It’s always a possibility that I’m insane, but normally a fairly unlikely one.
The baseline hypothesis is (say) p = 0.999 that I’m sane, p = 0.0001 that I’m hallucinating. Let’s further assume that if I’m hallucinating, there’s a 2% chance that hallucination is about time travel. My prior is something like p = 0.000001 that time travel exists. If I assume those are the only two explanations of seeing a time traveler, (i.e. we’re ignoring pranks and similar), my estimate of the probability that time travel exists would shift up to about 2% instead of 0.0001% -- a huge increase. The smart money (98%) is still on me hallucinating though.
If you screen out the insanity possibility, and any other possibility that gives better than 1 in a million chances of me seeing what appears to be a time traveler with what appears to be futuristic technology, yes, the time traveler hypothesis would dominate. However, the prior for that is quite low. There’s a difference between “refusing to update” and “not updating far enough that one explanation is favored”.
If I was abducted by aliens, my first inclination would likewise be to assume that I’m going insane—this is despite the fact that nothing in the laws of physics precludes the existence of aliens. Are you saying that the average person who thinks they are abducted by aliens should trust their senses on that matter?
Ah. In that case, I think we’re basically in agreement. To clarify: I only used the time travel as an example because that was the example that VAuroch used in his/her comment. I agree that even taking into account your observation of time travel, the posterior probability for your insanity is still much larger than the posterior probability for genuine time travel. You do agree, however, that even if you conclude that you are likely insane, the probability of time travel was still updated in a positive direction, right? It seems to me that Nominull (the person to whom I was originally replying) was implying that your probability estimate shouldn’t change at all, because that’s “clearly impossible”/”fictional evidence” or something along those lines. It is that implication which I disagree with; as long as you’re not endorsing that implication, we’re in agreement. (If Nominull is reading this and feels that I am mistaken in my reading of his/her comment, then he/she should feel free to clarify his/her meaning.)
It’s always a possibility that I’m insane, but normally a fairly unlikely one.
The baseline hypothesis is (say) p = 0.999 that I’m sane, p = 0.0001 that I’m hallucinating. Let’s further assume that if I’m hallucinating, there’s a 2% chance that hallucination is about time travel. My prior is something like p = 0.000001 that time travel exists. If I assume those are the only two explanations of seeing a time traveler, (i.e. we’re ignoring pranks and similar), my estimate of the probability that time travel exists would shift up to about 2% instead of 0.0001% -- a huge increase. The smart money (98%) is still on me hallucinating though.
If you screen out the insanity possibility, and any other possibility that gives better than 1 in a million chances of me seeing what appears to be a time traveler with what appears to be futuristic technology, yes, the time traveler hypothesis would dominate. However, the prior for that is quite low. There’s a difference between “refusing to update” and “not updating far enough that one explanation is favored”.
If I was abducted by aliens, my first inclination would likewise be to assume that I’m going insane—this is despite the fact that nothing in the laws of physics precludes the existence of aliens. Are you saying that the average person who thinks they are abducted by aliens should trust their senses on that matter?
Ah. In that case, I think we’re basically in agreement. To clarify: I only used the time travel as an example because that was the example that VAuroch used in his/her comment. I agree that even taking into account your observation of time travel, the posterior probability for your insanity is still much larger than the posterior probability for genuine time travel. You do agree, however, that even if you conclude that you are likely insane, the probability of time travel was still updated in a positive direction, right? It seems to me that Nominull (the person to whom I was originally replying) was implying that your probability estimate shouldn’t change at all, because that’s “clearly impossible”/”fictional evidence” or something along those lines. It is that implication which I disagree with; as long as you’re not endorsing that implication, we’re in agreement. (If Nominull is reading this and feels that I am mistaken in my reading of his/her comment, then he/she should feel free to clarify his/her meaning.)