Saturday, May 23, 2009

Show Me the Polyhedra!

24-trapezoidal combo
of 7.5 RT & 6 RD, color coded

by David Koski

Sometimes the PR around the concentric hierarchy we like to jazz about runs into resistance from skeptics, who say polyhedra are not all that relevant and maybe lead to gayness to boot, so lets get back to algebra, easier on the eyes and our delicate constitutions.

However, polyhedra are merely the canonical stand-ins for a non-virtual world of dogs, dishwashers and racoons, all with moving parts, all modeled with polyhedra in the virtual analogs (like in Over the Hedge). They're everywhere in other words, very hard to get away from them. You're sitting in one, 24/7, if we might agree on that grammar.

Sometimes in my 2nd or 3rd grade classes (following along with my daughter), I would have us think about V, F and E as distinguishable topological features in any scene or painting, also with tactile aspects e.g. an F is a flat surface, possibly smooth. V + F = E + 2 makes more sense once you've imbued it with all this "surround sound" and taken it out in the jungle as it were (edges = vines, good for swinging if you have a Tarzan complex, possibly short-lived).

The pre-frequency versus frequency distinction we make in similar terms, of reality versus verisimilitude. On low budget special effects, you'll simply substitute a model boat for a real one and splash it around, simulating a perfect storm. Because of sliding scale powering rules, relating 1st, 2nd and 3rd powering according to topological aspects again (radials, areas, volumes), the physics changes as we range through the size spectrum.

Strategies that work for a real-sized praying mantis, wouldn't work at the Godzilla scale, but that doesn't keep the motion picture studios from messing with the physics. They do it in Star Trek all the time. People pay good money to see reality distorted (good therapy, good escapism -- take your pick).

So in pre-frequency, where we care only about shape (angle), we don't really have any physics to speak of, just pure geometry. We might do some literary allusions, talk about cyber stuff, in keeping with the ethereal nature of this so-called "Platonic realm" (some cultures wouldn't call it that though).

In frequency, we don our BS detectors and start smelling the fishy stuff. Science is a lot like police work in that folks will dream up all kinds of moneymaking schemes, and yet the science just isn't there to back them up. AI gets to be like this. OLPC makes a lot more sense.

In my own case, Isaac Asimov was an influence in that he harped on using credible science in his plot lines a lot, not just fantastic elements. This gave his science fiction a satisfyingly didactic flavor in that you knew some of his speculations might be transferable to a real world context someday, i.e. you might use what you'd learned, reading in the car, to pass a chemistry test down the road.

We're fortunate in the Fuller School in that our geometry works, checks out, and the literary stuff is of high quality, and furthermore the physical specimens, the domes and trusses, the house and the car, do a lot of credible load-bearing, i.e. there's nothing all that bogus on the M-side or the P-side in our U=MP.

That high level of metaphysical integrity means our curriculum is fairly easy to teach, compared to a lot of the competing material, which is far more obfuscatory and riddled with pitfalls.

Go ahead and poke around, see what you think after an hour or two. We know a lot of you come back for more, sometimes as paying customers.

We thank you for your business.

EuroPython 2009
28th June to 4th July 2009
Birmingham, UK