Tuesday, June 29, 2010

Disaster Zone

At the time of the great flooding of New Orleans, I wrote about Tillamook in an idyllic Oregon setting. This might have seemed far removed from the devastation in the Gulf, soon to be followed by hurricane Rita, hitting Texas, and the BP hemorrhage.

With all these past and looming natural disasters, plus BP's, you might wonder why humans also inflict disaster upon themselves. Could any species be this dysfunctional and survive?

Oregon is facing its own day of reckoning. A subduction earthquake, hitting about 9 on the Richter scale, is expected off the coast, based on previous patterns. Some planning (PDF) has occurred (Alan Potkin could advance the art).

Were we to live more lightly on the Earth, per aerospace ecovillage scenarios (ala Project Earthala), we could get off with less loss. We wallow in a dark age though, postponing engineering maturity.

My thanks to Glenn for updating me on some of the math future buzz. He also brought by the right crimping tool and workspace light, and supervised while I replaced the heating element in my oven, pretty much in an apprentice role. The part itself was hard to find. I credit the hard worker at W.L. May for pinpointing something in stock. She's a genius (seriously: it's an old Magic Chef in a retro style kitchen, hard to find parts).

Monday, June 28, 2010

Mortality Again

Losing all of ones personal files off a laptop may be a serious psychological blow. Retreating to the est model of 1s, 2s and 3s, this definitely triggers a 1. That model was ridiculously stark and austere by the way, like the training itself.

I'm crying inside about some of what I've lost.

I am grateful for my life and the people in it.

Loss is an occasion for suffering which is a manifestation of love. Attachments are not bad, just potentially painful.

Losing my dad so suddenly on October 13, 2000, was very hard. I flew to Lesotho to close out the estate. Mom was in the hospital in Bloemfontaine and not expected to live. She helped me manage from her hospital bed, so many bones broken.

I am proud of myself for holding it together under duress, could not have done so without my community. Eugene Norcross-Renner offered to accompany me, an offer that touched me deeply even though I ended up going alone. Gayle helped me get a plane ticket on short order. Dawn kept things running for the month I was gone.

Annis and George Bleeke, who were planning to visit for Annual Session, which my parents were organizing, came to this tragic scene and helped me organize the estate sale and off-load a lot of stuff (I shipped other stuff back to here).

I am proud of my sister for flying out to take over nursing mom back to where she could travel.

Losing my wife Dawn to breast cancer was also all about community, for both of us. She prayed her death would be a healing. She lived bravely and brought joy to many.

Someday I will need to surrender this body. Like many who contemplate their own passing, I don't want to leave a lot of hassles and loose ends.

I'd like my love to live on, my gratitude to my community.

Thinking also of Ed Applewhite, George Hammond, John Talmadge, and Elise Boulding.

Wednesday, June 23, 2010

End the Qyooban Embargo!

For quite awhile now, I've been using the word "Qyoob" to parody the word "Cube". "Qyoob" has a kind of Persian or Arabian Nights look and feel (Al Qyoob), which creates some valuable artistic distance for some readers.

Looking back at the Euro cultures, we see "four square" and such inter-twining attributes as "upright" "normal" "orthodox" and "upstanding" -- not to mention "regular guy" and "square deal".

Sound familiar?

Remember, the "beatniks" didn't want to be "squares" in an age of hyper-dimensional "cubism" -- were perhaps prototypical of the "buckaneers" in that way.[0]

"So what?" you ask, "what has any of this to do with Philosophical Investigations?"

Well, when undertaking a philosophical investigation, in the Wittgensteinian tradition, it pays to take in the lay of the land, to map out the surrounding grammar.

Connotations matter, not just denotations.

The goal, to fight the bewitchment of our intelligence by means of grammar, will be more effectively reached if we've actually done some homework.[1]

To get how these key vocabulary words weave their meanings, one actually needs to study them in action, not just assume one "already knows" as a kind of gedanken experiment.

To assume one "already knows" is to bleep over the whole point of Wittgenstein's philosophy, which is to get you to actually investigate, not take "it" -- whatever meaning -- for granted.

Back to Al Qyoob: the prevailing caliphate starts drilling children early on to think of "squaring" and "cubing" as mathematical equivalents of "2nd powering" and "3rd powering".

Some rather subtle mathematics inheres in this difference twixt saying "squared" and "to the second power", as the former presumes a shape, whereas the latter leaves the door open to different shapes, such as a triangle -- or a tetrahedron in the case of 3rd powering. [2]

My recent essay Aristotle was Right! is an opening salvo from the newest NeoPlatonists, one might say, as it challenges philosophers to revisit their ancient ties to the Polyhedra (and their inter-relationships).

Geometrical thinking is a primitive form of logical reasoning.[3] Before we had modal logic or a theory of logical types (ala Russell), we had the golden ratio, vesica pices, and the accepted methods of construction and proof.

Architecture was accomplished by these processes. Real work got done.

The story going forward, starting from Aristotle's claim that pyramids fill space (dismissed as bogus in superficial treatments), wends its way to recent times, to the geometrical explorations of a lone geometer named Sommerville.[4]

Sommerville circles a certain tri-rectangular tetrahedron as the simplest candidate that follows some specific rules in his mathematical language game, namely that:
(a) to count as "space filling", the tetrahedra must face bond (as is typical in such studies) and

(b) the space-fillers in question must not rely on mirror images of one another (i.e. sometimes a left and a right fill space, but not something alone).
Said tri-rectangular tetrahedron is found in Regular Polytopes by Coxeter (Wittgenstein's student, contributor of a venue for the Blue / Brown Book notes I think it was), where it is referenced by page number from our NeoPlatonist work. [5] There it is dubbed the Mite, or Minimum Tetrahedron, because of its space-filling role (no need of mirrors -- nor smoke for that matter).

In this referring work (dedicated to H.S.M. "King of Infinite Space" Coxeter), said Sommerville shape is in turn dissected, into the two As and 1 B particle, also described and depicted by Robert Williams in his groundbreaking work The Geometrical Foundation of Natural Structure. [6]

The Qyoobans have been embargoing this information (hence the term "Qyooban Embargo"), as evidenced by Math World, which on the page about space-filling polyhedra pointedly eschews mentioning any of the tetrahedra meeting Sommerville's rules.[7] These would be the Mite and two Sytes in current parlance, a tetragonal disphenoid (Rite) and another one (Bite), all three illustrated in the chart by Guy Inchbald.[8]

Furthermore, the Qyoobans censor and/or forbid sharing about the alternative model of 3rd powering, whereby said Mite and Sytes have volume 1/8 and 1/4 respectively, vis-a-vis a cube of volume 3 (no longer unity). Their public school systems deny their own citizens access to this heritage. Write to Congress?

Having their beloved Qyoob (a hexahedron) booted from His Eternal Throne is tantamount to heresy for them, hence the Embargo or Boycott, easy to document for the history books. The sense of entitlement among these Qyoobans (not to be confused with Cubans) is legendary. Talk about road hogs!

Those philosophers paying any attention to this little tempest in a teapot (not!), are probably aware that the dike is breaking, and that Qyooban philosophers are soon to be held accountable for their intentional and insistent dumbing down of our common heritage (logic).

Their overly high price tags may be questioned, even as their bigoted and ethnocentric behaviors fall into disrepute. All math is ethno-math.

I'm thinking Wittgenstein's philo will come out smelling like roses though. His investigatory style has proved a real asset. Hooray for the linguistic turn.

To summarize:

If you want the benefit of a liberating gestalt or enlightenment (as the fly escapes the fly bottle), then you'll need to find all those pesky little strings the Lilliputians have used, to tie down their Gulliver (our hero), to trap him with their small-minded meanings.

"Snip snip" go the Philosopher's Scissors (similar to Occam's Razor). Don't let those lab-coated Qyoobans nab you in their straitjacketed way of thinking.

Qyoobism tends to be overly-confining, awkwardly unimaginative, some say a symptom of its insecurity in its logico-authoritative role (arrogated).

Cubes are unstable unless triangulated, as any honest architect-engineer will tell ya.

Lets end the Qyooban Embargo.


[0] Of beatniks vs. squares, also buckaneers:

[1] from a recent journal post:
Lots of comparing notes occurs among the spin doctors, with secondary sources echoing primary ones in disseminating the latest bewitchments (the great Austrian philosopher Ludwig Wittgenstein used this term "bewitch" in a technical sense, in the context of investigating the hypnotic powers of "language games").

[2] "Triangling and Tetrahedroning"

[3] Aristotle was Right! (remember the Mite)

[4] D. M. Y. Sommerville (1879-1934), see:
Which Tetrahedra Fill Space? by Marjorie Senechal, Mathematics Magazine, Vol. 54, No. 5 (Nov., 1981), pp. 227-243.

[5] One of several portals to said Neoplatonist philo:

[6] He changes the meaning of B-particle from its original source, but is otherwise on target:
R. Williams, The Geometrical Foundation of Natural Structure, Dover, New York (1976), see footnote 20 on pg. 136.

[7] No mention of Mites or Sytes (as of June 23, 2010):

[8] The Archimedean honeycomb duals by Guy Inchbald, The Mathematical Gazette 81, July 1997, p.p. 213-219.

Kirby Urner is a RadMath teacher living in Portland, Oregon.

Need Something? Check here: http://ludwig.squarespace.com/wittrslinks/

Saturday, June 19, 2010

Wanderers Summer Retreat

We're packed around the table again. Lots of plastic. Our Blue House ethics have shifted against plastic, which doesn't mean we don't have any. I went to the supermarket, determined not to get anything with plastic in the packaging (I got glass, cardboard and metal). I paid with plastic.

This is potluck time, so some of the plastic contains food. Tara joined us. She's booted into the wifi with my old laptop. She's at the table, I'm on the steps.

For those just joining us, this is the boyhood home of Linus Pauling, one of Oregon's favorite sons. He received two (unshared) Nobel Prizes, although the one for peace you could say goes to Ava Helen as well. Their papers are collected at Oregon State University.

Our patron and sponsor, Doug Strain, helped endow the reading room, as well as restore this magnificent old home. Doug co-founded Electro-Scientific Industries, which also supplied a facility to Quakers in the late 1950s, where they practice their faith to this day, two remodels later.

Our group, called Wanderers, gets its name from (a) the ancient Greek word for "planets" (they wander the sky, especially in a geocentric coordinate system -- simpler spirals if you look from a heliocentric point of view) and (b) a quote by Mandelbrot that goes like this:
Science would be ruined if it were to withdraw entirely into narrowly defined specialties. The rare scholars who are wanderers-by-choice are essential to the intellectual welfare of the settled disciplines.
-- Benoit Mandelbrot
We're looking at close up pictures of Mars on the Web, mostly gray scale.

Gus Frederick of Silverton is a Mars nut, actually a good presenter on an interesting topic. This isn't about Martian Math so much, which is something I write about.

Carol is home prepping for her next journey. She lost some pills, I lost some money. Our exchange student (per Census interview) is out and about.

Some traffic on PSF channel today; another Synergetics boot camp on Synergeo (ongoing).

Art Kohn and I spoke at some length in the alcove (near the food table), about family matters, about image processing and the Hubble space telescope.

This latter topic led Art to recommend Case Closed by Gerald Posner, laying to rest all those conspiracy theories around the assassination of JFK. The computer-stabilized version of the Zapruder film helps clarify the single bullet theory.

Jon Bunce and Don Wardwell sang an old Woody Guthrie song Pastures of Plenty. Jon and I then yakked about Subgenius literature, the bleeding head of Arnold Palmer in particular. We're an eclectic group, so pretty open to a wide range of topics.

Best wishes to Dr. Tag. I mentioned our internationalization work on the PSF list again. Not every Python-related chat room uses Latin-1 after all.

I started screening the first of a series on spatial geometry that's been showing on Portland community access TV, after screening O Superman by Laurie Anderson.

After a just few minutes into the polyhedra, Don and I heard yelling and cheering so went outside to see what was happening. A large number of naked and/or partially clad cyclists (skateboarders, roller skaters, unicyclists) were turning onto Hawthorne, protesting exposure to exhaust fumes, other machine world insults and indecencies. The procession was over a mile long, maybe longer.

Friday, June 18, 2010

Git Mo Stupid

"Too stupid to close Gitmo" was the verdict, last time we checked the score.

It's mighty hard to put any faith in those "counter-terrorist" twits after seeing their bogus blog posts in defense of that operation, an embarrassment for [what little remains of] "intelligence" in those circles.

No career path to an elite inner circle by that route apparently. Just cruft on the c.v., might as well say "unemployable".

I'm not blaming the White House though, even back to Bush, who wanted it closed too. Few people know that, as they can't believe presidents get lied to (especially presidents).

This defying of presidents is what "the woodwork" is good at (the so-called spineless bureaucracy -- aka "banana republic" -- which hides behind anonymity, posing as patriotic).

USAers don't seem to understand how their credit rating so much depended on what they might offer the future. Overlooking the debt was easier when the policies made some sense.

Endless "war on terror" is wearing thin, especially when there's so much positive futurism waiting in the wings, on hold while the world sits through this tortuous little stage number.

At least we're making some headway on the voting machines and attendant infrastructure. If they're not NSA approved, then we know they're unworthy. Or did I get that backwards? Good to see The Washington Post is on top of it, vigilant as ever.

Any truth in the rumor that the Pentagon wants to commandeer Gitmo as a HQS to monitor the oil bleed? Certain BP executives might need to be watched, asked a few questions.

Wednesday, June 16, 2010

Bruno (movie review)

As with Borat, the comic index of this film depends a lot on the viewer's assumptions about how scripted it is, i.e. which characters know this is a spoof and which do not?

The DVD version, which my daughter inherited from somewhere, has the movie with commentary, and that clears up some questions.

However, given Sasha is good at fooling people, how much of the commentary are we to believe in turn? Was Harrison Ford really "in on it"? Perhaps not.

I'm reminded of Werner Herzog's commentary regarding the filming of Fitzcarraldo. I took that as a spoof as well, in cahoots with his cast, the film savvy, Mick Jagger, Jason Robard and friends.

I viewed Bruno (twice, once with commentary) with a gay rights activist and community organizer, who thought, as I do, that Sasha is brilliantly brave, and knows how to do poignant social commentary.

Borat, Bruno and Ali G represent a new form of cultural anthropology, wherein the anthropologist learns enough about a culture to offend, enrage, excite and otherwise perturb it.

This is the opposite of trying to stay out of the limelight while taking notes.

I found myself reminiscing about Team America: World Police after it was over, a likewise penetrating spelunking exercise within the collective unconscious. Talk about "special operations"!

Sunday, June 13, 2010

Supporting Troops

I'm using "troops" rather loosely, to mean roving bands or remotely deployed teams of experts ("away teams").

When I was a young boy, a "troop" was a multiplicity of soldiers, only later reducing to a singular individual, i.e. a "trooper" became a "troop". Other linguists have remarked on this trend.

Later still came "An Army of One" (a marketing campaign).

The idea of embedding journalists or chroniclers (log makers, bloggers) as a part of the away team was a post-Vietnam War development.

A perception had developed around the Pentagon that too many journalists were loose canons and were seeing and reporting on events they should not, such as atrocities, murders of innocents, the agony of the troops.

The hellish nature of war motivated an insistence that it stop. Television played a big role. Young people (Global U students) especially resisted accepting their work / study assignments overseas. Others rebelled once they arrived at the scene.

A system of self-censorship was set up such that the media today are much more self-controlled. Pictures of atrocities get passed around on memory sticks, often mixed with pornography, but the general public is mostly spared from vicariously experiencing the horror of war.

Reporters violating the new code of ethics lose privileged access, and are punished for betraying their roving band, with whom they should have bonded to form a seamless team.

In the meantime, the public has been trained to harden itself against disturbing imagery, to become more accepting of inhumane behavior (witness Gitmo etc.).

Per C.G. Jung's posthumously published Man and His Symbols (which I borrowed from the Quaker meetinghouse today, along with Uncovered: the War in Iraq) people have the ability to "lose their souls" by means of various ego-dynamics. There's a picture of a band of Australian aborigines suffering from soul loss, amidst psychological analysis.

A TV-watching public sinks into unconsciousness under the watchful management of its spin-doctor anesthetizers, who continually remix the memes to keep the war tolerable and securely remunerative for its sponsors.

Lots of comparing notes occurs among the spin doctors, with secondary sources echoing primary ones in disseminating the latest bewitchments (the great Austrian philosopher Ludwig Wittgenstein used this term "bewitch" in a technical sense, in the context of investigating the hypnotic powers of "language games").

Some of the troops I'm thinking about have been thankfully reassigned to perform humanitarian duties, such as during the tsunami in South Asia. A lot of the same national guard type logistical skills pertain.

Coordination and planning, command centers and communications, all come into play. Some of the same military bases play a role.

The overlap is such that it's not always obvious which troops are engaged in which operations, or whether these ops are "special" or "covert" in any way.

In these pro-human operations, the embedded chroniclers are often keen to get the images and words out to a public, not just to show the heroism of the troops, but to garner public support in the form of actual goods and services.

Once a need becomes clear, sponsors step forward, either as individuals, as private companies, or as government agencies.

People at home or in coffee shops may wire funds directly, and take credit for doing so, on Facebook or whatever. Perhaps they send other forms of support (such as I've been doing, and chronicling on Facebook).

The chroniclers (bloggers, TV crews, filmmakers) are not under such pressure to keep the lid on their stories, as there's less fear of a negative backlash or reprisals. I'm not "spilling the beans" so much as "sharing the beans" (insider philosophy talk).

This image of civilians supporting humanitarian services from behind the front lines derives from many a war-time design pattern. People spend their time and energy making uniforms, boots, meals, other equipment for these troops.

In today's high tech military, a single troop is a million dollar investment over time, in terms of training, transport and equipment.

This high level of investment towards humanitarian endeavors marks a big step towards the amelioration of specific problems in many areas of the world. That same sense of good will flows towards the sponsors, for supporting the troops.

Yes, the military is a wealth redistribution and government jobs program. This is not news.

Having some of the programming serve humanitarian ends only means that the endeavor is somehow profitable to humanity.

Some characterize this difference as "adding intelligence" which might imply sponsorship by specific government agencies. Let's see which ones take credit.

Saturday, June 12, 2010

Aristotle Was Right!

I put an "oops" here because a tetrahedron is not a polygon, nor need its faces be equal.

On the other hand, its four faces are polygons, and they might be equal.

The regular tetrahedron of four equilateral triangles is not a space-filler.

The tetrahedral disphenoid, on the other hand, with four equal isosceles triangles, is a space-filler, meaning Aristotle was right: tetrahedra do fill space.

Misinformation from Math World:
A space-filling polyhedron, sometimes called a a plesiohedron (Gr├╝nbaum and Shephard 1980), is a polyhedron which can be used to generate a tessellation of space. Although even Aristotle himself proclaimed in his work On the Heavens that the tetrahedron fills space, it in fact does not.
In fact the tetrahedron does fill space, just not the regular one

Per Which Tetrahedra Fill Space? by Marjorie Senechal in Mathematics Magazine, Vol. 54, No. 5 (Nov., 1981), pp. 227-243:
"Aristotle did not state explicitly that he meant regular tetrahedra... some scholars continued to defend Aristotle on the grounds that he had not explicitly required regularity..."
As well they might.

What other tetrahedra fill space, all by themselves? Which one is minimal, in the sense that it builds the others?

OCN Branding

We started Radical Math in Portland, Oregon, offering a first course through Portland Free School on March 13, 2010. Our venue: SE Belmont around 30th, at Flipside (since vanished).

RadMath teaches what we call Verboten Math, which is considered somewhat on the subversive side, not suitable for textbooks.

Mathematicians tend to welcome our stirring the pot, as argument and debate stimulate interest in often dry topics.

RadMath inherits from the Oregon Curriculum Network's "digital mathematics" curriculum.

Glenn Stockton focused on Neolithic Math whereas I was more into Martian Math.

Would you like to help sponsor? Help produce mathcasts?

Going down in history as a true radical, in conformist times when diversity was threatened, might be your reward.

Wanna win some brand loyalty from some of tomorrow's freest thinkers?

ConceptNet in Python

How might you build your own ConceptNet for a specific knowledge domain?

What "graphs" would you create, what "webs"?

In the case of a spatial geometry web, would you maybe have Mite, Syte and Kite as entries?:

IsA(Syte, two Mite)
IsA(Kite, two Syte)
IsA(Mite, A A B).

Make any sense?

This math is somewhat esoteric by today's standards, but if you're at MIT, maybe you know what I'm talking about.

Or is this stuff still verboten there too?

Tuesday, June 01, 2010


Spring 2010
:: spring 2010 ::

World events backdrop: oil continues to spew, repeating events of 25 years ago according to Glenn, when the same sequence of repairs was attempted to no avail. Going through the motions. And the jigsaw puzzle of nations continues to defy solution, because nations are the product of lesser minds, were never God-given (human contrivances, an attempt at self-organization -- many valuable lessons learned).

The neighbors actually did repaint Sunnyside Piazza, looking good. I wandered by there with my camera, between computer jobs. We went looking for Hebrew brand beer at Zupan's, which we found in Pomegranate flavor, but it's the double IPA we were looking for. Dead Guy was on sale, along with another one. Thai soup with sandwich. Shades of Gothenberg. I miss Vilnius as well, glad Aiste is a Facebook friend, though I can't decipher most of what she writes. Greetings to Sir Laura, and to Steve Holden in Hong Kong (both PSF, Aiste should be if she's not).

Trey and Mike D. delivered some planters. LinZ did her Food Not Bombs run today. I filled in last week so she could work on repairing her rib cage.

The idea of a Beauty Pageant for Queen of the Space-fillers sounds kinda retro sexist, rather Rose Parade (there's a Rose Queen, high schools compete). Part of the fun is no hexahedron even makes the first cut. King Qyoob is thrown from his throne. Then there's this business of not being even-handed, being biased. Our Queen should be able to conceal her bias (orientation), is how the analogy works. I'm alluding to the B-module, which shows up as either left (+) or right (-), yet outwardly she has all the same shapely angles, either way.

The logjam of nations, in some sense a failure, in some sense lasting karma, in some sense a projection of our obedience to eternal principles, is captured in the movie The Terminal with Tom Hanks. The airport shows lots of octet-truss shots. The limbo of "nowhere / everywhere" is what airports seem good at projecting, that "space between nations" (like where the duty free shops tend to be). The Global University has roots in this limbo. Many of our students have no passports, no travel documents, no citizenship in any country. They fell through the cracks. World Game includes them, as more than statistics.

I got some polyhedra in the mail today, Made in Korea. My thanks to Gary of Pedagoguery Software of Canada.

Notice how I have no problem continuing to mention countries -- a familiar calculus. I like the stamps, money, flags and souvenirs. I also recognize virtual nations, closer to states of mind in some ways.

Imagine a Buddhist state of Samsara, with Nirvana the state capital (like Olympia of Washington). Or would Nirvana be more like Orlando? Is Nirvana an "after life"?

Many Xtians have questions about these "exotic cults" (as they might think of them, if not getting much tourism). Even Quakers are exotic to most Xtians, especially those of the "unprogrammed" variety (how does one deprogram an unprogrammed Friend?).

The folks in Louisiana have suffered plenty without this additional catastrophe of course. New Orleans is like Baghdad, though in the latter case, the disaster was man made, self inflicted. In both cases actually, counting the death-dealing oil plumes.

Poor engineering (e.g. FEMA trailers, decaying dikes) might be underlined as a cause of suffering in all of these scenarios. Poverty of mind, of the imagination, results in self-fulfilling "I told you so" prophesies coming true.

A more exultant engineering, clearly aimed at serving all humanity, would be easier to resonate with. Sometimes I think the free software movement got that ball rolling.

"World domination" in that geek subculture meant an end to domineering "owner enforced" selfishness. The workers co-owned the code, reaped the fruits of using their own heads -- what's under the "thinking cap" in capitalism. "Brain in body, body in mind" is what some say, projecting "mind" as like "the Matrix". That's pretty est-like (branching off Zen?).

Having wars about nations seems dark ages and retro, given how they're on the ropes to begin with, with the flagship USA taking on debt like there's no tomorrow. GST is switching the circuits, to where we speak more sensibly about energy inputs and workflows. "Not with a bang but a whimper" is how it would be, to ignite a big row over that which was never God-given.

The planet Earth on the other hand... now here's a Promised Land worth protecting. We'd need a Global University to do that. Maybe MIT will show us how it's done. Princeton? Cal Tech? Standford? We'll need a blend.

Speaking of Standford, we've been hearing from Keith Devlin's corner, where an Apollo Project for sharing precision thinking is planned, at least in a small corner thereof. I've not been able to trace the connections between Dr. Devlin and Dr. Benson, in case there's some overlap in the realm of Algebra. From my angle, it's more a Cult of Athena business (wisdom, defense, also music), with Algebra City a source of algorithms. We're feeding Pentagon Math with that NCLB Polyhedron and Polynomial: sounds cryptic, I realize. Other blog posts explain.

Trevor posted about still-standing Dymaxion Deployment Units or DDUs. Bucky was helping to get the idea of inexpensive, manufactured housing off to a good start. Bulter continued to reap the benefits of vending commercialized living quarters.