The Past and the Future in the Present

Author(s): Crutchfield, James P.; Ellison, Christopher J. | Abstract: We show how the shared information between the past and future---the excess entropy---derives from the components of directional information stored in the present---the predictive and retrodictive causal states. A detailed proof allows us to highlight a number of the subtle problems in estimation and analysis that impede accurate calculation of the excess entropy.

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