Wheeling & Dealing

I was gratified to learn that the Laughing Horse collective would accept a collection like mine as a sponsored shelf.

The principled management would rather close shop than sell out to ideologically undermining material, so an endorsement at this level is not just a trivial formality.

I explored this option with other book collectors today. Some of us may have duplicate volumes, if not willing to part with only copies. Grunch of Giants might soon be available in multiple copies, along with Cosmic Fishing and maybe Tetrascroll.

This change in direction might be perceived as outreach to a more geeky readership. Mike D. is already at the hub of One Laptop per Child in Portland. I've connected him with Ed Cherlin and others, Ed having some core responsibilities re Pycon 2012 in the Bay Area.

Portland bills itself as a capital of open source, is hosting both OS Bridge and OSCON this summer (I'm lurking on the planning list for the former, know O'Reilly has control of the latter). We're glad to get OSCON back from San Jose.

So does that mean it's easy for your average Portland-based high school math teacher to get an in-service credit for some Introduction to Python course? Not easy enough I'd hazard. I was up front with STScI about our uphill battles in this regard. Scientific calculators still monopolize the vista, with spatial geometry languishing in the lurch (except in a few elite venues?).

Will all this spirited initiative translate into new Free School classes at Laughing Horse, in Apache, in Django, in Pippy on the XO? Quite possibly. Or is Free Geek still doing those? Perhaps more cross-pollination is in order? I'd be a willing attender of these classes, as well as a presenter, which activities would from my perspective involve extending an already-thriving Pauling Campus subculture. We also both have video collections.

I'd be happy to sit in on some free and/or donation requested Django classes, given I'm currently hacking on /projects/ktraks, plus looking over Patrick's shoulder on his operational buzzbot with a Django front end. We could reach out to more children with Turtle Art as well. Maybe Ed himself would send us a video, or we could stream something live, ala Alan Kay addressing EuroPython.

The upcoming Flextegrity book is going to focus more on the graphical content than the lexical. I'd written something experimentally lyrical as possibly suggestive however this isn't like a recap of Tetrascroll (a poetic work); the nuts and bolts come across in the load-bearing prototypes themselves, more than in just the verbal descriptions thereof. The tactile / kinesthetic experience is likewise illuminating, hence our outreach to schools of design.

Jim reminded me in our meeting this morning (at Lyrik) that Edgar Allen Poe is one of Baltimore's celebrated favorite sons. I hadn't realized or remembered that. Now I'm thinking "Eureka!" (good to know). Baltimore has a kind of Gothic Gotham flavor that deserves explicit celebration.

Back in 97214

I connected with Patrick and Glenn today.

Glenn and I started our morning with Acme Coffee Shop (its real name) as I wanted to introduce myself to the owner. This shop is around the corner from the Pauling Campus with a back end facing the same parking lot.

Lindsey was in there recently talking up getting them a free piano. She's turned herself into a mini-Hubble, tracking heavy pianos people want to get rid of, in some cases still good, easily tunable and/or fixable. Of course moving them is an art in itself.

She'd like to intern at Immortal Piano or one of those.

The upright at our house likewise needs student-intern attention, might still serve to give music theory lessons (like the Yamaha gave when I was away in Baltimore).

Then Glenn and I went to Barebones (by way of Red Square, also on Belmont) which has replaced Muddy's (same server slot). We had simple fare (fresh bagels and bottled beer, some hand made apple pie), enjoyed the sparse ambiance.

We then went around the corner to where Flipside had once been, the site of our first radical math class for Portland Free School.

Glenn remarked on the professional nature of the new dry wall that'd gone in (we were looking through the window).

Glenn has recently acquired a new kite, one of those Oregon beach soaring models. He got it at a rummage sale for $1.

Patrick and I stared at Django code and managed to make some headway on a more user-friendly front end for his buzz bot. He's already using the BB's back end, harnessing its services to help with some Hollywood "what if" business. He's amazed how much money rides on decisions backed by practically no analytics or psychometrics e.g. a "sample size" of "five similar films" -- what does that even mean?

Lindsey has been in Portland for about a year, as of today. We're marking the anniversary of her arrival from Georgia, at the end of a long drive across country. In addition to pianos, she shares Mike D's focus on XOs, has other geeky plans for Laughing Horse -- which may be on the verge of closing after all these years, given the paucity of volunteers. When it's open, it tends to do some brisk business in books, T-shirts, other merchandise which in turn helps to pay bills.

I've parked a Dymaxion Projection in there a couple times, more as a symbolic gesture than as a real for-sale item -- same as I did for the Burning Man crew. Maybe contact BFI if you want copies.

In Other Words, which used to be in our neighborhood (as did Laughing Horse -- on Division) now serves fresh coffee. So could Acme could benefit from some science magazines? Inquiring minds want to know.

Glenn and I should do our next Flextegrity workshop at one of those tables. That might net 'em some new customers, plus Ken is one great portrait painter, with some example works already displayed.

I'm cooking Together Friends lentils this evening, back to the brown ones. I tried this dish with red lentils recently and effed it up, though the hodge podge tasted pretty good, especially with soy sauce. This time I think I pulled it off, as I'm more experienced with lentils of this variety.

Last night we went out with Sam Lanahan on Flextegrity business. Tara doesn't appreciate fish, got the chicken strips instead. The cheesecake was just out of the freezer but still tasted OK (I don't eat it much, though did encounter some top-of-the-line example of that edible material in Fairfax, Virginia recently).

Although I'm scheduled to teach Martian Math this summer, it's not like I'm eager to abandon Project Earthala. A focus on Mars does not entail a loss of focus on Earth.

On the contrary, our geography-aware curriculum is about upgrading our diverse domestic civilizations to a point where we might one day realistically contemplate achieving such an esoteric goal as installing some human-habitable research facility on some other planet or moon.

We have a lot of homework to do, and studying doesn't happen when our students have so little security in so many necks of the wood. We retard the Zeitgeist by letting the Global U stay so far from "ship shape". What curriculum deficiencies might we address? What "more with less" learning strategies might we adopt?

Astronauts train in giant swimming pools. Undersea cities will likely presage true space colonies. Your geodesic domes had better not leak too dramatically under water. What math might we teach to keep these submarine dome-dwellers dry?

Might we need Old Man River City and others like it, to sustain our skilled work groups of ground-based personnel? "We need to address depleted infrastructure and move on to the next thing" hardly seems that controversial an hypothesis.

The Eisenhower Administration got the freeway network going (the I-net). Today's "freeway system" is more about fiber optics perhaps, with Google the new General Motors.

Speaking of ship-related skills, Glenn taught me some more tricks with string and rope during our circuit today. He also had his handsome handmade sling along for show and tell purposes. He's been making these things since boyhood, gradually improving on his designs. Boys Life was an influence, a popular magazine, not unlike Make: in some ways, disregarding the gender bias.

The math curriculum we're imagining has a lot in common with scouting programs, with a mix of stereotypically "boy" and "girl" type skills. Home economics, gardening, self defense and weaponry, navigation and mapping, diet and health... there's a math angle to each of these, as well as multiple timelines to simulate and contemplate.

Games like Civilization help students integrate the variables into sometimes non-linear relationships, with comic books and cartoons helping to fill in and flesh out what might otherwise come across as dry-as-bones statistics and demographics.

Of course anything so practical and outdoorsy must seem like a radical departure from the more commonplace and mostly sedentary approaches to matters mathematical -- because it is. These would be your more experimental pilot programs, not just run of the mill and not necessarily widely available in 2010. Geocaching R Us.

Getting our curriculum off the ground will be remain difficult minus an influx of trained personnel with an ability to impart some of these skills. Trainers are in short supply around the world, as is logistics capability. Afghanistan is absorbing much of this talent.

As we saw with Katrina and will see again if / when a disaster next strikes, if the guard for that state is mostly deployed in some remote, poorly-directed overseas misadventure, then it's unlikely the citizenry will accept some nebulous "war on terror" as a legitimate excuse.

Since when was it OK to rob the domestic front of its trained protectors? Many governors have asked themselves this same question.

I joined a thread at the Math Forum regarding other aspects of the curriculum. Having recently observed first hand how programming skills remain in demand in the aerospace sector, I was again nudging the math teachers to maybe pick up some of that slack even pre-college.

This is not some new party line I just invented for the mid-term elections of 2010. This is a tune people have been singing since computer programming became somewhat affordable to many schools in the mid-to-late 1970s, with the advent of the personal computer with languages like BASIC and LOGO.

Later, a more Unix-like environment would migrate to the personal desktop, in the form of Linux and FreeBSD, and some additional computer languages would percolate through the popular mindset.

Languages such as LISP, Scheme, APL, Smalltalk, ISETL, ABC and so forth, would migrate from their mainframe settings onto home computer hard drives.

Of course no rule says high schools must confine themselves to running what home computers might run, but as a rule of thumb one wishes to have some continuity in that regard, if only to keep parents somewhat in the loop.

Tomorrow I'm to meet with Dr. Bob Fuller, my mentor on the First Person Physics project. This isn't the same gig as the Nebraska-based initiative (as in Lincoln), but it sounds like there may be some commonalities, e.g. a focus on delivering the information in ways health care professionals might find especially useful.

The focus on biomedicine was a characteristic of some of Dr. Urone's books as well.

Dr. Fuller is a student of Dr. Robert Karplus when it comes educational theory and techniques. A Love of Discovery sits in my living room on the "time capsule" (semi-cylindrical shelves) between a book by Linus Pauling and Wolfram's thick tome.

Dr. Tag has been bouncing around the Middle East for the last few weeks. We connected by Google chat yesterday, me just back from Baltimore, Maryland, and she in Damascus at some outdoor cafe.

Perhaps an Islamic bank might want to work with Acme? The one in Whittier seems to be doing OK (mom went to one of their meetings).

I'm not sure what financial services Portland even offers of that genre. Some branches are little more than a few cubes in some "cube space" I would imagine (we used to have an official CubeSpace in one of our banks, where I used to show up for work sometimes, or for user group meetings).

Tara is home sick. Our $500/mo health insurance policy covers 0% of her $80+ antibiotics and 0% of the $200+ doctor visit. As MoF winner RBF put it in Grunch of Giants: the "system" has been gamed (contrived) to serve only those making $100K/yr or more. That's not an American design, hence his call to arms (including cyber-spatial) against this alien GRUNCH (his books tended to be acronym cities -- search these blogs for decoder rings).

Like I'm guessing the interest on the debt for Star Wars alone is probably sufficient to restore education budgets to their higher 1970s levels (relative to GNP).

Eco-tourism could easily pick up the slack when it comes to needing skilled engineers, including those in an aerospace pay grade. The insolvency of the "ray gun" school is hardly a state secret at this point. Investors aren't buying what can't be sold (an economic truism I realize).

Speaking of economics, buzz in the financial press suggest the SEC plans to use Python more. I wonder if this might be owing to its new decimal type (just speculating again, though not without evidence).

Basically any silo is free to suck down a copy of Python and use it for whatever work / study programming. The license is liberal in that way.

In sci-tech circles, it's the NumPy module that gets a lot of appreciation, plus other stuff on top of it.

The Panda3D project started out under Disney and was published with a Pythonic API following its further development as an open source project under Carnegie Mellon Entertainment Technology Center. What kinds of course-ware might we develop around this asset?

Python Gig

Thanks to Holdenweb, I was given an opportunity to visit the Johns Hopkins campus in Baltimore, to present a three day Python training to people working with the Space Telescope Science Institute (STScI).

STScI is a management and data analysis hub for the Hubble space telescope, and will also provide ground support for the James Webb Space Telescope (JWST).

I arrived at Dulles (WDC) on Sunday and stayed a night in Fairfax, Virginia. I am grateful to my kind host for making so many of the arrangements.

Design Science

Given all the jitters in space program circles, these EPCOT-like proposals to "colonize Earth" by using aerospace level technology are gaining new appeal.

The PR around such terms as "dwelling machines" (a variant of "smart house") is worth monitoring.

Perhaps people are finally ready to stand back and take a new look at their energy ecology. Futuristic artifacts make more sense when changes appear inevitable, with or without said artifacts.

I've been surveying the "peak oil" literature again, finding lots of awareness of the "design science revolution". Apocalyptic scenarists, if tempered at all in their doom saying, tend to steer towards these "more with less" aesthetics of aerospace and high efficiency.

Squandering fuel on commutes is seeming increasingly crazy.

Fuller cites "planners" as among those most empowered to think in big picture terms. Planning around lifestyles that don't require a daily commute might require some rezoning.

More communal kitchens are feasible, including in suburban settings. The metaphor of a campus might become less of a metaphor in that case, especially in light of all the student exchange going on (a lead counter to xenophobia around the world).

Our hopes to showcase some of these alternative future lifestyles clearly manifest in Portland, not least in connection with the Pauling Campus in zip code 97214. Sponsors looking for product placement opportunities have been stepping forward.

Having humans rewarded for not commuting while getting important work done nevertheless, will likely involve greater use of optical fiber.

Dreams around urban agriculture, less tied to fossil fuels for transport, and of eco-villages designed from the ground up to do more with less, seem semi-mainstream by this point.

Wanderers 2010.4.3

Tonight was about eco-tourism, which means developing budgets to keep environments pristine, in a state people would gladly pay to experience, and/or save for others to experience.

Lynne Taylor gave the presentation, showing lots of pictures from her eco-tour in Australia, mixed with other maps, screen shots from Google Earth (or so I recall). Jeff Goddard produced the projected slide show, which Lynne reviewed quickly afterwards, for my benefit.

I got here late, having caught the 14 back from downtown. This wasn't the first time PPUG and Wanderers had met on the same night.

Barry was attuned to the trimaran Groupama 3 that'd recently broken an around the world sailing record.

PPUG 2010.4.13

I made a quick visit to Portland Python User Group on the 16th floor of a downtown sky tower this evening, at the WebTrends office.

We're having sponsor-provided pizza but did not manage to secure permission from management to consume beer.

Our first presentation is on the "baker" module. This provides a customizable decorator that lets you export a bunch of functions to your external command line environment.

Jason has a proposal in the EuroPython. The GIS in Action conference, where I spoke last year, is about to get started, at PSU this year. The wheels keep turning.

Jason is quickly covering some 2.7 features, mainly new dict methods. He's noting that 3.x features have been back ported, but isn't sure what all these new features are. Dictionary and set comprehensions" are a neat. Adam is showing us those.

Kyle is showing us execnet. This lets you send Python code through an ssh connection for execution on remote Pythons, Jythons or whatever. The "channel" created by makegateway() uses its own serializing protocol, although you can specify a different one.

I'm busy cramming for a gig, supposedly an introduction to Python. I should probably get back to that. We must have like 40 people here, only one of us female. Lindsey (FOSS witch) is sending some grammatical remarks (corrections) through the ether, so is here in spirit.

Discogs & Python by Kevin Leweandowski (founder and CEO of Discogs) is about the Discogs database, which is wiki-like. The database has about 2 million entries, 4 million unique users a month, runs on about 30 servers. His latest architecture uses some Python ports of Ruby stuff: Routes, and WebHelpers (is that through Pylons?).

Kyle really appreciates the Python interactive console, one of its most unappreciated features (saves time in development, maintenance etc.).

If I leave now, I'll have a short time with Wanderers.

Radical Math and Python

Figure 1: Inscribing a Cube in a Rhombic Triacontahedron

by D. Koski

Loyal readers of these non-fiction blogs will have discovered a Russian novel's number of characters, along with numerous "mug shots" of polyhedra, repeated in many contexts.

For example, I phoned David Koski this morning to double-check on the face diagonals of the Rhombic Triacontahedron of volume 7.5 which shape, you may recall, intersects the volume 6.0 Rhombic Dodecahedron of radius 1 (or of diameter 1/2 if accounting in diameters). The 7.5 volumed Rhombic Triacontahedron has a radius of Φ/√2 compared to that of a sphere of radius 1.0.

These polyhedra are both members of our august Concentric Hierarchy of Polyhedra, a famed inner circle of polys, including the Platonic Five, that comprise our Zen Garden.

David had a ready answer: given a Cube inscribed as above has 2/5ths the Triacontahedron's volume, the 7.5 volumed RT would contain a Cube of volume 3. This is convenient, as it's the Cube volume we had already, based on two unit volume Tetrahedra intersecting each other to form its corners.

What's cool is that every time you intersect a Platonic with its dual, you get a polyhedron with rhombic faces (squares count as rhombs, and so the Cube is one of them).

When you criss-cross those rhombic faces, you divide them into four right triangles (the face diagonals of rhombs intersect at 90 degrees -- something to prove in a Euclidean geometry class). The point at the body center forms the fourth vertex of these four tri-rectangular tetrahedra per rhombic face.

In the case of the Cube and the Rhombic Dodecahedron, the fall-out from so carving the faces are Mites, or minimum tetrahedra. One gets 24 and 48 of them respectively, each weighing in with volume of 1/8. Cube: 1/8 * 24 = 3. Rhombic dodecahedron: 1/8 * 48 = 6.

In the case of the Rhombic Triacontahedron, the fall-out is the T-module shape. To be an actual T-module, you'll want your Triacontahedron to weigh in at precisely 5. This gives each of the corresponding 120 T-modules a volume of 1/24, i.e. 1/3rd that of the Mite and the same volume as the A and B modules (the Mite is comprised of 2As and 1B).

Below is David's instructive vZome as to how the Cube and Rhombic Dodecahedron are both comprised of Mites.

Figure 2: sharing a MITE

by D. Koski

Note that a Rhombic Triacontahedron of volume 5 would contain an inscribed cube (per Figure 1) of volume 2, i.e. 5 * 2/5 = 2. This is a good candidate for a 2-volume in the concentric hierarchy, which already has volumes 1, 3, 4, 5, 6, (Φ² + 1) 3√2, 5 Φ²√2, 20 and 24.

"relative volumes"
(Python + POV-Ray)

Note: the above information is premised on using Tetrahedral Accounting, not widely practiced or known about as late as 2010, Dr. Arthur Loeb's brilliant essays notwithstanding.

A wily underground of Radical Math teachers, some with friends in high places, willingly circumvented the Bucky Boycott (an anti-USA PR campaign) and taught this "verboten math" on the sly -- a risky-yet-necessary business given the high stakes involved.

Python, Athena's archetypal protector (she's our goddess of wisdom, intelligence and defense) is also literally a computer language. Python proved useful for encoding such radical math as the above, keeping it alive and kicking through a dark age of rampant ignorance and tyrannical subjugation.

My First Critic

Some of my fiercest critics hide out. This guy, Frank Zubek, is at least up front with his counter-points. If he succeeds in confusing you, maybe check Color Plate 3? Don't forget to order his Elusive Cube. Be the first on your block to share one. CubeIt! by Huntar is also worth having, if the mighty MITE is your game.

close encounter with Martian Math

:: MITEs Cube with pg. 71 of Regular Polytopes ::

Globalization

The term "globalization" has many negative connotations, such as loss of ethnic identity, change at too fast a pace, disruptive economics. I'm not on some mission to dismiss what's really difficult as somehow easy. Along with Jungians, others with a psychological focus, I'm aware of an inward process as well as an outward one. Humanity is giving birth to its next collective self in some dimension. People look to their religious traditions, other wisdom literature, for guidance in these unprecedented times. We have each other.

I wandered into Tibet Spirit today, after working all morning on a Python-related project. I read some of the meditations, wished the proprietor well. This was after driving Tara's community service project report to her school (3.4 miles round trip). She was home fighting a cough. I spoke with my mother by cell phone (the only phone we have anymore).

My thanks to Glenn Stockton for his help today with the office.

I thought about Mecca today as well, the pilgrimages people make. One may reason against these practices, yet from another standpoint, here is how people have made a way together, created community. Precession. Side effects. Gravity. Tension. I do not disrespect or sit in judgment. I join the prayerful in their eagerness to find a way forward that has integrity. My contributions should be a help, not a hindrance. We pray to serve and to find alternatives to violence, out of compassion for ourselves in our own suffering. Let us work together. May Allah have mercy when we stray or delay, and write new teachings in our hearts.

Easter Sunday 2010

In celebration of Easter, Tara and I joined the Boltons' extended family, plus a nuclear family from China that has lived in North America for some twenty years.

The Chinese family had recently traveled across America by train, from Portland to Boston, with a change in Chicago. They had a sleeper compartment and took in a lot of country they had never seen from an airplane: eagles on the frozen Mississippi, owls on the leg to Seattle.

I had some Flextegrity along, for conversation purposes, a product of Glenn Stockton's workshop with supplies from the company, the four-frequency tetrahedron of 35 plastic injection molded hubs, each of 6 identical components, made somewhere on the Chinese mainland.

Tara joined the other young girls, and an older guy, in hunting for eggs and chocolate. Tara has a special liking for Cadbury eggs. That used to be a Friendly company (as in "Quaker"). I wore my Friendly hat, a professorial jacket, black and blue jeans and shirt. Tara was more stylish.

Later, I visited with Glenn, returning said tetrahedron. We discussed Hinton's work. Charles Hinton was a contemporary of Edward Abbott's of Flatland fame. Geometry was entering a new chapter back then, with talk of hyper-dimensions, starting with four.

In the Greek view, height, width and depth constituted three independent dimensions, which took care of conventional space. The "unconventional dimensions" per Hinton and others, might have to do with "higher consciousness" -- not an unusual view and one which continues to permeate the literature, although one perhaps more commonly thinks of mundane "time" as a fourth dimension, complete with world lines and so forth.

Linda Darlrymple Henderson's The Fourth Dimension and Non-Euclidean Geometry in Modern Art provides a useful account of fourth dimension talk at the start of the 1900s. Fuller was a player by then, as was P.D. Ouspensky. When Fuller finished writing 4D Timelock, he rushed a copy to the latter, per Dr. Henderson's chronicle.

I replied to Alan about the Coupler on Synergeo, fitting in mention of Descartes' secret notebook. I was going over Descartes' angular deficit in the context of Fuller's critique of the calculus with Glenn, jumping from Bishop Berkeley's excoriations.

Tara took public transportation to Clackamas to see a movie with her friend. I wrote our trip to Hillsdale on the mileage sheet, then walked around the neighborhood with LW who was seeking candles. Cooking and cleaning ensued (also blogging).

Non-humans played an important role in this year's Easter, starting with Suzanne's possum on Facebook, through the squirrels in our attic, to the new pug puppy at our lunch. The pug ate a carrot off the Flextegrity tetrahedron (see Fig. 1). From the Amtrak train, many animal tracks had been visible, though no actual bears had been seen.

Last night, Tara educated me about the steampunk aesthetic, one of several styles that have traction at her school. She sent me a detailed email, including pictures, spelling out more of the lifestyle taxonomy. Steampunk has a neo-Victorian flavor, which got me thinking about Neal Stephenson's writings.

Tara is reading about Clarence Darrow and studying the issue of jury nullification for district debates. We had a discussion about corporate personhood over dinner last night, with me citing Thom Hartmann's research into the bogus beginnings of this idea, and with LW linking to Europe's social democrats. Regarding these social democrats, Tara worried about any tyranny of the majority that might give outlet to rampant xenophobia. Should ethnic costumes be banned just because Preppies don't like them? What would the Goths think?

Treating corporations as programmable machines does not negate the value potentially added by the people who control them. Some Quaker corporation (e.g. Global Data Corporation) might deliberately drop the corporate personhood dogma and revert to becoming such a machine. The new business rules would be expressed in the software, and with the government's blessing. We're designing new institutions from scratch, borrowing from cultural templates, but not mindlessly imitating them. Academia could help with the blueprints (class definitions), as could some national labs. Plus let's work with Native Americans to pioneer these new ethics. This proposal might make for some interesting steampunk science fiction if nothing more.

Fig 1: flextegrity dog

A View from Abroad

to Poly list, by DK

Dave Koski and I were on the cell again tonight.

I ranted a bit.

Two points:

(a) Not including much if any Bucky in K-12, where some of his contributions clearly belong, in geometry, history, literature, is a clear signal to the world that some ulterior motive trumps obvious relevance. Study what America teaches its young. What diplomats or politicians put out, is far less of an indicator than what goes down in K-12. We're talking about a positive, hopeful futurist whom many a world leader embraced. To actively exclude this information is a forceful declaration of a commitment to go in a different direction, a commitment renewed daily in schools across the country. Just mentioning geodesic domes in a geometry textbook sidebar is hardly saying much. Where are the whole number volume ratios?

(b) Not making more hay around the minimum space-filler, so-called because it's a tetrahedron without left or right handedness, seems bizarre. Math World doesn't mention it on its page on space-filling, with or without Fuller's terminology (he called it a Mite). True, spatial geometry is somewhat esoteric to begin with, but a minimum space-filler... even K-12 should have room for such a thing.

Here's from Math World. Notice how tetrahedra are not mentioned at all in the paragraph below, even amidst an attempt to be exhaustive:

In the period 1974-1980, Michael Goldberg attempted to exhaustively catalog space-filling polyhedra. According to Goldberg, there are 27 distinct space-filling hexahedra, covering all of the 7 hexahedra except the pentagonal pyramid. Of the 34 heptahedra, 16 are space-fillers, which can fill space in at least 56 distinct ways. Octahedra can fill space in at least 49 different ways. In pre-1980 papers, there are forty 11-hedra, sixteen dodecahedra, four 13-hedra, eight 14-hedra, no 15-hedra, one 16-hedron originally discovered by Föppl (Grünbaum and Shephard 1980; Wells 1991, p. 234), two 17-hedra, one 18-hedron, six icosahedra, two 21-hedra, five 22-hedra, two 23-hedra, one 24-hedron, and a believed maximal 26-hedron. In 1980, P. Engel (Wells 1991, pp. 234-235) then found a total of 172 more space-fillers of 17 to 38 faces, and more space-fillers have been found subsequently.

What you find instead is that Aristotle was wrong: tetrahedra do not fill space. "Although even Aristotle himself proclaimed in his work On the Heavens that the tetrahedron fills space, it in fact does not."

The more nuanced dismissals remember to say he said "regular tetrahedra," however this oft repeated factoid just goes to obscure the fact identical non-regular tetrahedra do fill space.

Mites face-bond to make two more space-filling tetrahedra (called Sytes by Fuller), though these are not as primitive, given their decomposition into component identical space-fillers.

Dave is looking at some Catalans these days, duals to the Archimedeans. The cuboctahedron and icosidodecahedron have the rhombic dodecahedron and rhombic triacontahedron as their respective duals. He's studying the dual concept more generally, going off some of the data in the Robert Williams compendium.

These latter are combinations of duals themselves: the rhombic dodecahedron is a combination of the cube and octahedron; the rhombic triacontahedron is a combination of the icosahedron and pentagonal dodecahedron.

I doubt many people will read a lot of Synergetics with gusto. That's a hard text. Glenn routinely expresses his frustration with it, as do I. Not everyone reads philosophy, period.

Related post to Math Forum: Recap: Letter to Arne Duncan etc. (March 31, 2010)

Work / Study Programs

Global U student LW has been traveling along with Paul Treanor through the highways and byways of Amsterdam, looking at Google Street Views.

I took a little workshop with Glenn this morning, in his GlobalMatrix Studio on the Pauling Campus. I got to snap some more acrylic icosahedra together (a fun skill), then paid with a lunch at Oasis.

His prototype Flextegrity kit is looking good but I won't say much about it yet. Glenn and Sam did some inventory recently, meaning Glenn got to see the energy-efficient two wheeler Sam let me ride. The three of us plan to meet again tomorrow.

During our lunch at Oasis, Leslie Hickcox put me in touch with a Sky Trams guy who used to be with Boeing. He's into high speed rail and like that. I was amused by the little cartoon about the year 2000, made in some Other America; "very sexist" I told him, smiling broadly.

That got me thinking about the for-academic-credit work / study approach to some of these railroad jobs.

These are programs helping companies recruit their future engineers (of many varieties) and so are not about taking away jobs. We're presuming friendly town-gown relations.

This is about internships, apprenticeships. Students sample jobs, learn lore.

Some of those enrolled may have no strong leading to commit to railroad building as a career focus, are up front with this thinking, and yet are willing trainees for the semester, bring relevant skills.

The resulting mix in the temporary communities will prove more diverse as a result, and this is a net positive. Biologists and ecologists in training, a few nurses, out with the surveyors and track layers, doing some cross-training and coming to understand one another better: something to write home about.

Temporary campus communities would need to set up along the way, sometimes in picturesque circumstances. Core staff would include those working full time in a more dedicated capacity, perhaps with Siemens or Bombardier.

When you get back to your dome village, you have classes in other subjects, like computer programming or TV editing. There's a cafeteria, private living spaces. We don't presume the typical construction site trailers. Perhaps Princeton is supplying some of the programming.

Some temporary campus facilities may grow into small towns, provided this marks a return to passenger railway days, with some trains making lots of local stops (perhaps on a siding).

The trend has been in the other direction, so there'd have been a cultural shift twixt then and now, maybe thanks to peak oil, frustration with suburban living, nostalgia for saner lifestyles.

Given this whole work / study approach is from Another Tomorrow, lets be imaginative and simply assume North Americans have returned to the notion that trains are good, and lots of remote living along the railroads is once again a preferred lifestyle. Or maybe this is somewhere closer to Mongolia?

You've got optical fiber, lots of bandwidth, local clinics with skilled health care personnel.

Yes, there might be a runway within a couple hundred miles, but no regular commercial service. Sometimes an executive team will visit by small jet, especially if the rail line is still under construction. These bases come and go though, just as the villages do. They're built with dis-assembly and removal already a part of the plan -- a new kind of architecture.

Back at the campus, lets tour around: more horses than motor vehicles? Electric ATVs? No supermarket for hundreds of miles? How many children? How many elderly?

A given campus might host facilities for alumni, company veterans. Even though you don't visit the construction site every day, don't operate heavy equipment, you're still able to teach, work on memoirs, collate experiences, play with young children. The Global U is for life-long learners.

The trains sometimes leave box cars with stuff off the ships, ordered on-line. The new "smart homes" fit in one container.

This isn't about "commuting to work" necessarily, so much as being where the school is located, and both working and studying.

Is this school a religious institution? The more permanent towns will have their cemeteries, their sacred spaces. If the school starts a vineyard, then the trains may have orders to pick up, as well as drop. The idea of a civilian-friendly rail-based economy will have reasserted itself.

Smart curricula will combine experiences, integrating the new knowledge and skills, encouraging positive synergies. For example, the dodecacam you used at the job site (while working on the railroad) will feature in your learning to program, as you upload to the company server.

As a materials engineer, you will analyze data from the work site. As a field biologist, you will have your specimens to study. As a geologist, you might have collected a few gems. Apprentices will mingle with more experienced personnel, learning the ropes.

A railroad is a stand-in for many a project requiring off-the-duff tool use.

A semester in North America, or Russia, or wherever, working on an interesting mega-project, would be a feature of several university majors.

Consider Old Man River City (OMR). Where would the workers come from?

If they're also students in some cases, then the build site would have more of an Arcosanti flavor.

Light Speed

Readers of Synergetics (a philosophy) may accept that nature is going as fast as she can, yet is sometimes traveling in knots. The result is a spatial unfolding, time-wise experienced, that might seem quite slow and mundane. "Light speed" is not extraordinarily fast then, is more what we'd consider normal in this namespace, invented by R.B. Fuller in collaboration with E.J. Applewhite.

Einstein's philosophy did not hold the speed of radiation unfettered in vacuo to be "very fast." It assumed this speed to be normal, and all other lesser speeds manifest in physical Universe to be occasioned by local interferences, shunting independent phenomena into local circuit repatternings. (529.24)

I tackled the garage again today, with Glenn and LW coaching. The student quarters are dingy by local standards, not Reed College quality to put it mildly. The principal enemy is clutter. As a typical homeowner, I'm saddled with the archeological detritus of middle age, having been married, raised children, turned gray. I treasure a lot of these materials, which span generations and connect many people and events, but that doesn't justify collecting and keeping a whole boat load.

TM got invited to the beach. NC pushed off with Gideon.

A thread on education policy, openly critical of the Obama administration, continued to get my attention. The idea of a "manufactured crisis" is preposterous, given the times, the events we're witnessing. I weigh in with some rant in favor of more domestic international schools, exchange student programs, and tearing down the "Berlin Wall" between computer and mathematics topics at the high school level. I even call on the Russians for help, echoing Ronald Reagan's request to Gorbachev. These are longstanding themes in math teaching circles, with experiments going back to at least the dawn of the personal computer.

Last night, we screened another three videos from the book store, this one about an Air Force pilot and officer, enjoying a leisurely tour flying some big planes in Vietnam, then suddenly having a crisis of conscience over what was being carried out and refusing to support combat operations any further. He reminded me of Ralph McGehee in some ways. The Air Force put him in a mental hospital, which led him to eventually enter the medical profession and find his way to El Salvador to treat victims of the war in Central America. This guy seemed amazingly courageous. He'd also become a Quaker. Dr. Charlie Clemens.

Glenn was kind but stern about getting rid of garbage, old papers etc. LW has her stuff down to one car load. If you're an acquaintance near or in 97214 who could use some children's books, toys, some good clothing, some dishes, other supplies or decorations, I might have what you're looking for, feel free to get in touch. Garage sales are always a possibility.

Through the Wikieducator list and other sources, I'm tracking Google's decision to lift censorship in China by moving to simplified Chinese on the HK servers. I think of these as "events in Cyberia" wherein nations, virtual nations, other nebulous groups, engage in noospheric activities. There's a lot of spying and prying, which may sometimes change the map of how Global University services get delivered.

Using a Fuller Projection may be useful in this context as it reminds us to see extra-nationally as well as nationally. Even if the challenge is to remember the capitals of 50 states, associated with some 50 stars, it makes sense to provide a more global perspective, given the international flavor of this curriculum.

The Dymaxion airocean world map is only one of many devices that could provide man with a total information-integrating medium. We are going to have to find effective ways for all of humanity to see total Earth. Nothing could be more prominent in all the trending of all humanity today than the fact that we are soon to become world man; yet we are greatly frustrated by all our local, static organizations of an obsolete yesterday. (537.34)

You'll see how I walk this very talk if you follow my links through edu-sig, where I'm yakking about Rich Data Structures again. In more recent terminology, I'm sharing Supermarket Math, talking about how things work in terms of databases. We also take up TCP/IP in my classes, often screening Warriors of the Net.

Tonight's videos were somewhat horrific. Friends should avoid overdosing on Gothic documentaries. Quaker schools, aspiring Zen centers such as this one, other alternatives to violence programs, need to find a balance between studying the world's ills and working for positive change. To the extent we're able to make headway with disaster relief and healing, we'll be ready to face more challenges. Success stories make a difference. The Berlin Wall came down.

Responding to Op-Ed

[ originally posted to math-teach, hyperlinks added, typos fixed ]

>> Business leaders certainly have the right to make their voices heard in the ongoing debate. But public schools do not exist exclusively to meet their needs. The crisis they have manufactured to justify their criticism is nothing new. To understand the basis for this assessment, I refer you to my op-ed that was published in the international edition of the New York Times on Jan. 14, 2008 ("The 'crisis' of U.S. education" -- see http://www.nytimes.com/2008/01/14/opinion/14iht-edgarddner.1.9196672.html ).

This op-ed piece seemed somewhat full of non sequiturs.

Yes, these documentaries and reports showing the relative quality drop are disturbing and stir up anxiety.

What doesn't follow is that these were phony, fake or manufactured 'crises'.

Rather, these concerns gave rise to many responses, including some challenges to authority and adventuresome departures (e.g. Bill Gates from Harvard).

A lot of skeptics said the personal computer could never take off.

We needed risk takers and we got some. New Math made a difference, even if the name and branding were quickly buried.

In other words, if you go back over the same events and say the crises were real, and people responded (at least some of them did), then you might still get the same outcome.

This outcome is nothing to wildly celebrate. The USA is still mired in poverty and is apparently unwisely consoling itself that its curriculum must actually be OK because other countries are even worse basket cases. Another non sequitur.

The author is quite correct that the support of teachers is needed, and also the support of students.

Of each other.

It's not like threatening politicians with a loss of votes is going to change the situation on the ground, vis-a-vis whether much teaching and/or learning is really happening or not.

I thought the analysis from Singapore was pretty good: the USA system is less fixated on exams (although ETS works in that direction), depends more on creative risk taking.

OK, so where are the teachers willing to take risks and challenge authority, and what does that look like?

Or are we thinking it's students who should take all the risks?

Accusing businesses of manufacturing a crisis seems like a cop out to me. The economy is very clearly in a bad state and probably one of the most galvanizing things we might do to pull out of it is overhaul the education system in a way that gets a lot of people working in new roles i.e. institution building is in order.

No, I'm not just talking about "charter schools" (don't all schools have a charter -- some more recent than others?).

For the sake of debate and argument, I might also take the position that approximately no schools in the USA are "world class" right now.

That's just not what we've got, based on the curriculum I'm seeing.

I'm not saying this as a simplistic way of blaming teachers though.

Perhaps it's those same business leaders who just aren't being clear enough?

If all that's coming across is a sense of "fake crisis" then maybe the business community needs to spell it out in a lot more detail -- perhaps by sponsoring some showcase schools and showing directly and immediately what it would like to see more of.

We'd hope for a lot of diversity, with attainable reforms on display, not just pie-in-the-sky. The newer curriculum itself should start to come through, not just images of students working with it. Adult viewers could use some updates as well. Am I just talking about PBS then? Is the BBC planning anything similar?

Like why not make it a TV series? But maybe not fiction this time, and less scripted? We've got this "reality TV"genre going, but just use it to play silly games. Does anyone want to risk something more real? One school might be inner city somewhere, another in the hinterlands,
another built from scratch in the course of the episodes. Could we convert some spare aircraft carriers, even if just moored in harbor, make them into boarding schools perhaps. Just an idea -- other ships?

I'm thinking of Disney's bold vision of an Experimental Prototype Community of Tomorrow (EPCOT). What would the school be like, in said community? Jet packs? Probably not. More use of GIS / GPS, better spatial geometry? Probably.

The Japanese likely have ideas and talents to contribute. This idea that we're all divided up into nation-states who viciously compete, like in some Olympics, is itself a bit dated (a lot dated). The business community does a lot of problem solving trans-nationally, out of necessity.

Maybe that's a next step for teachers too? Again, some creative use of our shared media (not just the Internet) could start moving us in a more positive direction.

In the meantime, I remain thoroughly persuaded we're in something of a crisis. Lots of homeless, lots of tents, lots of FEMA trailers... you don't need me to spell it out for ya do ya? Oh yeah, lots of wars, lots of preventable deaths by starvation... I'd say by definition the curriculum is broken, or we wouldn't be so messed up.

Perhaps it sounds "idealistic" or "utopian" to want to address serious economic problems (which all fall under the category of health care, broadly interpreted) but from a business point of view there's pressure to find life supportive investments, stuff to do with time/energy that isn't just empty squandering.

An educated population is more likely to self-organize around such projects, whereas an ignorant one will just sit on its duff and blame the King, falling into some prehistoric pattern, of treating presidents like monarchs, then as scape goats -- not what the USA's founders had in mind (too immature).

Basically, it's complacency which has no appropriate role in this picture. If you think the status quo is OK, you're on the fringe, out to lunch. Change is needed. Risk taking is needed.

The only questions involve what, when, where and how, not whether, and many of these questions may be closer to answered than we'd like to admit sometimes i.e. it's convenient to always postpone doing the right thing, but at some point impractical.

So I'll end with an appeal to pragmatism, and a question: what shall we do now?

Maybe you don't like my TV-related proposals. So what are your better ideas. "More funding and smaller class sizes" should go without saying.

Be more specific. Talk about real changes to what's being taught, and how. Talk about how you might teach American History for example, up to the present day.

What if you couldn't rely on that textbook you teach from, what would you teach instead? What full length documentaries might you assign? What YouTubes might you project? What, you don't have a clue?

Yes, I'm walking this talk, as are many teachers I respect. I enjoy comparing notes with peers.

Remember, take risks.

More Kites!

Dave Koski has been bouncing off Scott Vorthmann with these new vZome studies. I've a privileged onlooker.

Related: Kite Sighting

Another Day

I was heading off with Glenn today, who arrived at my steps the moment I walked out the door. On the way, I noticed Mosley was out, cruising the street: a small dog belonging to one of the neighbors. He'd escaped. The neighbors were gone.

Thanks to cell phone technology, we resolved the situation or at least I think we did. LW was caretaking Mosley when I exited the scene, is now serene on the couch.

The meeting with Sam and Glenn went well, our server knowing all about Platonic polyhedra and crediting Minnesota schools, as well as his getting geometry, a math with clear objective content. Bridgeport Ale House. 97214 is truly global university, reaching out to sister zips. Tour through sometime, when in the mood to study. Visit Powell's maybe?

At the lunch meeting I showed some video from the Radical Math class Glenn and I had provided. I'd taken these with the Flextegrity camera (a Canon). I need to burn these to DVD, a process started thanks to Dave Fabik.

Remembering Dawn Wicca

:: dawn's pilgrimmage ::

Four of us gathered to commemorate the anniversary of Dawn Wicca's passing, on March 17, 2007.

Laurie Todd, Chris Ferguson-Cradler, Elizabeth Braithwaite and myself.

We all shared memories and perceptions, thinking of our dear life partner and friend.

I read aloud from my blog, shared pictures.

We also talked about why civilizations fail, or succeed as the case may be.

Chris, present at Tara's birth, has a new grandchild. Elizabeth's son is starting spring break, is in college. Laurie, our host and neighbor, employs Tara after school, and knew Dawn well before I did.

I took refuge in writing and walking today, did some cooking (those lentils again) and cleaning, other work. I thought much about the importance of community (sangha), of teachers. Dawn taught me a lot, more than I know.

Public Policy (2 of 2)

[ from math-teach @ Math Forum, typos fixed, hyperlinks added ]

On Mon, Mar 15, 2010 at 8:40 AM, Joe Niederberger wrote:

> So, the evidence as it stands, lends (strongly) towards the view
> that addition is basic, multiplication derived. It says you can
> always correctly view it that way if you choose to.
>
> Joe N.
>
> p.s. Pam, this is a bit related to the little intuition you
> sent me in your last email.
>

Somehow I thought we were done with this question.

We don't only care about Real Numbers.

Sometimes, we don't care about Real Numbers at all.

Matrices multiply. Adding them may be pretty worthless.

Vectors add, but don't multiply (with each other), although quaternions do.

We preview these meanings of "multiply" with younger students, not by drilling them in all kinds of arcane algorithms, but by giving them a heads up as to the multiplicity of types in the "math objects zoo".

Your nomenclature may vary, but the basic concepts are as traditional and conservative as you need them to be.

At more advanced levels, it pays to show the family resemblances between the different kinds of addition and multiplication.

At these levels a more abstract algebra approach enters in, and we share about closure, inverse, neutral element (identity element), associativity (matrices are associative, not commutative, w/r to that binary operation we call "multiplication" w/r to them).

Using clever little logic games, encouraging free play and discovery with finite groups is not out of reach. I'm not going to make extravagant claims for their pedagogical value, but nor am I going to sneer and jeer like some know-it-all pundit.

Back to my iconoclastic / radical agenda, here are pictures of a robust classroom-ready 4-frequency tetrahedron made of plastic icosahedra held together by strong springs:

(flextegrity by Sam Lanahan, sculpture by Glenn Stockton)

Of course no classroom has such a thing, as we're looking at a prototype fresh from the factory, woven to suit. With 4-frequency, you first get a nucleus.

The edge and face centers are easy to apprehend. 4-frequency means five members along an edge, plastic icosahedra in this case. So there's a middle one that's easy for students to grasp.

Having something heavy and robust adds measurably to the quality of the kinesthetics upon passing this around -- makes a lasting impression.

This is not salesmanship as I can't offer any for sale. More like advertising my Radical Math agenda, a product I believe in (obviously) and consider open source in large degree i.e. I'm not the gatekeeper (nor bottleneck). The truth is out there.

What might be a real world application for getting into polyhedral numbers ala sphere packing? The tetrahedral numbers? The triangular numbers?

Well, here's a write-up of a recent nanotechnology lecture we got in Portland, Oregon recently, where I think the connections are pretty clear (note Coxeter paper for further reading, if you want to go deeper into this stuff):

http://worldgame.blogspot.com/2010/03/towards-nanoscience.html

Kirby

Public Policy (1 of 2)

[ from math-teach archive, hyperlinks added ]

On Tue, Mar 16, 2010 at 9:52 AM, Joe Niederberger wrote:

> What of old decrepit terms like "imaginary numbers"?
> (Apologies to Euler.)
> Come to think of it, is "complex number" unnecessarily
> frightening our kids?
> Shouldn't some of these be rechristened?
>
> Joe N.
>

I say keep "imaginary numbers" handy (as a synonym) and don't touch "irrational" either.

It's important to our storytelling, our lore, that irrationals were a big challenge for greek philosophers.

Also, having roots of negative numbers was considered radical in its day.

Remember Lewis Carroll and Alice in Wonderland if you ever worry about math being too wild 'n crazy. It's supposed to be a refuge and source of solace for those seeking like-minded Harry Potter types or whatever.

"Do not sanitize if you know what's good for ya" might be the motto, and read Alice in Wonderland and some Wittgenstein while you're at it. Here's a useful crossroads, where these paths meet:

http://coffeeshopsnet.blogspot.com/2009/10/on-wittgensteins-philo.html

Irrational numbers (and hence "the reals" as rationals + irrationals) and imaginary numbers were basic innovations, akin to "tetrahedral mensuration" in their day. As such, they took hundreds of years to percolate outward, to where we're now worried about whether we're frightening little children.

Until we had roots of negative numbers, lots of modeling was out of reach. The polynomials forced us into them, or that's one way to tell the story. We should focus on how we got to them and what they gave us in return (the ability to model electrical phenomena for example).

Given the highly conservative anti-innovation climate we're seeing today (citing this recent post by Gary **), I'm wondering if our age will be known for any risk taking at all. Mostly, people hunkered down and denied that change might be advisable, even necessary.

You actually had people calling themselves "math teachers" who refused to share about Mites, Sytes and Kites! So much elementary math was "verboten" in early 2010. Makes ya wonder what they were thinking (if anything) eh?

Ben Franklin was a radical, and also an "off your duff" mathematician, sitting out there with his kite, waiting for lightning to hit.

That's a role model for children (he took wise precautions remember -- two strings to that kite), so lets make sure Ben Franklin and his kite keep getting some airplay.

I'm encouraged that NCTM has kites as a motif this year, as that's a hook for Alexander Graham Bell and his kites as well.

The NCTM lesson plan on Tetrahedral Kites is a buried gemstone amidst a lotta schlock IMO, as it's daring to question the authority of cubist thinking, even if only just a little. It's a chink (crack) in the armor.

http://illuminations.nctm.org/LessonDetail.aspx?ID=L639

Maybe Texas and Alaska are withholding support because everyone else is such a wuss?

Kirby

** http://mail.geneseo.edu/pipermail/math-thinking-l/2010-March/000659.html

Towards Nanoscience

Dr. Daniel Tomalia regaled us with stories on Thursday night, dwelling especially on his meeting with Linus Pauling, whom he met many years back. Their conversation stretched into the evening, and Dr. Tomalia was left with the distinct impression that he had met a great man.

This story was apropos as the lecture series is named for Linus Pauling and a lot of us meet in his boyhood home. Moreover, Pauling is the only person to have received two unshared Nobel Prizes, the second for peace, and Dr. Tomalia wanted to suggest that nanotechnology might herald an era of disarmament and far less warfaring, as humans learned to do yet more with less.

Next to these hopeful visions were peoples fears, revealed in subsequent Q&A, that nanotechnology would simply widen the gap between the haves and have nots, plus might become weaponized and used to target specific populations (biological warfare in other words). Of course these are key concerns that any serious scientist must address, both in words and with career moves, if seeking to retain the public's trust.

Dr. Tomalia suggests that nanotechnology is just that, a technology. His hope is to move it towards becoming a science by helping with the generalizations, the heuristics. He has a lot of good ideas along those lines, involving classifying components as hard and soft, corresponding roughly to inorganic and organic.

He has approximately six of each type of component. For example, buckminsterfullerene may be used as a hard core for attaching tree-like structures called dendrimers. RNA or DNA he calls S6 (soft six) and occurs naturally in such nano-structures as the viruses. Using this nomenclature, he builds something like a periodic table that is both descriptive and predictive as to chemical properites -- seems a good start.

In terms of synergetic geometry, I could see where control over dendrimer shape and size would correspond to Fuller's sphere packing cartoons. The core information, like a seed, is what governs the shape of the resulting dendrimer, which may be grown outward to various sizes or frequencies.

Shape corresponds to angle, and relates to the formula 2 P FF + 2, where P stands for whatever prime number product and FF (frequency to the second power) corresponds to size or number of layers. In the case of the cuboctahedron or icosahedron (shape), the prime number characteristic is 5. In the case of the cube, 3. In the case of the octahedron, 4. This is a kind of mathematical analogy helping to anchor the heuristics Dr. Tomalia was sharing with us.

1, 12, 42, 92, 162...

I was trudging in the rain from Blue Moon for this one and missed Skip Rung's introduction. Skip heads the ONAMI lab on the Hewlett Packard campus in Corvallis. Our Linus Pauling group went on a field trip there not so long ago. I noticed the Zome tool buckyball building kit.