## Thursday, January 29, 2009

### More Geometric Studies

On Tue, Jan 27, 2009 at 10:03 PM, kirby urner <kirby.urner@gmail.com> wrote:

<>

> I think it might help if more people passed this "IQ test"
> this today with Patrick, making my Guinness jump up
> and down. I said people who can't pass this are "morons"
> (drew a diagram):
>
> http://worldgame.blogspot.com/2005/12/iq-test.html
>

So I'd back up to this part and say this is me (Kirby) being a lot like Terry, coming on strong, using strong words ("morons"), sounding like I'm bruising for a fight.

But probably not everyone here even knows what I'm yakking about, even though my 'IQ test' makes it clear. So maybe I should say something more?

The idea with the Python generators is you have this math object O that you kick, as in kick(O), except we say next(O), but either way you get the next term in the series or sequence, just like in any math book. Maybe its the Fibonacci numbers, or something chaotic.

Anyway, big in late 20th century math are "polytopal numbers" that increase as a shape expands, layer by layer. At one time this was called "gnomon studies" but these days it's all very hyperdimensional, with the XYZ special case having whatever quirky properties, such as a longer literature, more links to the past.

So let's take an example. I hand you a ping pong ball with 12 crammed around it. Already, a huge literature. Where are those twelve? They define the corners of some shape, let's agree. Then add another layer, of 42 balls, and another, of 92. A crystallographer is nodding along by now, tapping her pencil, as this is the sequence of (a) cuboctahedral numbers or (b) icosahedral numbers.

So if you go to Sloane's On-Line Dictionary of Integer Sequences and enter 1, 12, 42, 92 you'll go to a page giving the literature, with a link to my grunch.net website actually, as there you have the virus story in some detail, mixed with intrigue, hints of a cover up. My investigative reporting is 2nd to none eh?

So once you're fluent in sphere packing and know 1, 12, 42, 92 in your sleep, then you're ready for rhombic dodecahedra. I won't go into them here except to say Kepler, the astronomer guy, was really into 'em. Unless you've read a lot of Arthur Koestler, you may not know this side of the guy, but geometers do, Sir Roger and like that.

Anyway, that's your final on-ramp to 6, 4, 3, 1 the thing my IQ test is about, coming in from like 20 (relates to 12-around-1).

Then that 1, that tetrahedron (finally!) splinters (oh no!) into 24 "A modules", which are what those genius geeks at Winterhaven learned about.

Lew, I'd say any school in the country is free to teach about "A modules" like Mr. Bright let me do, but what teachers believe they have any independence or authority anymore? They're all "ETS slaves" in my book, timid, cowed (except at Winterhaven maybe -- Mr. Bright rides a [Motto Guzzi], probably has tattoos).

A and B modules have volume 1/24, and build all these other guys, very Lego. There's the T module, same volume... more stories.

It's not like we should force this stuff, but at least maybe mention (because maybe they won't find out otherwise?): Medal of Freedom, long list of degrees, patents, everything you need to prove you're a huge success, yet when the journalists write their retrospectives, it's all about "what a failure he was". Why?

Hey, good question. Go figure.

Something their editors tell 'em? "Put a spin on it boy!" -- reminds me of Spiderman movies.

So, PPS has done the "A modules" segment, got that photographed and documented in my blog, Saturday Academy too. Score one for freedom and democracy (nyah nyah).

Notice I don't get any flak for subverting the dominant paradigm in this way. It's not like mathematicians ever nixed it, said it was wrong. Like I told IEEE at Portland Center Stage: "I have no competition." They fly me to Sweden, to Lithuania, always say the same thing. Everyone nods. No one copies. Very Yes Men in some ways.

http://www.grunch.net/synergetics/mathsummit.html (over 10 years ago, same spiel)

To me it's a no brainer this is a story worth telling, sharing with students, Reed kids for example. And as an American Transcendentalist, you can bet that I do, all over my resume, everywhere else. Kind of a trademark you might say.

Kirby
4D