The world's greatest paradox is The Sleeping Beauty paradox

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261252

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Very challenging conceptually


It is a deep study of perspective which can be seen in different world views that people have where two different views are both correct depending on POV.

The paradox is a study of epistemology (the study of knowledge and belief).
  • Sleeping Beauty is put to sleep on Sunday.
  • A fair coin is flipped.
  • If Heads : She is woken up on Monday, interviewed, and put back to sleep (with amnesia) then not woken again until Wednesday and experiment is over.
  • If Tails: She is woken up on Monday, interviewed, put back to sleep (with amnesia), then woken up again on Tuesday, interviewed again put to sleep the awoken on Wednesday and experiment is over.
    The question:
    When she is woken up for an interview on Monday or Tuesday or both (and she knows the setup but not the day), what should she say is the probability that the coin landed Heads from her perspective?
 
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261252

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Here I change the test where she is woken only on Monday but the answer will not change because she does not know it is Monday and got rid of Wednesday awakening as it is superfluous

Sleeping Beauty is put to sleep on Sunday. A fair coin is flipped. If Heads: She is told she will be woken up on Monday, interviewed, and put back to sleep (with amnesia) then not woken again. If Tails: She is woken up on Monday, interviewed, put back to sleep (with amnesia), then woken up again on Tuesday, interviewed again. The question: When she is woken up for an interview on Monday (and she knows the setup but not the day), what should she say is the probability that the coin landed Heads from her perspective?
 
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261252

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Even better remove the days to get to the puriest form of the question



A coin is flipped.
If Heads: you wake her once.
If Tails: you wake her twice (with amnesia between).
When she wakes up, what probability should she assign to Heads?"
 
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261252

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even better get rid of sleeping beauty and you are being tested


Given that you are having a conscious experience right now, and you know that Heads would produce one such experience, while Tails would produce two — what is the probability that the coin landed Heads?


From the coin flipper's POV the answer is clearly 1 in 2 but what is it from yours ?




This is not a probability question but a thought experiment about how we experience existence
 
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OntGuy2010

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Dear friend, if Sleeping Beauty is put to sleep and woken up so many times, with or without amnesia, she would be so pissed off at the end of the experiment, that even if you take the probability of heads times the integral over all existence divided by the sum total of the infinite series of the number of days, she would not give less of a ^%$# what the correct answer would have had been! 🥳
 
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Zoot Allures

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Sleeping Beauty wakes up on Monday if heads and Monday and Tuesday if tails. But, it seems to me, regardless of day she thinks

"If it is Monday coin was either head or tails but if it is Tuesday coin was only tails"

She has no idea which day it is

So, if tails she wakes up twice and if heads she wakes up once so it is twice as probable coin is tails, from her perspective.
But it is still 50% chance it is tails for if it is heads there is no Tuesday wake up but she does not know if there is a Tuesday wake up so she sees twice as many possible tails. The coin flip is 50/50 that never changes and Sleeping Beauty know it. The question is not about the flip, she knows it is a fifty % chance of being tails but her question is what are the odds I am in a tails world right now ? There are 2 possible awakenings if it landed tails but only one if it landed heads

You have to frame the proper question

Whoever thought of this paradox is clever but I like 261252 version better in post 4 as it gets right to the issue without 3 days of wakeups with a fictious character as you are now the one asleep so you see the problem through your eyes not a third party
 
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onomatopoeia

onomatopoeia

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The probability of the coin flip is always 50/50, even if the most recent sequence of flips has resulted in all heads or all tails. Probability and actual outcome are two different things.

The probability of winning the Lotto 6/49 is approximately 1 in 13.8 Million. That doesn't mean that if 13.8 million people buy a ticket, there is a 100% chance that there will be exactly one winner.
 
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rhuarc29

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I mean, I see why some would get 2/3 chance its tails answer, because there are twice as many awakenings in the Tails "path" as the Heads "path".
However, in my mind the number of awakenings does not influence the chance of Heads or Tails. Merely the opposite: the Heads or Tails influences the number of awakenings. People who choose 2/3 as their answer have the causality reversed or bidirectional, when it isn't really.
 
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Zoot Allures

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rhuarc29 said:
I mean, I see why some would get 2/3 chance its tails answer, because there are twice as many awakenings in the Tails "path" as the Heads "path".
Click to expand...
exactly
rhuarc29 said:
However, in my mind the number of awakenings does not influence the chance of Heads or Tails. Merely the opposite: the Heads or Tails influences the number of awakenings. People who choose 2/3 as their answer have the causality reversed or bidirectional, when it isn't really.
Click to expand...
It is a puzzle about how rational decisions are influenced by perspective which is what makes it so interesting.

As well as being conceptually challenging. I had to think about it for some time before I
understood the puzzle and I am still not sure I fully understand it.
 
Valcazar

Valcazar

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rhuarc29 said:
I mean, I see why some would get 2/3 chance its tails answer, because there are twice as many awakenings in the Tails "path" as the Heads "path".
However, in my mind the number of awakenings does not influence the chance of Heads or Tails. Merely the opposite: the Heads or Tails influences the number of awakenings. People who choose 2/3 as their answer have the causality reversed or bidirectional, when it isn't really.
Click to expand...
That's the bit about "how are you framing the question".
What you think the question actually is changes the answer.

Think of it another way.
If the coin lands heads, she is awakened 1 time.
If the coin lands tails, she is awakened 99 times.

She is woken up, what should she guess the coin was?

Do you think of it in terms of "given how many possible times I was woken up, which path am I on?" or do you think of it as "what are the two possible coin flip outcomes"?
The difference is starker when you make it 99 to 1 but the problem remains the same.

The philosophical bit is which do you think is the "real" question?
 
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Zoot Allures

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Valcazar said:
Think of it another way.
If the coin lands heads, she is awakened 1 time.
If the coin lands tails, she is awakened 99 times.

She is woken up, what should she guess the coin was?

Do you think of it in terms of "given how many possible times I was woken up, which path am I on?" or do you think of it as "what are the two possible coin flip outcomes"?
The difference is starker when you make it 99 to 1 but the problem remains the same.

The philosophical bit is which do you think is the "real" question?
Click to expand...
I think you mean she is woken 100 times if it is tails

She is woken the first time when either heads or tails then 99 times more only if it was tails

So the odds of a tails world awakening is 99 out of 100 but if she sees through the question she will realize the odds are 50% for the flip

The odds of her being in a tails awakening is 99% as she has no idea which awakening she is in but the odds of the flip is still 50%

You could fool her and wake her only once regardless of flip and her answer will be the same
 
Valcazar

Valcazar

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Zoot Allures said:
I think you mean she is woken 100 times if it is tails
Click to expand...
No. I made it 99.
It doesn't really matter.
The point is just to pull it away from 1/2 and 1/3.

So the odds of a tails world awakening is 99 out of 100 but if she sees through the question she will realize the odds are 50% for the flip

The odds of her being in a tails awakening is 99% as she has no idea which awakening she is in but the odds of the flip is still 50%
Click to expand...
Right.
Is the probability space awakening or is the probability space the coin flip?
It's the same as before.

You could fool her and wake her only once regardless of flip and her answer will be the same
Click to expand...
Why would her answer be the same?
If you mean that the reality can be different from the information she is given, then sure.
 
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Zoot Allures

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Valcazar said:
Why would her answer be the same?
If you mean that the reality can be different from the information she is given, then sure.
Click to expand...

because she has no idea which awakening she is in so each awakening ,be it the first or last, gets the same answer
 
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261252

Nobodies business if I do
Sep 26, 2007
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Zoot Allures said:
because she has no idea which awakening she is in so each awakening ,be it the first or last, gets the same answer
Click to expand...

Sleeping beauty has no way to know which awakening she is in because the rules are she forgets the awakening after being interviewed


She does not think "I was awakened yesterday so this must be Tuesday so the coin was tails"

she thinks there are more awakenings if the coin was tails so I am probably in tails awakening
 
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Big Rig

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Valcazar said:
But that just becomes a question about lying to her.
Click to expand...
No

She is never told which awakening she is in so each awakening is the same to her so only giving her one awakening instead of two, while a lie, does not change the thought experiment

From her POV she is twice as likely in a tails world even though she fully understands the coin flip was 50%

The odds of it being tails is not the question she is answering
 
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Valcazar

Valcazar

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Big Rig said:
No

She is never told which awakening she is in so each awakening is the same to her so only giving her one awakening instead of two, while a lie, does not change the thought experiment
Click to expand...
It completely changes the thought experiment.

From her POV she is twice as likely in a tails world even though she fully understands the coin flip was 50%

The odds of it being tails is not the question she is answering
Click to expand...
I don't think you're explaining yourself clearly.
In the original she knows the effects of each result.
In yours, she doesn't.

They are completely different situations.

Am I misunderstanding how you've altered the terms?
 
TakeOffHoser

TakeOffHoser

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Every time she wakes up, her butthole hurts for some weird reason, I have no idea why.
 
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Big Rig

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Valcazar said:
It completely changes the thought experiment.



I don't think you're explaining yourself clearly.
In the original she knows the effects of each result.
In yours, she doesn't.

They are completely different situations.

Am I misunderstanding how you've altered the terms?
Click to expand...
i have not altered anything i really think you have missed it

It is about her waking up and not knowing which awakening she is in
she knows the flip is 50% but she is twice as likely to be woken in an awakening where the coin was tails
 
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