= 27d567bc2d48d9f40e9ccc20ea370b15)
jimrandomh comments on The I-Less Eye - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (83)
I respectfully disagree.
Suppose I bet that a 30-digit random number generator will deliver the number 938726493810487327500934872645. And, lo and behold, the generator comes up with 938726493810487327500934872645 on the first try. If I am magically certain that I am actually dealing with a random number generator, I ought to conclude that I am hallucinating, because p(me hallucinating) > p(guessing a 30-digit string correctly).
Note that this is true even though p(me hallucinating the number 938726493810487327500934872645) is quite low. I am certainly more likely, for example, to hallucinate the number 123456789012345678901234567890 than I am to hallucinate the number 938726493810487327500934872645. But since I am trying to find the minimum meaningful probability, I don't care too much about the upper bounds on the odds that I'm hallucinating -- I want the lower bound on the odds that I'm hallucinating, and the lower bound would correspond to a mentally arbitrary number like 938726493810487327500934872645.
In other words, if you agree with me that p(I correctly guess the number 938726493810487327500934872645) < p(I'm hallucinating the number 938726493810487327500934872645), then you should certainly agree with me that p(I correctly guess the number 123456789012345678901234567890) < p(I'm hallucinating the number 123456789012345678901234567890). The probability of guessing the correct number is always 10^-30; the probability of hallucinating varies, but I suspect that the probability of hallucinating is more than 10^-30 for either number.
Choosing a number and betting that you will see it increases the probability that you will wrongly believe that you have seen that number in the future to a value that does not depend on how long that number is. P(hallucinate number N|placed a bet on N) >> P(hallucinate number N).
Yes, I completely agree. To show that I understand your point, I will suggest possible numbers for each of these variables. I would guess, with very low confidence, that on a daily basis, P(hallucinate a number) might be something like 10^-7, that P(hallucinate a 30-digit number N) might be something like 10^-37, and that P(hallucinate a 30-digit number N | placed a bet on N) might be something like 10^-9. Obviously, p(correctly guess a 30-digit number) is still 10^-30.
Even given all of these values, I still claim that we should be interested in P(hallucinate a 30-digit number N | placed a bet on N). This number is probably roughly constant across ostensibly sane people, and I claim that it marks a lower bound below which we should not care about the difference in probabilities for a non-replicable event.
I am not certain of these claims, and I would greatly appreciate your analysis of them.