Tangents as Local Truth
Derivative as instantaneous constraint
What you’re seeing
A point moves periodically along y = sin(x). The tangent line uses the same phase parameter — no drift.
f(x)=sin(x)
f′(x)=cos(x)
f′(x)=cos(x)
Least Action Principle
All paths explored — one survives
Why the straight path wins
All curves fluctuate, but deviations are pulled back toward a baseline. This is a discrete Euler–Lagrange analogue.
Why this resolves Zeno
Infinite subdivision does not diverge because each perturbation is damped. Infinity collapses into a finite attractor.
Harmonic Context
Local motion is governed by global structure