Standard physics treats the coupling between two oscillators as a fixed number you tune by hand. This essay is about what happens when you let it be alive instead.
When couplings evolve according to a single principle — maximize coherence — they spontaneously organize into a binary field of alive and dead bonds. Topological defects nucleate out of random initial conditions. The system settles at the BKT critical point, not because we put it there, but because that is where topology and dynamics meet. And the fine structure constant α = 1/137.036, the thing physicists have stared at for a century, drops out as a byproduct of all of this — with zero free parameters.
This is a story best told with moving pictures. Each section below is short, interactive, and self-contained. Read in order, or skip to what draws you.
A note on interactionNumbers in the prose that look like this can be dragged left and right to change them. Watch the figures respond. Sliders in panels work the usual way. Everything runs in your browser — no data leaves your machine.
Companion to the paper The Coherence Learning Rule on the Diamond Lattice: From Coupled Oscillators to the Fine Structure Constant, Sharpe 2026. Source at github.com/project-89/coherence-lattice-alpha.