But then that doesn’t hold up to any decent Bayesian probabilistic analysis.
When you trace the chain of causality for why they thought it was “God” that spoke to them in the first place, you find that they use very vague heuristics for identifying speakers-in-dreams as “God” as opposed to “Some Mathematically-genius Alien”, and then that the source of those heuristics is even more vague and unlikely to be accurate: Biblical readings, inferences from the bible, third-hand accounts from some person who listened to some priest who read the Bible, etc.
So the final compound probability that their source of information was good and they correctly applied the right heuristics and their conclusion that “God” was communicating to them was correct and that it was actually a communication in a dream rather than a dream about a communication and that the proof was given by this communication rather than subconsciously arrived at by the non-mathematician friend somehow… is not very high.
(well, depending on some priors, obviously… if your priors for “God exists” and “God frequently communicates with people through dreams” are very high to begin with, the above starts sounding much more plausible)
I didn’t say I’d think God was involved. I said the deliberately vague, conjunction-fallacy-avoiding phrasing “I would think something more interesting than a typical dream was going on.” That means I’d update P(God spoke to him OR aliens spoke to him OR he’s secretly a genius mathematician and trolling me OR he’s got serious math talent he can’t access consciously OR [more hypotheses I won’t bother generating because this didn’t happen]), with the most likely possibility being that my friend is a genius troll. Then I’d do more experiments.
Ah, yes. I took you to imply you would acknowledge the friend without telling him that he’s probably wrong, or that you’d update disproportionately higher the probability that “God spoke to him in his dream”. i.e. I had assumed an uncharitable interpretation. Doing more experiments on the basis that something interesting happening has suddenly become very likely sounds like a healthy (well, scientifically-healthy) thing to do!
Re. downvote: One single downvote usually doesn’t mean much for posts where I expected karma to remain near 0 anyway. Despite the name and intended purposes of this site, there are still systematic downvoters, karma trolls, generic trolls and biased people around. I’ve noticed (and corrected, hopefully) at least one instance where I was systematically being biased against a certain user and downvoting their comments more frequently than I should. I suspect not everyone is as careful with this.
But then that doesn’t hold up to any decent Bayesian probabilistic analysis.
When you trace the chain of causality for why they thought it was “God” that spoke to them in the first place, you find that they use very vague heuristics for identifying speakers-in-dreams as “God” as opposed to “Some Mathematically-genius Alien”, and then that the source of those heuristics is even more vague and unlikely to be accurate: Biblical readings, inferences from the bible, third-hand accounts from some person who listened to some priest who read the Bible, etc.
So the final compound probability that their source of information was good and they correctly applied the right heuristics and their conclusion that “God” was communicating to them was correct and that it was actually a communication in a dream rather than a dream about a communication and that the proof was given by this communication rather than subconsciously arrived at by the non-mathematician friend somehow… is not very high.
(well, depending on some priors, obviously… if your priors for “God exists” and “God frequently communicates with people through dreams” are very high to begin with, the above starts sounding much more plausible)
I didn’t say I’d think God was involved. I said the deliberately vague, conjunction-fallacy-avoiding phrasing “I would think something more interesting than a typical dream was going on.” That means I’d update P(God spoke to him OR aliens spoke to him OR he’s secretly a genius mathematician and trolling me OR he’s got serious math talent he can’t access consciously OR [more hypotheses I won’t bother generating because this didn’t happen]), with the most likely possibility being that my friend is a genius troll. Then I’d do more experiments.
Note: I didn’t downvote you.
Ah, yes. I took you to imply you would acknowledge the friend without telling him that he’s probably wrong, or that you’d update disproportionately higher the probability that “God spoke to him in his dream”. i.e. I had assumed an uncharitable interpretation. Doing more experiments on the basis that something interesting happening has suddenly become very likely sounds like a healthy (well, scientifically-healthy) thing to do!
Re. downvote: One single downvote usually doesn’t mean much for posts where I expected karma to remain near 0 anyway. Despite the name and intended purposes of this site, there are still systematic downvoters, karma trolls, generic trolls and biased people around. I’ve noticed (and corrected, hopefully) at least one instance where I was systematically being biased against a certain user and downvoting their comments more frequently than I should. I suspect not everyone is as careful with this.