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denis_bider comments on Leave a Line of Retreat - Less Wrong

59 Post author: Eliezer_Yudkowsky 25 February 2008 11:57PM

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Comment author: denis_bider 26 February 2008 03:55:17AM 0 points [-]

I should however note that one of the last mathy posts (Mutual Information) struck a chord with me and caused an "Aha!" moment for which I am grateful.

Specifically, it was this:

I digress here to remark that the symmetry of the expression for the mutual information shows that Y must tell us as much about Z, on average, as Z tells us about Y. I leave it as an exercise to the reader to reconcile this with anything they were taught in logic class about how, if all ravens are black, being allowed to reason Raven(x)->Black(x) doesn't mean you're allowed to reason Black(x)->Raven(x). How different seem the symmetrical probability flows of the Bayesian, from the sharp lurches of logic - even though the latter is just a degenerate case of the former.