Source
Seth (2010), “Measuring Autonomy and Emergence via Granger Causality”, Artificial Life 16(2): 179–196, LIT-1170, read in full in NOTE-935 from the deposited published version.
What was actually shown
Definitions. G-autonomy ga_{X|E} = log(var(ε without X’s own lags)/var(ε full)) (Eq. 3). G-emergence ge_{M|m} = ga_{M|m}·(1/N)Σ gc_{mᵢ→M} (Eq. 4), with Taylor-expanded regressors for the nonlinear version (Eqs. 5–6).
A constructed system (Eq. 7, Table 1). G-autonomy is zero for white noise and for a variable driven only by white noise, and high for variables with their own autoregressive terms. The set of G-causalities does not fix the G-autonomies.
Predator–prey (§3). Predator G-autonomy orders the four conditions as built, and the evolved controller beats the rule that uses internal state.
Boids (§4). G-emergence of the centre of mass and Granger causation from it to the boids are higher in the hand-chosen flocking condition than in rigid or random motion, linear and nonlinear alike.
What could have come out otherwise: G-emergence could have failed to separate the three boids conditions, or been highest for the rigid formations.
What this does not say
- That G-emergence measures emergence independently of the analyst. It is positive when micro factors are missing or the predictor is limited, and would be zero with the system itself as predictor (§5.2).
- That downward Granger causation is downward causation. It is Granger causation from macro to micro, which Seth calls “ontologically innocent”. An intervention on the centre of mass that leaves the boids at that time unchanged does not exist, so it is not an interventional effect in THEORY-704’s sense (CLAIM-334).
- That evolution promotes autonomy in general. One model, one evolved controller, conditions ordered by construction.
- Anything about consciousness. §5.3’s link to volition is a hypothesis, untested.
- That the measure is robust. Fig. 6’s smoothness is by inspection.
Connections
- THEORY-497 (ΦID) and THEORY-257 (dynamical independence) are later accounts of the same phenomenon. Dynamical independence asks only that the micro history add nothing to the macro variable’s self-prediction. G-emergence asks for dependence and autonomy at once.
- Hoel et al.’s complaint that Granger emergence is not causal (NOTE-726) is one Seth accepts.
- TERM-058 defines Granger causality in the record’s own words.