Open Thread June 2010, Part 4

Will_Newsome

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

This thread brought to you by quantum immortality.

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

This thread brought to you by quantum immortality.

I'm in the process of digging into the math, so hopefully some point soon I'll be able to back up my suspicions in a more rigorous way.

This doesn't sound right to me. Imagine you're tossing a coin repeatedly. Hypothesis 1 says the coin is fair. Hypothesis 2 says the coin repeats the sequence HTTTHHTHTHTTTT over and over in a loop. The second hypothesis is harder to locate, but makes a stronger prediction.

I was talking about the number of predictions, not their strength. So Hypothesis 1 predicts any sequence of coin-flips that converges on 50%, and Hypothesis 2 predicts only sequences that repeat HTTTHHTHTHTTTT. Hypothesis 1 explains many more possible worlds than Hypothesis 2, and so without evidence as to which world we inhabit, Hypothesis 1 is much more likely.

Since I've already conceded that being a Perfect Bayesian is impossible, I'm not surprised to hear that measuring locate-ability is likewise impossible (especially because the one reduces to the other). It just means that we should determine prior probabilities by approximating Solomonoff complexity as best we can.

Thanks for taking the time to comment, by the way.

Then let's try this. Hypothesis 1 says the sequence will consist of only H repeated forever. Hypothesis 2 says the sequence will be either HTTTHHTHTHTTTT repeated forever, or TTHTHTTTHTHHHHH repeated forever. The second one is harder to locate, but describes two possible worlds rather than one.

Maybe your idea can be fixed somehow, but I see no way yet. Keep digging.