A formal equivalence class algebra, in the sense of the groupoid section of the Appendix, can now be constructed by choosing different origin and end points S 0; S ∞ and defining equivalence of two states by the existence of a high probability meaningful path connecting them with the same origin and end. Disjoint partition by equivalence class, analogous to orbit equivalence classes for dynamical systems, defines the vertices of the proposed network of cognitive dual languages, much enlarged beyond the spinglass example. We thus envision a network of metanetworks, in the sense of Ciliberti et al. Each vertex then represents a different equivalence class of information sources dual to a cognitive process. This is an abstract set of metanetwork ‘languages’ dual to the cognitive processes of gene expression and development.
KeywordsEquivalence Class Free Energy Density Allometric Scaling Disjoint Partition Mathematical Appendix
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