Statistical physics: transport, percolation, criticality, and tipping points

Networks do not usually fail gradually -- they hold, and hold, and then collapse all at once past a tipping point. This page gathers conjectures that borrow the mathematics physicists use for exactly that kind of behaviour: percolation theory, which predicts the sudden collapse of a connected network once too many links fail; phase transitions, where one state suddenly gives way to another; and self-organized criticality, where a system creeps toward a tipping point and gives off early tremors before it goes. The claim tested here is a strong one: that a real historical process -- an amber-trading network, a tin-supply route, a currency going bad -- fits one of these equations exactly, not just resembles it loosely.

Gresham's phase transition and Tin percolation collapse both test whether a network -- a currency system, a metal-trade route -- fails the way percolation theory predicts, collapsing suddenly once connectivity drops below a threshold rather than degrading gradually. Amber advection and Obsidian regime shifts each track a traded material, amber and obsidian, as if it were a substance diffusing and occasionally shifting into a new distribution regime. Hollow ways are slime mold reads worn hollow paths cut into hillsides as behaving like a slime mould's efficient, self-organizing network rather than a centrally planned road system.