The Geometry of Logic

Mathematics don't get their just deserts, so I thought it might be prudent for mathematicians to calculate the geometry of language, and make sure the linguists get it right.

It helps to read the title and the first paragraph, but I can skim through 20 pages of physics, math, or whatever, and point out exactly where they make logic errors and assumptions, without ever reading a word, just by the shapes of the paragraphs. In other words, language itself expresses the geometry of logic, that trained mathematicians can describe, helping the lawyers to define reality for the rest of us. Try it for yourself, you might be surprised how fast you can get good at it.

The theoretical implications are that logic and geometry express particle-wave duality, which is why the geometry of logic only becomes apparent in language. Languages all obey Zipf's law, for a hyperbolic distribution of words. In general, the more causal your math, the more parabolic, while theories like Relativity and Quantum Mechanics obey a hyperbolic curve. Parabola's can emerge from hyperbolic curves, suggesting everything expresses both humble efficiency and elegant simplicity.

This is a contextual geometry, where the same principle in quantum mechanics applies where, more is different. Think of a giant puzzle you assemble, where each piece you add will frequently confuse the Big Picture. Quanta have proven to be predictable in enormous numbers, yet they still become impossible to predict one at a time. This pattern obeys a multifractal equation, a Fractal Dragon emerging from a Mandelbrot, or what can also be modeled after four modified Bayesian probabilities, forming a torus. This is how your neurons organize.

Note that this particular geometry I'm describing is just for logic, because humor is taboo in academia, so I developed it as a foot in the door. It's actually a simplification of the next geometry, while the next geometry I write should go down the rabbit hole. Very psychedelic possibly. This is just for logic, the next covers Spooky Quantum Mechanics, adding the emotional logic to the geometry, with each geometry I create including some way to measure the geometry of the singularity in the real world. What they all look like combined, is the mystery.