= 27d567bc2d48d9f40e9ccc20ea370b15)
Jack comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (335)
Variation Alpha:
10 people. If heads, one of the ten is randomly selected to be revived. If tails, all ten are revived. (If you like, suppose that the ten are revived one at a time on consecutive days - but it doesn't make any difference.)
Variation Beta:
Same as Alpha except the 10 people are clones of yours, with mental state identical to your own.
Variation Gamma:
Same as Beta except the cloning is done after you fall asleep.
Variation Delta:
Same as Gamma except that the way the clones are not created all at once. Rather, successive clones are created on subsequent days by erasing one days' worth of memory of the previous clone.
It seems clear to me that in variation Alpha, 1/11 is the answer and not 1/2. And clearly variation Delta is isomorphic to the Sleeping Beauty problem (except with 10 days rather than 2). And clearly each step from Alpha to Delta doesn't change anything essential.
Right?
Nice way of formulating the problem.
In variation Alpha we know beforehand of a particular event that will happen with P=1 if tails and P=1/10 if heads. Call this event "Jack wakes up and thinks a thought". So when we see that event we can conclude 1/11.
But in Beta and the remaining variations there is no such event. A clone can't tell which clone it is, going into the experiment my anticipated experience does not differ based on whether or not heads comes up. Either one of me will be woken up or 10 identical copies who don't know about each other will be woken up. "Jack wakes up and thinks a thought" happens at the same probability for heads and tails. At no point does any copy of me get new information to revise from 1/2.