers no benefits (and this can't be exploited by the contestant). Except if I recall correctly there is no problem there with what we would like it to be, and what it turns out to be from a Bayesian analysis. Can you rephrase that, I don't understand what you mean. From a Bayesian standpoint, you repick. So, no apparently false conclusion. This however makes the Bayesian answer look stupid as fuck. Repick what? Are talking about the modified Monty Hall problem or the mad philosopher? I'm still not following. Monty Hall. In that situation you need a probability distribution of what kind of strategy the other agent follows. This is actually what strong poker players do when they meet a new opponent. They make assumptions based on prior experience as well as any information they can get their hands on. It's very much a Bayesian approach but it's hard to quantify because of the number of different variables that goes into it. I mean, I guess you could say that when you have an intelligent agent the Bayesian approach gives no sensible answer if you have no information whatsoever on his strategy. I guess that's true, but that's true for any other view too. In this case the position of the prize is just a distraction. The question is really about the strategy of the host. Specifying that we know nothing about the strategy and then asking for a number that directly depends on it seems disingenuous. What does that have to do with Bayesian analysis giving a straight up illogical answer in this case? What's the answer of the Bayesian analysis in your opinion? + Show Spoiler +Have you made an assumption on the host's strategy? Explicitly or implicitly?
The explicit is that the host flips a fair coin, and that coin flip which you do not observe determines what the host does. And Bayesian analysis says it is 1/2. But betting 1/2 would lose you money. You can see it easier by modifying the problem such that heads results in a wake amnesia sleep wake etc cycle for an arbitarily large number of days, and that on the last day, you walk free after tea. Then the problem becomes bettering on whether or not you walk free after tea, and if you bet 1/2 you sure as hell are going to be losing lots of money.
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You have to look at it from the perspective of the famous mathematician Sean Plott. If it feels like a funday, then there is 100% chance it's monday. Otherwise it's tuesday.
+ Show Spoiler +I said famous, and mathematician. Day[9] is both, although he isn't famous for his mathematics.
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On January 04 2013 16:58 jrkirby wrote:You have to look at it from the perspective of the famous mathematician Sean Plott. If it feels like a funday, then there is 100% chance it's monday. Otherwise it's tuesday. + Show Spoiler +I said famous, and mathematician. Day[9] is both, although he isn't famous for his mathematics.
LOL.
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Baa?21242 Posts
On January 04 2013 16:58 jrkirby wrote:You have to look at it from the perspective of the famous mathematician Sean Plott. If it feels like a funday, then there is 100% chance it's monday. Otherwise it's tuesday. + Show Spoiler +I said famous, and mathematician. Day[9] is both, although he isn't famous for his mathematics.
cute 
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On January 04 2013 16:51 EtherealDeath wrote:
The explicit is that the host flips a fair coin, and that coin flip which you do not observe determines what the host does. And Bayesian analysis says it is 1/2. But betting 1/2 would lose you money. You can see it easier by modifying the problem such that heads results in a wake amnesia sleep wake etc cycle for an arbitarily large number of days, and that on the last day, you walk free after tea. Then the problem becomes bettering on whether or not you walk free after tea, and if you bet 1/2 you sure as hell are going to be losing lots of money.
Ok, let's backtrack. Clearly we aren't talking about Monty Hall anymore but some version of OP's game.
Either way you didn't answer if the philosopher asks the question every time. That's the key assumption not whether he wakes up Sleeping Beauty or not.
Under the assumption that he does ask the question every time he wakes Sleeping Beauty up the answer is 1/3 not 1/2. Or 0 for the arbitrarily large case. Note 0 is a nonsensical answer but the assumption that the philosopher lives forever is nonsense so that's expected.
Under different assumptions the answer is different. I.e. if we're betting for money and we expect the philosopher to try to maximize his EV the right play is to guess heads 50% and tails 50%. That's not a Bayesian answer.
It turns out that simply saying that the philosopher tries to maximize his EV gives no new information, it's exactly the same as asking what the philosopher's strategy is while specifying that we know nothing about it. *
*It turns out that if we play the Nash equilibrium (guess tails 50% of the time) then the philosopher really is indifferent between any strategies. Since we are playing a game where he can observe our strategy but we can't observe his, he can play anything he damn well pleases and still get an EV of 0. So assuming rationality on his part gives no new information and we're back to the original problem of asking about something we explicitly said we know nothing about.
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let's make it a game theory problem and say you don't know his strategy :D
edit: wait, if you guess 1/2 and the mad philosopher always asks, you lose....
edit: keep in mind that he's a philosopher so he knows what you're thinking
edit: I think I'm too drunk to talk about this goodnight
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On January 04 2013 17:24 sam!zdat wrote:
let's make it a game theory problem and say you don't know his strategy :D
edit: wait, if you guess 1/2 and the mad philosopher always asks, you lose....
edit: keep in mind that he's a philosopher so he knows what you're thinking
What's the exact rule? If he says: "Did the coin land heads or tails?" and we bet I won't lose by answering randomly. How could I?
If he asks: "What's the probability it's Monday" of course I lose. edit: Or equivalently he asks what's the probability the coin landed tails. /edit He's asking me to guess a real number between 0 and 1 that he determined beforehand.
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Sorry, one last clarification. For the case when you can only take the side that the coin landed tails:
Clearly this is a bet you should not take. The rational strategy from the philosopher is to only ask this question when the coin actually landed heads. So assuming a rational (if mad) philosopher the probability of the coin having landed tails after the philosopher offers the bet is 0. So no odds is fair and we should just refuse the bet.
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On January 04 2013 17:20 hypercube wrote:Show nested quote +On January 04 2013 16:51 EtherealDeath wrote:
The explicit is that the host flips a fair coin, and that coin flip which you do not observe determines what the host does. And Bayesian analysis says it is 1/2. But betting 1/2 would lose you money. You can see it easier by modifying the problem such that heads results in a wake amnesia sleep wake etc cycle for an arbitarily large number of days, and that on the last day, you walk free after tea. Then the problem becomes bettering on whether or not you walk free after tea, and if you bet 1/2 you sure as hell are going to be losing lots of money. Ok, let's backtrack. Clearly we aren't talking about Monty Hall anymore but some version of OP's game. Either way you didn't answer if the philosopher asks the question every time. That's the key assumption not whether he wakes up Sleeping Beauty or not. Under the assumption that he does ask the question every time he wakes Sleeping Beauty up the answer is 1/3 not 1/2. Or 0 for the arbitrarily large case. Note 0 is a nonsensical answer but the assumption that the philosopher lives forever is nonsense so that's expected. Under different assumptions the answer is different. I.e. if we're betting for money and we expect the philosopher to try to maximize his EV the right play is to guess heads 50% and tails 50%. That's not a Bayesian answer. It turns out that simply saying that the philosopher tries to maximize his EV gives no new information, it's exactly the same as asking what the philosopher's strategy is while specifying that we know nothing about it. * *It turns out that if we play the Nash equilibrium (guess tails 50% of the time) then the philosopher really is indifferent between any strategies. Since we are playing a game where he can observe our strategy but we can't observe his, he can play anything he damn well pleases and still get an EV of 0. So assuming rationality on his part gives no new information and we're back to the original problem of asking about something we explicitly said we know nothing about.
You are over analyzing and sticking in extra assumptions/strategies where non exist. The only point is that yea it should be 1/3 but it you calculate it using Bayes theorem it is 1/2.
And the EV is yours not his. Pretend he is a robot programmed to not fuck with you but follow the rules precisely as written.
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man i got 1/3 
I simplified the problem statement a lot. The problem I did look like this:
Day0:
A single state of sleep S0
Day1:
2 states, a wake state W1, and a sleep state S1
Day2:
1 state, a wake state W2
S0 transition to W1 with probability 1/2 (head)
S0 transition to S1 with probability 1/2 (tail)
Both W1 and S1 transition to W2 with probability 1
I made a blatant assumption that P(Day0) = P(Day1) = P(Day2) = 1/3, this let me simplify some expressions.
Basically this let us condition some events on which day it is. I feel this is a bit ridiculous, but Bayesians put bullshit priors on random stuff anyways hehehe
Now we are after this query:
P(T | Wake), i.e. what's the probability of tail given the princess is awake at the moment (of the question from the wizard)
P(T | Wake) = P(Wake | T) * P(T) / P(Wake) //bayues rule
We now compute the components
##
Computing P(Wake):
P(Wake) = P(W1) + P(W2) //If ur wake, ur in one of the 2 wake states
= P(Day0)P(W1 | Day0) + P(Day1)P(W1 | Day1) + P(Day2)P(W1 | Day2) +
...P(Day0)P(W2 | Day0) + P(Day1)P(W2 | Day1) + P(Day2)P(W2 | Day2) //decompose based on which day it could be
= 0 + P(Day1)P(W1 | Day1) + 0 +
...0 + 0 + P(Day2)P(W2 | Day2) //most of these are 0...
= 1/3 * P(W1 | Day1) + 1/3 * P(W2 | Day2)
P(W1 | Day1) = 1/2 // because P(W1 | Day1) = P(S1 | Day1) = 1/2 depending on your coin toss
P(W2 | Day2) = 1 // because ur wake no matter what on day2
Thus:
P(Wake) = 1/3 * 1/2 + 1/3 * 1 = 3/6
##Computing P(Wake | T)
P(Wake | T)
= P(Day0)*P(Wake | T, Day0) + P(Day1)*P(Wake | T, Day1) + P(Day2)*P(Wake | T, Day2)
= 0 + 0 + P(Day2)*P(Wake | T, Day2)
P(Wake | T, Day2) = P(W1 | T, Day2) + P(W2 | T, Day2) = 0 + 1 = 1
Thus:
P(Wake | T) = 1/3 * 1 = 1/3
##Finally:
P(T | Wake)
= P(Wake | T) * P(T) / P(Wake)
= (1/3 * 1/2) / (3/6)
= 1/6 / 3/6
= 1/3
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wouldn't the probability on waking on monday be 25% and the probability of waking on tuesday 75%?
if the coin flips tails you wake on tuesday, 50% chance of this happening. if the coin flips heads you have 25% of waking on monday and 25% of waking on tuesday.
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Russian Federation823 Posts
There's no philosophy in this, just math. I might solve it later if i have time.
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On January 04 2013 19:21 kusto wrote:
There's no philosophy in this, just math. I might solve it later if i have time.
The problem is about giving credence to a certain proposition in a particular thought-experiment situation. Of course it is philosophy (epistemology). Academic philosophy is (or rather: can be) way closer to math than you might expect.
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Russian Federation823 Posts
On January 04 2013 19:04 evanthebouncy! wrote:man i got 1/3 I simplified the problem statement a lot. The problem I did look like this: Day0: A single state of sleep S0 Day1: 2 states, a wake state W1, and a sleep state S1 Day2: 1 state, a wake state W2 S0 transition to W1 with probability 1/2 (head) S0 transition to S1 with probability 1/2 (tail) Both W1 and S1 transition to W2 with probability 1 I made a blatant assumption that P(Day0) = P(Day1) = P(Day2) = 1/3, this let me simplify some expressions. Basically this let us condition some events on which day it is. I feel this is a bit ridiculous, but Bayesians put bullshit priors on random stuff anyways hehehe Now we are after this query: P(T | Wake), i.e. what's the probability of tail given the princess is awake at the moment (of the question from the wizard) P(T | Wake) = P(Wake | T) * P(T) / P(Wake) //bayues rule We now compute the components ## Computing P(Wake): P(Wake) = P(W1) + P(W2) //If ur wake, ur in one of the 2 wake states = P(Day0)P(W1 | Day0) + P(Day1)P(W1 | Day1) + P(Day2)P(W1 | Day2) + ...P(Day0)P(W2 | Day0) + P(Day1)P(W2 | Day1) + P(Day2)P(W2 | Day2) //decompose based on which day it could be = 0 + P(Day1)P(W1 | Day1) + 0 + ...0 + 0 + P(Day2)P(W2 | Day2) //most of these are 0... = 1/3 * P(W1 | Day1) + 1/3 * P(W2 | Day2) P(W1 | Day1) = 1/2 // because P(W1 | Day1) = P(S1 | Day1) = 1/2 depending on your coin toss P(W2 | Day2) = 1 // because ur wake no matter what on day2 Thus: P(Wake) = 1/3 * 1/2 + 1/3 * 1 = 3/6 ##Computing P(Wake | T) P(Wake | T) = P(Day0)*P(Wake | T, Day0) + P(Day1)*P(Wake | T, Day1) + P(Day2)*P(Wake | T, Day2) = 0 + 0 + P(Day2)*P(Wake | T, Day2) P(Wake | T, Day2) = P(W1 | T, Day2) + P(W2 | T, Day2) = 0 + 1 = 1 Thus: P(Wake | T) = 1/3 * 1 = 1/3 ##Finally: P(T | Wake) = P(Wake | T) * P(T) / P(Wake) = (1/3 * 1/2) / (3/6) = 1/6 / 3/6 = 1/3
You must have made a mistake somewhere - your computations are quite complicated, i did it similar to EtherealDeath and 3/4 is the correct answer.
What you're searching for is p(T | waking up on Mo) + p(T | waking up on Tuesday) = p(T | waking up on an unknown day).
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Russian Federation823 Posts
On January 04 2013 20:26 Prog wrote:Show nested quote +On January 04 2013 19:21 kusto wrote:
There's no philosophy in this, just math. I might solve it later if i have time. The problem is about giving credence to a certain proposition in a particular thought-experiment situation. Of course it is philosophy (epistemology). Academic philosophy is (or rather: can be) way closer to math than you might expect.
OK, then the problem is the word "credence", which might have inherited some unpractical definitions.
For me, it's just the probability p(coin was Tails | i have woken up on any day) - with this premise, the problem is perfectly solvable.
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On January 04 2013 18:41 EtherealDeath wrote:Show nested quote +On January 04 2013 17:20 hypercube wrote:On January 04 2013 16:51 EtherealDeath wrote:
The explicit is that the host flips a fair coin, and that coin flip which you do not observe determines what the host does. And Bayesian analysis says it is 1/2. But betting 1/2 would lose you money. You can see it easier by modifying the problem such that heads results in a wake amnesia sleep wake etc cycle for an arbitarily large number of days, and that on the last day, you walk free after tea. Then the problem becomes bettering on whether or not you walk free after tea, and if you bet 1/2 you sure as hell are going to be losing lots of money. Ok, let's backtrack. Clearly we aren't talking about Monty Hall anymore but some version of OP's game. Either way you didn't answer if the philosopher asks the question every time. That's the key assumption not whether he wakes up Sleeping Beauty or not. Under the assumption that he does ask the question every time he wakes Sleeping Beauty up the answer is 1/3 not 1/2. Or 0 for the arbitrarily large case. Note 0 is a nonsensical answer but the assumption that the philosopher lives forever is nonsense so that's expected. Under different assumptions the answer is different. I.e. if we're betting for money and we expect the philosopher to try to maximize his EV the right play is to guess heads 50% and tails 50%. That's not a Bayesian answer. It turns out that simply saying that the philosopher tries to maximize his EV gives no new information, it's exactly the same as asking what the philosopher's strategy is while specifying that we know nothing about it. * *It turns out that if we play the Nash equilibrium (guess tails 50% of the time) then the philosopher really is indifferent between any strategies. Since we are playing a game where he can observe our strategy but we can't observe his, he can play anything he damn well pleases and still get an EV of 0. So assuming rationality on his part gives no new information and we're back to the original problem of asking about something we explicitly said we know nothing about. You are over analyzing and sticking in extra assumptions/strategies where non exist. The only point is that yea it should be 1/3 but it you calculate it using Bayes theorem it is 1/2.
Nope, you just miscalculated.
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What you're looking for is P(Tails|Waken up)
By Bayes theorem
P(Tails|Waken up) = P(Waken up|Tails)*P(Tails, a priori)/P(Waken up) = 0.5*0.5/0.75= 1/3
I could go back and check your math, but in these cases the Bayes theorem always gives the same result as the traditional way of counting elementary cases. If you get a different result you messed up somewhere since the two ways are mathematically equivalent.
edit:
On January 04 2013 15:58 EtherealDeath wrote:Hopefully I didnt fuck something up in my head. Ok so we want Pr(Monday | tea), so Pr(tea | Monday) * Pr(Monday) / Pr(Tea). Pr(tea | Monday) = Pr(Heads) = 1/2 if we do it Bayesian. Pr(Monday) = 1/2 (pick a day at random, unbiased manner) Pr(tea) = 3/4 fuck it never mind lololol I inserted a 1 randomly in my head.
Which is exactly the same as you got, so I don't understand the problem.
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Its 1/3 for tails and 2/3 head imrite ?
So she is wrong edit: didn't read properly OP, its the mad scientist who is talking. Anyway it is just a point of view problem. The correct answer (if she hasn't forgotten the rules of the game) should be that it is more likely to be head than tails.
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On January 05 2013 00:37 Boblion wrote:
Its 1/3 for tails and 2/3 head imrite ?
So she is wrong.
Reading comprehension fail on my part 
She's actually right numerically: P(Monday|tea) does equal 1/3 and the calculation is right. Checking by counting cases there are two cases of Tuesday AND Tea and only one of Monday AND Tea, so 1/3 is correct.
But it's not obvious how you get P(Tails|tea) = 1/3 from that. So, it's really a different calculation that doesn't say anything about P(Tails|Tea).
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On January 04 2013 21:09 kusto wrote:Show nested quote +On January 04 2013 20:26 Prog wrote:On January 04 2013 19:21 kusto wrote:
There's no philosophy in this, just math. I might solve it later if i have time. The problem is about giving credence to a certain proposition in a particular thought-experiment situation. Of course it is philosophy (epistemology). Academic philosophy is (or rather: can be) way closer to math than you might expect. OK, then the problem is the word "credence", which might have inherited some unpractical definitions. For me, it's just the probability p(coin was Tails | i have woken up on any day) - with this premise, the problem is perfectly solvable.
What's the probability "I have woken up on any day"
that's a hard one
edit: remember that propositions should tell you what possible world you are in
edit: anybody who answers 1/3 must then account for arbitrarily large case
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Several people have mentioned they got 3/4, that is not a commonly argued answer, how did you get this?
edit:
you have to consider also, say he asks on sunday
"what is the probability that the coin will be tails"
ezpz 1/2
then she goes to sleep and wakes up and gains no information at all
then he asks
"what is the probability that the coin was tails"
ermmmmmmmm now it's harder
but no information was gained?!?
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Now that i'm thinking about it the main problem is that the affirmation of the mad guy is incredibly vague. And OP isn't really clear about what we are discussing here. It seems that we have to take the girl point of view.
Problem is that she lost her memory and well the girl can't really answer anything other than "well if you say so it was tails and we are tuesday". If she remembers the rules she can add a bit more and describe the whole experiment (like several people tried to do in this thread) but i have no idea about what she is supposed to answer other than that. I mean she could always say "no you a liar" but eh i guess she has to believe him...
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I'll jump on the occasion to ask a question about probabilities : when you say that there's 1/2 chances that it's tails, is it out of the infinite, as in if you threw a coin ad infinitam it would split between two equal occurrances of tails and heads? If so, isn't it theoretically possible to throw a coin every minute for a whole century and only obtain tails ? And if so, doesn't it mean that probabilities are, strictly speaking, empirical observations?
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^
Every time i have to read one of your post i'm like wtf is wrong with you. You are probably the most confused and confusing guy on TL. I mean there are some really dumb guys and smart guys on TL but at least even if their stupidity (or intelligence) is sometimes hard to understand at least it makes sense. On the other hand you are always playing with words which is something extremly annoying. You also seem to always make a confusion between theory, concepts and real life and this is unhealthy imo. You are STERILE and always babbling.
1- Yes tails and heads are the only outcome as described by OP (although you could argue you can get the "edge" of the coin irl).
2- Yea you can obtain tails or heads forever, its called luck.
3- Probabilities are RULES. The outcome (irl) is the empirical observation.
Wtf is so hard about this ?
User was warned for this post
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I don't see what's wrong, it's just a fun question to me. And since TL is full of smart users, I can simply ask my questions and grow as a person.  I know we've been in heated discussions but hey, if you can teach me something, I won't reject it.
(Note that I never make a confusion between theory and real life, I'm just curious about words in general, that's all. I still eat when I'm hungry and then p... do my thing after a couple of days.)
I don't understand what you imply by saying that probabilities are rules, could you explain a little more ?
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Words are words. You can make everything happen with words lol.
Anyway i can see a coin. Can you see probabilities ? That should be enough to answer your question lol. Call it a convention, a concept, a rule, w/e. Happy now ?
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in before "but blind people can't see coins" arggggggggggggg.
I won't answer this one !!!
(Well i could, they can sense coins with their hands but then "what about if they don't have hands ?"etc... it never ends with people like Kukaracha lol).
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No, the question is less tricky than that!
For example, if I throw a coin, I'll say "there's a 50% chance that the outcome is tails" (excluding any other event as in the coin being desintegrated by a bomb, the observers dying of a heart attack, etc). Then I'll throw it a couple of times and I'll be left with something like 40% of tails and 60% of heads. My proposition wasn't empirically verified, although it doesn't invalidate the original "rule" (it seems like an appropriate term). In fact, if the proportions are a division of an infinite number, how can you divide an infinite number ?
Also, if I were to make an educated guess and place a bet on any of the two possibilities, I may consider that each has the same chances of appearing. However, if I throw the coin there's always the possibility that I'll only obtain tails for a very long time, as what seems very long to me is nothing in comparison to an infinite duration. As such, although my choice is correct in theory, it may not be appropriate for me as the life span of a human being is minuscule in comparison of the duration concerned by the 50/50 proportion.
(For example, if I roll a dice with 6 faces, I might consider the fact that there is a 1/6 chances that each face will appear, and place my bets accordingly, except that the game will only last a couple of minutes in the billions of years that constitute our mathematical context, and that the chances that I will roll only sixes aren't that small when you look at the big picture.)
The second question being : aren't probabilities irrelevant when compared to an infinite number? How is it that they seem to be verified empirically? Why are results constant?
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On January 05 2013 02:29 Kukaracha wrote:
For example, if I throw a coin, I'll say "there's a 50% chance that the outcome is tails"
It is only true if the coin is fair... another concept... but does perfect fairness exists ? That's a question for you Kukaracha.
On January 05 2013 02:29 Kukaracha wrote:
(excluding any other event as in the coin being desintegrated by a bomb, the observers dying of a heart attack, etc). Then I'll throw it a couple of times and I'll be left with something like 40% of tails and 60% of heads. My proposition wasn't empirically verified, although it doesn't invalidate the original "rule" (it seems like an appropriate term).
Dude that's where you are getting lost. We are discussing in this thread a "fantasy" problem (its called math for a reason lol) whereas you want to discuss the result of a real coin flip. Now i have to tell you that irl you don't make the rules except if you are god or some crazy shit lol. You have no fucking idea about the fairness of your coin and its "rules", hence all the empirical rolls and shit. You could also use a bit of basic physics knowledge and weight your coin etc... anyway the result is that you will never know the exact "rules" whereas in a fantasy problem you are MAKING the rules.
On January 05 2013 02:29 Kukaracha wrote:
In fact, if the proportions are a division of an infinite number, how can you divide an infinite number ?
Classic Kukaracha, a random question completly unrelated.
On January 05 2013 02:29 Kukaracha wrote:
Also, if I were to make an educated guess and place a bet on any of the two possibilities, I may consider that each has the same chances of appearing.
However, if I throw the coin there's always the possibility that I'll only obtain tails for a very long time, as what seems very long to me is nothing in comparison to an infinite duration. As such, although my choice is correct in theory, it may not be appropriate for me as the life span of a human being is minuscule in comparison of the duration concerned by the 50/50 proportion.
(For example, if I roll a dice with 6 faces, I might consider the fact that there is a 1/6 chances that each face will appear, and place my bets accordingly, except that the game will only last a couple of minutes in the billions of years that constitute our mathematical context, and that the chances that I will roll only sixes aren't that small when you look at the big picture.)
The second question being : aren't probabilities irrelevant when compared to an infinite number? How is it that they seem to be verified empirically? Why are results constant?
Oh god you are stuck in a an infinite loop of auto mindfuck it seems. I can't do anything for you lol. As i said you are STERILE.
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Just curious, i need some empirical data lol.
Poll: Who is the biggest retardkukaracha (5) 71% boblion (2) 29% 7 total votes Your vote: Who is the biggest retard (Vote): boblion
(Vote): kukaracha
Just to be clear the empirical data is about TL users opinions, not me or Kukaracha.
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On January 05 2013 01:06 sam!zdat wrote:Show nested quote +On January 04 2013 21:09 kusto wrote:On January 04 2013 20:26 Prog wrote:On January 04 2013 19:21 kusto wrote:
There's no philosophy in this, just math. I might solve it later if i have time. The problem is about giving credence to a certain proposition in a particular thought-experiment situation. Of course it is philosophy (epistemology). Academic philosophy is (or rather: can be) way closer to math than you might expect. OK, then the problem is the word "credence", which might have inherited some unpractical definitions. For me, it's just the probability p(coin was Tails | i have woken up on any day) - with this premise, the problem is perfectly solvable. What's the probability "I have woken up on any day" that's a hard one edit: remember that propositions should tell you what possible world you are in edit: anybody who answers 1/3 must then account for arbitrarily large case
In the arbitrarily large case the probability of tails (under the condition that the princess is woken up) goes to zero.
Don't see how you can say that "no new information was gained". The fact that she was woken up IS new information.
This isn't about Bayesian inference at all: simple counting gives the same result.
It's exactly the same mechanism as Monty Hall or the Coin Toss puzzle.
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^
Her only source of information is the mad guy.
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On January 05 2013 03:14 Boblion wrote:
^
Her only source of information is the mad guy.
Are you agreeing or disagreeing?
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The thing is that being awake doesn't help her to know if it is tails, head or the day, but as i said before OP question isn't really clear.
sam!zdat mind to give your "answer" ?
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On January 05 2013 03:00 Boblion wrote:Just curious, i need some empirical data lol. Poll: Who is the biggest retardkukaracha (5) 71% boblion (2) 29% 7 total votes Your vote: Who is the biggest retard (Vote): boblion
(Vote): kukaracha
they guy who goes batshit with ad hominem wins in my eyes.
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On January 05 2013 03:25 Boblion wrote:
The thing is that being awake doesn't help her to know if it is tails or head or the day, but as i said before OP question isn't really clear.
But it does. She knows that the coin landing heads or tails would change the probability of her being awake. So it's not surprising that being awake changes the probability of the coin having landed heads or tails in turn.
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But she doesn't know what will happen next. Maybe the mad guy lied and it is monday and she will go to sleep again ?
I think that this problem has no solution from her pov.
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sleeping beauty knows everything you know, she only has amnesia for things that happen on monday.
the philosopher is not a liar, and he asks every time they have tea.
he can ask her two things, consider both:
what is the probability that the proposition 'the coin was tails' is true?
what is the probability that the proposition 'it is now monday' is true?
the second one is harder because it involves an indexical. But if on sunday the probaility is .5 that tails, and she gains no information when she wakes up because both outcomes produce same phenomenological experience, then it seems answer must be .5. But if she always guesses tails she will be wrong more than half the time, so the probability can't be .5.
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you'll notice that the wikipedia article has a section titled 'solutions' and none title 'solution'
in samizdat's blog, no appeals to wikithority are permitted
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I wrote answerS in my last post :p
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On January 05 2013 04:13 sam!zdat wrote:
sleeping beauty knows everything you know, she only has amnesia for things that happen on monday.
the philosopher is not a liar, and he asks every time they have tea.
he can ask her two things, consider both:
what is the probability that the proposition 'the coin was tails' is true?
what is the probability that the proposition 'it is now monday' is true?
the second one is harder because it involves an indexical. But if on sunday the probaility is .5 that tails, and she gains no information when she wakes up because both outcomes produce same phenomenological experience, then it seems answer must be .5. But if she always guesses tails she will be wrong more than half the time, so the probability can't be .5.
That's silly, of course she gained new information. If you want to be anal about it the information was gained at the moment when the rules were explained to her. At that point she already knows that whenever she awakes there'll be a 1/3 chance that it's Monday and the coin had landed Heads, a 1/3 chance that it's Tuesday and the coin landed Tails and a 1/3 chance that it's Tuesaday and the coin landed Heads.
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so on sunday when the philosopher explains sleeping beauty will b e correct if she says that 'there is a 1/3 probability that the coin will have been tails'?
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On January 05 2013 02:52 Boblion wrote:
It is only true if the coin is fair... another concept... but does perfect fairness exists ? That's a question for you Kukaracha.
It's a good question, true. Let's stay on the track of fantasy settings though!
On January 05 2013 02:52 Boblion wrote:
Dude that's where you are getting lost. We are discussing in this thread a "fantasy" problem (its called math for a reason lol) whereas you want to discuss the result of a real coin flip. Now i have to tell you that irl you don't make the rules except if you are god or some crazy shit lol. You have no fucking idea about the fairness of your coin and its "rules", hence all the empirical rolls and shit. You could also use a bit of basic physics knowledge and weight your coin etc... anyway the result is that you will never know the exact "rules" whereas in a fantasy problem you are MAKING the rules.
But would you deny that we make many, many educated guesses in real-life settings? Poker, stock exchange... It's true that the coin example would be flawed IRL because it can't be calculated accurately enough, but my questions remain.
On January 05 2013 02:52 Boblion wrote:Show nested quote +On January 05 2013 02:29 Kukaracha wrote:
In fact, if the proportions are a division of an infinite number, how can you divide an infinite number ?
Classic Kukaracha, a random question completly unrelated.
I personally find that it is an interesting question and I believe that people who have studied maths could provide a sort of answer, no?
On January 05 2013 02:52 Boblion wrote:
Oh god you are stuck in a an infinite loop of auto mindfuck it seems. I can't do anything for you lol. As i said you are STERILE.
* I am FUN
Btw I call bullshit on that poll, I'm obviously awesome. But I don't want to derail this any further (sorry sam!zdat).
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derail away I don't care, I derail everybody else's threads
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See what's curious about this problem is we seem to have two different claims:
"it is the case that X"
"it is the case that when I perform an utterance claiming X I will be correct"
and the probabilities of these two things are different.
somebody get me an aspirin
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On January 05 2013 05:46 sam!zdat wrote:
so on sunday when the philosopher explains sleeping beauty will b e correct if she says that 'there is a 1/3 probability that the coin will have been tails'?
She would be correct to say: "When you awaken me you will have thrown tails with a probability of 1/3."
She might add: "However when you do not awaken me the probability of you having thrown tails is 1. You will wake me up with a probability of 3/4 and not wake me up with a probability of 1/4. This leads to a total probability of throwing tails as (3/4)*(1/3) + (1/4)*1 = 1/2"
Think of it this way: I throw coins and record the results on separate pieces of paper. Now the probability for any particular piece containing the text "Tails" is 50%. Now I announce that I'm throwing out half of the pieces that have "Tails" written on them. Have I changed the probability of the pieces that I didn't touch?
+ Show Spoiler +The answer of course is yes, now each paper is less likely to have Tails written on them. Even the ones I didn't touch.
The key is that I changed the underlying distribution. Saying: "The probability that this piece of paper has Tails written on it is 50%" is imprecise. The precise way to say it is that the piece of paper is part of a distribution that is 50% heads 50% tails. The probability isn't intrinsic to the piece of paper, it's a consequence of it being part of a particular distribution. If I change the distribution I change the probability.
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On January 05 2013 06:27 sam!zdat wrote:See what's curious about this problem is we seem to have two different claims: "it is the case that X" "it is the case that when I perform an utterance claiming X I will be correct" and the probabilities of these two things are different. somebody get me an aspirin
You insist in saying P(tails) and P(tails|waken up) are the same thing. They are not.
Of course the probabilities of the two things are different because you changed the meaning of X.
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On January 05 2013 06:27 sam!zdat wrote:See what's curious about this problem is we seem to have two different claims: "it is the case that X" "it is the case that when I perform an utterance claiming X I will be correct" and the probabilities of these two things are different. somebody get me an aspirin
I smell the despotic obfuscation of truth-in-performativity abound......
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On January 05 2013 00:28 hypercube wrote:What you're looking for is P(Tails|Waken up) By Bayes theorem P(Tails|Waken up) = P(Waken up|Tails)*P(Tails, a priori)/P(Waken up) = 0.5*0.5/0.75= 1/3 I could go back and check your math, but in these cases the Bayes theorem always gives the same result as the traditional way of counting elementary cases. If you get a different result you messed up somewhere since the two ways are mathematically equivalent. edit: Show nested quote +On January 04 2013 15:58 EtherealDeath wrote:On January 04 2013 15:53 sam!zdat wrote:
how do you get 1/4? Hopefully I didnt fuck something up in my head. Ok so we want Pr(Monday | tea), so Pr(tea | Monday) * Pr(Monday) / Pr(Tea). Pr(tea | Monday) = Pr(Heads) = 1/2 if we do it Bayesian. Pr(Monday) = 1/2 (pick a day at random, unbiased manner) Pr(tea) = 3/4 fuck it never mind lololol I inserted a 1 randomly in my head. Which is exactly the same as you got, so I don't understand the problem.
I was calculating the probability that it is Monday, given that we are sitting down for Tea, not the probability that the coin is tails given that we woke up.
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On January 05 2013 06:43 EtherealDeath wrote:Show nested quote +On January 05 2013 00:28 hypercube wrote:What you're looking for is P(Tails|Waken up) By Bayes theorem P(Tails|Waken up) = P(Waken up|Tails)*P(Tails, a priori)/P(Waken up) = 0.5*0.5/0.75= 1/3 I could go back and check your math, but in these cases the Bayes theorem always gives the same result as the traditional way of counting elementary cases. If you get a different result you messed up somewhere since the two ways are mathematically equivalent. edit: On January 04 2013 15:58 EtherealDeath wrote:On January 04 2013 15:53 sam!zdat wrote:
how do you get 1/4? Hopefully I didnt fuck something up in my head. Ok so we want Pr(Monday | tea), so Pr(tea | Monday) * Pr(Monday) / Pr(Tea). Pr(tea | Monday) = Pr(Heads) = 1/2 if we do it Bayesian. Pr(Monday) = 1/2 (pick a day at random, unbiased manner) Pr(tea) = 3/4 fuck it never mind lololol I inserted a 1 randomly in my head. Which is exactly the same as you got, so I don't understand the problem. I was calculating the probability that it is Monday, given that we are sitting down for Tea, not the probability that the coin is tails given that we woke up.
Yea, I got that later. Anyway, I couldn't find your calculation for P(Tails|Tea). Do you have any issues with mine?
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Why are you guys talking about tea? The tea is utterly irrelevant I just put it in there because it sounds like something Lewis Carroll would write.
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On January 04 2013 14:51 sam!zdat wrote:
Then the philosopher asks:
Sleeping Beauty, my ravishing somnolent darling, what credence do you ascribe to the proposition that "the Coin was tails"
That's the important point. While you could make an argument that a question about whether it was Monday or not could be deemed to be a 1/3 probability that isn't the question. Sleeping Beauty's awakeness has no effect on what the coin ended up so the probability is 1/2.
edit: Thinking about it more I don't think you could argue the Monday being 1/3 thing either. Yes there are three times she wakes up but P(Heads|Monday) and P(Heads| Tuesday) are the same result so they both have probability of 1/2.
edit: Ok I'm an idiot the Monday thing is 1/3. Point still stands about the probability.
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“I say let the world go to hell, but I should always have my tea.”
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On January 05 2013 06:29 hypercube wrote:Show nested quote +On January 05 2013 05:46 sam!zdat wrote:
so on sunday when the philosopher explains sleeping beauty will b e correct if she says that 'there is a 1/3 probability that the coin will have been tails'? She would be correct to say: "When you awaken me you will have thrown tails with a probability of 1/3."
So what is the difference in the formal structure of claim "you will have thrown tails" and "when you awaken me you will have thrown tails"? Then when she actually wakes up and considers the claim "you have thrown tails" should she believe 1/3 or 1/2? Remember that she didn't gain any information about the world, and before she went to sleep the probability was 1/2.
She might add: "However when you do not awaken me the probability of you having thrown tails is 1. You will wake me up with a probability of 3/4 and not wake me up with a probability of 1/4. This leads to a total probability of throwing tails as (3/4)*(1/3) + (1/4)*1 = 1/2"
Yes, so that's how you know on Sunday that the probability is 1/2. But when she wakes up she doesn't know what day it is. What should she answer about her belief that the coin was tails?
Think of it this way: I throw coins and record the results on separate pieces of paper. Now the probability for any particular piece containing the text "Tails" is 50%. Now I announce that I'm throwing out half of the pieces that have "Tails" written on them. Have I changed the probability of the pieces that I didn't touch? + Show Spoiler +The answer of course is yes, now each paper is less likely to have Tails written on them. Even the ones I didn't touch.
The key is that I changed the underlying distribution. Saying: "The probability that this piece of paper has Tails written on it is 50%" is imprecise. The precise way to say it is that the piece of paper is part of a distribution that is 50% heads 50% tails. The probability isn't intrinsic to the piece of paper, it's a consequence of it being part of a particular distribution. If I change the distribution I change the probability.
you're assuming that distributing items in a set in space is the same as distributing them in time. Is that true?
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On January 05 2013 06:45 hypercube wrote:Show nested quote +On January 05 2013 06:43 EtherealDeath wrote:On January 05 2013 00:28 hypercube wrote:What you're looking for is P(Tails|Waken up) By Bayes theorem P(Tails|Waken up) = P(Waken up|Tails)*P(Tails, a priori)/P(Waken up) = 0.5*0.5/0.75= 1/3 I could go back and check your math, but in these cases the Bayes theorem always gives the same result as the traditional way of counting elementary cases. If you get a different result you messed up somewhere since the two ways are mathematically equivalent. edit: On January 04 2013 15:58 EtherealDeath wrote:On January 04 2013 15:53 sam!zdat wrote:
how do you get 1/4? Hopefully I didnt fuck something up in my head. Ok so we want Pr(Monday | tea), so Pr(tea | Monday) * Pr(Monday) / Pr(Tea). Pr(tea | Monday) = Pr(Heads) = 1/2 if we do it Bayesian. Pr(Monday) = 1/2 (pick a day at random, unbiased manner) Pr(tea) = 3/4 fuck it never mind lololol I inserted a 1 randomly in my head. Which is exactly the same as you got, so I don't understand the problem. I was calculating the probability that it is Monday, given that we are sitting down for Tea, not the probability that the coin is tails given that we woke up. Yea, I got that later. Anyway, I couldn't find your calculation for P(Tails|Tea). Do you have any issues with mine?
Hmm I suppose that could work actually.
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On January 05 2013 06:46 sam!zdat wrote:
Why are you guys talking about tea? The tea is utterly irrelevant I just put it in there because it sounds like something Lewis Carroll would write.
Have you read what I wrote?
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On January 05 2013 06:46 imallinson wrote:Show nested quote +On January 04 2013 14:51 sam!zdat wrote:
Then the philosopher asks:
Sleeping Beauty, my ravishing somnolent darling, what credence do you ascribe to the proposition that "the Coin was tails" That's the important point. While you could make an argument that a question about whether it was Monday or not could be deemed to be a 1/3 probability that isn't the question. Sleeping Beauty's awakeness has no effect on what the coin ended up so the probability is 1/2.
yes, good. But then how do you explain the EV? The fact remains that she'll probably be wrong if she says "the coin was tails"
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On January 05 2013 06:50 hypercube wrote:Show nested quote +On January 05 2013 06:46 sam!zdat wrote:
Why are you guys talking about tea? The tea is utterly irrelevant I just put it in there because it sounds like something Lewis Carroll would write. Have you read what I wrote?
oh, you mean "tea" to signify "I'm currently awake"?
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On January 05 2013 03:10 hypercube wrote:
Don't see how you can say that "no new information was gained". The fact that she was woken up IS new information.
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.
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On January 05 2013 06:51 sam!zdat wrote:Show nested quote +On January 05 2013 06:46 imallinson wrote:On January 04 2013 14:51 sam!zdat wrote:
Then the philosopher asks:
Sleeping Beauty, my ravishing somnolent darling, what credence do you ascribe to the proposition that "the Coin was tails" That's the important point. While you could make an argument that a question about whether it was Monday or not could be deemed to be a 1/3 probability that isn't the question. Sleeping Beauty's awakeness has no effect on what the coin ended up so the probability is 1/2. yes, good. But then how do you explain the EV? The fact remains that she'll probably be wrong if she says "the coin was tails"
I think I've been thinking about this wrong. It's not whether its heads or tails that's really being asked.
edit: For an outside observer its definitely still 50-50. Not so sure from her perspective.
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Ah, good! what is really being asked?
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On January 05 2013 06:18 Kukaracha wrote:
But would you deny that we make many, many educated guesses in real-life settings? Poker, stock exchange... It's true that the coin example would be flawed IRL because it can't be calculated accurately enough, but my questions remain.
I have never denied the usefulness of maths lol. Obviously we have to use this knowledge to make guesses in real-life settings but we are making assumptions, we are theorizing. Again do not mistake the maths with the "real" stuff. Everyone with basic probabilities knowledge can understand the "maths" behind poker (and make the assumption that cards are dealt randomly) on the other hand if you know and understand perfectly the Pseudorandom number generator of a poker site you gonna be rich real quick. There are more things than just the "maths" in poker, you can also get some information by observing the other players (or their cards lol). Knowing the maths will help you tho and on the long run you should be able to beat a guy who have no idea about the basic strenght of the hands. Or you could get unlucky.
Stock exchange is way more complicated and i don't really want to discuss this but it is definitly not just about maths (or you could argue that our maths models are not strong enough yet) and there are way too many things involved. Insider trading will make you richer than having 300 IQ and a Fields medal. Or you could go to jail lol. But let's just say that it is like a giant poker game with millions of players and a crazy amount of cheating and randomness.
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On January 05 2013 07:08 sam!zdat wrote:
Ah, good! what is really being asked?
It's a question of whether it's heads or tails as a function of what day it is. That made like zero sense.
There are two possibilities for what day it is.
Monday can only occur if it's heads in which case it is 100% heads.
Tuesday can occur if it's heads or tails so you have double the chance of getting Tuesday. If it's Tuesday its 50-50 heads or tails.
P(Mon|Heads)=1/3 x 1 = 1/3
P(Tues|Heads)=2/3 x 1/2 = 1/3
P(Tues|Tails)=2/3 x 1/2 = 1/3
So P(Heads) = P(Mon|Heads) + P(Tues|Heads) = 2/3 and P(Tues) = 1/3
So go with tails.
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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?
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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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But when she wakes up surely there is a one half chance that she is in a world in which the coin was heads, and she will see prince charming again, and a one half chance in which the coin was tails, and she will not.
(sorry if I'm mixing up heads and tails I'm sure I have)
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On January 05 2013 06:55 sam!zdat wrote:Show nested quote +On January 05 2013 03:10 hypercube wrote:
Don't see how you can say that "no new information was gained". The fact that she was woken up IS new information. 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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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?
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What exactly is the arbitrarily large case in this case?
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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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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
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I just realized this discussion is turning me into a Calvinist. Oh dear lord
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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.
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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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As long as you don't understand Kukaracha's existential problems you are fine. Trust me.
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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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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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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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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?
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On January 05 2013 07:56 sam!zdat wrote:Show nested quote +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
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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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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yeah, think about it and see if you can tell me what the 2 different beliefs are that give you different answers. that's the key I think but I'm not sure exactly how to say what it is. Like I say, the non-indexical proposition is definitely 1/2, and the indexical proposition seems to be 1/3, but how to apply probabilities to indexicals is not clear to me.
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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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if you think them at the same time, then yeah I'd say they have to have the same credence
cute example though ^.^
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Which is not surprising at all, considering that the beliefs "p" and "p is true" have the same conditions of satisfaction.
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Right, but that seems not to be the case in the thought experiment, which is what is troubling
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Good lord what's the problem here samzdat this was solved on the first page.
Bayesianism 1 - 0 samzdat
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What's your solution?
If you think it's easy that means you don't understand yet, I promise
edit: we can just generalize the above law to apply to all things, actually. That's the first dogma of the church of samizdat
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On January 05 2013 09:30 sam!zdat wrote:
What's your solution?
If you think it's easy that means you don't understand yet, I promise
I think you're right, can you perhaps add a little bit about Bayesianism into the OP??
This requires prior knowledge which I don't have, and there's all sorts of stupid questions being asked and alternate problems and solutions throughout the thread.
From what little I've read about Bayesianism and the question I *think* you're asking in the OP it all seems very simple to me, if you could perhaps clarify them both that would be helpful =)
+ Show Spoiler +not seeing the problem here
If you want I can just read the OP as it is and give you my answer =/ Seems pointles if you're 100% certain I don't even understand the question lmao
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according to bayesianism she should change her credence in some proposition "the coin was tails" if and only if she gains some information about the world. It seems that she gains no information about the world, but it also seems like her credence will change. how to reconcile this?
yeah take a stab at it. what do you think
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Here I go, how to make a fool of yourself 101:
She doesn't need to "gain" information about the world, she has already accumulated information throughout her life.
She understands the inherent skullduggery in the philosopher's questioning and gives the appropriate answer...
You need to specify if he must ask her this question when she wakes up or if he can opt not to ask if her the question, and she is aware of this too.
If he promises that he will ask her the question any time that she wakes up then she will reply
"The coin is less likely to have flipped tails than heads"
if he doesn't say anything on the matter there's 3 options.
1. You make a random guess based on your previous life experience with mad philosophers
2. You try to determine what his aims are, work out how he will attempt to exploit your guessing pattern and play some kind of reverse double bluff on him.
3. Acknowledge that both are equally likely since he hasn't revealed if he will ask you the question every time or not, attribute a 50/50 chance that he does ask every time/doesn't ask every time which means overall heads is always the winning coin anyway, if you take this approach and I think it's the most "Bayesian" if my understanding is correct it will be something like 1/2 + 1/3 all divided by two.
How did I do  ?
edit: If you think it's easy that means you don't understand yet, I promise
I smell a sig.
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haha, assume he asks you every time. don't worry about his strategy, he has none. he explains everything beforehand.
the problem is that on sunday it's obvious that the coin has .5 chance tails.
when she wakes up (she doesn't know what day) she has gained no information (she can predict exactly what this waking up experience will be like) but all of the sudden it seems like the chance is 1/3 (that is, if you repeat and she always answers tails she will be wrong 2/3 of the time)
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Philosopher: Sleeping Beauty, my ravishing somnolent darling, what credence do you ascribe to the proposition that the Coin was tails ?
Sleeping Beauty: I say that proposition will be wrong 2/3 of the time/is most likely wrong sir.
(my sleeping beauty is good at maths so would answer 50|50 before she slept after she woke up 1/3 | 2/3)
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yes, good, so what if instead of 2 days vs 1 day it is infinity days vs 1 day? Should Sleeping Beauty say there is a vanishingly small chance that she will go free, or a 1/2 chance that she will go free?
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If it's infinity days vs one day she will say beforehand its 50/50 if I'm going to leave here, when asked "do you think you're about to leave" after waking up and drinking tea, as before would give a different response, and would reply "I'm more certain that I'm not about to leave than I could ever be about anything".
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You don't find that conclusion absurd?
Try to imagine that you are in her situation.
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Well I was about to post another option is that she's either in Loop A or Loop B and both are equally as likely as each other, so she may simply reply "I don't know, both are equally likely"
I don't know enough about Bayesianism to give you a definitive answer.
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You don't have to know anything about bayesianism. It's just a probability problem. The only thing about bayesianism is that (some, maybe) bayesians think you can solve every problem ever if you just think with probability. this I think demonstrates otherwise
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In terms of probability on any given day that she wakes up, there's only one day ever that she will be released and an infinite number of days where she will not be released. She also knows that both these alternative scenarios, waking up on the right day and being released or being in an infinite loop and never being released are equally likely. I don't know exactly how she would respond... would you care to make some comments of your own?
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Hmm okay reading something about it now....
The prior probability = 50/50
The two conditional probabilities are
1. one
2. infinity
If the two conditional probabilities are equal, the posterior probability equals the prior probability.
Since they're not she will give the answer of "I'm 99.999**% certain that I'm not going to be set free."
I see why you've raised this issue, but I think it more highlights the counter-intuitive nature of statistics and probabilities to the human mind rather than shows that Bayesianism itself is flawed.
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But isn't the probability 1/2 that she will be set free? One half of all sleeping beauties in this situation see prince charming again.
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Yes, at the outset of the problem it's a 50/50 chance that she will be set free.
Once she enters into the process of drinking potions, sleeping, waking up and drinking tea since she is going to be asked this question only once if she gets the good side of the coin and an infinite number of times if she gets the bad side of the coin the probability that this one particular day is the good day is 1 in infinity...
Sorry, a better way of saying this would be:
On any given day, because she doesn't know if it's the first day or nth day, from her perspective the chances are 50/50 that she will be let free, either she tossed heads or tossed tails.
However, as people pointed out if you said tails every time you would be wrong 2/3 times for 1 day vs 2 day, so the actual probability of the question you're asking is very different to what a non-mathematician would intuitively answer.
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so how can her belief change if she gains no information?
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Her "belief" never changes, she is just aware of how probability works and would tell you right from the outset that her chances are 50/50 to flip the heads/tails, but once she enters into two possible loops one comprising of one day and the other infinite days then her response must change accordingly.
The information gained is "I have just woken up, drank tea and been asked the question."
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So of all the sleeping beauties that enter this situation, all of them correctly reason that there's vanishing hope for them ever to escape, and all of them are correct, even though half of them go free? What is the belief that we are discussing, exactly?
edit: and that's not information, because she already knew that that would happen
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I can't follow you guys lol. Poor girl(s). The mad guy should just kill her.
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The philosopher begins on day 1. He takes the first sleeping beauty and conducts the experiment. Let's say for the sake of argument she flips heads. She wakes up, answers "I'm never getting out of here" and is correct. She goes back to sleep, and repeats this process ad infinitum, and is correct every day forever.
The philosopher continues on day 2. He takes the second sleeping beauty and conducts the experiment. Let's say for the sake of argument she flips tails. She wakes up, answers "I'm never getting out of here", is wrong and so set free. The philospher then wakes up the first sleeping beauty who says "I'm never getting out of here" and is again correct. She goes back to sleep, and repeats this process ad infinitum, and is correct every day forever.
The philosopher continues on day 3. He takes the third sleeping beauty and conducts the experiment. Let's say for the sake of argument she flips heads. She wakes up, answers "I'm never getting out of here" and is correct. She goes back to sleep, and repeats this process ad infinitum, and is correct every day forever. The philospher then wakes up the first sleeping beauty who says "I'm never getting out of here" and is again correct. She goes back to sleep, and repeats this process ad infinitum, and is correct every day forever
Every day he catches a sleeping beauty but sadly only gets to keep every second one that he finds.
Regardless, over time he accumulates an infinite number of sleeping beauties, and an infinite number of them answer "I'm never getting out of here" and are correct 99.999**% of the time, only once every second day would a single sleeping beauty out of an infinite number of sleeping beauties be correct in guessing that she was about to leave.
Prior to entering into this bargain the chance of the coin flipping heads or tails is 50/50, yes, and the chances of you being a new heads rolling sleeping beauty or a new tails rolling sleeping beauty is still 50/50 after the potion, sleep and tea, yes, but the chances of you being that "lucky" new subject in his experiment on any given day as opposed to just one of his infinite sleeping beauties is...... 1/infinity.
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On January 05 2013 07:14 Boblion wrote:Show nested quote +On January 05 2013 06:18 Kukaracha wrote:
But would you deny that we make many, many educated guesses in real-life settings? Poker, stock exchange... It's true that the coin example would be flawed IRL because it can't be calculated accurately enough, but my questions remain.
I have never denied the usefulness of maths lol. Obviously we have to use this knowledge to make guesses in real-life settings but we are making assumptions, we are theorizing. Again do not mistake the maths with the "real" stuff. Everyone with basic probabilities knowledge can understand the "maths" behind poker (and make the assumption that cards are dealt randomly) on the other hand if you know and understand perfectly the Pseudorandom number generator of a poker site you gonna be rich real quick. There are more things than just the "maths" in poker, you can also get some information by observing the other players (or their cards lol). Knowing the maths will help you tho and on the long run you should be able to beat a guy who have no idea about the basic strenght of the hands. Or you could get unlucky. Stock exchange is way more complicated and i don't really want to discuss this but it is definitly not just about maths (or you could argue that our maths models are not strong enough yet) and there are way too many things involved. Insider trading will make you richer than having 300 IQ and a Fields medal. Or you could go to jail lol. But let's just say that it is like a giant poker game with millions of players and a crazy amount of cheating and randomness.
But that's the problem : we make assumptions, "educated guesses" but I don't understand how we can really make an "educated guess" that the coin effectively has a 50% chance to show tails in the time span that interests us. We could obtain heads during our whole lifetime since a century is just an infinitesimal portion of... the infinite. The "rule" that tails and heads appear with a 50% chance each wouldn't be invalidated. And yet it seems that we can observe a certain balance in the occurrance of tails and heads; how come? There surely is a mathematical explanation that the odds appear consistantly in such a small time span. How come you can beat another poker player by making educated guesses, although the probabilities don't necessarily have to be verified within the extremely limited duration of the game?
And stock exchange wasn't such a bad example I think... probabilities come into play, just like in behavioural finance.
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Aren't you counting one person a bunch of different times, though? You say "an infinite number of them answer 0 and are right" but isn't that just one person answering over and over again?
edit:
what's the difference between a "sleeping beauty event" and an "answering event"? you are treating them the same
edit
On January 05 2013 10:58 Boblion wrote:
I can't follow you guys lol. Poor girl(s). The mad guy should just kill her.
this is the correct answer, you win.
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On January 05 2013 11:34 sam!zdat wrote:Aren't you counting one person a bunch of different times, though? You say "an infinite number of them answer 0 and are right" but isn't that just one person answering over and over again? edit: what's the difference between a "sleeping beauty event" and an "answering event"? you are treating them the same edit Show nested quote +On January 05 2013 10:58 Boblion wrote:
I can't follow you guys lol. Poor girl(s). The mad guy should just kill her. this is the correct answer, you win.
On January 05 2013 10:56 sam!zdat wrote:
So of all the sleeping beauties that enter this situation, all of them correctly reason that there's vanishing hope for them ever to escape, and all of them are correct, even though half of them go free? What is the belief that we are discussing, exactly?
edit: and that's not information, because she already knew that that would happen
Multiple sleeping beauties entering the situation.
Day 1: Finds sleeping beauty, keeps her.
beauty count :1
Day 2: Finds sleeping beauty, loses her.
beauty count :1
Day 3: Find sleeping beauty, keeps her.
beauty count :2
Day 4: ....
So no, it's not just one person. It's an infinite number of sleeping beauties because he keeps every second one.
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right, so of all the sleeping beauties, half of them go free, but of all the answering events, a vanishingly small number of them will be correct if claiming "I will go free"
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On January 05 2013 11:33 Kukaracha wrote:Show nested quote +On January 05 2013 07:14 Boblion wrote:On January 05 2013 06:18 Kukaracha wrote:
But would you deny that we make many, many educated guesses in real-life settings? Poker, stock exchange... It's true that the coin example would be flawed IRL because it can't be calculated accurately enough, but my questions remain.
I have never denied the usefulness of maths lol. Obviously we have to use this knowledge to make guesses in real-life settings but we are making assumptions, we are theorizing. Again do not mistake the maths with the "real" stuff. Everyone with basic probabilities knowledge can understand the "maths" behind poker (and make the assumption that cards are dealt randomly) on the other hand if you know and understand perfectly the Pseudorandom number generator of a poker site you gonna be rich real quick. There are more things than just the "maths" in poker, you can also get some information by observing the other players (or their cards lol). Knowing the maths will help you tho and on the long run you should be able to beat a guy who have no idea about the basic strenght of the hands. Or you could get unlucky. Stock exchange is way more complicated and i don't really want to discuss this but it is definitly not just about maths (or you could argue that our maths models are not strong enough yet) and there are way too many things involved. Insider trading will make you richer than having 300 IQ and a Fields medal. Or you could go to jail lol. But let's just say that it is like a giant poker game with millions of players and a crazy amount of cheating and randomness. But that's the problem : we make assumptions, "educated guesses" but I don't understand how we can really make an "educated guess" that the coin effectively has a 50% chance to show tails in the time span that interests us. We could obtain heads during our whole lifetime since a century is just an infinitesimal portion of... the infinite. The "rule" that tails and heads appear with a 50% chance each wouldn't be invalidated. And yet it seems that we can observe a certain balance in the occurrance of tails and heads; how come? There surely is a mathematical explanation that the odds appear consistantly in such a small time span. How come you can beat another poker player by making educated guesses, although the probabilities don't necessarily have to be verified within the extremely limited duration of the game? And stock exchange wasn't such a bad example I think... probabilities come into play, just like in behavioural finance.
Help me with this guy please.
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How can I help? I believe that probability is ontologically meaningless. It's just a useful lie.
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On January 05 2013 11:51 sam!zdat wrote:
right, so of all the sleeping beauties, half of them go free, but of all the answering events, a vanishingly small number of them will be correct if claiming "I will go free"
right, so before you're just a sleeping beauty with a 50/50 chance of going free or being kept, but once you enter "the process" you're involved in an "answering event", and "vanishingly small" is confusing because you don't know where you are on the spectrum, it's *already* and *always* an *infinitely* small chance in being correct.
For infinite sleeping beauties chances = 1/infinity*infinity
(probably a lot more complicated way of describing that but it will do lol)
For a single sleeping beauty chances = 1/infinity
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On January 05 2013 11:52 sam!zdat wrote:
How can I help? I believe that probability is ontologically meaningless. It's just a useful lie.
Well at least you think it is useful lol.
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On January 05 2013 11:51 Boblion wrote:Show nested quote +On January 05 2013 11:33 Kukaracha wrote:On January 05 2013 07:14 Boblion wrote:On January 05 2013 06:18 Kukaracha wrote:
But would you deny that we make many, many educated guesses in real-life settings? Poker, stock exchange... It's true that the coin example would be flawed IRL because it can't be calculated accurately enough, but my questions remain.
I have never denied the usefulness of maths lol. Obviously we have to use this knowledge to make guesses in real-life settings but we are making assumptions, we are theorizing. Again do not mistake the maths with the "real" stuff. Everyone with basic probabilities knowledge can understand the "maths" behind poker (and make the assumption that cards are dealt randomly) on the other hand if you know and understand perfectly the Pseudorandom number generator of a poker site you gonna be rich real quick. There are more things than just the "maths" in poker, you can also get some information by observing the other players (or their cards lol). Knowing the maths will help you tho and on the long run you should be able to beat a guy who have no idea about the basic strenght of the hands. Or you could get unlucky. Stock exchange is way more complicated and i don't really want to discuss this but it is definitly not just about maths (or you could argue that our maths models are not strong enough yet) and there are way too many things involved. Insider trading will make you richer than having 300 IQ and a Fields medal. Or you could go to jail lol. But let's just say that it is like a giant poker game with millions of players and a crazy amount of cheating and randomness. But that's the problem : we make assumptions, "educated guesses" but I don't understand how we can really make an "educated guess" that the coin effectively has a 50% chance to show tails in the time span that interests us. We could obtain heads during our whole lifetime since a century is just an infinitesimal portion of... the infinite. The "rule" that tails and heads appear with a 50% chance each wouldn't be invalidated. And yet it seems that we can observe a certain balance in the occurrance of tails and heads; how come? There surely is a mathematical explanation that the odds appear consistantly in such a small time span. How come you can beat another poker player by making educated guesses, although the probabilities don't necessarily have to be verified within the extremely limited duration of the game? And stock exchange wasn't such a bad example I think... probabilities come into play, just like in behavioural finance. Help me with this guy please.
You don't need any help, he's just trolling or is seriously confused.
The answer is, there are infinitely more combinations of heads and tails than there are strings of just heads or just tails, therefore the probability of rolling just heads or tails for a century is so absurdly low that we're talking about you'd have to flip a coin for longer than the universe has been around to get that kind of a spree, that's why.
For a simple example.
one toss:
heads
tails
two tosses:
heads, heads
tails, tails
heads, tails
tails, heads
three tosses:
heads, heads, heads
tails, tails, tails
heads, heads, tails
heads, tails, heads
heads, tails, tails
tails, tails, heads
tails, heads, tails
tails, heads, heads
four tosses:
no way am I typing all that out
See how the second group got much bigger proportionally at 3 tosses? It's even more so at 4, then 5....
We call this exponential.
On January 05 2013 11:52 sam!zdat wrote:
How can I help? I believe that probability is ontologically meaningless. It's just a useful lie.
You don't believe that.
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On January 05 2013 12:09 Reason wrote:
you'd have to flip a coin for longer than the universe has been around
crucial observation, good work. most people don't think about time
Show nested quote +On January 05 2013 11:52 sam!zdat wrote:
How can I help? I believe that probability is ontologically meaningless. It's just a useful lie. You don't believe that.
I absolutely do.
edit: I don't believe there is actually any such thing as randomness. Only things that appear to be random, and because of computational intractability cannot be proved either way.
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I'm still not sure about him. I just don't know if he is an idiot with a fairly large vocabulary (which makes him more annoying since he can't make a coherent sentence) or if he is just what people call "a troll". Usually "trolls" are rude, outrageous and try to be provocative. Kukaracha just seem childish and absurd. Reminds me of shitty plays like Waiting for Godot or Happy Days lol.
I don't know if he is genuinely absurd or if he is just trying to mimick that kind of "humor" but either way it's kinda sad.
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On January 05 2013 12:30 Boblion wrote:
I'm still not sure about him. I just don't know if he is an idiot with a fairly large vocabulary (which makes him more annoying since he can't make a coherent sentence) or if he is just what people call "a troll". Usually "trolls" are rude, outrageous and try to be provocative. Kukaracha just seem childish and absurd. Reminds me of shitty plays like Waiting for Godot or Happy Days lol.
Dontchoo be talking bad 'bout Beckett now, ya hear? Waiting for Godot may not be his best work, but I'm betting you've never seen a really good production of it. Happy Days I'm still on the fence about, so I'll give you that much.
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I despise most Absurdist fictions. I find it pathetic and degrading. Their nihilistic nature is disgusting and i rank this "genre" lower than action movies or shitty Scifi books. But you are right i have never seen the plays. I had to read them and write commentaries tho. What a pain. That's the kind of brainwash you have to endure in highschool nowadays instead of reading beautiful and exciting books.
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Kukaracha is misunderstood, and Boblion has no sense of humor
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On January 05 2013 12:43 sam!zdat wrote:Kukaracha is misunderstood, and Boblion has no sense of humor
well someone who can't appreciate absurdism definitely lack some taste.
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I find the pejorative use of the word "pathetic" rather pathetic and degrading, especially when it comes to declaring an honest critical perspective. But hey, they're your words, and you are free to "despise" that which you wish. Disdain can be fun, that much is always true.
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On January 05 2013 12:13 sam!zdat wrote:Show nested quote +On January 05 2013 12:09 Reason wrote:
you'd have to flip a coin for longer than the universe has been around
crucial observation, good work. most people don't think about time Show nested quote +On January 05 2013 11:52 sam!zdat wrote:
How can I help? I believe that probability is ontologically meaningless. It's just a useful lie. You don't believe that. I absolutely do. edit: I don't believe there is actually any such thing as randomness. Only things that appear to be random, and because of computational intractability cannot be proved either way.
Why do you think this way?
When I think about it.... I'm familiar that every human made "random" thing isn't really random, it's just some kind of complex process that appears to be random.
Is this what you think is in fact true of everything?
Try to define random for me :O
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Well i can appreciate some absurd jokes but when you are writing fucking absurd plays there is something really wrong about it. That's like eating a burger with gold cutlery lol. I seriously believe that absurdism is the lowest kind of humor.
The worst thing is that when you are 16-17 you have no idea about the meaning of the words culture and art and hence you have to study this crap and write about it like if it is amazing. That's why it is degrading: you can feel it is garbage but if you have to study it in class it must be good right ? Deep stuff uh ? Must think extra hard uh ? Oh and i forget it is super fun too. You only understand why it is truly awful when you start to read some serious philosophy. If i could come back in time i would put my "litterature teacher" to shame and make her reconsider her miserable existence lol.
edit: Just to be clear Beckett is by far the worst kind of absurd humor i had to endure. At least Jarry usually uses some forms of mockery (a way better source of humor !) in his Ubu and Apollinaire probably lost it when he went to war so i can't really blame him lol.
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On January 05 2013 13:05 Boblion wrote:
Well i can appreciate some absurd jokes but when you are writing fucking absurd plays there is something really wrong about it. That's like eating a burger with gold cutlery lol. I seriously believe that absurdism is the lowest kind of humor.
The worst thing is that when you are 16-17 you have no idea about the meaning of the words culture and art and hence you have to study this crap and write about it like if it is amazing. That's why it is degrading: you can feel it is garbage but if you have to study it in class it must be good right ? Deep stuff uh ? Must think extra hard uh ? Oh and i forget it is super fun too. You only understand why it is truly awful when you start to read some serious philosophy. If i could come back in time i would put my "litterature teacher" to shame and make her reconsider her miserable existence lol.
so much hate, just because you can't appreciate it doesn't mean it's garbage. and the bold part doesn't put you in good light, the angry kid in you seems to have forgot to grow up for some parts.
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Hate is one of the main sources of humor
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idk I think beckett is pretty crucial if you want to understand things
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Reason, the reason I don't believe in randomness is that I can't really figure out what that would be. So I can't define it for you. Can you?
I hold with Einstein that "God does not play dice"
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Well the problem of Beckett is that his works are nihilistic. The only thing it will make you understand is that everything is pointless and futile, or that there is nothing to understand. And then you end up like Kukaracha and you start to ask some dumb questions all the time lol.
I don't really believe in randomness too btw.
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I have to be a nihilist to enjoy reading a literary document par excellence of a man's personal encounter with the abyss of the Sublime?
edit: I mean of course enjoy is a strong word when it comes to Beckett. Appreciate.
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His Sublime seems like a vacuum to me :p
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yeah man it's the fucking abyss
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The real abyss is way more exciting tho. There are plenty of cool fishes. Don't know if i would call them sublime but a TV documentary about those life forms would be definitly more exciting for me than the tribulations of Vladimir and Estragon.
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idk man, I think that deep ocean stuff is only called 'the abyss' by metaphorical comparison to the actual abyss
edit: but yeah that shit's dope
edit: one of the main things about beckett is that you read it and then realize that there was absolutely no point in reading that, but parts of it were really cool
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Right time to draw up some conclusions for your thread instead of waffling on about Beckett and Absurdism.
Random is basically pure chance/no pattern. Sticking to coins, if you flip a coin 100 times, though heavily geared towards 50 heads flips & 50 tails flips, due to the undeniable ontological reality that is probability, most of the time it won't actually be 50/50.
If you flipped 100 coins 100 times and averaged all the results it would probably be pretty damn close to: 100*50 heads and 100*50 tails.
(assuming a fair coin)
Anyway the point is the distribution, the particular order in which these outcomes arrive are.... "random". There isn't some higher power or some absolutely kickass coinflipper exerting influence over whether it's a heads or a tails on any given flip, it's purely random whether the next flip is a heads or a tails even though we can be relatively certain they will flip roughly equally over time.
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I have to uninteresting things to add to this thread.
One is that probability is the most broing maths subject.
Two is that sam!zdat, you need to study a lot of quantic theory. I'm pretty sure your teachers would become crazy.
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Hey all! I'd like to preface my response by saying that I've never studied philosophy before, so please don't take me too seriously because I just wanted to post my thoughts and dive right into the discussion.
Well, I think that because the question was directed at the sleeping beauty, the answer does not matter. I mean, if the beauty has no memory of Monday because her memory was erased or because she slept through it, then there can be no answer that she can give right? She will have no proof, and should she decide to give an answer, it'd almost be as if she was acting as the coin itself. If she says the coin was tails, then the coin must be tails to her. But I'm only assuming that the philosopher does not give her any further hints. So I guess this is a little like sollipsism, but what do I know anyway?
This problem feels a little bit like the whole "if a tree falls in a forest and nobody is around to hear it, does it make a sound?" problem, where the sound the tree makes is the tea session on Monday. We don't know whether it was, but we do know the end result - the tree fell. The beauty woke up on Tuesday.
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On January 06 2013 00:38 Azera wrote:
Hey all! I'd like to preface my response by saying that I've never studied philosophy before, so please don't take me too seriously because I just wanted to post my thoughts and dive right into the discussion.
Well, I think that because the question was directed at the sleeping beauty, the answer does not matter. I mean, if the beauty has no memory of Monday because her memory was erased or because she slept through it, then there can be no answer that she can give right? She will have no proof, and should she decide to give an answer, it'd almost be as if she was acting as the coin itself. If she says the coin was tails, then the coin must be tails to her. But I'm only assuming that the philosopher does not give her any further hints. So I guess this is a little like sollipsism, but what do I know anyway?
This problem feels a little bit like the whole "if a tree falls in a forest and nobody is around to hear it, does it make a sound?" problem, where the sound the tree makes is the tea session on Monday. We don't know whether it was, but we do know the end result - the tree fell. The beauty woke up on Tuesday.
She is being asked to assess the statement and indicate how likely it is to be correct or incorrect.
It may be Monday when she is being asked the question, and her guess does not dictate what actually happened when the coin was flipped.
Yes if a tree falls and no one hears it it does make a sound, because that's how physics works.
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Ah! I didn't read the problem well enough. The chances of it being Monday makes the problem even more of a doozy.
Is there actually an answer to this or not?
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On January 05 2013 12:09 Reason wrote:
The answer is, there are infinitely more combinations of heads and tails than there are strings of just heads or just tails, therefore the probability of rolling just heads or tails for a century is so absurdly low that we're talking about you'd have to flip a coin for longer than the universe has been around to get that kind of a spree, that's why.
[...]
See how the second group got much bigger proportionally at 3 tosses? It's even more so at 4, then 5....
We call this exponential.
Alright, but what troubles me with the exponential factor is that it leads to infinity, which doesn't seem to make sense in my mind.
Just like that imaginary monkey will plagiarize Shakespeare some day, we can say that a series of 52594876 tails in a row is bound to happen. So how is it less likely to happen now than later? Isn't life itself an unlikely and yet very present occurrance?
And what is a probability anyway? Does it make any sense if we consider time as linear? And isn't the law of large numbers a weird conclusion? I'm not discussing the validity of it, but I'm struggling to understand what a probability is exactly.
On a sidenote, I may be confused but I think that it should be the most common state of a curious, sincere man, and I may seem childish but I'm really just asking questions (which is, in my books, a quality at all "abstract" times).
I just don't understand very well why people get angry at my curiosity, although they worship thinkers who are by definition people who ask questions too. Certainties can only get you so far, intelectually speaking - although it is probably a confidence boost and a valuable shortcut, true.
On January 06 2013 01:04 Reason wrote:
Yes if a tree falls and no one hears it it does make a sound, because that's how physics works.
It depends of our observation. If the phenomenon is perceived (but not heard), we can surely make a claim that there was a sound; however, if no one is around at all, then the tree doesn't exist by default, following the same pragmatic course of thought that leads to use the laws of physics as a conclusion.
(Because for any conceivable object, it seems that we consider by default that it does not exist until something else indicates that it does.)
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On January 06 2013 01:34 Kukaracha wrote:Show nested quote +On January 05 2013 12:09 Reason wrote:
The answer is, there are infinitely more combinations of heads and tails than there are strings of just heads or just tails, therefore the probability of rolling just heads or tails for a century is so absurdly low that we're talking about you'd have to flip a coin for longer than the universe has been around to get that kind of a spree, that's why.
[...]
See how the second group got much bigger proportionally at 3 tosses? It's even more so at 4, then 5....
We call this exponential. Alright, but what troubles me with the exponential factor is that it leads to infinity, which doesn't seem to make sense in my mind. Just like that imaginary monkey will plagiarize Shakespeare some day, we can say that a series of 52594876 tails in a row is bound to happen. So how is it less likely to happen now than later? Isn't life itself an unlikely and yet very present occurrance? And what is a probability anyway? Does it make any sense if we consider time as linear? And isn't the law of large numbers a weird conclusion? I'm not discussing the validity of it, but I'm struggling to understand what a probability is exactly. On a sidenote, I may be confused but I think that it should be the most common state of a curious, sincere man, and I may seem childish but I'm really just asking questions (which is, in my books, a quality at all "abstract" times). I just don't understand very well why people get angry at my curiosity, although they worship thinkers who are by definition people who ask questions too. Certainties can only get you so far, intelectually speaking - although it is probably a confidence boost and a valuable shortcut, true. Show nested quote +On January 06 2013 01:04 Reason wrote:
Yes if a tree falls and no one hears it it does make a sound, because that's how physics works. It depends of our observation. If the phenomenon is perceived (but not heard), we can surely make a claim that there was a sound; however, if no one is around at all, then the tree doesn't exist by default, following the same pragmatic course of thought that leads to use the laws of physics as a conclusion. (Because for any conceivable object, it seems that we consider by default that it does not exist until something else indicates that it does.)
Yes, life is extremely unlikely by our understanding but due to the size and age of the universe and from our limited understanding of it it seems reasonable there is actually a lot of life out there, unforunately possibly farther away than we will ever reach. To answer this sort of thing more precisely we need more information and better technology, and prior to actual verification I suppose we could never be certain.
It's just as likely for 52594876 tails to happen at any given time as it is to happen at another time, but it's a very unlikely occurrence. The thing with a coin is because it's 50/50 for each increasing flip in the series there are only two possible strings of outcomes that are pure tails or pure heads, and an exponentially increasing number of heads and tails combinations. We can say eventually one million tails in a row will be flipped for certain if : someone is endlessly flipping a coin and the universe lasts forever. The problem is someone isn't endlessly flipping a coin and the universe probably won't last forever.
That said, again, I could start flipping a coin right now and flip a million tails in a row, but it's so infinitely unlikely and statistics and probability when dealing with complex things like this (for example if a coin has two sides that are both heads we can say it's 100% certain that we'll never flip tails, but most of the time statistics and probabilities are used for more complicated questions, in fact that's pretty much the only time they're used and the very reason they were invented because you don't need maths to tell you that, it's common sense) can only tell you that say in a million years flipping the coin once per second the chances of flipping a million tails in a row would be something absurd like 0.0000000000000001%. I've just pulled those numbers out of my hat and in fact it's probably much, much less likely even than that.
Sorry, I wasn't really paying much attention to your comments and didn't mean to be offensive by calling you confused, I thought you were just asking deliberately difficult and (to me) nonsensical questions in order to confuse Boblion to amuse yourself. If you were being genuine you have my sincerest apology.
If no one's around then the tree still exists because you are referring to it. You've already stated that there's a tree.
You can't say "there's a tree in a forest but there's no one in the universe left alive to see it, therefore it doesn't exist" because you've already stated that it does.
Our extensive yet incomplete understanding of physics allows to make the statement "if there is a tree and it did fall, when it fell it made a sound" simply because that's the way the universe has been found to work.
You could I suppose say that since we don't have a complete understanding (and possibly never will) of how the universe works that we can only be 99.999999999% certain that the tree makes a sound when it falls, but every single piece of data we've ever accumulated indictates that it does and we've never found any data to the contrary, you could only claim a lack of absolute certainty as a result of absolute understanding, but it wouldn't really be useful in any way to do this.
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On January 06 2013 01:34 Kukaracha wrote:
Just like that imaginary monkey will plagiarize Shakespeare some day,
It probably won't, because the universe isn't big enough.
The library of Babel is way, way, way, way, way, way, way bigger than the universe.
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So, self-indication vs self-sampling...
are we getting anywhere here =p?
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I don't know, you tell me, I forgot what the question was. Did you solve it?
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I don't believe there is an accepted "solution" and I think you're very well aware of that 
I'm clearly naturally leaning towards the self-indication assumption though I did so before I even knew what it was lol.
Do you feel the same way or would you care to play the advocate for the other side so we can explore this issue?
As it is people have just thrown out some responses the vast majority of which are similar to mine...
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On January 06 2013 01:34 Kukaracha wrote:
Just like that imaginary monkey will plagiarize Shakespeare some day,
If an old specie of primates has evolved into humans i don't really know why it would be impossible for them to write books. It would take a while to get to Shakespeare level tho 
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My only solution to this puzzle is to say that probability makes no sense when you are talking about indexical propositions. The answer is 1/2, and only 1/2. When he asks "is it Monday?" there is no coherent answer to that question involving probability.
edit: but I'm not satisfied by saying this, either.
edit: but like I say this is a big part of the reason why I'm skeptical that probability is anything other than a heuristic.
edit: I mean that when you talk about probability, you are talking about epistemology and not ontology. Propositions about probability don't tell you anything about the world, they just tell you about your concept of the world. If sleeping beauty always answers 1/2, she'll always be right about the probability even though if she guesses tails she'll be wrong 2/3 of the time.
Which goes to show that there's a difference between saying:
"X is 1/2 probable"
and
"If I guess X I will be right 1/2 of the time"
Because the fact of the matter changes the conditions under which the utterance is made, and so you get the self-sampling problem. The question is, how many other things are like this?
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Can you explain indexical propositions in general and in the context of the sleeping beauty puzzle, and make an effort to dumb your language down more
"The question is, how many other things are like this?"
I don't know, but I don't think many.
As for propositions about probability not telling you anything about the world... well I think it's sort of an issue of time.
Probability can't and doesn't claim to be able to tell me what the next flip of the coin will be, it merely assures me and quite correctly so that there's an even chance of it being heads or a tails. Probability can tell you an awful lot about the world, it just can't tell you about the state of the world at a specific point in time.
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Heads is 1/2 probable. If I flip a coin and guess heads 1/2 the time, I will be right 1/2 the time
Your situation has been specifically engineered to show there's a difference between those two statemens and my ^ above situation has been engineered to show that they're the same. She's right about the probability prior to the answering scenario by saying 1/2 but she would be incorrect, I believe, once actually involved in the experiment.
So I suppose you could end up with "X is 1/2 probable is not *always* equal to 'If I guess X I will be right 1/2 of the time'" but I don't think that's really what's been established here and thus why there's no accepted solution to this problem.
I know there's another similar and much simpler example :
There's three cups and one contains the ball. You have to get the ball. You make two guesses at first. Your first guess is wrong, so there's two cups left and one contains the ball. You get offered the choice to swap or stick with your original guess. You always swap, because it improves your chance of getting the right cup from 1/3 to 1/2, even though this seems counter intuitive to say the least. I still don't "understand" it, really.
As far as I'm aware there's absolutely no debate about this and it can be proven and tested in a laboratory or in your own home if you're a bit of a nerd, which leaves me confused because it seems identical to this problem yet it seems to be troubling the educated world a bit more than the old cup 'n' ball scenario.
Your thoughts?
edit: I was aware of the cup 'n' ball scenario prior to reading this thread, so it has obviously heavily influenced my responses and is probably why I'm in favour of the self-indication assumption.
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On January 06 2013 04:40 Reason wrote:Can you explain indexical propositions in general and in the context of the sleeping beauty puzzle, and make an effort to dumb your language down more
An indexical is something that points. Words like "now" "here" "I" "you" and so on are indexicals. Normal propositions don't use them. There is no way to formalize the proposition "it is now Monday" in first order logic.
"The question is, how many other things are like this?"
I don't know, but I don't think many.
Maybe not, but what is "like this" exactly? I think it's worth thinking about.
As for propositions about probability not telling you anything about the world... well I think it's sort of an issue of time.
Probability can't and doesn't claim to be able to tell me what the next flip of the coin will be, it merely assures me and quite correctly so that there's an even chance of it being heads or a tails. Probability can tell you an awful lot about the world, it just can't tell you about the state of the world at a specific point in time.
Right, so probability tells you what you don't know about the world. You don't know whether this coin will be heads or tails, and probability lets you say more exactly what it is that you don't know.
You use the word "chance" but I don't think you actually know what it means! Can you say what you mean?
"Heads is 1/2 probable.
if I flip a coin and guess heads 1/2 the time, I will be right 1/2 the time."
Your situation has been specifically engineered to show there's a difference between those two statemens and my above situation has been engineered to show that they're the same.
So mine wins. In philosophy you engineer thought experiment to show exceptions. Then you have to reconcile your theory with the exception.
She's right about the probability prior to the answering scenario by saying 1/2 but she would be incorrect, I believe, once actually involved in the experiment.
But she doesn't gain any information, so the probability can't change.
So I suppose you could end up with "X is 1/2 probable is not *always* equal to 'If I guess X I will be right 1/2 of the time'" but I don't think that's really what's been established here and thus why there's no accepted solution to this problem.
Well, I argue that that is precisely what has been established here, and it's very troubling. My guess is that the second one is not well formed, and we don't really know what we are saying when we say "if I guess X I will be right 1/2 of the time."
I know there's another similar and much simpler example :
There's three cups and one contains the ball. You have to get the ball. You make two guesses at first. Your first guess is wrong, so there's two cups left and one contains the ball. You get offered the choice to swap or stick with your original guess. You always swap, because it improves your chance of getting the right cup from 1/3 to 1/2, even though this seems counter intuitive. As far as I'm aware there's absolutely no debate about this and it can be proven and tested in a laboratory or in your own home if you're a bit of a nerd, which leaves me confused because it seems identical to this problem yet it seems to be troubling the educated world a bit more than the old cup 'n' ball scenario.
Your thoughts?
Yeah this is the Monty Hall problem, it's solved.
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What makes the Sleeping Beauty problem different from the Monty Hall problem aside from rhetorical embellishments?
I think once we establish the key difference(s) we can approach this in a more constructive fashion and also perhaps find similar scenarios.
When I say chance I'm referring to likelihood or.. probability lol.
Probability doesn't tell me if the coin will be heads or tails next, it tells me it's equally likely to be either.
That's kind of useful if say you're going for an operation and the doctor says "there's a 2% chance of serious complications and you could die" you don't just say " LIAR, YOU DON'T KNOW WHAT'S GOING TO HAPPEN" you accept the information he has given you, because it is indeed useful.
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On January 06 2013 04:52 Reason wrote:
What makes the Sleeping Beauty problem different from the Monty Hall problem aside from rhetorical embellishments?
Memory loss.
I think once we establish the key difference(s) we can approach this in a more constructive fashion and attempt to find similar scenarios.
Good thinking!
When I say chance I'm referring to likelihood or.. probability lol.
Philosophy 1, Reason 0
That's kind of useful if say you're going for an operation and the doctor says "there's a 2% chance of serious complications and you could die" you don't just say " LIAR, YOU DON'T KNOW WHAT'S GOING TO HAPPEN" you accept the information he has given you, because it is indeed useful.
Yeah, it's definitely useful. All models are lies, but many of them are useful.
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How does her own memory loss effect the probability of the outcome or the credence that can be attributed to the statement?
Why are models lies?
Philosophy 1, Reason 0
I respectfully disagree, please elaborate.
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On January 06 2013 04:58 Reason wrote:
How does her own memory loss effect the probability of the outcome or the credence that can be attributed to the statement?
That's what we've been talking about for all these pages.
Why are models lies?
Because if there were a model which weren't a lie, it would just be the thing you were trying to model, and it would be pointless.
Show nested quote +
When I say chance I'm referring to likelihood or.. probability lol.
Philosophy 1, Reason 0 I respectfully disagree, please elaborate.
Because you can't define what you mean by 'chance' and I count that as a victory for Philosophy.
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On January 06 2013 05:04 sam!zdat wrote:Show nested quote +On January 06 2013 04:58 Reason wrote:
How does her own memory loss effect the probability of the outcome or the credence that can be attributed to the statement?
That's what we've been talking about for all these pages. Because if there were a model which weren't a lie, it would just be the thing you were trying to model, and it would be pointless. Show nested quote +
When I say chance I'm referring to likelihood or.. probability lol.
Philosophy 1, Reason 0 I respectfully disagree, please elaborate. Because you can't define what you mean by 'chance' and I count that as a victory for Philosophy.
This reads just like the Monty Hall problem to me =/
I don't understand.
I explained what I meant by chance. Likelihood or probability.
edit: From what I've read everyone has just treated it like the Monty Hall problem and given you a bunch of mathematical proofs, if that's what you were hoping for then fine. I don't get it and I don't think others do either from their responses.
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United Kingdom3482 Posts
On January 06 2013 05:04 sam!zdat wrote:Because if there were a model which weren't a lie, it would just be the thing you were trying to model, and it would be pointless.
Just because a model is not 100% accurate, which is always the case or it wouldn't be a model, doesn't mean it's a lie, it means it's an approximation. The only case where it would be a lie is if you tried to claim it was 100% accurate or even more accurate than it actually is.
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On January 06 2013 05:30 Reason wrote:
I explained what I meant by chance. Likelihood or probability.
Those are just synonyms.
edit: From what I've read everyone has just treated it like the Monty Hall problem and given you a bunch of mathematical proofs, if that's what you were hoping for then fine. I don't get it and I don't think others do either from their responses.
It's like the Monty Hall problem, but much harder.
On January 06 2013 05:31 imallinson wrote:Show nested quote +On January 06 2013 05:04 sam!zdat wrote:
Why are models lies?
Because if there were a model which weren't a lie, it would just be the thing you were trying to model, and it would be pointless. Just because a model is not 100% accurate, which is always the case or it wouldn't be a model, doesn't mean it's a lie, it means it's an approximation. The only case where it would be a lie is if you tried to claim it was 100% accurate or even more accurate than it actually is.
An approximation is one kind of lie. Another kind of lie is claiming that your approximation is not a lie.
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On January 06 2013 05:43 sam!zdat wrote:Show nested quote +On January 06 2013 05:30 Reason wrote:
I explained what I meant by chance. Likelihood or probability.
Those are just synonyms. Show nested quote +
edit: From what I've read everyone has just treated it like the Monty Hall problem and given you a bunch of mathematical proofs, if that's what you were hoping for then fine. I don't get it and I don't think others do either from their responses.
It's like the Monty Hall problem, but much harder. Show nested quote +On January 06 2013 05:31 imallinson wrote:On January 06 2013 05:04 sam!zdat wrote:
Why are models lies?
Because if there were a model which weren't a lie, it would just be the thing you were trying to model, and it would be pointless. Just because a model is not 100% accurate, which is always the case or it wouldn't be a model, doesn't mean it's a lie, it means it's an approximation. The only case where it would be a lie is if you tried to claim it was 100% accurate or even more accurate than it actually is. An approximation is one kind of lie. Another kind of lie is claiming that your approximation is not a lie.
So by giving you synonyms don't you think I know what I mean by something?
I don't know why you'd randomly ask me to define a word anyway...
I'm going to read this entire thread again and then comment tomorrow but from what I've seen I don't think we're really getting at the root of the problem here.
I'm still of the opinion that it's just the Monty Hall problem re-written and I know that's not true, but unfortunately "memory loss" isn't a sufficient enough explanation for me.
I'll try to figure this out myself I guess... might be useful to quote the Monty Hall problem in the OP for new readers and explain specifically what's different about this and why it's not been solved, quote the opposing positions and give a bit of background etc... meh.
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On January 06 2013 04:58 Reason wrote:
How does her own memory loss effect the probability of the outcome or the credence that can be attributed to the statement?
It's not the memory loss that changes the probability. It's the fact that the mad philosopher changes the distribution between the two questions.
It's equivalent to putting 2 red and 2 blue balls into a box and asking what the probability of picking red is.
Then taking out a red one and asking for the probability of picking out a red one again.
The whole discussion about memory loss is a red herring and samizdat already admitted as much. Even on Sunday Sleeping Beauty knows that her answer will change by time she wakes up.
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On January 06 2013 05:49 Reason wrote:Show nested quote +On January 06 2013 05:43 sam!zdat wrote:On January 06 2013 05:30 Reason wrote:
I explained what I meant by chance. Likelihood or probability.
Those are just synonyms.
edit: From what I've read everyone has just treated it like the Monty Hall problem and given you a bunch of mathematical proofs, if that's what you were hoping for then fine. I don't get it and I don't think others do either from their responses.
It's like the Monty Hall problem, but much harder. On January 06 2013 05:31 imallinson wrote:On January 06 2013 05:04 sam!zdat wrote:
Why are models lies?
Because if there were a model which weren't a lie, it would just be the thing you were trying to model, and it would be pointless. Just because a model is not 100% accurate, which is always the case or it wouldn't be a model, doesn't mean it's a lie, it means it's an approximation. The only case where it would be a lie is if you tried to claim it was 100% accurate or even more accurate than it actually is. An approximation is one kind of lie. Another kind of lie is claiming that your approximation is not a lie. So by giving you synonyms don't you think I know what I mean by something?
No... absolutely not... In fact giving synonyms is a sure proof that you DON'T know what you mean...
I thought by the way you said it that you understood this.
I don't know why you'd randomly ask me to define a word anyway...
It's not random, it's the very crux of the issue!!
(edit: lololol)
I'm going to read this entire thread again and then comment tomorrow but from what I've seen I don't think we're really getting at the root of the problem here.
Probably not, I admire your perseverance <3
I'm still of the opinion that it's just the Monty Hall problem re-written
My appeal to authority says no. Nobody thinks this is identical to Monty Hall problem, afaik.
and I know that's not true, but unfortunately "memory loss" isn't a sufficient enough explanation for me.
Yeah it's not, it's just pointing. @hypercube it's definitely not a red herring, the problem is that she KNOWS she will lose her memory. If she didn't know it would be totally unproblematic.
I'll try to figure this out myself I guess... might be useful to quote the Monty Hall problem in the OP for new readers and explain specifically what's different about this and why it's not been solved, quote the opposing positions and give a bit of background etc... meh.
If you want to write up the monty hall problem, I will edit it into the OP.
On January 06 2013 05:50 hypercube wrote:Show nested quote +On January 06 2013 04:58 Reason wrote:
How does her own memory loss effect the probability of the outcome or the credence that can be attributed to the statement?
It's the fact that the mad philosopher changes the distribution between the two questions.
No, he asks one question which is equivocal.
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Might not have time to read through this again and get my thinking cap on today so I'll settle for defining chance/probability/likelihood just now so it's out of the way.
When I said the "chances" of something happening, what I meant was this:
x = the number of times a particular event with multiple outcomes is repeated
y = the number of times that a particular outcome will be the end result of x repetitions of the event, on average
c = "the chances" (of the particular outcome in question happening in a single repetition of the event)
y/x = c
Was that really necessary lol? 
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x >= y
c = x/y >= 1 doesnt really make sense.
More like y/x = c ?
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Shhh that's what I wrote.
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Right, so if you can only define probability in terms of multiple events, is it sensical to talk about the probability of one event as anything other than a useful lie?
Also, how do you "repeat the same event"? Heraclitus is skeptical. At best you can repeat events that are very much like it.
But it's a nice definition. It still gives us the conclusion that
X
The utterance of X expresses true proposition
Can be different probabilities at a given moment. tres bizarre
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I stepped into the same river twice once, I swear.
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Someone trying to challenge Heraclitus. That's cute lol.
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On January 07 2013 05:21 farvacola wrote:
I stepped into the same river twice once, I swear.
I smell an equivocation
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On January 07 2013 05:27 Boblion wrote:
Someone trying to challenge Heraclitus. That's cute lol.
One can never challenge the same Heraclitus twice
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I don't really know what you want to prove. By "Heraclitus" i mean his ideas. But if you want to challenge the existence of time go ahead lol.
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Consider for a moment that the trace of human history exists like that of a flowing and ebbing river; a stream of information and context whose appearance and consistency find themselves inexorably tied to instantiation of contact. The Heraclitus of today and the Heraclitus of yesterday might seem quite the same in the minds eye, but they are most surely different, for time has passed!
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On January 07 2013 05:51 farvacola wrote:
Consider for a moment that the trace of human history exists like that of a flowing and ebbing river; a stream of information and context whose appearance and consistency find themselves inexorably tied to instantiation of contact. The Heraclitus of today and the Heraclitus of yesterday might seem quite the same in the minds eye, but they are most surely different, for time has passed!
You are trying so hard to be funny and yet you fail to realize that yea we are different every day, every hour, every second until our death. That process is called ageing lol.
Quoted for posterity tho. I think i will have to update my previous poll. Here comes a new challenger for Kukaracha lol.
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Oh! Oh!
are you identical to yourself across time? I have a puzzle about that too!
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That what I wrote appears as a joke to you might be a casualty of written forum communication, for I am not challenging the ideas of Heraclitus, merely reiterating them for my own enjoyment. Critique of absurdism aside, I do not think we disagree
Edit: and the quote! Oh dear, you do mistake me.
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Told you absurdism is dumb duh and that's why your joke wasn't funny
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Cayman Islands24199 Posts
she should drink a lot of tea and go to sleep again. then the next time she'll know if she drank a lot of something. yea.
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you think you're SOOOOO clever don't you, oot
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Cayman Islands24199 Posts
well, this is kind of like asking the agent to evaluate from 2 perspectives, while driving in a bifurcated tunnel
one perspective looks straight ahead, which gives always 2 possibilities in that the coin is either up or down
the other perspective looks horizontally, seeing multiple possible observer agents that he could be. so 3 instances.
reminds me of zeno's paradox if anything(are we there yet vs where are we). world is not broken, just 2 kinds of probability accounting (evaluating the coin itself, vs evaluating observer instances)
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yeah, definitely two kinds of probability accounting. The point is just that the bare fact of there being two kinds of probability is troubling for a certain naive understanding of what we are talking about when we are talking about probability. I think the idea of incommensurable flavors of probability is useful for upsetting some overly reifying tendencies in statistical thinking.
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EPT![[image loading]](http://i.imgur.com/grLQs.png?1)
