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CCC comments on Probability is in the Mind - Less Wrong

60 Post author: Eliezer_Yudkowsky 12 March 2008 04:08AM

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Comment author: CCC 24 May 2013 10:39:19AM 0 points [-]

Before the camera gets switched, what prior probability does B9 assign to the possibility that its favorite ball is blue?

I'd imagine something like <error in world model: concept 'blue': no definition found>. It would be like asking whether or not the ball is supercalifragilisticexpialidocious.

If B9 has recently been informed that 'blue' is a property, then the prior would be very low. Can balls even be blue? If balls can be blue, then what percentage of balls are blue? There is also a possibility that, if some balls can be blue, all balls are blue; so the probability distribution would have a very low mean but a very high standard deviation.

Any further refinement requires B9 to obtain additional information; if informed that balls can be blue, the odds go up; if informed that some balls are blue, the odds go up further; if further informed that not all balls are blue, the standard deviation drops somewhat. If presented with the luminance formula, the odds may go up significantly (it can't be used to prove blueness, but it can be used to limit the number of possible colours the ball can be, based on the output of the black-and-white camera).