There are 2^1001 equally likely (in the prior) scenarios, by combinations of coin flips. Applying evidence, anthropic or otherwise, means eliminating possibilities which have been excluded by the evidence and renormalising what’s left. Doing this leaves two equally likely scenarios, that the original coin was tails and the other 1000 flips were heads, or that all 1001 flips were heads. The chances of the original coin being heads are therefore, still, 50-50. Keep flipping.
If this is meant to highlight some of the horribly flawed thinking that comes with anthropic evidence then you’ve done an excellent job. You’ve imposed an assymetry between “dieing” and “surviving the game and moving on”, but no such assymetry exists. Both possibilities would equally prevent you from being in the situation you describe.
You are assuming that we have absolute certainty in the game, but evidence as strong as 1000 heads in a row digs up a lot of previously unlikely hypotheses. Do you think this would change the answer?
Oh I’d definately be questioning my assumptions well before the 1000th head. Taking a good hard look at the coin, questioning my memory, and whatever else. As Sherlock Holmes most definately didn’t say but probably should have, “When all possibilities have been eliminated, the answer most probably is something you simply haven’t thought of”. I don’t think I’d be privileging any flawed theories of anthropic evidence and embracing the idea quantum suicide for fun and/or profit until I’d eliminated a fair few other options though.
There are 2^1001 equally likely (in the prior) scenarios, by combinations of coin flips. Applying evidence, anthropic or otherwise, means eliminating possibilities which have been excluded by the evidence and renormalising what’s left. Doing this leaves two equally likely scenarios, that the original coin was tails and the other 1000 flips were heads, or that all 1001 flips were heads. The chances of the original coin being heads are therefore, still, 50-50. Keep flipping.
If this is meant to highlight some of the horribly flawed thinking that comes with anthropic evidence then you’ve done an excellent job. You’ve imposed an assymetry between “dieing” and “surviving the game and moving on”, but no such assymetry exists. Both possibilities would equally prevent you from being in the situation you describe.
Good analysis.
You are assuming that we have absolute certainty in the game, but evidence as strong as 1000 heads in a row digs up a lot of previously unlikely hypotheses. Do you think this would change the answer?
Oh I’d definately be questioning my assumptions well before the 1000th head. Taking a good hard look at the coin, questioning my memory, and whatever else. As Sherlock Holmes most definately didn’t say but probably should have, “When all possibilities have been eliminated, the answer most probably is something you simply haven’t thought of”. I don’t think I’d be privileging any flawed theories of anthropic evidence and embracing the idea quantum suicide for fun and/or profit until I’d eliminated a fair few other options though.