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Forum » Math/Philsophy bros GTFIH for a simple problem that will blow your mind
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Thread: Math/Philsophy bros GTFIH for a simple problem that will blow your mind

post 1523061431 10-18-2017, 04:39 PM
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Originally Posted By Omnivium⏩
But the 1/3 one assumes she picks heads every time which it doesn't say anywhere in the question
Yeah, look at what the question is asking. 'What is your certainty that it's heads?'

Her answer should be "Given that I am awake and the coin probability is 50/50, I am 33% certain that it is heads"
post 1523061481 10-18-2017, 04:39 PM
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Originally Posted By tylerluxai⏩
I think that's giving her a random prediction rather than the case for always chosing heads vs always choosing tails. What would be *really* cool is if it was 1/3 for heads but something totally different for tails. Unfortunately it's just 2/3 I think. Looking for a browser JS library to run the sim on a neural network at the moment.

Also, good work on the code
The first one is giving her random predictions, and is formulated from experimenter's pov. Second was if she chooses all heads, and is formulated from her POV.
post 1523061621 10-18-2017, 04:41 PM
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Originally Posted By wincel⏩
The first one is giving her random predictions, and is formulated from experimenter's pov. Second was if she chooses all heads, and is formulated from her POV.
That's weird that if she randomly guesses heads or tails it evens out. Are you sure brah? I always make code that has bugs in it so I'm just making 100% certain this is properly set up.
post 1523061721 10-18-2017, 04:41 PM
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Originally Posted By wincel⏩
...The code demonstrates that if she guesses heads, she is right only 1/3 of the time, rather than the 1/2 you are saying. And there aren't 3 days. Where are you getting 3 phucking days? There are only 2 motherphucking days, Monday and Tuesday. WTF
Because it can be any number of ****ing days and it's sill 50%

I'm pointing out the variable you're creating that doesn't affect the odds of her guessing correctly. Time or repitition has 0 impact on odds in the state question is asked

And no she wouldn't say its 33% chance of heads youre doing way too much and phucking up what's constant and what isn't boyo
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post 1523061851 10-18-2017, 04:43 PM
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Originally Posted By tylerluxai⏩
That's weird that if she randomly guesses heads or tails it evens out. Are you sure brah? I always make code that has bugs in it so I'm just making 100% certain this is properly set up.
Yeah it is weird. That's the subtlety of it. See my code. There are no bugs afaik. It works out to being 50% chance if she randomly guesses, and formulated from POV of experimenter. What's even funnier is that when she guesses heads every time from her POV, even if she is only right 33% of the time, the actual number of heads and tails is still 50:50 as expected. lol this is why probability doesn't really translate well to english. It is better to look at the logical flow of the program to see the difference.

MATLAB is like one step removed from pseudocode, so you could probably write that sim up in another language and check it out. You should get the same results.
post 1523062541 10-18-2017, 04:52 PM
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I think the answer is that as the experiment is repeated, the odds approach 1/3.

Is that even a valid answer? Assume she wakes up 999,999 times instead of 1 extra time. Because she has no idea how many times she woke up, the odds of the single experiment are 1/2. If you repeat this experiment, she would know her odds are closer to 1/3.
post 1523070141 10-18-2017, 06:12 PM
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Originally Posted By tylerluxai⏩
That's weird that if she randomly guesses heads or tails it evens out.Are you sure brah? I always make code that has bugs in it so I'm just making 100% certain this is properly set up.
Why is this weird at all? You are guessing randomly at a flipped fair coin. Of course it will be 50/50 in the results. Having her guess randomly is also completely irrelevant to this problem.

Also, why are you guys even bothering writing simulations? That all could be figured out-the whole 2 to 1 ratio of incorrect heads guesses- with extremely simple math and logic. This is like someone writing a code to see if two fair dice come up double six on average once every 36 times.

Whoever was saying the sims show that the conditional probability for heads from her POV is 1/3....no, it still depends on interpretation and your take on credence. Halfers are arguing 1/2 chance from her POV....
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post 1523070331 10-18-2017, 06:14 PM
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Originally Posted By DemiBrah⏩
She doesn't know what the variable result entails that's the entire point of the experiment
The amnesia-inducing drug makes her forget each awakening, not the details she was told beforehand on Sunday, thus she should still know the odds are 66% the coin was tails, no?
post 1523074061 10-18-2017, 06:50 PM
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where n is number of times the experiment is run

As the experiment is run more than once, she should be exponentially less certain that the probability is 50-50
If the experiment is run one time, the (n-1)/n coefficient is 0 so 1/3 disappears and it becomes 50-50

Edit: It works for n = 1, but haven't done proof by induction or anything
post 1523074551 10-18-2017, 06:55 PM
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Originally Posted By skinnyfat88⏩
The amnesia-inducing drug makes her forget each awakening, not the details she was told beforehand on Sunday, thus she should still know the odds are 66% the coin was tails, no?
Where does it say she's told how the experiment works? That isn't a thing


Oh didn't see that LMFAO

But it's still 50/50 regardless because it's a single coin toss regardless of how many times she awakes therefore it's still 1/2 chance she'll be right once or twice, but over the course of two days there's a second 50% chance she'll be right/wrong again. The chances that she'll be wrong over the course of two days isn't in question, but per interview no?
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post 1523075491 10-18-2017, 07:05 PM
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There are 3 possibilities she can wake up on H-M, T-M, and T-T. One of those has heads on it. But that doesnt mean that there's a 1/3 chance that the coin landed on heads. Because it doesnt take into account the coin flip.

Imagine the exact same scenario, but they use a coin that has a 99.99% chance of heads and 0.01% chance of tails. There are still 3 possibilities she can wake up on H-M, T-M, and T-T. Do you still believe there is a 1/3 chance of it being heads? Or am i missing something here.
post 1523076101 10-18-2017, 07:10 PM
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I think my equation works if you run it through the sigmoid function? Right now it works for large numbers of n and n = 1, but I need to use the activation function in between
post 1523082221 10-18-2017, 08:10 PM
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Answer is 50:50, since it's a single event coin flip, if her goal was to be correct the most number of times it'd be 1/3.

OP, whats the difference between the question quoted in op and the one from here?

https://www.quantamagazine.org/solut...emma-20160129/
The famous fairy-tale princess Sleeping Beauty participates in an experiment that starts on Sunday. She is told that she will be put to sleep, and while she is asleep a fair coin will be tossed that will determine how the experiment will proceed. If the coin comes up heads, she will be awakened on Monday, interviewed, and put back to sleep, but she won’t remember this awakening. If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday, again without remembering either awakening. In either case, the experiment ends when she is awakened on Wednesday without being interviewed.

Whenever Sleeping Beauty is awakened and interviewed, she won’t know which day it is or whether she has been awakened before. During each awakening, she is asked: “What is your degree of certainty* that the coin landed heads?” What should her answer be?

*(This is sometimes worded as “credence,” “degree of belief,” “subjective probability” or “subjective certainty.”)
Also the MIT essay had a different question,(on monday what are the odds it was a head flip) and the princeton guy didnt even state the question in his writings.

Or maybe everyone bends the question to match their answer?
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post 1523084771 10-18-2017, 08:31 PM
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Originally Posted By Stafor⏩
Answer is 50:50, since it's a single event coin flip, if her goal was to be correct the most number of times it'd be 1/3.

OP, whats the difference between the question quoted in op and the one from here?

https://www.quantamagazine.org/solut...emma-20160129/



Also the MIT essay had a different question,(on monday what are the odds it was a head flip)and the princeton guy didnt even state the question in his writings.

Or maybe everyone bends the question to match their answer?
Where are you seeing this? He calculates P_(H|W): heads given she wakes up at least once during the experiment.
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post 1523086411 10-18-2017, 08:46 PM
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Originally Posted By wincel⏩
u guys need to realize that being woken up at all and knowing the experiment does add some new information...there are 2 ways she wakes up with tails and 1 way she wakes up with heads, all with equal probability. That's why it's 1/3. It's also 2/3 that it is a Monday if you ask her what day of the week she thinks it is.
I disagree that there is new information. She wakes up with zero memory. What is the new information?

That she's awake? She knew she would be awaken on both heads or tails. This is not new info?

Also, waking up on H-M, T-M, or T-T does not all have the same probability. When she gets woken up, there is a higher chance that it is H-M, than T-M or T-T.
Originally Posted By iceypain⏩
it is new because it gives additional information about what has happened i.e. that is isn't both tuesday and the coin was heads because then she wouldn't be awake. to start there were 4 possible outcomes: awake monday heads, awake monday tails, awake tuesday tails, asleep tuesday heads...being awake eliminates one of the 4.
Knowing that it is not H-T is not new information. Imagine this, prior to the experiment they ask her ," What is the likelihood that you wake up on H-T?" She will say 0. So learning that its not H-T is not new information.
post 1523096171 10-18-2017, 10:32 PM
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Originally Posted By goodapple⏩
I disagree that there is new information. She wakes up with zero memory. What is the new information?

That she's awake? She knew she would be awaken on both heads or tails. This is not new info?

Also, waking up on H-M, T-M, or T-T does not all have the same probability.When she gets woken up, there is a higher chance that it is H-M, than T-M or T-T.



Knowing that it is not H-T is not new information. Imagine this, prior to the experiment they ask her ," What is the likelihood that you wake up on H-T?" She will say 0. So learning that its not H-T is not new information.
Ah. THIS is an interesting point, and is really at the crux of the issue (I imagine thirders would argue it). If one looks at the variant experiment with tails meaning she is awoken 1 million days in a row, and heads just on Monday...if she awakes, is it more likely she is in H-M, or T-#574,379? For the thirders out there...put yourself in that position. You just wake up. Are you betting on H-M or T-#574,379?

Also, right on about the non-new info. I still can't see how anyone would think there is new info being produced by her waking up.
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post 1523274791 10-20-2017, 11:07 AM
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Good work wincel, but the problem I have is when you have her guess randomly, of course its going to come out 50/50, thats literally what random guessing means.

It's still 'new' info in that you are currently woke up. In a milion tails and 1 heads, are you truly going to believe this is 50/50 wake up, or one of a long long line of tail wake ups?
post 1523280951 10-20-2017, 12:02 PM
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Originally Posted By KMadigan777⏩
Good work wincel, but the problem I have is when you have her guess randomly, of course its going to come out 50/50, thats literally what random guessing means.

It's still 'new' info in that you are currently woke up. In a milion tails and 1 heads, are you truly going to believe this is 50/50 wake up, or one of a long long line of tail wake ups?
I see what you are saying man, but I just don't agree this is new info, since she knew she would be woken up at least once during the experiment a priori (and I realize no argument will convince either of us otherwise).

In terms of the million day variant, I see these longer extensions as intuitively supporting the 50/50, if anything. If you are woken up during this 1 million day variant, and then told it was heads, are you going to be shocked beyond all belief? I don't think I would be, since I know it was the other half chance of the 50/50 flip. The thirder position would say you should be absolutely shocked.
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post 1523288311 10-20-2017, 01:10 PM
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Originally Posted By numberguy12⏩
I see what you are saying man, but I just don't agree this is new info, since she knew she would be woken up at least once during the experiment a priori (and I realize no argument will convince either of us otherwise).

In terms of the million day variant, I see these longer extensions as intuitively supporting the 50/50, if anything. If you are woken up during this 1 million day variant, and then told it was heads, are you going to be shocked beyond all belief? I don't think I would be, since I know it was the other half chance of the 50/50 flip. The thirder position would say you should be absolutely shocked.
I would be shocked. To me someone brought up the similarity to the monty hall door and I see it as similar. Out of a thousand doors, if you pick the right one, you WOULD be surprised right? Much more likely you picked the wrong one (just like more likely you are stuck on the tails route).

***
It brings up some degree of religious/spiritual issues if you believe the original problem is the 2/3 (I do) because it has implications of 'what is more likely, this is just some low random chance of us being alive, or is there something happening behind the scenes?
post 1523296561 10-20-2017, 02:22 PM
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Originally Posted By KMadigan777⏩
I would be shocked. To me someone brought up the similarity to the monty hall door and I see it as similar. Out of a thousand doors, if you pick the right one, you WOULD be surprised right? Much more likely you picked the wrong one (just like more likely you are stuck on the tails route).

***
It brings up some degree of religious/spiritual issues if you believe the original problem is the 2/3 (I do) because it has implications of 'what is more likely, this is just some low random chance of us being alive, or is there something happening behind the scenes?
Absolutely some similarities to the question of existence. You could always bypass both the creator and the unlikely chance of our existence by answering it with the anthropic principle: the mere fact we are observing the universe is placing restraints on the universe and its conditions for life (so it's not unlikely, per say, but rather 100% certain).

To the first point, I still wouldn't be shocked within the context of a single experiment, and the experimenter told me upon waking it was heads. Part of our disagreement here is a discrepancy in sample space- your sample space is the set of all wakenings, and so are including all the tails wake-ups. My sample space is different- it is more akin to the number ofexperiments. This is why all those sim trials above are meaningless to the halfer position. In just one experiment, and that's what we have here, say it was heads....why even bother with all those tails wake-ups? There could be 1, or 100, or a trillion. Nothing changes the fact it is still 50% you are in the heads. Im not seeing how someone could be absolutely shocked if they wake up and the experimenter says it's heads.

With my sample space (if it even makes sense to define a sample space in this type of problem), is more like,

Experiment 1: Beauty guesses right
Experiment 2: Beauty guesses wrong
Experiment 3: Beauty guesses wrong
Experiment 4: Beauty guesses right
....etc etc

With your sample space:

Awakening 1: Beauty guesses right
Awakening 2: Beauty guesses wrong
Awakening 3: Beauty guesses wrong
Awakening 4: Beauty guesses right
.....etc etc
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post 1523449131 10-22-2017, 05:36 AM
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Originally Posted By numberguy12⏩
Absolutely some similarities to the question of existence. You could always bypass both the creator and the unlikely chance of our existence by answering it with the anthropic principle: the mere fact we are observing the universe is placing restraints on the universe and its conditions for life (so it's not unlikely, per say, but rather 100% certain).

To the first point, I still wouldn't be shocked within the context of a single experiment, and the experimenter told me upon waking it was heads. Part of our disagreement here is a discrepancy in sample space- your sample space is the set of all wakenings, and so are including all the tails wake-ups. My sample space is different- it is more akin to the number ofexperiments. This is why all those sim trials above are meaningless to the halfer position. In just one experiment, and that's what we have here, say it was heads....why even bother with all those tails wake-ups? There could be 1, or 100, or a trillion. Nothing changes the fact it is still 50% you are in the heads. Im not seeing how someone could be absolutely shocked if they wake up and the experimenter says it's heads.

With my sample space (if it even makes sense to define a sample space in this type of problem), is more like,

Experiment 1: Beauty guesses right
Experiment 2: Beauty guesses wrong
Experiment 3: Beauty guesses wrong
Experiment 4: Beauty guesses right
....etc etc

With your sample space:

Awakening 1: Beauty guesses right
Awakening 2: Beauty guesses wrong
Awakening 3: Beauty guesses wrong
Awakening 4: Beauty guesses right
.....etc etc
listen here you incel. the lady is told the experiment BEFORE she is drugged.

so she KNOWS going into it that the probability that it will be tuesday when she wakes up is 1/3.

when it is tuesday, the coin DEFINITELY landed tails. the other 2/3 of the time, the coin has a 50/50 chance of being heads or tails.

do the math on this and overall she KNOWS that it is a 2/3 chance to land tails and a 1/3 chance to land heads. you're just obfuscating an extremely simple problem with your overly long replies
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post 1523568601 10-23-2017, 09:54 AM
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I was thinking about this some more from an 'expected value' way. Imagine that every time she wakes up, she guesses which path she is on, if she is right she gets a dollar.

On the heads path she guesses wrong. On the tails path she guess correctly twice, therefore a profit of 2$. Given there are 3 wakes ups, she has a better expected value (2/3) compared to the 1/3. Further evidence of the 2/3
post 1523993471 10-26-2017, 08:04 PM
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Anyone who is part of the 1/2 explain why the expected value thing is wrong, because this seems like it seals the deal.
post 1523998001 10-26-2017, 08:57 PM
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Originally Posted By KMadigan777⏩
Anyone who is part of the 1/2 explain why the expected value thing is wrong, because this seems like it seals the deal.
Uhh because that's not the question.

The question is what's the odds the coin being heads.

That doesn't change.

The question is being misinterpreted .

In statistics the first thing you learn is that you can't have ambiguity.

And even if that WAS the question, it would still be incorrect because people are adding up the odds without multiplying the denominator.
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Talk about math and I am into it.
post 1616105191 09-10-2020, 07:54 AM
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Lol I remember this thread. 1/2 back then and still 1/2 today
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post 1616116051 09-10-2020, 10:10 AM
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How can this be unsolved? You can just write a program that does this 1000000 times and record the answers.
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post 1616117961 09-10-2020, 10:30 AM
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Originally Posted By HerderofGoats⏩
How can this be unsolved? You can just write a program that does this 1000000 times and record the answers.
No computer simulations are needed here. It comes down to interpretation of “what is Beauty’s credence the coin landed heads”.

It’s almost like the Monty Hall problem where the answer is ambiguous, unless certain assumptions are made.

I think the most natural interpretation of this problem is we are counting by coin tosses, and Beauty’s estimation of the probability heads came up is 50/50 since she receives no new information, that’s just my interpretation though.
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post 1616118871 09-10-2020, 10:39 AM
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Originally Posted By numberguy12⏩
No computer simulations are needed here. It comes down to interpretation of “what is Beauty’s credence the coin landed heads”.

It’s almost like the Monty Hall problem where the answer is ambiguous, unless certain assumptions are made.

I think the most natural interpretation of this problem is we are counting by coin tosses, and Beauty’s estimation of the probability heads came up is 50/50 since she receives no new information, that’s just my interpretation though.
The Monty Hall program isn't ambiguous, it has a clear answer and so does this one.

If you did this 10,000 times and she said she believed it was heads every time she was woken up then she would be correct 1/3 of the time.

I recognize though that different interpretations change the view of which question needs to be solved which changes the answer but if the question is worded as it is on the Wikipedia page then a rational sleeping beauty would believe that each time she was awoke there was a 1/3 chance the coin landed on heads.
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post 1616120781 09-10-2020, 10:55 AM
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Originally Posted By HerderofGoats⏩
The Monty Hall program isn't ambiguous, it has a clear answer and so does this one.

If you did this 10,000 times and she said she believed it was heads every time she was woken up then she would be correct 1/3 of the time.

I recognize though that different interpretations change the view of which question needs to be solved which changes the answer but if the question is worded as it is on the Wikipedia page then a rational sleeping beauty would believe that each time she was awoke there was a 1/3 chance the coin landed on heads.
-The Monty Hall problem is technically ambiguous as stated: it depends on assumptions for the host’s actions. We are not given if the host randomly picks one of the remaining two doors, or specially picks one with a goat, when he reveals a goat door. If it’s the former, it’s 1/2 vs 1/2 and doesn’t matter if you switch, if it’s the latter, is 1/3 vs 2/3 and makes sense to switch. It would be more plausible if the host purposely picks a goat door, but this is not in the problem as stated.

-For the sleeping beauty problem, you are indicating a specific interpretation to count awakenings vs experiments, but many do not look at it this way. There really is no answer to that no new information issue from the 1/3 crew. As for me, if i was doing this for one single experiment, and it was 1 trillion awakenings for tails, and 1 for heads for a 50/50 coin flip.....I am all the sudden awake....I still know it’s just as likely I’m on the heads side, vs on the string on tails sides. Under your interpretation it would be nearly infinitely small chance im on the heads side, which doesn’t make much sense to me. The important thing is no new information is obtained, so Beauty’s credence of the coin flip result shouldn’t change.

A lot of this comes down to interpretation, which I don’t like, and also is common with a lot of these popular philosophy-type problems. We are not asking a precise question like “does there exist an odd integer x such that 3<x<5” (no)
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