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Jade comments on Crisis of Faith - Less Wrong

57 Post author: Eliezer_Yudkowsky 10 October 2008 10:08PM

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Comment author: Jade 11 January 2017 02:53:48AM 1 point [-]

Would you say the origins of other religions become more mysterious if there never were whatever magical beings those religions posit? Would you think it likely that Guanyin was real human of unknown gender? Do the origins of fictional stories become more mysterious if there never were the fictitious characters in the flesh? Did Paul Bunyan exist, as there were similar lumberjacks?

You're not supposed to tie yourself to any hypothesis, even if mainstream, but rather update your probability distributions. Bits of the NT weren't written until long enough after the supposed death of Jesus that people wouldn't have been like, 'Who you talkin' about?' And I doubt they would've cared whether the character existed, like no one cares whether Harry Potter existed, because it's the stories that matter.

Comment author: Salemicus 12 January 2017 11:36:08AM 0 points [-]

Would you say the origins of other religions become more mysterious if there never were whatever magical beings those religions posit?

Yes, of course.

The least mysterious explanation of Paul Bunyan stories is that there really was a Paul Bunyan. And the closer the real Paul Bunyan hews to the Bunyan of the stories, the smaller the mystery. P(stories about Bunyan | Bunyan) > P(stories about Bunyan | !Bunyan).

But just because a story is simple, doesn't necessarily make it likely. We can't conclude from the above that P(Bunyan | stories about Bunyan) > P(!Bunyan | stories about Bunyan).

Comment author: CCC 12 January 2017 05:19:42PM *  1 point [-]

Hmmm. To mess around with equations a bit... what can we say about P(Bunyan | stories about Bunyan) and P(!Bunyan | stories about Bunyan), given P(stories about Bunyan | Bunyan) > P(stories about Bunyan | !Bunyan)?

Let's genaralise it a bit (and reduce typing). What can we say about P(A|B) and P(!A|B) when P(B|A) > P(B|!A)?

Consider Bayes' Theorem: P(A|B) = [(P(B|A)*P(A)]/P(B). Thus, P(B) = [(P(B|A)*P(A)]/P(A|B)

Therefore, P(!A|B) = [(P(B|!A)*P(!A)]/P(B)

Now, P(!A) = 1-P(A). So:

P(!A|B) = [(P(B|!A)*{1-P(A)}]/P(B)

Solve for P(B):

P(B) = [(P(B|!A)*{1-P(A)}]/P(!A|B)

Since P(B) = [(P(B|A)*P(A)]/P(A|B):

[(P(B|A)*P(A)]/P(A|B) = [(P(B|!A)*{1-P(A)}]/P(!A|B)

Since P(B|A) > P(B|!A)

[(P(B|A)*P(A)]/P(A|B) > [(P(B|!A)*P(A)]/P(A|B)

Therefore:

[(P(B|!A)*{1-P(A)}]/P(!A|B) > [(P(B|!A)*P(A)]/P(A|B)

Since probabilities cannot be negative:

[{1-P(A)}]/P(!A|B) > [P(A)]/P(A|B)

.[1-P(A)]*P(A|B) > [P(A)]*P(!A|B)

...which means that either (1-P(A)) > P(A) or P(A|B) > P(!A|B), and quite possibly both; and whichever of these two inequalities is false (if either) the ratio between the two sides is closer than the inequality that is true.

To return to the original example; either P(Bunyan | stories about Bunyan) > P(!Bunyan | stories about Bunyan) OR P(!Bunyan) > P(Bunyan).

Also, if P(Bunyan | stories about Bunyan) > P(!Bunyan | stories about Bunyan) is false, then it must be true that P(Bunyan|stories about Bunyan) > P(Bunyan).

Comment author: Jade 16 January 2017 03:00:52AM *  1 point [-]

You left out the 'magical' part of my question. If magical beings exist(ed), then everything becomes more mysterious. That's partly why we don't pester JK Rowling about what extra-special boy Harry Potter was based on. We don't even suspect comic superheros like Batman, who has no magic, to have been based on a real-life billionaire. We certainly don't have scholars wasting time looking for evidence of 'the real Batman.' Modern stories of unlikely events are easily taken as imaginings, yet when people bucket a story as 'old/traditonal', for some people, that bucket includes 'characters must've been real persons', as if humans must've been too stupid to have imagination. https://en.wikipedia.org/wiki/Fakelore