The problem vexing the minds of experts is as follows: Sleeping Beauty agrees to participate in an experiment. On Sunday she is given a sleeping pill and falls asleep. One of the experimenters then tosses a coin. If “heads” comes up, the scientists awaken Sleeping Beauty on Monday. Afterward, they administer another sleeping pill. If “tails” comes up, they wake Sleeping Beauty up on Monday, put her back to sleep and wake her up again on Tuesday. Then they give her another sleeping pill. In both cases, they wake her up again on Wednesday, and the experiment ends.
The important thing here is that because of the sleeping drug, Sleeping Beauty has no memory of whether she was woken up before. So when she wakes up, she cannot distinguish whether it is Monday or Tuesday. The experimenters do not tell Sleeping Beauty either the outcome of the coin toss nor the day.
They ask her one question after each time she awakens, however: What is the probability that the coin shows heads?
To emphasize this answer, imagine head: they wake her the once, but tails, they do it 100 times before the experiment ends. The coin flip odds are still 50/50, but the odds that on a random waking she sees tails is overwhelming. — noAxioms
Without memory of prior awakening or knowledge of what day it is, she would have to answer 1/2. What SB remembers is she was put to sleep and she awakens. The coin is tossed once in her memory.They ask her one question after each time she awakens, however: What is the probability that the coin shows heads?
I thought I saw this problem posted before in the Lounge? — L'éléphant
The Sailor's Child problem, introduced by Radford M. Neal, is somewhat similar. It involves a sailor who regularly sails between ports. In one port there is a woman who wants to have a child with him, across the sea there is another woman who also wants to have a child with him. The sailor cannot decide if he will have one or two children, so he will leave it up to a coin toss. If Heads, he will have one child, and if Tails, two children. But if the coin lands on Heads, which woman would have his child? He would decide this by looking at The Sailor's Guide to Ports and the woman in the port that appears first would be the woman that he has a child with. You are his child. You do not have a copy of The Sailor's Guide to Ports. What is the probability that you are his only child, thus the coin landed on Heads (assume a fair coin)? — wiki
Sleeping Beauty receives no new non-self-locating information throughout the experiment because she is told the details of the experiment. Since her credence before the experiment is P(Heads) = 1/2, she ought to continue to have a credence of P(Heads) = 1/2 since she gains no new relevant evidence when she wakes up during the experiment.
This version looks a lot clearer to me, and the question at the end looks like a deception. 2 possible worlds, contain 3 possible identities. So other things (ie coins) being equal, I am more likely to be one of two than one of one. So P. (only child) is 1/3 notwithstanding P. (heads) is 1/2, because tails is twice as fruitful as heads. — unenlightened
If you chose The Siren, you would feel like The World's Idiot for the rest of your life. — hypericin
She can't. The instruction reads that she has no memory of prior awakening or what day it is. She doesn't even know that the experimenter tosses the coin, because they do it when she's put back to sleep. The question to her is "what are the odds that a coin will land heads (or tails)". Since she must know what a coin is, and what heads and tails is, she must answer "1/2".To answer correctly, sleeping beauty must evaluate the probability she is experiencing each of these events. — hypericin
The probability that the coin will land heads and she will be woken on Monday is 1/2.
The probability that the coin will land tails and she will be woken on Monday is 1/2.
The probability that the coin will land tails and she will be woken on Tuesday is 1/2. — Michael
Bet on heads or tails. If tails, you get to repeat the same bet again, on the same toss — hypericin
This is straightforwardly true, but from the perspective of an observer of the experiment. But to answer the problem you must adopt SB's perspective. That makes all the difference. — hypericin
But SB is asked on every wakening, and is woken twice as much on tails. This must influence the odds — hypericin
Influences the gambling odds, even though the coin toss is fair in both cases — hypericin
Let's say that I wanted to bet on a coin toss. I bet £100 that it will be tails. To increase the odds that it's tails, I ask you to put me to sleep, wake me up, put me back to sleep, wake me up, put me back to sleep, wake me up, and so on. Does that make any sense? — Michael
No, I'm in the double halfer camp now. The post right above explains my current thinking.
((This is, I don't know, maybe the third time I've argued with Michael about something and then concluded he was right all along.)) — Srap Tasmaner
So you've switched back to being a thirder? — Michael
Let's say that I wanted to bet on a coin toss. I bet £100 that it will be tails. To increase the odds that it's tails, I ask you to put me to sleep, wake me up, put me back to sleep, wake me up, put me back to sleep, wake me up, and so on. Does that make any sense? — Michael
I switched back shortly after that post; it's right there in the thread. The argument that convinced me was this: consider a variation, "Informative SB", in which Beauty is told she will be awakened twice either way, but if it was heads she will be told at the second interview that it was heads and that this is her second interview; at none of the others will she be given such information. — Srap Tasmaner
The absence of that thing is informative, it amounts to "it was tails or this is your first interview," and this is true as well for stock SB. Being asked is itself information you can condition on. — Srap Tasmaner
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.