Towards quantifying a wider reality: Shannon exonerata

Abstract

In 1872 Ludwig von Boltzmann derived a statistical formula to represent the entropy (an apophasis) of a highly simplistic system. In 1948 Claude Shannon independently formulated the same expression to capture the positivist essence of information. Such contradictory thrusts engendered decades of ambiguity concerning exactly what is conveyed by the expression. Resolution of widespread confusion is possible by invoking the third law of thermodynamics, which requires that entropy be treated in a relativistic fashion. Doing so parses the Boltzmann expression into separate terms that segregate apophatic entropy from positivist information. Possibly more importantly, the decomposition itself portrays a dialectic-like agonism between constraint and disorder that may provide a more appropriate description of the behavior of living systems than is possible using conventional dynamics. By quantifying the apophatic side of evolution, the Shannon approach to information achieves what no other treatment of the subject affords: It opens the window on a more encompassing perception of reality.