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Synergetics: A Contrarian’s Namespace

“Enough GST already, tell us about Synergetics.” I get it. I’ve posted a lot about the former, but not a whole lot about the latter. By the way: I continued updating this particular essay all through October, 2018, including changing the title.

Also by the way: I’m in open rebellion against the practice of putting the period inside the quote marks at the end of a sentence. I’ll be sometimes breaking that rule. Medium lets me.

Fuller was a contrarian and grew up bucking “the establishment” before most people had a vocabulary large enough to include such a word. He talks about the average size of people’s vocabularies significantly growing over the course of his lifetime (1895–1983). Financial literacy was also increasing. Today we share Fintech with children, starting earlier than ever with cryptographic language games.

In my experience, “the establishment” and “the environment” arose as parallel four-syllable words, oft cast as duking it out (wrestling). Environmentalists would either work “inside” or “outside” the system. When you hear or read the word “system” you’re meant to conjure geometric imagery in the namespace of synergetics: picture a ball made of triangles. Lots of triangles make for stability. There’s a lot of visualization required of the synergetics reader, if the prose is to be grokked fully.

Everyone “knows” that space is three dimensional, right? I’m not sure if Euclid knew. Four not-co-planar points determine a volume, he has that encoded. A “volume” is an inhabitant of “space”. Volume takes up volume (room).

Kant proved that space was a priori roomy, but did he insist on “three dimensional”? I’ve been working on tracking that down, yay or nay.

Kant did find something irreducible about “space” in one’s experience. We’re simply not mentally equipped to imagine no room for changes or differences. There’s wiggle room.

In Descartes’ day, people spoke of “res extensa” meaning stuff taking up room. We have a sense of roominess, of inside versus outside, of concavity versus convexity. How many “dimensions” is all that? We’re taught to say “three” but how self-evident is that really?

Fuller actually hoped he could change our thinking on that question, expanding our minds to accept more than one possible answer.

No, I’m not talking about Einstein’s “time”, although Fuller does talk about time a lot, including as a dimension.

He truly means to challenge the notion that we’re duty-bound to agree that space is 3D. Out of allegiance to whom? He has some counter-reasoning to share, or call it counter-intelligence.

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But wait, it gets worse.

Bucky also wanted to make you question another aspect of your schooling.

You’ve been schooled to say “2 squared” when you write “2 to the 2nd power”, and “2 cubed” when you’re using a 3rd power.

“So why squares and cubes?” asks our Greenwich Village Bohemian rebel, “why not triangles and tetrahedrons?”.

Note about the picture below (“excerpt from Synergetics”): the regular tetrahedron is not, by itself, a space-filler like the MITE is (we’ll get to that later) and the growing tetrahedron in the right column subdivides into a mix of octahedrons and tetrahedrons. There’s more in the original figure (990.01) to make that clear.

The octahedrons weigh in at four times a tetrahedron’s volume (same edge lengths) , which is why the 2nd from the top (four tetrahedrons fitting around a single central octahedron) has a total volume of eight (4 + 1 + 1 + 1 + 1). And so on. The volumes as accounted in “tetravolumes” follow the same sequence (1, 8, 27, 64, …) as what we call the “cubes”. “But do they have to be cubes?” was Fuller’s question, and he showed us why he thought “no” was a good answer.

We see the same numbers, for both areal and volumetric growth, but accept an alternative geometrical modeling, not only the squares and cubes like we learn about in school. Squares and cubes seem exclusively entitled to rule (to serve as rulers) in the only maths we’re given to understand. Synergetics is a new kid on the block.

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excerpt from Synergetics

Our Bohemian rebel contrarian started dressing like a banker later, when he finally realized people focused on his ideas more when not distracted by his fashion sense. He was on the lookout for venture capital and needed to project the aura of a businessman. He could stay radical under the hood.

The suit and bow-tie persona helped him camouflage his radically “out there” design science agenda, which would later inspire a generation of Jay Baldwin types, those engineering savvy Whole Earth Catalog people eager to try something new. They pioneered new lifestyles, and sometimes showcased their new artifacts at Burning Man.

Fuller would stride on stage holding his “unit volume 3rd powering device”, what poet Gene Fowler called a “6sys” but what the rest of the English and Greek speaking world knows as a “tetrahedron” and he would want to make it important, even as important as a cube. This was sacrilege.

The shape we call a tetrahedron is at the center of Dr. Fuller’s religion, although calling synergetics “a religion” does sound a bit off the mark. Is synergetics a “designer religion” that’s perpetually reinvented? Lets allow anthropologists to fight over the right answer.

RBF claimed he was engaged in a project to bridge the humanities to the maths (intentional plural, English spelling) and the sciences, or what many in North American states call “STEM” (science, technology, engineering, mathematics), a hodgepodge meaning “not the Humanities” which latter some have branded PATH.

Not only is the tetrahedron his unit of volume, which grows and shrinks as a 3rd power of linear change, but it’s spun as “4D” or “four dimensional”. We don’t get simpler than a simplex. One might suggest “sphere” but that’s the analog limit we never reach from the digital side, is complex in contrast. One might suggest “a circle” but are you looking down on that circle? What’s that between you and this other then, if not space?

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four blue basis vectors to corners of six black edge framework

Four rays vector off from a common center, defining four facets. A cage with six bars. What’s so “three dee” about that? If we make the tetrahedron the icon of some anchoring “4D talk” will we be able to continue? Are there games we might play, or does everything lock up in inconsistencies?

To some ears, it sounds silly, like a joke, that we could ever offer a defensible alternative to the “space is three dimensional” dogma. The schooled scoff. There’s no going up against the “space is 3D” dogma with such naive objections, is the common wisdom. The court of public opinion has rendered its verdict. Fuller mainly attracts other contrarians.

A huge theme park operates daily on the basis of “space is 3D” and no Don Quixote with a lance and pony is going to bring our gigantic operation to a halt. “Go away little man”. The windmills keep turning. But who said anything about stopping big wheels? Synergetics is a startup, not aimed at shutting down its competition. All maths are accepted, as correct in their own terms.

Methane, the feared global warming gas, trapped in great quantities beneath thawing frozen stuff, is tetrahedron shaped, with a carbon atom shared with four hydrogens.

gallium arsenide (pubic domain)

A tetrahedron-based chemistry forms a basis for quartz. Or look at diamond.

True enough, tetrahedrons are everywhere in nature. Bringing more attention to the tetrahedron can’t be all bad.

But we have to wonder at Fuller’s willingness to warp the language itself to give it the foreground treatment he believes it deserves.

Furthermore, he’ll sometimes even trash talk the cube, the very centerpiece of the prevailing orthodoxy.

Having offended us on two fronts, challenging our ideas about dimension and volume, Dr. Fuller then gets to work chipping away at the language in another way people hate: he starts making up new jargon, new shoptalk.

As if we didn’t have enough of that already. And as if it’s his role to be giving things names. What an upstart! We should leave naming to the high priests, right?

Adam got to do that (name primitives, such as “sky” and “dirt”), and Eve too presumably. So did they ever fight about what to call this or that?

I’m just thinking of a little sermon, about how the Snake in the Garden represents “forked tongue”. Man and Woman got to fighting, and maybe said some stuff they’d later regret. They learned about holding a grudge. Their time in paradise was over.

Suddenly, one of them was “evil” and it was pretty much downhill from there.

And yet they managed to have a big family (not just Cain and Abel as some suppose). We’re some billions strong lo these thousands of Bible years later (another namespace, the Bible is).

Synergetics is not biblical, but does feature numbered passages, which was fashionable in philosophy in Wittgenstein’s time.

Furthermore, Fuller does reinterpret the Genesis story, but in Tetrascroll, a “book” he wrote later. Eve becomes the ship, made of ribs (eaves) and, flipped over, becomes a shelter on land. Check it out. Ordinary books were produced from this limited edition stack of triangular panels.

Synergetics also names primitive stuff, like the A & B modules, tetrahedral slivers of the Platonics. Are we going to allow a known dissenter to get those words in edge-wise? Where could that lead? Might there be further transgressions?

Both Ludwig Wittgenstein’s Philosophical Investigations and his earlier tract (“the Tractatus” for short), featured numbered aphorisms.

Synergetics is likewise presented like some expandable (or shrinkable?) outline, with sections and subsections.

I mention these two philosophies in the same paragraph as I think LW’s philosophy of maths helps us come to grips with what RBF did to create his meanings operationally, more than by definition or by axiom.

We know a great deal about the workflow behind Synergetics thanks to a whole book on the subject: Cosmic Fishing by Ed Applewhite, author also of Washington Itself, a guidebook to his home city, and Paradise Mislaid, a meditation on the meaning of mortality.

More “against the grain” thinking: Synergetics refuses to model “gravity” properly, i.e. in strict accordance with Newton’s meaning.

Instead, he identifies a naturally occurring squeezing strategy, a way of tightening by increasing tension, and claims “gravity” for that.

“Gravity” is like when a fishing net hauls in fish, or when a balloon holds its shape against mounting internal gas pressure. The networking tension is at 90 degrees to what it’s complementing.

Yet he’ll come close to Newton when he talks about “falling in” and gravity increasing as a 2nd power of decreasing distance. His “gravity” seems more familiar then. Should he be allowed to have it both ways?

Fuller likes to overlay meanings, as we’re permitted to do in the humanities. His “metaphorical verities” are “tomographic” according to Applewhite, meaning they’re meant to stay metaphoric. Any strictly literal interpretation is special case, and “gravity” is ultimately about the generalizations. Think of “sense” versus “nonsense”.

Is Fuller trying to awaken the collective unconscious in his layered style of writing, more like a Norman O. Brown? Is he being deliberately evocative?

That it might have been poetry (per Applewhite) is why Synergetics remains a work in the humanities first and foremost (it’s mostly prose, after all). But with an intent to bridge to STEM, and thereby overcoming overspecialization (“devolution”) by crisscrossing the C.P Snow chasm, creating more traffic in both directions.

“Maintaining structural integrity (composure, equanimity) against a pressure to explode” is Fuller’s picture of what gravity does versus radiation. So “anti-entropy” then?

“Gravity” provides the “syn” in “synergetics” as in “syntropy”. How rad is that?

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random decal

Contrary to “gravity” yet always and only co-occurring — they’re complementary, two sides of the same coin — is “radiation” manifesting explosive, divergent behavior.

He again uses his “physics words” seemingly without much reference to the Standard Model, although he’s happy to yak about electromagnetism in some passages. But is he on the same wavelength as a doctor of physics?

He’s into sphere packing, the CCP especially, which he preemptively identified as “densest” before mathematicians had reached consensus on that question. Was that reckless?

He’s into the proton and neutron being inter-transformable and pretty much sticks to the Feynman view of them, though without mentioning Feynman by name, nor Dirac either. He diagrams their connecting particle physics in a couple places.

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sphere packing in the CCP

His “gravity” fades into “precession” which segues to “unpredictable” (as in “chaotic”). That’s not unlike how professionals talk about the three body problem.

We get to “butterfly” or “trim tab” effects pretty quickly. Precession keeps surprising us with whole-not-predicted-by-its-part behaviors. We call them “side effects” as in “unintended”, whereas that’s just how nature works (precessionally).

Gravity squeezes energy into special case events, makes energy follow the rules, which are as taut as tautologies. If the generalized principles are the strings, then the music of what’s happening is from their vibrations. Atoms only shine at certain frequencies.

Energy is constrained by the “generalized principles” many of which are recognized as such under the heading of “conservation laws” and likewise the “principle of least action”.

Synergetics seems close to physics in how it looks at natural laws as exceptionless, which doesn’t preclude their being sometimes probabilistic in their expression.

Fuller’s critique of the Real Numbers is summarized in his dictum “Nature is not using Pi”. His point is that physical processes have a noisy chaotic underbelly that we paper over with simplifying ideas about pure continuity. However, perfect continuity remains an abstraction over and above what energy needs. We have no measurements to suggest that “perfect pi” is anywhere used.

He’s willing to let ratios stay “approximate” because we’re energetically limited in our operations, regardless of what we think we imagine.

Conceptually, we may talk ourselves into “infinite precision” as a feature of a specific math, whereas in practice we’re never required to spend anything close to “infinite energy” to demonstrate such posited phenomena. Synergetics allows us to stay discrete and discontinuous.

He recycles the word “metaphysical” (out of fashion in some circles) for our growing mastery of universal generalizations. “More with less” comes about when we get greater performance with less expense, thanks to improving design savvy.

A kind of optimization goes on which we might characterize as stuff instantaneously “obeying” any number of physical laws. More metaphors.

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One of the rules Fuller goes on about is the Gibbs Phase Rule relationship between frozen (solid), flowing (liquid), and dispersed (gas) phases of matter, with their inter-proportions relating to ambient temperature and pressure.

Fuller makes a point of saying “flowing” is the least eccentric state to be in, compared with the other two. In being between two extremes, liquid comprises an average and home base.

My recommendation would be to study the Standard Model in some detail, as that’s an important edifice.

Don’t artificially narrow your research to Synergetics alone; but nor need we fear it as some spanner in the works, a monkey wrench in the machinery.

Consider shifting between them as different “gears” or as alternative ways to engage the same drive train.

Definitely take in Maxwell, Carnot, Laplace, Newton, Leibniz and Galileo. The list continues. Fuller does that too, establishing relationships with Newton, Euler, Gibbs, Socrates, Avogadro, Boltzmann, Einstein, among others.

He doesn’t try to work in everybody. A lot of the passages seem broad brush stroke. He mostly aims for flowing prose, but with forays into more crystalline logic and/or more disjoint speculations. The texture is deliberately uneven.

Because of all these transgressions, the backlash against using even his more straightforward jargon was to be expected, especially from the most defensive.

He slices and dices his regular tetrahedron into “A modules”, which show up in the octahedron (of volume 4) in complement with the “B modules” of same volume, different shape.

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24 A modules = Unit Tetrahedron

He goes on to name other tetrahedral slivers, components of a small vocabulary “concentric hierarchy”. These include the E, T and S, in addition to the A and B. Two As and one B make a MITE, a tetrahedron space-filler.

Practically no one is using this terminology, for fear of losing their standing in an intensely competitive environment. These terms just don’t come across as sufficiently well established. They’re too outside the mainstream.

But what about geodesic domes? They’re well integrated into the landscape as mainstream artifacts. I’ll end with those.

If you’ve followed the career of “Guinea Pig B” (what Fuller called himself), you’ll remember his fifteen minutes of fame and glory came in the world of architecture.

Synergetics (the two volumes) is much more concerned with full spheres and their subdivision. These spheres pack together, exhibit surface tension and so on. The domes derive from the spheres.

In addition to the Spheres and Domes, there’s a Gyroscope, an Equilibrium (the so-called VE), and a transformation called the Jitterbug (from the VE through Icosahedron, Octahedron, Tetrahedron, though some no-pause zero, to an inside-out VE). And don’t forget to “mind the gap” (the two rhombic triacontahedrons that differ by a tiny scale factor). A whole theme park of fun rides!

The “concentric hierarchy” is the Main Street through the center, where two tetrahedrons intersect each other, and beget each other. The rest, as they say, is history.

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concentric hierarchy

With the domes came all this shoptalk of “angle and frequency” which he generalized as far as he could, to all phenomena eventually.

“Frequency” has to do with vibration, resolution, precision, special cases.

“Angle” relates to shape, principle, gravity, regardless of size, and has more of that eternal Masonic meaning (check the logo, compass open at 60 degrees).

In the case of a dome, the higher the frequency, the higher the number of component triangles.

In the decades subsequent to the publication of Synergetics, research has continued. I’ve been one of several contributors to the subject’s momentum.

Cyberspace is big enough to accommodate the contrarian, the remote, the obscure and esoteric.

One example discovery, not mentioned in the two volumes: the ratio of the cuboctahedron to the icosahedron of same edge length, derived through Jitterbugging, is the S:E volume ratio. Cuboctahedron : Icosahedron :: S : E.

In the interim, computer science has helped us with its concept of “namespace”. That a common physics word, like “work”, might have different meanings, not just different connotations, in other walks of life, comes as no surprise. Namespaces allow us to keep “name collisions” from wrecking the logic of our operational code.

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from Python for Teachers

A handful of favorite words we all share do a disproportionate amount of load bearing. To keep confusion levels down, we need to stay clear about the context (the namespace). What A means by Y may not be what B means by Y. In “dot notion” we may contrast A.Y with B.Y to disambiguate.

If the context is Synergetics, we’ll expect some words to mean something else. Fuller.4D differs from Coxeter.4D which in turn differs from Einstein.4D.

Given that perspective, we may yet find that, as an alien tongue, the synergetics namespace grows on (or in) us. Sometimes new inventions in language come in handy down the road.

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