On 17 Jul 2010 at 20:10, ERIC P. CHARLES wrote: > 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".
If it's an "explanation" of any thing, I think it's an explanation of the manner in which we (or some of us) come to give an account of the situation. I'd rather call it a description of the situation, coupled with a description (not particularly explanatory) of our manner of coming to that account (e.g., how we assign labels "vertical" and "horizontal"). > 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. That depends on how the definition of "appears" appears. (And makes my point, above, about the us-ness of the how-ness of it all.) Sticks that lie in the (assumed horizontal) plane of the monocular viewer will have a distribution of apparent lengths (defined in some purely optical, non-perceptual, way: e.g., in terms of measurements taken with a pair of dividers on a 2D snapshot) that may be (and very likely is) markedly different from the distribution of apparent lengths of all the sticks; the viewer's assumptions (conscious or unconscious) about what is seen will play a large part in determining what conclusions (conscious or unconscious) the viewer draws about the distribution of attitudes of the sticks. (Affordances must come up here, eh?) If we had a 2D photo such as you suggest, Eric, it would be an interesting experiment to show it to various people turned at various angles. My prediction is that (absent clues about "true vertical") "appreciably more" of the sticks would be perceived as being "near the horizontal than near the vertical orientation" in every case (assuming, as I just realized I have been, that the 2D photo is viewed in a vertical plane, rather than lying on a desk or in one's lap or on the floor; in *those* cases, I'll now predict that ascriptions of verticality will be quite variable). Shephard points out (in his paper speculating on why humans have a 3D color space) that for terrestrial animals (at least, ones that live above the scale where things like surface tension of water and viscosity of the atmosphere are big deals in daily life), the vertical axis defined by gravity is highly salient. What, we may ask, would a porpoise or a porgy make of your photo? Lee Rudolph > 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 > > > ============================================================ 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
