On 7/8/09, Henry Baker <hbaker1@pipeline.com> wrote:
... If you read the popular science literature, then the "man in the street" version of physics spends an inordinate amount of time worrying about "these extra dimensions" & attaches a mystical significance to them.
However, how would such an extra "string-like" dimension be all that much different from the extra dimension used in 3D graphics "homogeneous coordinates", where the projection back into 3D is by dividing out the last coordinate ? After all, most "men in the street" ("street people?" :-) wouldn't attach much mystical significance to homogeneous coordinates, would they?
That's a nice analogy. Unfortunately, its implications are not reassuring. I taught Computer Graphics for a number of years, and my experience was that a large proportion of my class never came to terms with representing a point in 3-space using 4 components. Their reluctance is on the face of it incomprehensible. After all, in Data Representation courses they regularly meet distinct data structure implementations of the same abstract data type --- what's different about coordinate geometry? Another teacher recently suggested that the problem lies with the familiarity and intuitive appeal of the "real" (Cartesian) representation, acting to prevent the student from modelling the data in any other way. There's a larger-scale analogy of this phenomenon in the heliocentricity controversy which embroiled Galileo and Copernicus --- where again, a naturalistic preoccupation with "existence" of an object (the aether, in effect) obscured the fundamental matter of a spatial relationship (indeed, a geometric symmetry as considered by Klein). [It was highly diverting to read, some years ago, that the Vatican had apologised for this incident, and now agreed that the Earth does rotate around the Sun after all. Perhaps in another 250 years or so, they'll have got around to digesting Einstein! And as for the uncertainty principle, well, one does not like to contemplate the consequences ... ] Fred Lunnon