The lag between cause and effect. What a system does next depends on what you did to it before.
Drag left and right to lead him. Small changes of heart vanish into the slack — he counts those, and the count is public. Below, the loop draws itself: the green diagonal is a world without memory; the red path is the mule. You will always have walked farther than him. The gap is the hysteresis. He is not lazy. He is principled.
Not hysteria — different word, unrelated baggage. Hysteros simply means the one who comes after. The effect that arrives late to its own cause.
Magnetize a piece of iron, remove the field — the magnetism stays. Ewing, studying this stubbornness, names the lag hysteresis. The area inside the magnetic loop is real energy, lost as heat, every single cycle. Indecision has a price, and it's measured in joules.
Trying to mimic how squid neurons fire cleanly instead of chattering, Schmitt builds a circuit with two thresholds — one to switch on, a different one to switch off. The Schmitt trigger puts deliberate hysteresis into electronics. It is in essentially every chip you own, debouncing reality.
Barkhausen wraps a coil around iron, feeds it to a speaker, and slowly magnetizes the bar. Instead of a smooth rise he hears a rush of clicks — proof the domains flip in sudden discrete jumps, not gradually. The noise still bears his name. Magneto's cascade is real.
A furnace that switched at exactly 20° would flutter on-off forever at 19.99°. So thermostats hold a deadband: on at 18, off at 22. The gap where nothing responds isn't a flaw. It's the design. The system declines to care about small changes of heart.
Blanchard and Summers argue European unemployment shows hysteresis — push joblessness up and it does not fall back when the shock ends. The economy's present depends on its past. The loop applies to people now, and it is no longer charming.
UI debounce, alert thresholds that arm and disarm at different levels, agents that don't re-plan on every tiny observation. Engineers keep re-inventing the deadband because reality jitters and systems that react to everything react to nothing well. The mule was right all along.