Artifact

Lipton B2C
Unilever B2B

In a Quandary

:: Hurricane Katrina, Magee MS ::

I drove down to PKL today resolute to close shop, because of the only unfree wireless situation, only to discover a weak signal (not MetroFi's) which I'm currently using. I'll truck away some items anyway, as I still think closure is the most likely outcome, with a reopening somewhere else.

On math-teach we've turned our focus to teacher quality in Illinois, the computer science teachers are threshing about discrete math, while over on Synergeo (#30932) I'm dissing the Clinton administration for the bombing of Belgrade (consistently with my views at the time).

That's pretty much my beat these days, not making toons in ToonTown, which'd be my druthers. So maybe I'll get that promotion? I should have a talk with my boss. Plus I still have my other hats to wear.

Wanderers is hosting a 3rd talk in a series re Sacred Geometry tonight, Stockton and I having delivered the first two. Micheal Sunanda is bussing up from Eugene. He's another character I'd stick in my stable of stars in a heartbeat, had I a stable. Well, I've got these journals at least (my so-called blogs).

Speaking of journals, when is Earlham College ever gonna put George Fox's on line, John Woolman's, in blog format, with proper back dating? Too difficult? Hey, maybe that's not work Earlham ever signed up for! Other takers then? Friends'd benefit by having these earlier Quaker journals on line as blogs, easily linked from today's Quakers' postings.

Journey Home

Enroute back to Portland, we pulled off I-5 at Seattle's Northgate, to find our favorite Math 'n Stuff store on NE Roosevelt Way. The store will be moving soon, though perhaps not far.

In addition to some Christmas gifts, which I'm not going to write about, I invested in a second Cube-It! for myself, a toy of 24 colorful magnetic MITEs i.e. space-filling MInimum TEtrahedra of volume 1/8th in Buckminster Fuller's Synergetics.

Now that I have two of these puzzles, not only can I build the volume 3 cube, but the volume 6 rhombic dodecahedron as well, yay.

We'd hoped to visit the Dead Sea Scrolls at the Seattle Science Center, but the exhibit was sold out until evening, so we ascended the famous Space Needle instead.

Related posts:
More from MITEy Mouse (roar!) @ Math Forum
Half Coupler (in this blog, one year ago today)
Re T-modules and a volume 2 qyoob (October, 2006)

Family & Friends

:: family table in bellingham ::

:: élise ::

Lucky Day

Friend Chris is recovering from a successful surgery. We visited her on our way out of town.

I checked with Dawn's oncology clinic and they had my lost bag with all contents. I'd left it there on Friday, yet had persuaded myself that it'd been stolen.

Tara immediately inherited the Olympus Stylus 500, an early Xmas present. I'll stick with the new Stylus 720.

Plus I finally got to share Bodies with Dawn and Tara in Seattle this evening, having seen it by my lonesome in London in April.

Now we're staying in Tulalip and Stillaguamish country, further north, with good friends.

All in all, a great day. Giving thanks.

Even the traffic wasn't too bad, despite some heavy rain.

1-2-3 Testing...

:: 4-frequency tetrahedron on dog bed ::

:: tara tankha from druk-yul ::

photos by K. Urner
Olympus Stylus 720 SW

Lurching Forward

I enjoyed a satisfying conclusion to Pythonic Mathematics today, that was #7571 - Computer Programming from Chaos to Python. The students had turned raw Python syntax to Vpython gold, including a 3-or-4 frequency tetrahedron, moons around moons, and a mom and her kids did this "look, a real professor" number in the Park Blocks (I had the plastic 4-frequency in tow, attracted attention).

However, these triumphs are somewhat overshadowed by the loss of my OSCON bag and all its contents: iPod, digicam, new Russian geometry book... dried up cashews. Part of the torment is imagining the lucky dude who now has all that, and that's if it really was stolen, which I can't prove (more torment). I recall from some Tibetan Book of the Dead DVD that this is the hardest part: watching your killers play with your stuff. Anyway, maybe it'll turn up, along with Robin, my stolen car.

Back to the classroom: we watched excerpts of a Google Technical Talk, Guido rehearsing before OSCON 2006, talking about Python 3000. Then I shared Store Wars (Cuke versus Darth Tater) and the first few verses of Ramanujan (as many stared into their screens, completing projects). I recommended Python 411 and Dive Into Python (starting with the web version) as possible next sources of information.

As for source code, I looked at Pascal's Triangle (first time through) and Fibonacci generators (second pass -- tie back to triangular and tetrahedral sequences, plus Pascal's). I said something to the effect that these gentlemen needn't have been the first to ever conceive of such language games. So calling 'em is more an honor than a right.

I handed out the closed student evaluation forms, which get sealed and collected at the end of the final class by an SA HQS minion (cute colleague, some new kid on the block), i.e. are pretty much unseen by the instructor. Plus we send home parent forms in case an adult guardian wants to give feedback. Plus I get to fill one out about my students, my experience as the instructor. Plus I handed out signed certificates of completion, properly name embossed, like a credential of some kind.

Several of my students expressed in different ways their wish that ordinary school was more beefy like this, dense-packed with relevant multiplexing, with parents seconding the motion. I always make these "right on" noises, like gee I really empathize. That's why I teach through Saturday Academy, to fight for our Silicon Forest and its values, high standards. I've also been invited onto a curriculum advisory board for Portland Public Schools (PPS).

More Hermeneutics

Originally drafted on Synergeo, an eGroup, and therefore populated with references to other discussants -- Editor.

4D

Cliff is in the vicinity and that always reminds me of our shared interest in outfitting Synergetics with some Mathematica style claptrap (caltrop? -- look it up, Braley-sans-w knows), except in my case it's Pythonic harkening back to APLish (given my personal trajectory), more than Wolframic in its computerized expression [*], but that's not a problem for me if it ain't for Cliffie here.

Other names for the Quadrays namespace might be: Chakovians (after David Chako of Synergetics-L fame); Tetrays (Chako's preferred term); Caltrop Coordinates (vs. Cartesian); Simplicial Coordinates (but minus J.H. Conway's focus on the hypercross and Coxeter.4D) -- and maybe Klingon Coordinates in honor of the other big Conway (Damian).

What we do is shoot four "basis vectors" (pirating from linear algebra) to the corners (1,0,0,0) (0,1,0,0) (0,0,1,0) and (0,0,0,1). To reverse a basis vector is to flip its bits i.e. -(1,0,0,0) = (0,1,1,1) and so on. So we end up not needing negative signs in this canonical representation, though by another convention we might alternatively insist that the sum of the 4-tuples always be zero.

The Cartesians claim having 4 basis vectors is redundant, as they get by with just 3, but then they permit vector reversal to play a role in netting them 7/8ths of their space. Thanks to vector reversal and the three negative "not really" basis vectors, the Cartesians have 3 additional "ghost vectors" doing most of their dirty work i.e. pointing in that 7/8ths negatively tainted space, with only one octant (+++) remaining "positively pure" and therefore directly accessible without all the "bad neighborhood" connotations of a "non-basic" (e.g. +-+) address.

So in point of fact, the Cartesians are using essentially six reference vectors to the corners of a regular octahedron, not just three, whereas in Chakovians we're using just four, and not relying on vector reversal for back-handed access to anything.

3D

The four positive basis rays positively scale and vector-add to address any point in Positive Universe. Negative Universe is through-the-origin inside-outing of the reference tetrahedron. Your application may have no need for this other space, conjoined through (0,0,0,0), but it's there if you need it. Nor does it matter which you call Positive initially, though once you've invested, conversion may be time-consuming (just like both left and right XYZ coordinate systems have their followings).

My Synergetics on the Web @ grunch.net contains a thorough overview of Chakovians (./synergetics/quadrays.html), plus transforms for converting to-from XYZ, 4x4 rotation matrices courtesy of Tom Ace.

We don't insist on using these in public schools, e.g. won't be targeting any school boards for not, but we do bring kids through on field trips from time to time, just to remind 'em that XYZ thinking ain't all its cracked up to be in some circles.

Alternatives exist, some of them smart cookie.

Kirby

[*] e.g. in some versions of coords.py, imported by rbf.py for doing StrangeAttractors, rendering other concentric hierarchy graphics in the 4D++ IVM.FM (lots at my grunch.net and 4dsolutions.net websites).

Wanderers 2006.11.14

So tonight it was Barry's turn to induct us into the deep metallurgy of small microprocessors, the ones you program once for some permanent job in a car engine or, in Barry's case, a DC light dimmer.

Boats are wired for DC but don't come with a dimmer switch, usually. Barry's gizmo, a coventure, takes DC into a pulse width modulator, written in software, and matched with code to the interface, in this case either one or two switches, and rather complex behaviors.

A feature of this Motorola HC05 series chip is a ripple counter with some flag bits, such as COP. Unless you "kick the dog" every few cycles, COP'll flip and send a reset; useful for when poorly written code enters an infinite loop or whatever. You don't want simple coding errors to devalue the hardware, or maybe the code makes intelligent use of dog kicking internally. Either way, nice to know that COP is there.

So the boat owner chooses to wire either one or two switches, then meters DC power at tiny calibrations, or full on, though even this max brightness setting includes sleeping, i.e. going to low voltage for short intervals.

Given all the interrupts in this picture, 109 cycles a second mas o meno, with 256 intervals within each of those, there's lots of pushing registers to stack, running off someplace, coming back and popping the stack. Nesting subroutines is a source of subtle errors and stack overflows so Barry's code stays pretty flat. He's pretty much self taught, and being a smart guy, he made sure he did a good job of teaching it.

Safe to say, this was pretty unfamiliar stuff for a lot of those present, and Barry didn't get to the graphical (windowed) debugger until close to the end. That actually gave us stepped execution, break points, on a simulated chip, with registers, a next program line pointer (under 500 max lines), other flag indicators, and the very limited 64 bytes of RAM (right Barry?), all conveniently displayed.

I appreciated Barry's willingness to not hold back about the nitty gritty details, even though he knew we weren't tracking in all cases.

Cultural Anthropology

Based on this news that the yellow "support our troops" ribbon motif actually got off the ground during the Indian Wars, when brave horse-mounted Custer types headed off like knights in shining armour, protecting Betty Crocker security moms back home, I'm extrapolating the early emergence of a later counter-culture, in the form of those racoon hatted Daniel Boone types, civilian trackers and company traders, who became friendly with North America's natives, intermarried.

When cultures collide, you always get these Romeo and Juliet stories wherein a younger sister or someone falls head over heels for a pagan, Roman, Jew or whatever rival ethnicity, and it's a big family crisis. One brother encourages his gang members to slay the infidel love object, while another brother, usually played as a pacifist introvert type (i.e. a sissy who better understands women) betrays the rougher bro by leaking news of this plan, resulting in an ambush of the Goody Gang and lots of remorseful suicides, including by Romeo and Juliet. Curtain. Sigh. Such a tragedy.

This pattern gets repeated in our day's Lost to some extent, in the love story between the California Babe and the Elite Republican Guard dude. But in the context of this island, with its strong magnetic fields, the predictable unfolding gets scrambled, and California Babe gets shot by the trigger happy Latina Police Chick by mistake, leaving the Iraqi Dude to mourn and eventually forgive (that's about as far as I've gotten in the series).

More predictable was the CNN banter I heard while in Florida, these Anglo pundits angsting about Iraqis and their tribal loyalties, their lack of sophistication around democracy, USAers having just proved to themselves theirs has yet to be rendered incomprehensible by an insider technocracy in charge of the voting machines (an advancing AI army, like in Terminator).

I haven't studied the history in detail, but I bet if we go back we'll find the brave Custer types were just trying to prevent all those unsophisticated Indians from killing each other, and so would side with one underdog tribe after another, just to balance things out and to prove to all doubters that the Great White Father in Washington knew how to pick a winner every time.

T Module

:: an original koski T ::
(Portland Knowledge Lab Collection)

The T module recursively self-fills with tau-scaled versions of itself, in complement with a stop-gap or "unfinished business" mod called the Remainder Tet or R module, shown in orange.

Keep filling the R mod with smaller T mods if you like, but expect smaller terminal R mods.

Phi-scaled Ts and Rs together make a cube, other shapes.

Plus if you regard a golden cuboid (1 x phi x tau (tau = 1/phi)) as defining 7 edge lengths (3 XYZ + 3 face diagonals + 1 body diagonal), and choose those six at a time to get additional phi-scalable tetrahedra, then you've got the gist of David Koski's pioneering explorations.

And remember, two parallel accounting systems: lowest terms in canonical volumes; most economical physical assembly using actual left and right handed modules.

More Pythonic Mathematics

:: protocols ::

Today we dove into tcp/ip and the smoke signals that ride atop it: nntp, ftp, http... smtp.

Gnubees often say "the Internet" meaning just http (hypertext transfer protocol), the one used to serve web pages (through port 80 most likely), but long before Mosaic, Netscape, IE, Opera, Mozilla... FireFox, we had usenet (the newsgroups) and ways to swap files (ftp = file transfer protocol) -- and of course email.

All of these services working together define the Internet, not just http and its webwork of interconnected urls.

After this short intro, we watched Warriors of the Net, a mathcast I've used ever since my first Saturday Academy class at West Precinct.

:: mosaic ::

Then it was back to VPython and the challenge of connecting the dots in XYZ to make shapes, starting with the simplest, the simplex or tetrahedron.

This time we had stickworks.py with its Vector and Edge to aid and abet, and a few students had additional shapes in short order.

My Pythonic vectors always have their tail at the origin. If you want a line segment between any two points, feed those two vectors to the Edge class to get back your edge object, which displays in the VPython window when you trigger its draw method.

:: vector arithmetic ::

In preparation for Vpython sculpting, we went over some basic geometry using models made years ago in collaboration R. Z. Chu and Trevor. They're a bit rough around the edges but still usable, though the Vector Flexor broke a joint during my Wanderers presentation on Halloween, and the rhombic triacontahedron (see it?), scaled to volume 5, is definitely falling apart.

I pour these hard white beans from one shape to the other, reminding them of our everyday home base sculpture.

:: cargo cult geometry ::

I had a parent sitting through much of this class, even asking questions. That's new for Saturday Academy, but worth testing. Clearly some of these students are working with their parents at home on Python + VPython, even though we don't assign homework. I also learned one of the parents is a fellow alum, Princeton '83 (just three years behind me). We chatted about some of the class reunions we'd attended.

Next week: we plan to get more into animation, getting beyond static imagery. One of my students is interested in coding a planets-around-the-sun type toon. I turned him on to Celestia.

Synergeo 30350

> Marx was not caught up by the idea of not being enough-
> in fact he wrote that in the future will be plenty- though
> he didn't show me the statements of Marx in this matter-

Fuller boils it down to a very simple equation in Critical Path: assuming not enough to go around (Malthusianism), we get LAWCAP (lawyer-capitalism) versus Marxist schools of thought (workers of the world unite), each claiming the competition wasn't pulling its own weight i.e. "our side" has the right to be on the top of the heap (presumably where you find the best access to scarce life support).

Per dumbed down Hegelianism (he never boiled it down to 'thesis - antithesis -> synthesis' the way they teach in grade school) we've since moved on.

Grunch is focused on artifacts and competitive marketing/ branding, but also on open source energy planning and modeling, publicly sharing lots of relevant global data (vs. keeping it classified the way Malthusians had to, cuz the news was so grim, at least for the majority of humans). World Game is still a competitive game, but our top teams don't easily stuff into 20th century pigeon-holes.

Kirby