When I was growing up, I picked up on the "multi-dimensional meme" and on how "thinking in higher dimensions" was a hallmark of geometric IQ or something along those lines.
I'd say that's still the
case, and when people first encounter Bucky's 4D lingo and connect with
his being a recognized genius, past president of Mensa and so on, they
just assume he's thinking "multi-dimensionally" too, like one of those
super smart people, or at least intuitively gifted people. And in a way, he
is. But in what way?
Since studying computer science more, and developing an
appreciation for "namespaces", I'm better able to compartmentalize the
terrain of human discourse into "language games", thereby fragmenting
most monolithic meanings -- and lets throw "God" into the mix, most
assuredly i.e. there's no monolithic meaning attaching to monotheism
either.
Nowadays, I no longer spontaneously think of space as 3-D (especially with the hyphen (smile)). I have to work at it. I'm able to psych myself back into it through machine learning (ML), which is closely related to Coxeter-type polytope geometry, not least because they both thrived at the University of Toronto. Canadians have a higher geometric IQ than their neighbors to the south perhaps.
Through ML, I get back to the n-D meme and conventional Extended Euclideanism (EE), with "3-D" a visualizable subspace, a kind of Minecraft or Lego World for doing XYZ "three directional" physics.
We learn space has these independent
directions called the X, Y and Z. We learn to spontaneously
say "cubed" when confronted with a 3rd powering. Anything flat, like a pancake or screen, is "2-D" whereas the horizon betwixt the ocean and sky is "1-D".
"Schooled
people" (me one of them) all think in this way. However, since Synergetics
(Fuller's, not Haken's), I'm not so sure we sound quite as smart as we
used to. Osmosis has taken its toll. The Euclideans have no monopoly on philosophical underpinnings anymore, presuming they ever did.
In EE and ML, whether you had other family on board with you, were female or male, had a nice cabin or were in a certain age range, all become dimensions locating you along various axes, giving you a multi-dimensional "address" with a Euclidean distance to other addresses.
We'll compute some weighting factors using "neural networks"and pretty soon, in knowing your multi-dimensional Euclidean neighborhood, we'll also have a very educated guess as to whether you survived or drowned when the Titanic went down. Such is EE + ML.
If we're
Cambridge Analytica, we'll use our prowess with ML to scare you into believing we know "where you live" in the sense of knowing how you'll
vote in the next election. Or we know what to do to tilt you more in a specific direction (dimension), through tailored messages, targeted ads. We'll sell politicians on this idea we have these superpowers, leaving it to others to counter our grandiose claims.
The Minority Report (a dystopian movie) seems already here, or at
least some people would like you to believe they know the future. Any
wannabe priest caste has conventionally claimed clairvoyance, based on whatever passes for "tea leaves" in a given generation.
In
Synergetics, we part company with those saying they can visualize but a
single dimension, such as width but no breadth or height, or height
without width and breadth. Whatever we're visualizing, it's already in a container defined by the observer's apparent subjective distance from the observed. There's your space.
We find it quaint that 3Ders include, as one of their chief documents promoting "hypercross mysticism", a work not of mathematics, but of political satire. I'm speaking of Flatland of course, by Edwin Abbott, quite important to this namespace, as a kind of cultish tract.
When you start fresh with with a Kantian a priori
sense of space, it's a box, a container, ab initio. Then comes a creation story about successive dimensions (starting from zero) explaining why said paradigm box is
"3-D". We go to school for the privilege of learning this creation myth, as a part of our early indoctrination.
Fuller disrupts that genesis story and supplies another one, likewise firmly based in topology: space is one inseparable concept, indivisible into independent dimensions, one of containment, and the most primitive (in the sense of simple) container is naturally the tetrahedron (spheres stay complex and may be reshaped accordingly), a tetrahedron that says "four" way more loudly than "three".
Beyond timeless 4D space, we get to Time, which we may call a dimension too (as Einstein does), but then, while we're in time, lets not
forget to break it down further, into weight, density, molecular makeup, color, temperature... the "dimensions of chemistry "
we could call them, and indeed the word "dimension" does carry that kind
of water in many a namespace, including in ML.
For Fuller, there's 4D space + Energy, where Energy = Frequency i.e. a specific "program" full of physics happening. "Event space" we could call it. Shape alone is angles. Frequency steps up the mere eternal into the actually existent, the space of "special cases" in time/size.
Such was the state of Fuller's philosophical lingo, by the 1970s. "Angle + frequency" had become his shorthand for all physical information about stuff in general.
Going back and forth between namespaces sometimes does involve training the senses, inducing new perspectives. Gestalt psychology shares this notion of "aspect shifts" with philosophy.
Getting into Fuller's way of thinking does require a kind of re-education, and getting there may involve what we might call "brainwashing" if we're resolved to put a negative spin on it.
Or consider "brainwashing" something healthy, apply a positive spin.
If you haven't washed your brain in decades, maybe it's high time? Smile.
