On Sun, Jul 18, 2010 at 10:53 AM, Ted Carmichael <teds...@gmail.com> wrote:
> I agree with the comments on the psychology/perception issue. But I don't > agree with this: > > "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...." > > I just don't think that is possible. All you have to do is consider one > case (that supposedly has more sticks parallel), and then freeze the sticks > in place, and rotate the plane through the sphere so that it is now > perpendicular to the original plane. Clearly now the "parallel" sticks are > "perpendicular," so if there were more parallel before, now there are more > perpendicular. > > The plane is simply a place of reference. It makes no difference on the > number of sticks oriented one way or another. > > There is no one plane perpendicular to a given plane in three dimensional space, that only becomes a possibility in four dimensions. When you rotate a plane through 90 degrees in 3D you end up with a plane that intersects the original plane along a line. Some of the sticks parallel to the first plane are still parallel to the rotated plane. -- rec --
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