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.
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.