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Jack comments on A note on the description complexity of physical theories - Less Wrong
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But then if I observed any string of 30 outcomes I would have strong evidence for MWI (if the coin is fair, "p" for any specific string would be 2^-30).
You have to specify a particular string to look for before you do the experiment.
Sorry, now I have no idea what we're talking about. If your experiment involves killing yourself after seeing the wrong string, this is close to the standard quantum suicide.
If not, I would have to see the probabilities to understand. My analysis is like this: P(I observe string S | MWI) = P(I observe string S | Copenhagen) = 2^-30, regardless of whether the string S is specified beforehand or not. MWI doesn't mean that my next Everett branch must be S because I say so.