I just ran across this<http://plato.stanford.edu/entries/mathematics-explanation/>. (Call it the "horizontal force.")
There appear to be physical explanations that are non-causal. Suppose that a bunch of sticks are thrown into the air with a lot of spin so that they twirl and tumble as they fall. We freeze the scene as the sticks are in free fall and find that appreciably more of them are near the horizontal than near the vertical orientation. Why is this? The reason is that there are more ways for a stick to be the horizontal than near the vertical. To see this, consider a single stick with a fixed midpoint position. There are many ways this stick could be horizontal (spin it around in the horizontal plane), but only two ways it could be vertical (up or down). This asymmetry remains for positions near horizontal and vertical, as you can see if you think about the full shell traced out by the stick as it takes all possible orientations. This is a beautiful explanation for the physical distribution of the sticks, but what is doing the explaining are broadly geometrical facts that cannot be causes. -- Russ Abbott ______________________________________ Professor, Computer Science California State University, Los Angeles cell: 310-621-3805 Google voice: 424-2Blue2 blog: http://russabbott.blogspot.com/ vita: http://sites.google.com/site/russabbott/ ______________________________________
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