[ this story is my response to an email from a philosopher I correspond with, that I’ve not herein included, yet used to guide my response ]
I think if one is planning to grapple with Synergetics on its own terms, then one is eventually compelled to deal with Fuller’s novel use of “dimension”, which term (or tool) is not actually the name of some “thing” we can mentally point to or at.
Precision is established through usage (operationally) not through some instantaneous metaphysical “pointing”.
The idea of pointing “very exactly” to some speck (as one might with a telescope, to some distant star) is a metaphor, and a bewitching one at that.
Or so I believe Wittgenstein has shown, at least to my own satisfaction.
I won’t myself ever go back to the old Nominalism / Realism of “named ideas” — that would seem way too atavistic a maneuver. Given we’ve successfully exorcised said demon, why invite it back in?
Put another way, if one is defending or explaining Synergetics, one must come to grips with Fuller’s departure from the standard academic discourse on several fronts. Using the language of Synergetics to “suck up” to established usage is ill-advised in many cases, and only leads to confusion.
If you try too hard to put Fuller “on the same page” as other philosophers, you’ll miss his sometimes mocking tone, his making fun of schoolish views (not just Applewhite’s influence).
We’d do better to value his alien perspective for what it is (divergent), versus attempting a force fit.
Spatial volume (res extensa) is not 3D in the deliberately remote vocabulary of Synergetics, it’s 4D, because at minimum you’re inside a tetrahedron, if you’re inside anything at all.
Conceptualizing begins with containers. You’re inside and have insides. “I contain [thoughts, feelings, whatever], ergo I am”.
The logic called “mereology” begins here too, in recognition of the primitiveness of “inside” and/or “part of” versus “not part of” relationship.
A tetrahedron is 4 faced, 4 cornered. That’s a stronger fourness than the hexahedron’s 3ness perhaps. What’s so “3D” about the cube anyway, with all those extra faces? Are we allowed to ask such questions? Perhaps we’re only trying to free ourselves from some cultural conventions?
Sure, the three mutually orthogonal intersecting squares of an octahedron, define eight octants. Six spokes create eight sectors instead of four spokes creating four.
Do height, breadth and width really come apart, conceptually, as separable notions?
Does the idea of width-only — with neither height, nor breadth — defy conceptualization?
Whatever you visualize, aren’t you assuming a viewpoint on some room, wherein your visualized specimen now occurs at some focus? How do you get rid of the room itself? Kant said you can’t. So lets start with the room.
Room and camera are the same word in Latin. A tetrahedron is the minimal room. It’s the “hello, world” of polyhedrons.
Three edges define a zigzag, defining three more, connecting the same dots in a different order. Are those Zs the three dimensions then, inter-connecting the four non-coplanar points? And why do “right angles” matter so much again?
-Z + Z = Tetrahedron.
We may feel like we’re back in elementary school, struggling with early doubts about the wisdom of the ages. That was young Bucky in a nutshell, like a lot of us.
When he later proved to be a failure, by objective business standards (he did fine in the navy), he eventually wondered (after contemplating suicide) if that was because of all the “squares” running the show.
So why not fight them instead? Why not question the authorities even more deeply? He was pretty successful doing that, receiving many medals and awards, honorary degrees.
XYZ likewise suggests a sixness (a three and three, like -Z + Z), once all the “negative basis vectors” have been computed, giving the six-spoked jack.
The three “positive” unit vectors are helpless to reach 7/8ths of space minus assistance from their “negative” counterparts.
We’re allowed to turn a vector completely around and call that “in the same dimension” yet only one of the two vectors is an actual basis vector. (1,0,0) is more basic than (-1,0,0) because it points to the right?
These practices are mere conventions, not self evident truths. Suppose we want to try other conventions for a change. Is that verboten? Synergetics is objectively an experiment with alternative concepts. Does it hold water?
A caltrop has only four spokes. Four is less than six. If we’re talking about beacons, star patterns, the caltrop is more primitive than the jack.
“Codependent origination” of ideas (like concave vs. convex) might be a better solution to the height versus width versus breadth relationship. Sounds Asian.
No wire frame is less complicated, in the world of simply edges (or rods), than a tetrahedron.
A sphere is something to zoom in upon, to inspect more closely, and no empirical evidence of pure continua is out there. Spheres are complicated. Lets stick with edges, crossings, openings, or E, V, F per Eulerian topology.
It’s not that Synergetics doesn’t use root of 2. Synergetics is full of surds (radical signs). It’s that real world energetic phenomena are not “infinitely precise” in some sense that requires infinite precision.
The incommensurability concept (what we call irrationality) is neither denied nor eschewed in Synergetics, just Fuller thinks physics is not using pi to a trillion digits, and he’s empirically justified in thinking that. What’s the counter-evidence?
Anyway, he’s leaving academic “schoolish math” the way it is (much as Wittgenstein’s philosophy leaves everything as it is), and has no power nor even inclination to dismiss it. His freedom is only to create alternative neural pathways in response to intuitions — the same freedom all of us have, to think on our own.
Dismissing his alternative becomes more difficult in proportion to its causing light bulbs to go on within others. When Synergetics starts making sense to little kids, is when we know it’ll have a long half life.
Fuller wanted to carve out a namespace for himself that from his point of view was perspicacious, veil-lifting, revelatory. Synergetics shows how he went about developing that namespace, which is an evolving, regenerative, collaborative process.
He’d make mistakes and explain them.
The second volume retracts some speculations in the first.
He’d have likely used a software version control system had it been available.
Synergetics continues to evolve.
Fuller didn’t highlight that VE:icosa volume ratio in the Jitterbug is the same ratio as S:E module ratio, nor give that number a name (S factor), the way some of us do now.
Synergetics did not come to a dead halt in the 1980s.
I considered the latter far easier to develop with, and did so (cite my Jupyter Notebooks), but without suggesting this four basis vector apparatus was actually found in Fuller’s writings (go look, you won’t find it).
Cliff seemed to think he was teasing out an existing machinery, and therefore felt comfortable naming his apparatus “Synergetics Coordinates” as if Fuller had maybe invented them. I tried to counter this miss-perception.
To me, Synergetics is a work in the humanities, a literary phenomenon within the lineage of American Transcendentalism. The people who need to read Synergetics, professionally, if they expect to be fluent in their professed domain, are professors of literature, and of philosophy, such as we still have any.
However Synergetics is also a bridge to STEM topics on the other side of the C.P Snow chasm. Those who read in the humanities will find themselves in a set of guided meditations (reveries) involving the CCP (cubic centered packing, per conventional nomenclature) and much else besides.
Anyway, there’s something ironic about saddling Fuller with writing about “3D spheres” when he was adamant about using “4D” for all pre-frequency eternal spatial entities.
We know what you mean of course, as we’re all products of the same curriculum at that level, and thinking outside the XYZ box was never our forte.
For further reading: