Exaptation and torsion: toward a theory of natural information processing

Several conundrums are provoked by attempts to provide algorithmic descriptions of natural phenomena. A characteristic feature of natural computation is a breakdown in the formal simulation relation. This is called hermeneutic torsion, and is formally the failure to commute of a diagram describing homomorphisms between dynamical systems. This torsion is a source of computational power. For example, it is deeply involved with phenomena such as exaptation, wherein an existing structure is recruited for a novel function. Exaptation occurs continually at the macromolecular level and is fundamentally nonalgorithmic; our system-theoretic models of computation deal with structural descriptions for which a functional semantics must be assigned in advance, and a natural system continually 'diagonalizes out' of this semantics. This perspective clarifies the nature of computing power and encourages consideration of a new kind of transcomputational complexity.