Tools for the Future: Hidden Symmetries

Abstract

SummaryAdopting Maturan a’s and Varela’s perspective on the necessity of cognition—or Rosen’s view of “anticipation”—at every scale and level of organization of the living state it is possible to extend Yeung’s relation between information inequalities and finite group structure to a fundamental duality between an information-theoretic characterization of cognition in gene expression and the groupoid extension of simple symmetries. It appears that gene expression, responding to and hence “anticipating” environmental clues, in a large sense, may sometimes be characterized by groupoids of increasing complexity constructed from underlying finite groups. While higher organisms at later developmental stages may not be described so simply, Yeung’s powerful results suggest the existence of regularities built from finite groups during certain developmental periods via an extension of the spontaneous symmetry breaking/making formalism familiar from physical theory. Essentially, the S-shaped developmental curve serves as a temperature analog driving increasing levels of deeply underlying topological symmetries. This suggests, as in the characterization of complex geometric objects by “simpler” structures in algebraic topology, that a shift of perspective from gene expression networks and their dynamics to their underlying symmetries may provide deeper insight to ontology and its dysfunctions.