Path-Dependent vs. Ergodic Systems
January 11th, 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 fix the arm (perfectly) horizontally 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)
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