**Next message:**Eliezer S. Yudkowsky: "Re: politeness in posting"**Previous message:**Lee Corbin: "Re: Fun With Bayes' Theorem"**In reply to:**Lee Corbin: "Re: Fun With Bayes' Theorem"**Next in thread:**Lee Corbin: "Re: Fun With Bayes' Theorem"**Reply:**Lee Corbin: "Re: Fun With Bayes' Theorem"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

Lee Corbin wrote:

*>
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*> I'm sorry; you're quite right. *Gloating* is never justified,
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*> and the real purpose of cute mathematical problems is the same
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*> as the purpose of any interesting tidbit that one might want
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*> to throw out. We're not trying to just show off; we expose our
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*> beliefs to criticism, and also hope that there will be an
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*> exchange of wisdom. We hope to be enlightened.
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You can sub in "illustrating previously unknown reasoning techniques" for

"gloating" if you so prefer. My point is that someone who answers "I bet

you think it's 1/3, but it's actually 1/2" is demonstrating deeper

knowledge than someone who answers "1/3", just as someone who answers

"1/3" probably has more (declarative!) knowledge than someone who guesses

"1/2".

*> Well, this has been enlightening indeed! All my life I felt
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*> deprived because I didn't know what the controversy surrounding
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*> the "Bayesians" and "Non-Bayesians" was, and at one point, it
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*> was the only intellectual controversy I knew of that I felt
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*> excluded from. Perhaps I've finally gotten involved.
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There are non-Bayesians? I've never heard of any non-Bayesians or any

"controversy". Where I come from, "Bayesian reasoning" is practically a

synonym for "normative rationality".

Maybe you're right. Maybe a *mathematician* answers 1/3 - the problem was

posed about mathematicians, after all. And I bet that a statistician

answers 1/3 as well. However, a sufficiently alert cognitive scientist

should answer 1/2.

So now we have *four* possible answers:

"1/2." (naive human)

"1/3." (naive mathematician)

"You'd think it'd be 1/3, but it's actually 1/2." (bayesian)

"It's actually 1/2, but all but the most alert mathematicians would answer

1/3." (actual answer)

*> Only one question remains:
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*>
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*> > (Vorlon voice:) "We are all Bayesian statisticians."
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*>
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*> 'zat so? You mean I missed out on the controversy after all?
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No - I just mean that the human brain runs on folk bayesian reasoning

rather than folk mathematics. No, scratch that, that's a lousy sentence.

What I mean is that, in this instance at least, the Bayesian answer is

much closer to the way our brains work than the mathematical answer.

-- -- -- -- --

Eliezer S. Yudkowsky http://singinst.org/

Research Fellow, Singularity Institute for Artificial Intelligence

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