-
When Rules Repeat: The Fixed Point Ladder
Markets as Reflexive Fixed Points
Markets are more than noisy aggregators of information: beliefs about prices help determine prices, which makes reflexivity a fixed-point problem with fat tails, non-ergodicity, and hysteresis.
-
When Rules Repeat: The Fixed Point Ladder
Power Laws, Extremistan, and Non-Ergodicity
Scale invariance becomes power laws; power laws move importance to extremes; extremes make averages unstable through time.
-
The Edge of Chaos
Sandpiles and Crashes: How Systems Tune Themselves to the Brink
The last essay left a loose end. Markets can sit near a critical edge where small shocks cascade, but critical points are usually finely tuned, so who keeps a market balanced there? The answer, found in a pile of sand, is that nobody does. Some systems walk to the brink on their own, and that is where their crashes come from.