Be advised: this thread is not for serious in-depth discussion of weighty topics (we have a link for that), this thread is not for anything Culture War related. This thread is for Fun. You got jokes? Share 'em. You got silly questions? Ask 'em.
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Notes -
Against Talking About Anthropics/Possible Worlds/etc in the Sleeping Beauty Problem
I get it. Anthropics is an interesting topic. Possible worlds has a long and rich philosophical history. I can get why people might want to expose more people to that stuff, kinda squint at the sleeping beauty problem, then think that it's close enough to spread the gospel.
But that's confusing people.
It's confusing them on what is otherwise a very simple math problem.
For those who haven't seen my last entry, I made some minor modifications, primarily adding a second person, so we have both Alice and Bob undergoing simultaneous experiments. The simplest version is that they each undergo approximately the same experiment, with the same coin, but opposite (the implications of heads for one person are like the implications of tails for the other). I also had some computer communication between them for some instructive purposes, but that's not even necessary here.1
Let's follow Alice and Bob a bit further. Suppose after their one/two awakenings, they're put back to sleep, memory again wiped. They're both finally awoken on Wednesday. "No more questions," the doctors say. "We took the liberty of interpreting your answers as wagers. We have your home address. We'll compute your payout and mail you a check with your results, revealing to you how the coin actually came out, how you answered the questions (because they won't remember), and what your payout is. Expect it to take 4-8 weeks."
Alice and Bob leave their respective rooms. They run into each other in the lobby.
Wait
Can Alice and Bob run into each other in the lobby? Aren't they, like, in different possible worlds or something? No, silly. That's confusing people. They're in the same world. They've been in the same hallway all along, separated by only a paper-thin wall.
Ok, so they run into each other in the lobby. They hit it off, decide to go out to a pub and grab a pint together. Naturally, the conversation turns to the strange experiment they each went through. Neither one is going to know how the coin flip actually went or what subsequently happened for another 4-8 weeks.
They begin to debate. How should they best guess what their results might have been? What if they'd like to wager against one another about the results? Should they have significantly different estimates of what they're going to see in their results? Should Alice think that there's a 1/3 chance that they're going to learn that it was heads, while Bob should think that there's a 1/3 chance that they're going to learn that it was tails? Did they truly "update" their probabilities during the course of the experiment?
No. Of course not. If either of them thought that, you could take their money. They should both think that it was 1/2 either heads or tails. This is because they didn't "update" some probability estimate. They didn't enter some weird different possible worlds, where never the physical Alice and Bob could ever meet again.
Instead, Alice and Bob are both capable of having a perfectly reasonable conversation. "Yeah, of course I think the probability of the coin flip was 1/2. It's just because of the weird observation function of the experiment that I computed that there was a different probability for what I was likely to observe." "Yeah, me too, but my observation function was the opposite, so I computed that I was likely to observe the opposite. But obviously, at the same time, the probability of the coin flip was 1/2."
They're just different probabilities with different meanings. You can just compute them from the observation functions.
1 - That time, I was trying to get people to figure out that they could have one individual's brain retaining multiple different probabilities, with multiple different meanings. I guess this time, I'll just try having multiple different minds meeting.
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