ciphergoth comments on Real-Life Anthropic Weirdness - Less Wrong

24 Post author: Eliezer_Yudkowsky 05 April 2009 10:26PM

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Comment author: ciphergoth 07 April 2009 04:57:20PM 2 points [-]

I mean that if we're to know the evidential weight of winning the lottery to the theory that we're on the holodeck, we need to know P(L|H), so that we can calculate P(H|L) = P(L|H)P(H)/(P(L|H)P(H) + P(L|¬H)P(¬H)).

Comment author: Hans 07 April 2009 05:33:11PM *  1 point [-]

I get your point now. But all we need to know is whether P(L|H) > P(L|~H)*.

If this is the case, then if an extremely unlikely (P(L/~H) -> 0) event L happens to you, this evidently increases the chance that you're in a holodeck simulation. In the formula, P(L|H) equates to (almost) 1 as P(L|~H) approaches zero. The unlikelier the event (amazons on unicorns descending from the heavens to take you to the land of bread and honey), i.e. the larger the difference between P(L|H) and P(L|~H), the larger the probability that you're experiencing a simulation.

This is true as long as P(L|H) > P(L|~H). If L is a mundane event, P(L|H) = P(L|~H) and the formula reduces to P(H|L) = P(H). If L is so supremely banal that P(L|~H) > p(L|H), the occurence of L actually decreases the chance that you're experiencing a holodeck simulation.

Indeed, I believe that was the point of the original post.

The core assumption remains, of course, that you're more likely to win the lottery when you're experiencing a holodeck simulation than in the real world (P(L|H) > P(L|~H)).

I'm not well-versed in Bayesian reasoning, so correct me if I'm wrong. Your posts have definitely helped to clarify my thoughts.

*I don't know how to type the "not"-sign, so I'll use a tilde.