Russ, This seems very weird to me (as, of course, it is intended to). First off, I'm not sure it is an "explanation" any more then a "proof by definition". Second, at least in the case of a 2D snapshot, there are just as many 3D configurations that appear perfectly vertical as appear perfectly horizontal.
I'll have to meditate more on the more general case. Eric On Sat, Jul 17, 2010 07:28 PM, Russ Abbott <[email protected]> wrote: >> >I just ran across <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: <a style="font-family: trebuchet ms,sans-serif;" href="http://russabbott.blogspot.com/"; target="" onclick="window.open('http://russabbott.blogspot.com/');return false;">http://russabbott.blogspot.com/</a> > vita: <a style="font-family: trebuchet ms,sans-serif;" href="http://sites.google.com/site/russabbott/"; target="" onclick="window.open('http://sites.google.com/site/russabbott/');return false;">http://sites.google.com/site/russabbott/</a> >______________________________________ > > > > ============================================================ >FRIAM Applied Complexity Group listserv >Meets Fridays 9a-11:30 at cafe at St. John's College >lectures, archives, unsubscribe, maps at http://www.friam.org > Eric Charles Professional Student and Assistant Professor of Psychology Penn State University Altoona, PA 16601
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