Path-Dependent vs. Ergodic Systems

JANUARY 11, 2008

Consider a metal arm fixed by a pin. If it is hung vertically then the arm, no matter where it starts, will always end up in the same position.

However, if you the arm is set on a perfectly flat horizontal surface then it will stay forever in its initial position. The first case is ergodic: we converge independent of the starting point to some particular configuration; while the second is ‘path-dependent’ (or dependent on initial conditions): where you end up depends crucially on where you start. The question:

Is animal / technological / historical / linguistic evolution ergodic or path dependent?

More generally, how ergodic or path-dependent are the following processes?

  • (Natural) Evolution
  • Technological change
  • Human history
  • Communication systems such as natural languages
  • Other symbol systems (e.g. games or mathematics)