Order, organization, and randomness: on the mathematical formulation of life

Life increasingly is understood in terms of information. I consider two attempts to formulate life in terms of mathematical information theory. G. J. Chaitin’s proposes to define life in terms of the relation between organization and algorithmic compressibility in biological information. More recently, William Dembski, Winston Ewart, and Robert J. Marks suggest that Dembski’s notion of specified complexity can be mathematically expressed in information-theoretic terms through the concept of algorithmic specified complexity. The mathematical approaches are similar and in both cases essentially dependent on the concept of randomness deficiency in algorithmic information theory: to subtract out the degree of randomness from an informational measure, yielding a remainder of organization (Chatin) or specified complexity (Dembski, Ewart, and Marks). I argue that these attempts must fail due the information-theoretic indistinguishability of organization and randomness. The failure is instructive, however, because it illustrates the inability of mathematical information theory to register biological organization.