The person controlling the holodeck (who presumably designed the simulation) needs to know the probability. But the person being simulated, who experiences winning the lottery, does not need to know anything about the inner working of his (simulated) world. For the experience to seem real enough, it’d be best, even, not to know every detail of what’s going on.
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)).
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.
Strictly speaking you need to know the probability that you’ll win the lottery given that you’re on the holodeck to complete the calculation.
The person controlling the holodeck (who presumably designed the simulation) needs to know the probability. But the person being simulated, who experiences winning the lottery, does not need to know anything about the inner working of his (simulated) world. For the experience to seem real enough, it’d be best, even, not to know every detail of what’s going on.
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)).
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.