Coupling Outpaces Measurement
Systems synchronize via coupling faster than observers can detect it via measurement.
Demonstrates the fundamental inequality: Tsync ~ 1/|λc| << Tmeas ~ Istruct/R
Coupling Channel
Two structurally similar systems contract onto a shared synchronization manifold. This is a physical process governed by the conditional Lyapunov exponent λc.
Measurement Channel
An external observer accumulates information through bandwidth-limited sampling. This is an inference process bounded by channel capacity R.
The Blind Spot
During the gap Tsync < t < Tmeas, functional equivalence has been established but cannot yet be verified. The systems “know” each other before observers can confirm it.
Why This Matters
This isn't just about oscillators. Whenever high-dimensional systems coordinate—neurons synchronizing, cells recognizing each other, immune systems detecting pathogens—there may be a regime where coordination outpaces external verification. The “noise” that generic observers discard often carries the coordination signal.
Try reducing observer bandwidth (k) to see how limiting information access widens the blind spot. Try disabling coupling to see what happens without the synchronization channel.