On Sun, Jul 18, 2010 at 8:41 AM, Ted Carmichael <teds...@gmail.com> wrote:
> Russ, I don't get this at all. Two points: > > 1) There are an infinite number of ways that a line can be parallel to a > plane; there is exactly one way it can be perpendicular to the plane. Is > that the point? > > 2) The degree of orientation around the X and the Y axises don't have > anything to do with each other. As far as the random distribution is > concerned, you just pick a random number out of 360 degrees for the X axis > orientation (the horizontal plane), then pick another random number of 360 > for the Y axis orientation (the vertical plane). > > Actually, that is the point, at least so I thought. A uniform distribution of orientations in 3D, which is equivalent to a uniform distribution of points on a sphere, has a uniform distribution in azimuth, but a biased distribution in elevation. Elevations are chosen so that the density comes out proportional to cosine(elevation) which corrects for the different areas of the latitudinal rings as elevation moves away from the equator. At first I thought that this explained the "horizontal force", but then I realized that the uniform distribution is a uniform distribution no matter which direction is designated as up. So no matter which bisecting plane through the sphere we examine, it will always have more sticks parallel to it than to the orthogonal pole. So this actually explains a "planar force". There more horizontal sticks than up/down sticks, but there are also more meridional sticks than left/right sticks. -- rec --
============================================================ 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
