Doesn’t there have to be some point at which we consider what happens after these strange types of events? Information is only information if it causes some real change. I’m confused about this, not making a point yet.
What if we make a change in the Sleeping Beauty protocol such that, instead of more time passing in the event of tails, Beauty is merely put to sleep and wakes up twice on the same day for tails, and once for heads? So, nothing that has been discussed concerning whether 1⁄3 or 1⁄2 is changed by this new protocol (that I could find in the hundreds of comments). Now, after the experiment, the day is the same no matter which way the coin flipped. If they don’t tell Beauty which way the coin flipped, what should be her expectation, from then on throughout her life, that the coin landed on heads? Clearly the answer to that question is 1⁄2. So why should Beauty answer differently after she’s walked out of the testing facility than she did during her last interview?
I think there’s a way in which our intuitions about objective time and subjective time are confusing these questions. In the original protocol, after Beauty leaves the facility and before she checks a calendar, it seems like maybe she should still be thinking she was in the two-day protocol. But as soon as she looks at a calendar, her knowledge state collapses to the correct conclusion: “If it’s Monday, it was heads; if it’s Tuesday, it was tails. Now I’m going to find some pancakes!”
So, I guess the conclusion I’m coming to is that during the experiment, unless there is a pay-off structure, Beauty is in an entangled state with the coin flip that is not susceptible to analysis, and so any expectations she has are meaningless in relation to reality, except as might interest psychologists. This is the case whether we go with the original protocol or the 1 day vs 2 half-days protocol I suggested.
I haven’t had a chance to thoroughly analyze the specific situations offered by LucidFox, but kudos and up-vote for making me think of something new!
Doesn’t there have to be some point at which we consider what happens after these strange types of events? Information is only information if it causes some real change. I’m confused about this, not making a point yet.
What if we make a change in the Sleeping Beauty protocol such that, instead of more time passing in the event of tails, Beauty is merely put to sleep and wakes up twice on the same day for tails, and once for heads? So, nothing that has been discussed concerning whether 1⁄3 or 1⁄2 is changed by this new protocol (that I could find in the hundreds of comments). Now, after the experiment, the day is the same no matter which way the coin flipped. If they don’t tell Beauty which way the coin flipped, what should be her expectation, from then on throughout her life, that the coin landed on heads? Clearly the answer to that question is 1⁄2. So why should Beauty answer differently after she’s walked out of the testing facility than she did during her last interview?
I think there’s a way in which our intuitions about objective time and subjective time are confusing these questions. In the original protocol, after Beauty leaves the facility and before she checks a calendar, it seems like maybe she should still be thinking she was in the two-day protocol. But as soon as she looks at a calendar, her knowledge state collapses to the correct conclusion: “If it’s Monday, it was heads; if it’s Tuesday, it was tails. Now I’m going to find some pancakes!”
So, I guess the conclusion I’m coming to is that during the experiment, unless there is a pay-off structure, Beauty is in an entangled state with the coin flip that is not susceptible to analysis, and so any expectations she has are meaningless in relation to reality, except as might interest psychologists. This is the case whether we go with the original protocol or the 1 day vs 2 half-days protocol I suggested.
I haven’t had a chance to thoroughly analyze the specific situations offered by LucidFox, but kudos and up-vote for making me think of something new!