ThisSpaceAvailable comments on Does model theory [psychology] predict anything? (book: "How We Reason" (2009)) - Less Wrong

2 Post author: Jonathan_Graehl 03 June 2013 03:11AM

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Comment author: ThisSpaceAvailable 04 June 2013 06:40:24PM 2 points [-]

I find those two puzzles to be rife with ambiguities. First, a "force" is not going affect the attitude; only a torque will do that, and as another poster has noted, there's a bit of a difference between "random force" and "random attitude". There's also the question of just what "random" means. The word "random" just means that there is some probability distribution; it does nothing to tell us what it is. Finally, there's the issue of starting orientation. If the needles start out vertical, then the most likely result is that they will end up vertical.

Comment author: Jonathan_Graehl 04 June 2013 09:39:59PM *  1 point [-]

I know - all of us over-precise folk had the same frustrations. But if you allow the problem to be "the things are in a (uniformly) random configuration ('attitude' - nice word choice!) and haven't bounced or even started in some known orientation", it's a fun problem to think about. A uniform orientation seems appropriate since it's maximum entropy given the word-problem constraints.

http://math.stackexchange.com/questions/87230/picking-random-points-in-the-volume-of-sphere-with-uniform-probability