Probably a main reason I spend a lot of time trying to breathe some life into forgotten history, is I want to revive the idea of an attainable sustainable future. I’m no longer a young man, so this can’t be about me personally as much, although I do have a stake in the outcome. Yet I find myself driven to “keep the memes alive”.

The forgotten history is like a fading memory of a whole civilization, the one we might have built, the subjunctive future. My dad subscribed to The Futurist, a magazine, and I absorbed the notion that the future is something we plan for. Dad planned for a living.

After graduating from Princeton, having focused on philosophy, I was less sure how to implement any plans. I taught high school full time, in Jersey City. Some nights I would take the PATH train from Journal Square to Manhattan and participate in Area Center programs.

The Centers Network, as it was called, had a future facing orientation. Journalists claimed it was a cult. Maybe it was. Neil Mahoney, one of the est Trainers (right, same thing), said “cult” meant “large Irish family”.

I’d found out about est from Walter Kaufmann, then a professor of philosophy at Princeton with a lot of name recognition, and then got into conversations with David Raymond, a Princeton local, about enrolling in Werner Erhard’s program.

By the time I moved to Jersey City, with a group of friends, to share a group house, I was already volunteering around the trainings and seminars. I’d learned a lot about the adult world I was entering, as people tended to share from the heart during these meetings.

Erhard himself had discovered Richard Buckminster Fuller and made him a role model. Here’s someone who thinks for himself and fights for a better future for all humans. This is what an evolved human being looks like.

Fuller had also written a two volume philosophy called Synergetics which I now felt compelled to take a look at. What did Fuller think “success for humanity” might look like?

Jumping back to 8th grade, my last year in Rome, Italy, I recall how the future was perceived as dark. Are we Living in the Golden Age? asked the cover of The Futurist. That issue was about the Club of Rome, a computer modeling group trying to develop coherent models of the whole world, with predictive powers.

The general tone in those days, like today, was pretty dire. Overpopulation, war, pollution, dwindling food supplies, famine… not a pretty picture and we were advised to prepare ourselves for the coming crunch. Has our shared vision of the future gotten any brighter?

Fuller was one of the few voices predicting possibly positive outcomes, but these were often based on sharing certain insights that apparently few but Fuller had yet had. Those already committed to a more dystopian scenario could accuse Fuller of trying to become a cult leader, or even worse, a messiah.

“The guy was a megalomaniac” some concluded, even if he didn’t necessarily come across that way in person. Others called him a “gentle genius” or even “engineer saint”. However, in 8th grade, I had only barely tuned in Fuller, let alone all the cynicism that surrounded him.

By the time I was through Princeton, my outlook was different. I’d taken courses at the Woodrow Wilson School called Problems of World Hunger, and here Erhard was forming his Hunger Project aimed at ending starvation as a leading cause of death around the world by the year 2000. Buckminster Fuller was on the board.

I was teaching high school mathematics in the Catholic high school, and starting to study Synergetics, along with other books the guy had written.

Given this juxtaposition of facts and events, it’s not surprising that I tried to extract from Synergetics what might make sense at a high school level. How might this philosophy impact my math teaching?

However, I also found myself going back to my readings at the university, in philosophy. What would teaching about Synergetics look like in a university context. On what syllabus? In which department? Should it be seen as American Literature? Applewhite considered it in the same lineage and Edgar Allan Poe’s Eureka!

At it’s most elementary, Synergetics is about the behaviors of wholes being unpredictable based on the behavior of parts alone. More than that, it’s about showing how Fuller’s private (proprietary?) language, meshed with the world.

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Like Neoplatonist philosophy, or even Euclidean philosophy, Synergetics is deeply invested in polyhedrons and geometry. The book is dedicated to H.S.M. Coveter, a geometrician based at the University of Toronto.

Fuller thought one of his core breakthroughs was to organize some simple polyhedrons into a concentric arrangement. They nest inside one another, sharing vertices. The face diagonals will be important, especially the cube’s, as its face diagonals define two mutually intersecting tetrahedrons.

Geometers through the ages have developed this concept of “dual”. The dual of a polyhedron is another polyhedron with the same number of edges, but the the number of vertexes and faces switched.

For an icosahedron, with twelve vertexes and twenty faces, the dual is the pentagonal dodecahedron, with twenty vertexes and twelve faces. Given V + F = E + 2, both have thirty edges.

None of this was new or original with Fuller. The formula V + F = E + 2 went back to Euler, and maybe Descartes, who encrypted it in fear of upsetting his contemporaries with knowledge not recognized as such by church authorities.

What was new in Synergetics was the emphasis on the tetrahedron in particular as somehow the most primitive of the Platonics. It has the fewest edges. Could we make up a whole number system wherein a tetrahedron of edges one, has a volume of one as well?

That proposal would seem to go against conventions in a big way. For one thing, the cube inscribing such a tetrahedron of edges one, would have edges half the square root of two.

But then we know from other theorems its volume would be thrice that of the tetrahedron’s. If so, then the cube’s edges must be cube root of three, by definition, not square root of two over two. A contradiction!

Here is where Fuller introduced a new wrinkle. Suppose we changed our model of multiplication such that 3 x 3 = 9 would be accompanied not by picture of a square of edges three, with an area of nine, but with a triangle of edges three and an area of nine? 3 x 3 x 3 would be a tetrahedron of volume twenty seven. Or geometric model of third powering is thereby changed.

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multiplying two numbers, 4 and 3, to get their product (green area), 12 units

A happy result of this innovation, is we indeed may work with a unit volume tetrahedron, of simple edge length, and a corresponding cube of volume three. The cube’s dual, the octahedron, sized to intersect at mid-edges, has volume four and complements the tetrahedron in filling space without gaps. The octahedron and cube combined, as duals of one another, nets another shape, the rhombic dodecahedron, of volume six. It appears we’re off to the races.

concentric hierarchy

With these few facts, and one core innovation, we get two outcomes: a way of sharing about polyhedrons in the early grades; a conversation in the philosophy of mathematics about changing meanings, such as the meaning of “third powering”. Both outcomes tie back to a larger body of writings containing upbeat messages about the future. Population will level off with higher living standards and more security for one’s few children. We’ve learned how to do a lot more with a lot less. Perhaps life on Planet Earth might get better.

However, in Operating Manual for Spaceship Earth, Fuller paints a picture of how things became so dire in the first place, and a lot of his story has to do with generalists, the bigger picture comprehensivists, needing to ward off challengers, and doing so by having them specialize.

What happened next was the “great pirate” generalists died off, mainly because they were only effective in dealing with tangibilities, not invisible frequencies. Science had discovered a huge realm of phenomena we could not directly tap with our senses. The great pirates did not have the right stuff for this new status quo, yet their specializing institutions, pushing us into various departments and compartments, continued to function on autopilot.

I started writing to academics in various philosophy departments. We had the internet by this time, and before that I would use snail mail. Given Ludwig Wittgenstein had focussed on the Philosophy of Mathematics, why not start a conversation about alternative models of 2nd and 3rd powering in a Wittgensteinian context.

Once that fire was lit, we would have an easier time getting text book publishers to understand their responsibility to include Fuller’s concentric hierarchy of polyhedrons in their grade school publishings.

However, the academic specialities are each centered around a core set of journals wherein an accepted set of conversations occupy the attention of those in the field. These journals offer the “publish or perish” opportunities required to win name recognition and authority within one’s principal area of practice. Since I had dropped out of academia to become a high school teacher, I was no longer in the realm of “publish or perish” in that sense.

Once the World Wide Web became a reality, I saw my opportunity to spark discussion through that medium. I’d moved from Jersey City back to Portland, Oregon. In between, I crossed paths with Bucky at Hunter College in New York City. “I never had a son before” I remember him saying. Like Arnold Mindell, whom I met years later, he had a way of letting himself go in public speaking, meaning he was not the censorious ego, at least not in my experience. He tapped in to the collective unconscious, and that gave him energy.

My Synergetics on the Web was the first on the Web devoted to Fuller’s legacy. He wouldn’t live to see it. He died in 1983, when I was sharing an apartment with my parents in Washington DC. Dad was between jobs, looking for new work. My high school friend from Manila, Glenn Baker, was in DC that year too, working as an archivist for the Center for Defense Information (CDI). I have some stories there too, which I’ll cycle back to later. My parents and I were on the way to Friends General Conference (FGC) when I got the news.

Fuller was really into telepathy by the way, but knew we didn’t have the theory or vocabulary to keep its promulgators from sounding kooky. Fuller was sensitive to how he was perceived by others. Like the physicists who later met at Esalen, Erhard a sponsor, they could see where such phenomena might be reflected in the data, but were less clear where it might fit in any theory.

At least physics as a discipline was willing to take on “consciousness” as a challenge. Kiyoshi Kuromiya, a Fuller collaborator I became friends with, in Philadelphia, had his own telepathy stories relating to Fuller. I talk about that some in My Dinner with Kiyoshi.

Neither my Synergetics on the Web, nor Synergetics itself, is arguing for a lot of “paranormal” or “extrasensory” phenomena. The concept of subdividing some content into smaller and smaller intervals is associated with “frequency”. Indeed, “frequency” is generalized to mean anything having to do with scale, size, or persistence in time. I was amused when around this time we heard that Dan Rather, the CBS news anchor, had been accosted by some back alley figure asking “what’s the frequency, Dan?” I was a fan of CBS, Katie Couric also. I later saw the Charles Kuralt van from On the Road at the Henry Ford Museum in Michigan. Steve Hartman took that on, and has done a great job.

Aside from “frequency” we have “angles” which define that shape of an object. Picture something complicated, like a sewing machine. As it grows and shrinks in size (perhaps because coming closer or moving to greater distance), the shape remains constant, and may be described in terms of central and surface angles.

In the Synergetics vocabulary we get this notion of “prefrequency” in the sense of Platonic. The generic regular tetrahedron and indeed the whole of the concentric hierarchy, may be represented independently of any specific time or materials. We imagine it. We dream about it. This kind of philosophical thinking, about “pure forms”, is not unique to Fuller by any means. On the contrary, philosophers have formalized such notions since ancient times. What’s innovative in Synergetics is the vocabulary or dictionary it introduces. In computer science, we could say “its namespace”.

Fuller did have a son of sorts, and a grandson. The relationship between those three was somewhat stormy. Werner Erhard was part of that picture. The grandson Jaime had become involved with est and all the rest. The son of sorts was Ed Applewhite (whom Fuller called “sonny”), a fan of Fuller’s since his teenage years. Ed had worked closely with Fuller during the Wichita House project, when post-war Beech Aircraft was casting about for additional business opportunities and Fuller talked them in to building the prototype of an affordable home.

However, Ed spent most of his career in the CIA, in places like Berlin and Lebanon. He was never shy about this experience in retirement and liked to have this biographical detail highlighted, as a way of proving that, even if not an academic, he had an intellect to be reckoned with. He went on to write Paradise Mislaid, about whether science had reached any consenus on what that nature of “life” might be. We say a virus is alive because… fill in the blank.

Given I’d become involved with est at Princeton, and continued volunteering in my Jersey City years, and now had Synergetics on the Web as a website, Applewhite was keen to figure out my role in this puzzle. He was not initially all that friendly.

For one thing, he was rather offended that I’d at first considered him a fictional character. I read his Cosmic Fishing, about the process of writing Synergetics with Fuller, and it seemed like “Applewhite” was a metaphor for Fuller’s own brain (always filing and retrieving).

Perhaps “Applewhite” was a pseudonym Fuller had adopted, as a clever way of introducing his mind/brain distinction. That Fuller’s brain, Applewhite, would be this CIA guy, seemed just the clever cover story one would want. Fuller was using encryption to telegraph that he was privy to government secrets. Something like that.

However, during my stint in DC, when dad was between jobs, I spent a lot of time in the library (Library of Congress of course) and I think it might have been there that I came across an article where Applewhite’s picture appeared. In fact, had I been diligent, I could have exploded my fantasy about Fuller using a pseudonym much earlier. I’d indulged in a silly hypothesis for far too long, not the first time nor the last.

Before long though, we became friends, Applewhite and I. He gifted me with a copy of Synergetics Dictionary, a four volume compendium of usage patterns showing how Fuller used his words in context. One could cross reference. He still had the original 5 x 8 cards in his Georgetown apartment, a cool place with the key lock in the elevator. One summer, he and his wife June came out to visit me in Portland.

What Synergetics was good for, according to Dr. Arthur Loeb, who ended up writing the preface, was wrapping one’s mind around a matrix or scaffolding the crystallographers identify as either the cube centric packing (CCP) or face centered cubic (FCC).

What’s curious about both of these is the apparent absence of any cubes. What’s so “cubic” about either. As a matter of fact, one may impose a grid of cubes on the CCP scaffolding, but Loeb was attracted to Fuller’s method: start with nuclear ball and pack successive layers around it, following the numeric progression of 12, 42, 92, 162… balls, the so-called cuboctahedral numbers, the same sequence as the icosahedral numbers.

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1, 12, 62, 92…

What Fuller got from Loeb was that he was helping scientists see old material in new ways. Synergetics did not invalidate any math, although at one point Fuller adds to an age old debate about Calculus.

He does so in an innovative manner, starting from what we call Descartes’ Deficit. Add up all the degrees around every vertex of a high frequency geodesic sphere. As the frequency increases without limit, the angles around any vertex approach 360, and yet each vertex contributes a discrete amount to the overall 720 degrees that’s missing (true for any hole-free polyhedron).

So do we really approach 360 at the limit if we know there’s a definite difference that adds to a set specific number? How can 720/V = 0 rather than some tiny positive number?

The point goes by quickly and is in no way core to Fuller’s work. Concerns about the logical consistency of the calculus go back to Newton himself. Fuller is participating in an age old conversation. The utility of the calculus is not in doubt.

By now you might be thinking that, with all these contact points with existing academic subjects, Synergetics must appear on at least some syllabi in some academic departments. The Philosophy Department would probably make the most sense. Literature Department?

But then many philosophers are wary of math beyond whatever modal logic they’ve carved out for themselves. The “not invented here” syndrome is quite pronounced. Agreeing to have conversations about the pedagogical value of Synergetics might be too risky, given what else is in the Fuller syllabus (see below).

Which brings me back to my first stint in DC, when my friend Glenn Baker worked for the Center for Defense information. Kiyoshi Kuromiya and Fuller had worked together on this lengthy book, Critical Path. In the speculative prehistory section, Fuller appears to go off the deep end in suggesting alternative origins of the human species.

He thinks the big-brained intelligent mammals of the deep, the dolphins and whales, must have some common origin with humans. He thinks planetary ecosystems are programmable and that the blueprints for life somehow got here by naturally occurring frequency transmissions. Is he into being the ultimate contrarian in questioning everything that’s accepted? How might anyone defend such a bastion of maverick ideas?

From my angle, I’ve wondered if Fuller had really just shot himself in the foot with that book. He’d been resisting going off the deep end in many dimensions, but couldn’t help himself this time?

He doesn’t have UFOs or ETs in Critical Path. It’s not Chariots of the Gods. However, since he believes intelligence has been around for a long time (even Big Bangers believe that), he posits nature somehow spreads intelligence from planet to planet by electromagnetism. He’s not the first to posit such an hypothesis, but his speculative telling seems pretty zany.

However, later in Critical Path he shares information which we could verify or discount. If his belief in Soviet submarine aircraft carriers is fake news, then we can see him as a culprit, either in on this scam, or its victim. That’s when I start asking my friend Glenn to dig into it. He found some tapes, of Fuller talking with CDI’s founding admirals and generals, about those same subs, but that hardly qualifies as a cross-check.

We would need to see info from another source. I wrote to the Washington Post, and the Pentagon, saying that if they wanted to either discredit or bolster Fuller, here was a way. Please confirm or deny the existence of these submarines. Given they were now a matter of public record (in Critical Path), the public was owed some official statements.

Instead, President Reagan awarded Fuller the Medal of Freedom, with Synergetics mentioned explicitly. By this time he’d come out, again in collaboration with Kiyoshi, with Grunch of Giants. In that book he declared an end to the nation-state era, beginning with the bankruptcy (financially and ethically) of the once great United States.

In conclusion, the Fuller corpus contains a core of concrete mathematics we might connect with, and share with students at an early age.

On the other hand, this core is surrounded by a twilight zone of questionable assertions and assumptions.

Is the idea that humans could greatly improve upon their planetary situation one of these questionable assertions? That’s a debate humans pursue independently of Fuller’s World Game investigations. His idea of World Game was to establish a clearinghouse for global data, not unlike what the United Nations is supposed to do. Lets study our prospects and make plans as a group activity. Isn’t that what democracy is all about?

Regarding Fuller’s claims that we might have a bright future aboard Spaceship Earth (his metaphor), it’s not like we’re bereft of any means for cross-validation on that score. Computer models have become more sophisticated since the Club of Rome days, when I was living there.

On the other hand, if Fuller imagined that humanity’s coming to incorporate at least the basics of Synergetics were somehow critical to his program…? Lots of wild cards. I’m thinking why not play it safe and at least pass the torch in this regard. His streamlining of some Platonic geometry using a tetrahedron as a unit of volume is at least worthy of “memification” (as opposed to “mummification”).

Lets find or found at least one public or private school willing to share the crystal core of Synergetics. Stay tuned.

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