recovery time

Red ball is recovering from a poke; blue is settled and only jostling. Slide toward shallow and poke again — the recovery time grows, the trace widens, the autocorrelation climbs.

// what to notice

flatten the valley and the ball takes longer to settle — and wanders wider, and each moment predicts the next more. slow recovery, rising variance, rising autocorrelation: the signs a basin is getting shallow. a thing to notice by, not a diagnosis.

// what this is

This is critical slowing down: as a system's basin flattens, its return rate falls, so recovery after a disturbance lengthens and noise-driven fluctuations grow slower and wider. Scheffer et al. (2009) collect it as a generic early-warning signal — one that shows up ahead of tipping points across ecosystems, climate records, and other dynamical systems. Critical slowing down itself is established. Reading resilience from the wobble this way is the proposal, and it is real but imperfect: the same signs have ordinary causes, false alarms and missed warnings both happen, and the ball here is an idealized linear model, not any particular system. It measures a tendency, not an outcome; it is not a prediction. This is not therapy and not a diagnosis — a way to notice by, nothing clinical. where this misleads.

// kin

recovery-time — the same early-warning signal, written up · the settling — displacement and return, with the manner of return set by one number