The evolution of university departments in the wake of natural philosophy’s demise, left a chasm, so-called by C. P. Snow (1905–1980), between STEM subjects and the humanities.
In today’s parlance, the new bridge over that chasm is brought to you by the letter “A” (sounds like Sesame Street) turning STEM into STEAM, with this “A” usually standing for “Art,” less often for “Anthropology.”
One of the more prolific writers and inventors of the 1900s, R. Buckminster Fuller (1895 -1983), sought to bridge the C. P. Snow chasm twixt STEM and the humanities with a newly invented language.
The words would be familiar enough in that outright neologisms (e.g “tensegrity”) would be few, but their meanings would depend on usage patterns internal to this new kind of thinking.
“Vector,” “gravity,” “radiation,” “frequency”: terms much-used in STEM, but contained in a customized namespace giving each a spin and trajectory. The vocabulary was deliberately remote (Synergetics 250.30). Words such as “metaphysical” and “love” were also in there, part of that C.P. Snow bridge — or was it a tunnel?
He called his new language Synergetics and wrote two books in it, along with a bunch of poetry (cite The Pound Era by Hugh Kenner). Had it not been for Ed Applewhite (1919–2005), Synergetics and Synergetics 2 might have been in free verse (cite Cosmic Fishing, Applewhite’s account of their collaboration).
Imagine showing up on a tropical island, with lots of pristine beaches, palm trees and coconuts. Was here where Tom Hanks found himself marooned in Castaway?
You’re a member of a team of anthropologists. We’ve come to study the indigenous mathematics the island dwellers use, and write numerous academic papers about it, do some documentary films.
In our own elementary school experience, the right angle was king. In multiplying 2 x 3, we would place sticks at 90 degrees to one another, making a rectangle of 2 x 3 = 6 unit squares.
In contrast, these islanders place their sticks at 60 degrees. Their area is likewise six, but in triangle-shaped units.
In middle school if not before, we moved to volume, and again the right angle was king. 2 x 3 x 4 is a rectilinear brick of 24 cubic units. Our islanders, in contrast, add a third stick to the previous two in a 60-degree-based fashion.
All three sticks poke up from a common origin, made of three 60 degree angles, the corner of a regular tetrahedron.
Their multiplication process gives the result we expect, 24 units, but the units are regular unit-volume tetrahedrons, instead of cubes.
Given we’re anthropologists writing about a STEMish topic, the relationship between multiplication and geometric models, we’ll likely want to get help from our colleagues in other campus buildings. We’ll need mathematicians to weigh in, on these alternative logical foundations and their ramifications.
Our work will be expected to have an inter-disciplinary flavor, but then that’s not unusual in anthropology. We also study the indigenous flora and fauna on the island, meaning we’ll be bringing in lots of biology. The writings of Gregory Bateson (1904 -1980) have this flavor. He was married to anthropologist Margaret Mead (1901 -1978).
Shifting genres now, to science fiction, lets imagine such humble Polynesian roots for this aforementioned chasm-spanning project in American literature, thereby tying our story back to Synergetics. These islands provide an idyllic backdrop, an Eden, for a new genesis story.
Lets cast Fuller as one of the anthropologists who learned from these islanders, and then went on to amplify his findings. He adapted what he learned from this culture to the global problem of providing adequately sheltered environments to the world’s billions, places to live and grow food.
In accepting a tetrahedron as an alternate model of 3rd powering, or D x D x D, the floodgates were opened to sweeping revisions, with ripple effects regarding how we share geometry, even with our own kids. Yet why adopt an either / or mentality? We know our cube-based ways of reckoning work. We have more than one tonal scale in music. New possibilities need not be regarded as existential threats.
A tetrahedron divides evenly, with no remainder, volume-wise, into an octahedron of the same edge length four times, and into a cube with same length face diagonals three times. With a regular tetrahedron as our unit, we’re free to capitalize on these elementary math facts.
That’s already more whole number volumes for polyhedrons than we’re used to getting, from our mainland schools. Add a space-filling rhombic dodecahedron, Kepler’s favorite, of volume six (in blue below), and we’re off to the races, so to speak.
Before long, thanks to RBF’s Synergetics, American literature was bridging the C.P. Snow chasm, between STEM and not-STEM, by means of a new canonical arrangement of polyhedrons in a concentric design. Art and design school students picked up on it. Many more in the humanities found STEM concepts more easily graspable, including the concept of coconuts closest packed in the CCP (cubic close packing).
Twelve coconuts of equal radius around a central one, aligned with the vertices of a cuboctahedron, is the beginning of the FCC (or CCP) lattice. Successive layers contain 12, 42, 92, 162 … coconuts, per a formula Fuller derived, and shared with H.S.M. Coxeter (cite The King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry by Siobhan Roberts). This lattice provides the scaffolding for the canonical concentric hierarchy.
Anthropology and Art fused in the form of all these new artifacts that appeared as a consequence of this bridging. 3D printers started churning out the new shapes: A, B, T, E and S modules, all tetrahedrons. Geodesic domes popped up in our landscape.
Although how all of these developments actually occurred is a longer story, having more to do with a “cold war,” where we’ve come to is much this same place, science fiction aside.
What happens next is anybody’s guess. No one expects this island’s culture to replace the mainland’s well-established cube-centric mathematics. At best the new thinking will dove-tail, providing another “hard currency” in the world of computation, inter-convertible with what we already recognize and know.
Ideally, anthropologists compare and contrast cultures without engaging in any military campaigns that would violate the Prime Directive or overly interfere. The freedom to teach ethno-mathematics in an open academic environment, helps us do our jobs responsibly. We’re here to investigate and explore, not clamp down, not persecute or prosecute.
Besides, all math is ethno-math, when you get right down to it. Ludwig Wittgenstein (1889–1951) showed us that much, within his trademark mix of philosophy and anthropology. Was Wittgenstein a transcendentalist too then? He eschewed the pragmatist label, that much we know.
If you’re interested in American literature, I recommend doing some more homework to help snag a front row seat on the action. Become an A-team player yourself.