Imagine that you have a single stick. It is flat on a table and pointing directly away from you--like a knife when sitting down to dinner. Now rotate the table about the axis of that stick. The table now intersect the original plane of the table at a right angle. But the original stick will still be parallel to the original plane. (Since you rotated the table about it using it as an axis it won't have moved.)
As a first generalization imagine that instead of a single stick one had an array or parallel sticks, e.g., a knife, a spoon, a couple of forks, etc. (No utensils at the top of the plate perpendicular to the side utensils, though.) Rotate the table again, and all the sticks will still be parallel to the original table plane. Some will now be above the original table and some will now be below, But none will be perpendicular to the original table plane. -- Russ On Sun, Jul 18, 2010 at 2:09 PM, Vladimyr Ivan Burachynsky <[email protected]>wrote: > On Sun, Jul 18, 2010 at 10:53 AM, Ted Carmichael <[email protected]> > 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. > > > > That seems reminiscent of the vision trick of Bumps(or Hollows) with > shadows. In some sense our brains are wired (Hard or Soft?) to prefer > certain short cuts of reasoning based on gravity or the assumption that the > sun is overhead and shadows always fall in a particular way. If the sticks > were oriented perpendicular to a plane it strikes me that most viewers would > inevitable prefer to say the sticks are lying in some other orthogonal > plane. It is striking that this discussion can not disentangle itself from > Human perception for very long before exposing it again. Perhaps the reason > we find difficulty accepting Gravity in this new form is that our brains > themselves are stuck using a short cut approach. In spite of most human > beings accepting a roundish earth, day to day we still assume it to be > flat.! > > > > We automatically orient to a level flat plane with our bodies upright. Our > plane of reference is preferred over all others. > > > > > > > > > > > > *Vladimyr Ivan Burachynsky* > > *Ph.D.(Civil **Eng.**), M.Sc.(Mech.Eng.), M.Sc.(Biology)* > > > > *120-1053 Beaverhill Blvd.* > > *Winnipeg**, **Manitoba* > > *CANADA** R2J 3R2* > > *(204) 2548321 Phone/Fax* > > *[email protected]* <[email protected]> > > > > > > -----Original Message----- > *From:* [email protected] [mailto:[email protected]] *On > Behalf Of *Russ Abbott > *Sent:* July 18, 2010 1:27 PM > *To:* The Friday Morning Applied Complexity Coffee Group > *Subject:* Re: [FRIAM] Entropic force > > > > Hey Roger, Your posts inspired me to track you down a bit. Nice website (The > Entropy Liberation Front <http://elf.org/puzzle>). Not many posts, though. > You should post more. I like your Puzzle Earth <http://elf.org/puzzle>. > Very nice--except that the cursor doesn't always grab what it should. > > > -- Russ > > > > On Sun, Jul 18, 2010 at 10:14 AM, Roger Critchlow <[email protected]> wrote: > > > > On Sun, Jul 18, 2010 at 10:53 AM, Ted Carmichael <[email protected]> > 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 -- > > > > > ============================================================ > 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 > > >
============================================================ 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
