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.

Radical Math

:: radical math @ flip side ::

Glenn Stockton and I were glad to jump into this event and give a free class on Radical Math.

This was an organizational meeting, as well as an opportunity to have classes. Marc is moving to Santa Cruz, having organized for Portland Free School for quite awhile. He was passing the torch.

I did a rather serious amount of writing building up to this event, posting mostly to Synergeo.

Radical Math, which uses a "backwards R" under a radical sign for a logo, is a developing curriculum that includes Fuller's concentric hierarchy. I call this piece Verboten Math because you'll find a lot of teachers avoid including it, despite Fuller's stellar and decorated career.

A lot of high hopes for humanity's future were wrapped up with these rather basic and primitive innovations, some of them pedagogical in nature. This heritage is being squandered, and it's radical to point this out.

I did my usual demo, pouring beans from one shape to another. Crystal, a new blog character as of this post, sometimes collects audio recordings for KBOO, only some of which make it on the air of course. She climbed a ladder and hung a recording device over our meeting table.

Glenn and I were consistent in emphasizing nature's 60-degree coordination in contrast to humanity's investment in 90-degrees as "normal" (orthogonal, orthodox). Our presentation was not too abstruse or esoteric. Anyone present could become a Radical Math teacher pretty easily. That so few dare to share Verboten Math is one of my chief concerns these days.

Dr. Nick joined us towards the middle of our class. He's a house guest in our "radical household" these days (one of the top five in the country). He mostly sat quietly.

Sister Walker, another member of our household, organized this event and anchored a class on event organizing. Appropriately, she wailed on the Flip Side Studio piano as a part of her presentation, as events she organizes typically include opportunities to share her music. She actively participated in the math class, drawing a benzene ring on the chalkboard while talking about chemical building blocks up through proteins, sounding somewhat like Dr. Tomalia.

Ali gave a class on Food Politics, which included a dissection of the Grunch. I might write more on that later.

I hadn't met Marc before. We exchanged some resources.

Crystal, who kicked around Eastern Europe for ten years, took a break to visit said radical household (within walking distance) and let me copy a few pix off her memory card (mostly of me and Glenn). We made it back to Flip Side in time for the final torch passing.

Carol Urner, who complements our radical household some months in the year, is on another east coast adventure. Per a recent voice-mail, her flight into DC had been canceled, she was in line with US Air at the Philadelphia airport. She'd just been through there for an AFSC board meeting.

Two Track Solution

The need to learn calculus to attract the attention of technical job recruiters proves a real bummer to many students.

The plan to develop a parallel track has encountered a serious obstacle however: the ongoing feud between imperative and lambda calculus programmers.

The debate is too abstruse to register in most magazines and journals directed at a popular audience, however administrators and would-be funding sources pick up on the negative vibe, the sense of an altercation, and withhold the necessary energy investments.

We all suffer as a result.

In the old days, when a metaphysical blood clot of this magnitude developed so close to the heart, you'd have teams of philosophers, well-read across disciplines, descending upon the scene and insisting that common ground be discovered, that the logjam be removed.

These days, however, the fact that Leibniz dreamed of computer programming languages is mostly forgotten, and academic philosophers get away with not caring about anything so central to computer science. Their favorite flavors of logic miss that boat entirely.

My frustration level is high on this score, as my "freedom train" of polyhedra, including the volume six rhombic dodecahedron, was supposed to run along this track, blessing it with our concentric hierarchy of core relevance, our signature matrix, our geometrical relationships bonanza.

Should we implement polyhedra as objects? Might we use Python? The functional programmers cry foul. The necessary reforms do not occur. Another day goes by when we could have been investing instead of squandering. The clock keeps ticking, the meter keeps running, as our shared heritage is withheld. What's dammed here is not just technical content, but lore.

Or would a simple turtle, drawing a plane-net for the T-module maybe be OK? What do the philosophers say? Do they say anything? Is there a philosopher in the house?

Morning Meetings

US C-17 emergency airdrop in Haiti, 18 Jan 2010. via Wikipedia.

Aimee has returned from her workshop for air disaster victims in San Francisco, mostly relatives of loved ones. She was one of only three who had actually lived through a plane crash.

She took the Coast Starlight to get there and back (it was on time both ways). United Airlines sponsored her trip, recognizing its healing potential.

We went out for coffee at Peet's at the corner of 37th and Hawthorne.

The 911 group is not harboring hostility towards any general population, realizes these were extremist fanatics, hell bent on wreaking as much havoc as possible.

The TWA 800 group remains sure this was a friendly fire incident, a missile that got away during a training exercise. Many expect the truth will eventually come out.

Aimee's plane went down on a busy street in East Portland. Many escaped the fuselage upon landing yet were killed when one of the engines exploded.

Glenn joined me for coffee next.

His mind has been affected (in a good way) by all that Flextegrity experience. He's persuaded that hands-on is the only way to go, when it comes to fathoming its potentials, so where to order some?

My posting to the Math Forum regarding tetrahedral calibration is crystal clear, mathematically secure, and philosophically mature. So what though, right? The Necklace Effect would have been more pronounced if we'd had that super bowl commercial.

My thanks to Trevor for the highly topical look at Geodesic Domes and Earthquakes. Various media will develop more stories in this direction, as a reminder of neglected heritage that might prove relevant going forward. Other media prefer we'd forget.

I'm meeting with Patrick this afternoon, regarding matters educational.

I posted a quick FYI to math-thinking-l regarding our off-list Elluminate session.