FROM MICHAEL
Why does the triangle not require memory? Slipped from my mind. Crack me up, boss.
FROM CURT
Math version: no matter where you organize the three points you end up with a triangle. no other geometry follows this convention. Logical version: the only thing necessary to form three dimensions is the same as the triangle: regardless of the relatinos between positive negative and stable equlibium you always end up with three dimensions independent of spin, rotation, and movement.
FROM MICHAEL
The geometry part makes complete sense. 3 points either produce a triangle; or a line (a degenerate triangle trapped in 1D, or states in a spectrum)
So if we arrange data geometrically (or alternatively, just look at a geometric figure which is our statistical approximation of it) we either get:
A. dimensions (axes), when points all don’t line on the same line, in the same plane, or hyper plane
B. States along an axis (spectrum of measurements) when any 3 of the points are colinear
Dimensions:
Something worth noticing:
A data set of N points produces at most N1 axes (called degrees of freedom in statistics, pardon me if you already know this). The N1 comes from the fact that a triangle produces 2 dimensions from 3 points, and a tetrahedron 3 dimensions from 4 points, and the higher dimensional math follows all the same vector relations (angle, length, area, volume)
A point I’m assuming is itself an “experience” or “measurement” and thus every point I’m referring to has an adversarial component (it was seen, it contacted our measuring device, and is not just “posited” like quarks or Higgs)
Side note, to help folks understand statistics
The standard deviation formula calculates the radius of a “sphere of best fit” in N1 dimensions, whose center is the mean. Your data points are scattered in N1 dimensional space, and your sphere just approximates the points as a clump. The larger the SD the more spread out the points are.
I have never heard this point explained in any textbook
essentially all statistics is derived from “moment” calculations in physics, where we assume data points have mass, and with the mean as a center of mass
Logic:
The logical part I don’t yet see all the permutations of with regards to SPACE only. Can’t operationalize it
I get how ternary logic = epistemology for all subjects
I was approaching the 3D logical part this way
Two objects or people who encounter one another can either

Combine (amass, build capital)

Annihilate (energy loss, heat, dissipation, fun)

Exchange (work, trade)
Even repulsion from one another is a form of trade (I give you your freedom over there, I’ll take my space here)
The ternary logic I see at all levels, math, economics, there’s always a ternary logic formed: either a decision (chemical reaction, mathematical proof) occurs now or the system decides later in time (current state “undecided”)
The challenge is I can’t see why reality always collapses somehow to three SPATIAL dimensions from an inductive standpoint. I can’t make that specific connection
Not that I suffer from this dilemma, I’m quite happy in 3D and am just as happy to say “don’t overthink it pal” when a physicist preaches onanistic dreams about how we could be living in 13 dimensions. I’m asking so I can win arguments from the naysayers who aren’t addicted to Platonism and feel like the “there has to be 3 dimensions” reveals me to be a crackpot
FROM CURT
You’ve got it flawlessly. The three points create space question is intuitive if we use a constructive logic: So you have three points, all are dyamically alterable in any number of dimension including time, as positive, negative charges and a stable equilibrium or a collapse which destroy’s the traiangle, destroys the line, and destroys the point back into the quantum background. Now, try to construct a fourth point somehow. How do you construct it without constructing another triangle? In other words, space can only emerge in three dimensions plus time. There is no other way to construct a fourth point.
But in simple form how does the universe create more than three dimensions? There is no way to do so. Because there is no possibility of creating a fourth dimension except with three more of the same dimensions. Where does the energy for any subsequent dimension come from? “How does that energy get to the next point other than by repetition of the only operational possibiilty the universe can construct. Instead, what happens is that charges, dipoles, proto particles, particles, atoms, molecules just do the same thing: built more of each other from the only three available dimensions. And once we get to another three available dimensinos we have a means of creating a new stable relation (atomic bond etc).
The underlying question is the same at the next level down. How can three dimensional space be created in the first place? By the same rules: this time as energy (point), spin(line(circle)), scale(space), and vibration (Motion (or time)). There just isn’t any way to create more dimensions. As they say in rural Maine: “Ya kahnt get they’ah, frum, hee’ya.”
Even with just these two examples we demonstrate spherical(Small) and planar(Large) three dimensional systems: the only two ways we know of, of describing spatial relations.
Now, I will get better at this narrative over time, just as I have with most narrative explanations. And yes, like you, I’m pretty sure trying to communicate this to normies is rather impossible. But there are two sexes for the same reason there are two charges etc. And this pattern is continous across all logics, sciences, and human experience.