James P. Crutchfield (Complexity Sciences Center and Physics Department, University of California at Davis, and SFI External Professor)
Abstract: We show why the amount of information communicated between the past and future — the excess entropy — is not in general the amount of information stored in the present — the statistical complexity. This is a puzzle, and a long-standing one, since the former describes observed behavior, while optimal prediction requires the latter. We present a closed-form expression for the excess entropy in terms of optimal causal predictors and retrodictors — both epsilon-machines of computational mechanics. This leads us to two new system invariants: causal irreversibility — the temporal asymmetry between causal representations — and crypticity — the degree to which a process hides its state information.
Joint work with Chris Ellison, Ryan James, and John Mahoney.