learning when solids flow.

a bingham plastic can behave like a rigid body under low stress, then flow like a viscous fluid when the stress is high enough. toothpaste shows how a material can wait for a threshold before moving as a coherent plug.

as some systems approach a tipping point, they recover more slowly from small disturbances. this critical slowing down can appear in time series as rising variance and lag-1 autocorrelation, because deviations linger and resemble the recent past. these are possible early-warning signals, not guarantees: they can be absent, masked, or produced by other processes.

alternative stable-state theory models a system as a ball in an attraction basin. ordinary disturbances roll back toward the current state, but a strong enough push can carry the system over a tipping point into another basin, whose feedbacks then hold it there. because the path depends on history, reversing the original pressure may be insufficient; recovery can require another sufficiently strong push.