Why on earth would you think you are in a “random” box?!?

If I rearranged the diagram so the 3 categories now corresponded to totally different time periods – would you *still* think that you are in a random box?

Drawing arbitrarily-labelled boxes and assigning them equal probability does not seem to be a sensible way to generate priors on this topic.

I mean the problem is that there is no random process that spits you out into society with uniform probability of being any baby (or wakes you up with uniform probability of being in any day of the sleeping beauty paradox). These paradoxes are seductive because [B]we assume that since we can’t say anything in favor of us being born now rather than then we can assign them equal probability.[/B] Really though the notion of probability doesn’t even really make sense here.

To take apart this paradox let’s me first show why we can’t have shown that the probability of being near the end of civilization is large. Suppose I’m god and I can just magic up these worlds and 999,999 times out of a million I set up the worlds to continue indefinitely with ever expanding population. If I magic up a whole bunch of these worlds and assign souls randomly to such worlds then it turns out that the probability of being in the last generation is very very low.

Thus since this situation is wholly consistent with what we’ve observed so far we can’t actually have the information necessary to conclude that the probability of the end of days coming soon is high. The error was taking our lack of any reason to distingush being born as any given baby in our universe as justification for supposing that the world is fixed but who you are in it is chosen via a uniform distribution from all the people.

Probability isn’t magic and it shouldn’t be used interchangeably with confidence. It’s just a fancy way of counting things.

First just consider the sleeping beauty problem. You enroll in some weird experiment and are told that you will be put to sleep then a coin will be fliped if the coin is heads then you are woken up the next day informed the experiment isn’t over yet and then put back to sleep after which your memory of waking up is wiped. If tails you aren’t woken up tomorrow at all. In either case you are woken up the day after tomorrow and put back to sleep until being released 3 days from now. Now when you are woken up during the experiment should you assign probability 1/2 or probability 2/3 to the coin coming up heads. By a similar argument to above there are strong reasons to say it is 2/3 (certainly you should act as if it is 2/3 and not make even odds bets on the coin being tails since you could lose 2 dollars on a heads and win 1 on tails).

Now apply the same argument to the scenario I gave above. Do the math and you find that merely given the fact that you currently exist you should boost the probability that there are infinitely many copies of yourself (in time/space/whatever) to 1.

(a) Anthropic puzzles (e.g doomsday argument)
(b) Born probabilities
(c) Puzzles of weighting subjective experiences
(d) Time asymmetry

(a), (b) (c) and (d) are all related, and I’m sure the key is some big generalization of SIA which has so far been missed. I leave pesky near-mode details to you folks.

(Hint: Categoization, analogical inference, and reference classes are the key, not Bayes, and similarity is the important measure, not probability. It is simply obvious that categorization is the key is solving these puzzles and it is more powerful than induction. Any LW/OB participant who has failed to spot these blinking obvious points is not a ‘super clicker’ I’m afraid).

Probabilities are measures of uncertainty; people would be well advised to attach them to all their beliefs.

put another way, as others have noted, you have no way to assign any probabilities of anything relevant to the inquiry. aren’t the odds best we are in a simulation? how do you figure the odds we’re not the bacteria in a petrie dish wondering why the universe seems to be finite, lack other bacteria, etc.? how do you figure the odds it’s not god hiding things from us? how do you figure the odds that all advanced civilizations move almost immediately to communicating via gravity waves or somesuch that we can’t detect? how do you figure the odds we’re not in a zoo, or quarantined?