Wanderers 2006.8.30

We had a lot of heated discussion at the Pauling House this morning, arising from the Sustainability Archetypes book and workshop experience that Milt Markewitz, our presenter, is in the process of writing and designing.

One diagram he uses is an XY grid with Mechanical vs. Organic along X, Malthusian vs. Cornucopian (different from Copernican) along Y. That generates the four quadrants around the origin (++, +-, --, -+ going clockwise, although Milt doesn't use such grade schooler signage, a potential source of unnecessary bias).

I predictably suggested a tetrahedron instead, with all six edge relationships given equal weight. Then I spent some energy oscillating between Power (-+) and Planet (+-), speaking in passionate defense of NavAms (a People ++), which Terry was ragging on as incapable of turning a Profit i.e. creating surplus (the fourth P --), nevermind the casinos (or the airline?).

I say "predictably" because, per this recent post to Synergeo (re hurricane Katrina), we buckaneers are always getting up off the XY plane whenever "four corners" are involved. That's just basic to General Systems Theory (GST).

Milt also shared about the book Finite & Infinite Games by James Carse. In the former (finite games), the purpose is to win, thereby ending the game, whereas in the latter (infinite) it's more about just keeping the game going (which sometimes means changing the rules). The latter encompasses the former, but not vice versa.

Milt told the story of two Cold War powers escalating through the Cuban Missile Crisis, up through the Reagan years, and culminating in Bush Sr.'s visit to Japan for a summit, after the fall of the Berlin Wall (the summit Bush barfed at). How far we'd come, I think was his point.

I followed up with an account of an earlier event, when Eisenhower was all set to talk turkey, after Russia'd been devastated by WWII, and DC held the nuclear card (another "I'm the only superpower" moment i.e. not a level playing field). That time, Russia's "shooting down" of the U2 spy plane derailed the president's bold plans for a lasting world peace (cite Prouty).

David Tver talked about issues confronting Nigeria, and personal choices he's had to make.

Later, I spoke passionately about this "4P" Tetrahedron, saying it's all good (it got us this far didn't it?), and how the naturally evolved integrity of humanity would keep us centered. As individuals, we wander in its phase space, changing character in complement with the environment (including other workshop participants).

Like, if we don't include the Dark Side (Power) consciously, then we'll just end up projecting it unconsciously, like all those Over the Hedge security moms behind keeping the troops in Iraq (a species of "power nester"). Christine found my point "archetypal."

Brian Sharp also joined us this morning, which I was pleased about (he asked about Dawn). We seemed to see eye to eye on a lot of issues this time, including on the vital importance of trusting our intuitions and senses (the wisdom of the body), including our undervalued sense of smell (likewise Nietzsche's focus).

Relevant web sites:
Appreciative Inquiry
Chaordic Commons
Grunch.net
Spirit Mountain Community Fund

More Dimension Talk

Sometimes, in my battles with HyperCross Dogmatists, I get sloppy and say Coxeter draws a sharp distinction between his (Coxeter's) meaning of 'four dimensional' and Relativity's, in his "introduction" to Regular Polytopes.

Actually, he makes this point on page 119:

Little, if anything, is gained by representing the fourth Euclidean dimension as time. In fact, this idea, so attractively developed by H.G. Wells in The Time Machine, has led such authors as J. W. Dunne (An Experiment with Time) into a serious misconception of the theory of Relativity. Minkowski's geometry of space-time is not Euclidean, and consequently has no connection with the present investigation.

H.S.M. Coxeter. Regular Polytopes. Dover Publications, 1973. pg. 119

Although Coxeter warns against attaching any mystical significance to the fourth dimension, in retrospect we see how talk of mortal limitations vs. transcendent superpowers would inspire a religious sense in many physicists and mathematicians:

Only one or two people have ever attained the ability to visualize hyper-solids as simply and naturally as we ordinary mortals visualize solids; but a certain facility in that direction may be acquired by contemplating the analogy between one and two dimensions, then two and three, and so (by a kind of extrapolation) three to four. (Ibid, pg. 119).

He footnotes Abbott's Flatland at this point, helping to feed a meme complex which persists to this day, e.g. in this film What the Bleep: Down the Rabbit Hole. In a rush to "be the next Einstein" (not a bad role model mind you) generations of science fiction reader have strived to join the shamanic inner circle of those chosen few able to view the HyperCross directly.

What I've tried to make clear over the years is that R. Buckminster Fuller was not on the HyperCross bandwagon, and although he used the 4D meme, he had his own meaning and namespace for it.

Given a next generation of philosophy student tackling Synergetics as a primary work (one among many), I feel it's important to point out these potentially tricky and confusing name collisions. Partly why I've been developing the notion of "namespace" with some rigor (with inspiration from Python especially) is to help keep our B2B and B2C channels clear.

Like, you maybe wouldn't want to do business with me if you thought I was just another garden variety hypercrosser (they don't make many like H.S.M. Coxeter these days, the Geometer to whom Synergetics is dedicated).

Related readings by me:
The Matrix
4D++
Another Wittgenstein Essay
HyperCross Dogmatics

"Namespaces are one honking great idea -- let's do more of those!"
-- from import this in Python.

Archived Political Cartoon (May, 1998)

technogeeks of the world unite!

(click for larger view)

Hexapent Family Tree

drawing by K. Urner
(rolling writer on 8.5 x 11" white)
click for larger view

Background reading:

Geometry and GIS (thread @ Math Forum)
Correcting a mistake (thread @ Math Forum)
Packinon (geodesics & classes)
Darwin @ Home (elastic interval geometry)
Other hexapent links: [1][2][3][4]

More Cast

Another strong writer I've collaborated with over the years is Gene Fowler, of which you'll find several, but this Gene wrote Waking the Poet, and corresponded with Bucky over the years, and with his myriad progeny.

Gene thinks in terms of Amerish, a science fiction name for a language we're going into, as speakers of American English. Co-modeling and sys-talk figure in to his version, which I've scanned at some length.

Plus he taught himself Delphi (Borland's OOized Pascal) and XML, all so he could express his vision in eWriter. Not bad for a self taught old guy who'd done some hard time on the inside (not the only Fuller Schooler to have done so).

Gene's vision with eWriter is that we should keep XML in the conscious forefront, the way we do punctuation. Sure, we stop thinking about punctuation as much, after we learn it, but it's still the writer's responsibility to manage it.

Gene wants to enlarge our notion of Amerish grammar, by adding XML into its native machinery, one might say.

But as I understand it, this would not necessarily mean our eyeballing XHTML all day long. We already know that if the markup is for style, then its point is to remain hidden in the final viewing.

The writer/author knows that it's there, as do the viewers, but as when watching a stage play, your mind shouldn't be with the props and lighting the whole time (not if you're there to be enthralled).

I think this Google Blogspot interface is actually a good example of what Gene was talking about: as a blogger, I'm mostly using a WYSIWYG (wizzy-wig) browser-embedded text editing tool, but if I click on Edit Html, I'm able to mess with the markup (reminds me of WordPerfect's "reveal codes").

As an Amerish speaker, I'm not dismayed that my responsibilities have increased. It's a small price to pay to engage in a shared space of world-readable files, all interconnecting everywhichway in a great global matrix, and in so many intelligent languages!

Related reading: in a gnu math thread @ Math Forum (Aug 20, 2006)

Project Earthala

Aimeé Ford Conner gave me the Earthala meme. Project Earthala is one of those high tech ecovillage communities we wonder if we'll ever live to see, even if only on reality TV.

I'd make mine a by-invitation sanctuary for weary travelers I've met along the way (Aimeé and Peter included). It's not like you have to live there permanently -- but some would want to.

We'd have TV-out, i.e. you could subscribe to our shows, already edited for content. Journalists might be invited to give alternative inside scoops, or sneak in or whatever.

Anyway, you know if there's a "mine" there'll be a lot of "not mines" -- so you needn't worry if my Project Earthala isn't on your itinerary. You'll have other stops in other villages, just as fun and good.

Bee Season (movie review)

A talented family with all its physical needs met, freely explores metaphysical issues.

These don't seem the happiest people in the world, but hey, karma is like that (lots to work through, and moving too quickly may be dangerous).

Each cast member takes a few steps along an inward/outward journey.

I wish more families were free to work out at this level, instead of spending so much time scrabbling for food, water and shelter. Moving too slowly may likewise be dangerous.

On the Waterfront

facing the hawthorne

notice of party

context of notice (taped to hull)

photos by K. Urner

HexaPent Housing

Trevor forwarded this link to my del.icio.us inbox.

People with claustrophobia wouldn't want time in these, even with flatscreens showing World Cup action.

But as working prototypes, they fit well in a Bucky Works context.

We need more low impact dwelling machines or "pods" with "feet" -- some models helicopter deliverable, and some to work around oil fields in the Alaskan tundra.

Eternal War of Incommensurability

A Math World
(click for larger view)

Although I maybe wasn't thinking this when I drew the above, the two Kingdoms depicted could as well be the two Kingdoms described below. See: Synergetics 987.044 & neighborhood, plus Incommensurable Icosahedra from my ISSN: 1059-1486.

Original context of the drawing: Boosting Bandwidth.

Memo to Wanderers

Posted to the wwwanderers.org Yahoo eGroup (added some HTML):

---

Received: by 10.78.165.13 with SMTP id n13mr1980834hue;
Sat, 05 Aug 2006 13:58:53 -0700 (PDT)
Date: Sat, 5 Aug 2006 13:58:53 -0700
To: wwwanderers@yahoogroups.com
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
From: "kirby urner"

RE:

Dieter Kotschick
The Topology and Combinatorics of Soccer Balls (American Scientist, Volume 94, pg. 350 -- July-August of this year).

Glenn Stockton's name appears in Math Forum in connection with his gifting me a photocopy of the cited article @ Pauling House (Wanderers' Meeting), followed by a quick recap of its contents FYI:

http://mathforum.org/kb/message.jspa?messageID=4988588&tstart=0

Having finally seen Da Vinci Code for the first time last night (read book a long time ago) I was surprised at how little it did to exploit a rich set of geometric relationships. Fibonaccis were not tied to Phi very clearly, despite Pentacle.

Of course for a non-specialist audience, there's only so much you want to get into.

A mental schema I use:

Kingdom A:
Periodic Crystal Lattices:
Sphere packing schemes: SCP, BCC, CCP
Rhombic Dodecahedron, octet truss (A.G. Bell's "kites")
http://worldgame.blogspot.com/2006/07/math-they-wont-teach-you.html

Kingdom B:
Aperiodic Lattices & Five-Fold Symmetry:
Icosahedron, Pentagonal Dodecahedron, Hexapents
Penrose tiles
http://www.4dsolutions.net/ocn/hexapent.html

In Fuller's scheme, these two neighboring Kingdoms are bridged by the so-called Jitterbug Transformation, which transformation I would expect to incorporate into some of our archived mathcasts (re: Math Casting see: http://mathforum.org/kb/thread.jspa?threadID=1425804&tstart=0 and of course my ToonTown proposal for PDX, a potential source for such vidclips).

Kirby

Looking Back

high level management dance

something I own?

photos by K. Urner, February 2006

Big Map

photo by Kurt Przybilla
23 Jul 2006
Asheville, North Carolina

Advice to Synergetics Teachers

I find one of the first things I need to get into, when lecturing on the Concentric Hierarchy (a semi-regular gig), is the Synergetics Constant thread.

Amateur mathematicians are disbelieving that a cube of edges sqrt(2) could possibly have a volume 3, as their mental model of powering is entirely cube-based. The pro mathemeticians understand the possibility of an alternative model, but Fuller's is alien and they have better things to study.

So Fuller has readers go through this whole exercise of looking at growing/shrinking tetrahedra, then triangles, to see how the 3rd and 2nd powering relationship (vis-a-vis a changing scale factor, applied to edges) doesn't change. Double the edges, eight-fold the volume, just like before.

Likewise, the Pythagorean Theorem admits to more than the standard square + square = square interpretation. That could be any shape (say a silhouette of Pythagoras [1]), as long as the proportions are properly metered (the shapes are all similar, such that shape + shape = shape).

Once we've been through this, and people realize the cube thing is cultural, it becomes a lot easier to dissect said volume-3 cube into a tetrahedron (either one) and its four 1/8th octas. Said tet = 1, so the remaining 2 (1+2=3), distribute among four 1/2 volumes, 8 of which give the volume- 4 octahedron and so on.

Then its long and short diagonals on the volume 6 dodeca and we're almost done. 12-around-1 for the volume 20 cubocta, embraced by the 2-frequency cube (x8 the original 3 volume = 24), and the jitterbug, to capture the five-folders (pentagonal dodeca, icosa, and rhombic triaconta mainly).

With that out of the way (the concentric hierarchy, which bow-ties in two Universes (positive and negative)), we get to the next standard objection: "but so many polyhedra are left out of account! What about all the Archimedeans, the zonohedra, the this that and the other?"

I have two answers for that:

(1) no one is stopping anyone from expressing Archimedeans in terms of A & B modules, E modules or whatever, or inventing modules of their own. Yasushi Kajikawa did some of the most important and pioneering work in this domain (published in the Japanese edition of Scientific American), before moving on to disaster relief shelter solutions (his focus at the SNEC summit @ Russell's in DC). Plus David Koski pioneered recursive self-construction of the T-mod (Ed forwarded his stuff to Stanford).[2]

(2) Second answer: Bucky's Synergetics is not intended as some comprehensive survey of all matters geometric. He salutes Coxeter, yes, as the paradigm geometer of our age, then dives head first into philosophical system-building, more in the tradition of Hegel and Kant (plus I apply my signature post-linguistic-turn Wittgensteinian spin). Don't think of Synergetics as a math book at all, and you'll be miles ahead of your peers, still struggling with a lot of misleading imagery.

So, to recap: explain how "the cube is cultural" to keep your momentum through the concentric hierarchy, which is conceptually satisfying once gotten (keeps your audience with you, even if skeptical), then handle the objection that Synergetics is neither comprehensive of geometry as a whole, nor finished in terms of what we might do with it (duh).

To help free their heads from musty and mystifying math associations, remind them it's really literature in some philosophical domain (note the citation to Plato) -- or do what I do and classify it as American Transcendentalism, a product of the 1970s Renaissance, a lot fed by the Apollo Project. Comparison to Poe's Eureka are more than apt, as E.J. Applewhite signified in his last public address (2004 Bucky Symposium @ GWU).[3]

Also, try to remain cool-headed and don't launch into any diatribes about how anyone calling themselves a "math teacher" should already know all this by now, as Fuller's early synergetics constant stuff was published circa 1950. Statistically speaking, it's less and less likely that your audience will have overlapped Bucky in any lifetime scenario sense, many of them having been born since the 1980s. Go with the Universe you're given, not the one you wish we'd had. Accept reality (even if it is only special case).

---

Notes:

[1] I saw this bust-of-Pythagoras demo @ OMSI one time (our local science museum, back when it was still adjacent the Zoo), plus similar teachings on the walls of Winterhaven (not my doing), a local public school and technology magnet (somewhat different spin than Benson's, also for techies).


[2] "Playing with Blocks"

[3] Ed @ GWU

More on the synergetics constant (3rd powering thereof)