MY PHILOSOPHICAL STUDIES I entered Princeton with a full head of steam, having developed strong reading habits at the International School in the Philippines. Isaac Asimov was a big influence, first his fiction, then his non-fiction. I also liked reading philosophy books, though I was unaware of Wittgenstein's stuff. I lot happened at Princeton of course, in my four years there. I was drawn to International Relations and applied to the Woodrow Wilson School, but in my interview I was pretty clear that I felt drawn to philosophy, to Wittgenstein's especially, and that's what I ended up doing, writing my thesis on 'Philosophical Investigations' (even for a BA, we needed to write a thesis). Richard Rorty was one of my thesis advisers. Walter Kaufman was a big name teacher at Princeton at the time and I took more than one of his classes. He was influential in my decision to check out this training for "est people" he'd written about in one of his books, and shared about during one of his open house sessions for students in his class (Princeton is very good about giving undergrads access to professors, one of its chief claims to fame -- we also met during office hours). This science fiction book about "est people" only came to my attention later, and I haven't read it yet even to this day, but in any case it was through participating with this 1970s-1980s philosophical lecture series (including seminars) that I became aware of Bucky Fuller and his network of people. FULLER'S PHILOSOPHY Fuller had a hopeful vision of the future and that in itself was appealing. Princeton hadn't instilled me with lots of hope. Having grown up overseas, amidst poverty, in a family working hard to improve the world, and now living in poverty in the USA, I was attracted to Fuller's brand of positive futurism, which claimed to be based on existing human capabilities, was not about changing human nature. For many decades, Fuller sat on some big philosophy he was going to publish someday. People who worked with him or took the time to track down a manuscript, would get a preview of what it was about. For example, Robert Williams got to see a 1960 manuscript version at the Washington University in St. Louis, Mo. and cites it on page 136 of his magnum opus 'The Geometrical Foundation of Natural Structure, A Source Book of Design' (1972, 1979), one of the best Dover books ever. That big philosophy finally made its debut in 1975 around the time I was entering Princeton. I don't recall hearing any news of it from within the department though. Fuller was the dome guy, some kind of architect and engineer, not the next Quine or Kripke. There would be no discussion of Fuller's contribution in the philosophical journals. His 'Operating Manual for Spaceship Earth' showed up on my international studies syllabus, but under optional reading (I forget if I got to it then, did later). Undeterred by this lack of preparation, I took the train into Manhattan from my Jersey City abode, where I was starting out post Princeton as a high school math teacher, and purchased the first of the two volumes, or maybe I bought them both at that time, I don't remember. Macmillan was right downtown and had these hard-to-find tomes. Arthur C. Clarke, former UN Secretary U Thant and some others were on the dust jacket, endorsing this as an important work. Fuller's chief collaborator, though not the source of the drawings, was one E. J. Applewhite, advertised as some formerly high level CIA guy. An intriguing package. Coming from Princeton philosophy, you could see where I might be curious to scope it out. These were difficult books. Fuller was consciously inventing his own philosophical language. All the metaphors would be geometric. He said he was out to bridge the C.P. Snow chasm between the 99% of humans who don't digest arcane math notations, and the 1% who do. His bridge would be this new kind of language, starkly geometric yet about truth, beauty, love, as well as about engineering topics, concepts we would need to stay warm, healthy and dry, even should a next ice age occur (geodesic domes, cloud nines...). The mix of philosophy, math and engineering was eclectic and off-the-charts different from anything I'd seen at Princeton, even with all that poking around in Firestone Library. Even Heidegger seemed easy to read by comparison. TETRAHEDRAL MENSURATION One piece of Synergetics that's fairly easy to distill and render concrete, is the part about tetrahedral mensuration, i.e. using the tetrahedron, instead of the hexahedron (cube) as a unit of volume, seeing where that goes. As a high school math teacher, I could appreciate what he was saying. No one had told me about space-filling rhombic dodecahedra in high school, so important to Kepler. The octet truss, geodesic dome, polyhedra in general, all were more available and accessible to me thanks to Fuller's explications. I could use this with my students. I could have lots more volumes / shapes stay friendly whole-number. Surely this aspect of his philosophy would spread and catch on, even if a lot of the more speculative stuff fell by the wayside? INITIAL CONTACT WITH FULLER I gradually got to know more of Fuller's network and also communicated with Fuller himself. I sent him a paper on General Systems Theory (GST), which sounds really dry, but it was more a poetic work, weaving in my mother's work with the Zabaleen, a Coptic Christian group living in rock quarries in south Cairo and doing the city's recycling as a way of feeding its pigs. I wrote the paper in Cairo in 1982 I think it was, and expect its in the Stanford Archive, as I know Bonnie said she'd found it when those papers were still with the Buckminster Fuller Institute in LA. Fuller wrote back on his fancy letterhead to say it was excellent. We later crossed paths at Hunter College in New York, where I believe a videotape was made. Through my connecting with Fuller, I got to meet and become friends with Kenneth Snelson, E.J. Applewhite, his daughter Allegra and many others. By this time, in 2010, I am one of the people who knows the most about Fuller's philosophy. Maybe that's a conflict of interest when it comes to writing for Wikipedia, but then you want writers who know their subject matter, so not so long ago I jumped in to lend a hand, turning what was marked as a stub page into something more substantive. I didn't start the page and only did some of the writing for it -- some of the most technical parts, having to do with tetrahedral mensuration. CAMPAIGNING FOR MATH REFORMS Back in the 1990s, I started writing to the National Council of Teachers of Mathematics, asking about phasing in this tetrahedral mensuration business, taking it seriously. I pointed out that the NCTM logo was pretty much a 2-Frequency tetrahedron, i.e. it would be easy to use the logo itself as leverage, to tie in to these concepts. What happened shortly thereafter is the NCTM decided it needed to change its logo. Were they worried about getting swept up in some tetrahedral nonsense? Were they afraid of some cult? est people? Fast forward to the present day, and you will find a buried lesson plan on the NCTM Illuminate site where tetrahedral mensuration is discussed. There's nothing mathematically incorrect about taking the topologically simpler tetrahedron and making that a unit of volume. The fact that this streamlines other volumes, lets you develop some mental geometry for thinking more like a chemist or engineer, is not capitalized upon. The "Tetrahedral Kite" this lesson plan builds is not explicitly associated with the octet truss, called a "kite" by Alexander Graham Bell, who devoted much of his energy and fortune to its study in the early 1900s (long before Fuller got to it). The octet truss, or tetrahedron-octahedron truss, is prevalent in modern architecture. In chemistry, it is known as the FCC and/or CCP lattice and is associated with closest packing of spheres, a core topic in 1900s mathematics. CONNECTING TO WITTGENSTEIN What does any of this have to do with Wittgenstein? We know Wittgenstein was somewhat engineeringly minded, so that might be a connection. Bucky and Ludwig also shared a desire to participate in the rough and tumble world outside the Ivory Tower, so that would be another commonality. But I think it's the idea of gestalt switches, and meaning as use that will glue these philosophies together. Fuller used his words differently, yet consistently, according to rules, and so provides us with a golden opportunity to introduce a clear example of how philosophy works. Reading some Wittgenstein will be a good on-ramp. We might also read some Norman O. Brown, Hugh Kenner etc. The college version is taking shape. I've also discussed the fact that H.S.M. Coxeter, to whom Fuller dedicated his two volume philosophy, was a student of Wittgenstein's during the Blue Book chapter. Coxeter was somewhat impatient with philosophies, both Wittgenstein's and Fuller's. Sometimes a namespace may be a proper name (linking to Sean's investigations), and symbolizes a domain, a body of writing, where a word gets its meaning or spin. MEANING AS USE: 4D IN THREE DOMAINS To take a concrete example which I've written about quite a bit already, including on this list, we have the concept of "dimension" in mathematics. There's no one single meaning for that term. You need a context. Around the turn of the last century, the Zeitgeist was such that people wondered about "the fourth dimension" a lot. What could that mean? Many writers we're putting out meanings around 4D, including P.D. Ouspensky, Claude Bragdon, Albert Einstein and many others. Over the course of the 20th Century, I'd say three principal meanings for 4D have developed, each of which may be associated with a proper name. How I've distilled it is as follows: Coxeter.4D Einstein.4D Fuller.4D Within each prefix-domain you'll find a characteristic meaning (use) of the 4D meme (concept). These are not all equivalent and there's no need for some "grand unification" any more than we need to "unify" checkers with chess. I will briefly describe these three meanings and then end this autobiographical account, perhaps to be continued at a later date (I will also add some end- notes, just in case anyone wants to keep exploring). 4D vs 4D vs 4D Coxeter.4D refers to a fourth orthogonal in a linearly independent set of basis vectors, all equally spatial. You may add as many such orthogonals as you like and you'll find a consistent mathematics at each of these dimension levels. Concepts analogous to spheres, touching or not touching, a definite distance between their centers, have mathematical meaning. The equivalent of a regular polyhedron in these higher dimensions is called a polytope and Coxeter's book "Regular Polytopes" is about the language games needed to structure this domain (namespace). Of course many other authors have contributed to this branch of mathematics besides Coxeter. We're talking about one of the great "cathedrals" (colla- borative works) of 20th century mathematicians. Einstein.4D refers to a fourth axis known as time, although once the theory of relativity is more developed, we find time and space mixing together with the concept of "interval" taking over as the chief metric. Depending on your home base coordinate system, you may see an interval as more time-like or more space-like. The algorithms and algebra are different from that of the polytopes. This is more of a physical theory than a purely metaphysical and/or abstract one. On page 119 of his 'Regular Polytopes', Donald Coxeter points out that science fiction writers sometimes get confused and think his use of 4D has something to do with time travel. To put it another way, to confuse time machines with tesseracts is to confuse Einstein.4D with Coxeter.4D. These are not the same domain. The rules are different, the game is different. Fuller.4D refers to the four spatial axes of the tetrahedron, which need not be seen as independent of one another in the sense that we always have this minimum "lump" or "piece of clay" to start with. In a language game involving wire frames, edges and nodes, we find the that the simplest topological network dividing an inside concavity from an outside convexity is this shape we call a tetrahedron or simplex. Its primitive fourness, in terms of points and/or faces, earns it this characterization of being a 4D object. To add time and/or mass, velocity, energy, is to add additional dimensions. How many we have or need in total is not set in stone, but at the minimal end of the spectrum, where we have as few dimensions as possible, we get down to this meaning of 4D, a kind of Cartesian concept of Res Extensa, akin to 3D except we've dispensed with the notion that adding perpendiculars constitutes anything so special. 90 degree angles are less a priori a point of fascination in this namespace (domain). Again, there's no suggestion here that its important to conflate these domains into a single one. This is not a picture of "warring kingdoms" either. Rather, we have these three sandcastles on the beach, all engaged in peaceful trade with one another. I call this 4D vs 4D vs 4D, but my "vs" is not meant to imply antagonism, merely contrast. "If you don't keep your language games separate, you'll just get confused" is another way of describing my motivation for deploying this "dot notation" (prefix dot attribute, e.g. Coxeter dot 4D). OK, that's enough of a slog for one sitting. Thank you for reading, if you got this far. I'll conclude with some provocative questions. Kirby End Notes: World Game Of key interest to Fuller was the global electrical grid, which started out as a patch work of disconnected grids that, over time, have become more and more integrated, what with longer line transmissions, improvements in conductivity. He felt it was high time to start work on an electrical hookup across the Bering Strait with would eventually connect Portland to points in the eastern hemisphere, although in terms of load balancing this might just mean Portland feeding Alaska at a time when the eastern grid was too busy to feed Alaska. Come nightfall though, and the drop in demand, you get these hemispheric economies of scale, such that unused capacity might be shunted across hemispheres. This idea has made enough engineering sense to keep simmering beneath the surface and when John McCain chose a Governor of Alaska as a running mate, this story had every potential to become national news. That might have been inconvenient for some editors, not wishing to open this "can of worms" (their view of it). The Bridge to Nowhere appeared as something to ridicule and despise, thereby keeping the relatively simple idea of an undersea cable from getting too much press. The idea continues to be debated in esoteric circles, including at the Linus Pauling Campus in Portland, Oregon, where we're well aware of the plan. Or see geni.org. GST General Systems Theory has gone through a lot of incarnations, was already a topic before I started contributing. When I started developing it, I wanted to be sure that we at least got the energy relationship with our Sun in the picture. Economics is sometimes confused about whether Earth is an open or closed system, thermodynamically speaking, whereas the answer is "wide open". The relationship of the Earth to the Sun is akin to that of a nonprofit agency (say a global university) getting a steady grant income. The Earthian biosphere radiates most of the money away (gets more than it might use) and is in no position to "repay" the Sun, let alone with interest. If one doesn't understand these basic facts of life, one doesn't understand GST. I call this energy "money" because it fuels the carbon cycle whereby we get exponential replication of biomass, that which we call life, also food, on Planet Earth. Having something edible for currency is not atypical in economics, and yes, money *does* grow on trees in this sense (coconuts etc.). Many authors continue contributing to GST to this day. Google it up in Washington Post maybe? INCONVENIENT TRUTHS These two threads, World Game + GST, account for some of the continued interest Fuller's philosophy receives. His work has been on display in a traveling exhibit, hitting some of the better art museums (Noguchi, Whitney, Museum of Art in Chicago...). The play about his philosophy is opening in Washington DC in June, having receiving many rave reviews in Portland in 2008 (I gave the IEEE lecture on election night, at Portland Center Stage). Were tetrahedral mensuration to gain ground in 10th grade geometry teaching, there's a danger of spill-over, i.e. students finding out about Fuller and his more hopeful positive futurism, his geodesic domes, Old Man River City, Cloud Nines etc. They (or their parents) might ask why it has taken more than 30 years for NCTM to have a lesson plan on Tetrahedral Kites using what it calls "non-traditional volumes" or why no mass published high school geometry textbook to this day mentions anything about a tetrahedral unit volume, and how this has already been developed. Fuller thought more focus on the tetrahedron was critical to humanity's survival, as too many would tune out science and math unless given these conceptual advantages. We might fall below a critical intelligence level and blow ourselves up because not enough people understood our option to provide for ourselves. People would feel too helpless and powerless because too over-specialized, too paralyzed with ignorance, too in the dark about everything. How to counter? World Game, with more global data (like Google Earth) and more attention to spatial geometry (like on television) would need to kick in. Perhaps we've only made it to 2010, because we've been countering like hell? Now we need to pass the torch, by reaching out to 10th graders. Lets talk about those kites. Our students might ask why a guy who made the cover of TIME, had numerous patents, awards and freely given PhDs from prestigious universities (not Internet degree mills), would today be marginalized as a kook, nutjob, crackpot etc. -- or simply forgotten i.e. what's the agenda at work here? Was it that he dared question the dogma of corporate personhood, was one of the first authors to do so? Ronald Reagan gave him a Medal of Freedom after that. Do we teach that in schools? And if we're dealing with a real, bona fide philosophy here, then why aren't we learning about it in our college courses? How does buckminsterfullerene fit into all this? All good questions for the philosophy professors I'm thinking. Stay tuned. ========================================== Need Something? Check here: http://ludwig.squarespace.com/wittrslinks/