Thursday, August 24, 2006

More Dimension Talk

Sometimes, in my battles with HyperCross Dogmatists, I get sloppy and say Coxeter draws a sharp distinction between his (Coxeter's) meaning of 'four dimensional' and Relativity's, in his "introduction" to Regular Polytopes.

Actually, he makes this point on page 119:
Little, if anything, is gained by representing the fourth Euclidean dimension as time. In fact, this idea, so attractively developed by H.G. Wells in The Time Machine, has led such authors as J. W. Dunne (An Experiment with Time) into a serious misconception of the theory of Relativity. Minkowski's geometry of space-time is not Euclidean, and consequently has no connection with the present investigation.
H.S.M. Coxeter. Regular Polytopes. Dover Publications, 1973. pg. 119
Although Coxeter warns against attaching any mystical significance to the fourth dimension, in retrospect we see how talk of mortal limitations vs. transcendent superpowers would inspire a religious sense in many physicists and mathematicians:
Only one or two people have ever attained the ability to visualize hyper-solids as simply and naturally as we ordinary mortals visualize solids; but a certain facility in that direction may be acquired by contemplating the analogy between one and two dimensions, then two and three, and so (by a kind of extrapolation) three to four. (Ibid, pg. 119).
He footnotes Abbott's Flatland at this point, helping to feed a meme complex which persists to this day, e.g. in this film What the Bleep: Down the Rabbit Hole. In a rush to "be the next Einstein" (not a bad role model mind you) generations of science fiction reader have strived to join the shamanic inner circle of those chosen few able to view the HyperCross directly.

What I've tried to make clear over the years is that R. Buckminster Fuller was not on the HyperCross bandwagon, and although he used the 4D meme, he had his own meaning and namespace for it.

Given a next generation of philosophy student tackling Synergetics as a primary work (one among many), I feel it's important to point out these potentially tricky and confusing name collisions. Partly why I've been developing the notion of "namespace" with some rigor (with inspiration from Python especially) is to help keep our B2B and B2C channels clear.

Like, you maybe wouldn't want to do business with me if you thought I was just another garden variety hypercrosser (they don't make many like H.S.M. Coxeter these days, the Geometer to whom Synergetics is dedicated).

Related readings by me:
The Matrix
Another Wittgenstein Essay
HyperCross Dogmatics
"Namespaces are one honking great idea -- let's do more of those!"
-- from import this in Python.