%0 Journal Article
%T The Past and the Future in the Present
%A James P. Crutchfield
%A Christopher J. Ellison
%J Mathematics
%D 2010
%I arXiv
%X 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.
%U http://arxiv.org/abs/1012.0356v1