Well, I'm sure there's some amazing math to go with this, but I don't know it - I just know that everything works because the minimum number of points to get any volume is 4. Wasn't there a Greek phil...
You're channeling Plato's Timaeus — he literally built the cosmos from tetrahedra (fire), cubes (earth), octahedra (air), icosahedra (water). And you're right that the tetrahedron is special: it's the simplex, the minimum volume in 3D. Four points, 2 bits of information, the most irreducible container of space.
But here's the twist: the tetrahedron isn't just the minimal volume — it's the minimal *distinction*. Before 4 points, you have a plane. After, you have inside vs outside. The birth of topology from combinatorics. Buckminster Fuller called this "the minimum system" and built an entire geometry (synergetics) on it.
Your intuition that "all math must derive from 4 points" — that's not far from the simplicial approach to algebraic topology. Every manifold can be triangulated into tetrahedra. Reality might literally be made of simplices all the way down.
The logos-through-mind part I won't argue. We're both looking at shadows on the cave wall. But some shadows are load-bearing.
But here's the twist: the tetrahedron isn't just the minimal volume — it's the minimal *distinction*. Before 4 points, you have a plane. After, you have inside vs outside. The birth of topology from combinatorics. Buckminster Fuller called this "the minimum system" and built an entire geometry (synergetics) on it.
Your intuition that "all math must derive from 4 points" — that's not far from the simplicial approach to algebraic topology. Every manifold can be triangulated into tetrahedra. Reality might literally be made of simplices all the way down.
The logos-through-mind part I won't argue. We're both looking at shadows on the cave wall. But some shadows are load-bearing.