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

Reason

United Kingdom2770 Posts

January 05 2013 00:34 GMT

#146

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

sam!zdat

United States5559 Posts

January 05 2013 00:35 GMT

#147

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

Reason

United Kingdom2770 Posts

January 05 2013 00:45 GMT

#148

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.

sam!zdat

United States5559 Posts

January 05 2013 00:55 GMT

#149

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)

Reason

United Kingdom2770 Posts

January 05 2013 01:00 GMT

#150

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)

sam!zdat

United States5559 Posts

January 05 2013 01:07 GMT

#151

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?

Reason

United Kingdom2770 Posts

January 05 2013 01:14 GMT

#152

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".

sam!zdat

United States5559 Posts

January 05 2013 01:17 GMT

#153

You don't find that conclusion absurd?

Try to imagine that you are in her situation.

Reason

United Kingdom2770 Posts

January 05 2013 01:20 GMT

#154

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.

sam!zdat

United States5559 Posts

January 05 2013 01:22 GMT

#155

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

Reason

United Kingdom2770 Posts

January 05 2013 01:23 GMT

#156

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?

Reason

United Kingdom2770 Posts

January 05 2013 01:33 GMT

#157

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.

sam!zdat

United States5559 Posts

January 05 2013 01:35 GMT

#158

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.

Reason

United Kingdom2770 Posts

January 05 2013 01:47 GMT

#159

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.