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Cosmological Complexity on Grandest Scales (published in Evolution, Complexite, Hierarchie, and Organisation: Modeles de la boucle evolutive, A.C. Ehresmann, G.L. Farre, and J-P Vanbremeesch (eds.), p 20, Paris; invited paper at Emergence, Complexity, Hierarchy, and Organization meeting, Amiens, France, 1996)
How are “computational” dynamics of organic components organized to form organisms? The semiotic dilemma is exemplified by noting that the terms organic, organism, and organization are all derived from the same root! The common semantic origin of these terms strongly suggests the existence of a common perceptual pattern underlies the phenomena of complex pattern generators. Presumably, these generators create cellular “computations.”
Which mathematical structures are sufficiently rich to support a unified representation of interdependence, of hierarchical degrees of organization and of nonlinear dynamics? It has been suggested that category theory is appropriate. A notation for a hierarchical structure of the natural sciences is created which is consistent with categorical logic. A notational sequence for composing one - to - one correspondences among the degrees of organization [Oo] of material objects of a cellular system is proposed. Necessary and sufficient conditions for simple and complex systems are described. Causality is also exemplified in terms of the boundary conditions sustaining the system — bottom - up, top - down, outside - inward and inside - outward. This scientific notation is contrasted with six species of signs of general semiotics.
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