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Vaniver comments on Does model theory [psychology] predict anything? (book: "How We Reason" (2009)) - Less Wrong
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Comments (27)
Vertical configurations are more stable, if I'm thinking about the problem correctly.
The question looks unclear to me because it's not clear if they're asking about statics or dynamics. If you look at the dynamics of the system, it seems clear that needles being vertical is an attractor, and we should expect randomly initiated particles to be more likely to be in the attractor as time goes on.
But suppose we neglect air resistance. Imparting a random force to the needles and a random attitude to the needles are different, because the first implies to me that most needles will have some angular momentum, and thus we need to look at paths on a sphere rather than points on a sphere, whereas the second makes shminux's interpretation the obvious one.
"random force" is surely odd phrasing, but that's what they used in their experiment. If the coins aren't affected by air (which, oddly, they didn't specify, but I suggested they shouldn't be), and haven't hit anything, then we can imagine most "random force" distributions to choose uniformly a random orientation (because the random distribution goes high, and enough time has passed to do so, even if the starting orientations are all the same). Most importantly, if we assume we can answer the question, then initial orientation can't matter because it wasn't specified.