Code Constraint
Low-dimensional codes constrain high-dimensional dynamics
Two Coupled Systems
System A drives System B through a code. Both are Kuramoto oscillator lattices with nearest-neighbor coupling. A runs freely with noise; B tracks A but only sees what passes through the bandwidth bottleneck.
Structured vs Unstructured
Toggle Fourier vs Random projection. Fourier modes (low-frequency) cause N_eff collapse. Random projections cause whitening—B stays high-dimensional but loses structure. This is the key finding.
N_eff Collapse
Watch N_eff (effective dimensionality). A's N_eff stays high (~17). B's N_eff collapses as k drops with Fourier, but stays high with random projection. Biology uses structured constraints.
Key Experiment
1. Drag slider from k=32 to k=4 (Fourier)—watch B collapse. 2. Click toggle to Random—B stays complex but uncorrelated. The constraint must match the structure to constrain without destroying.