General Science and Philosophy |
Authors: Stephen P. Smith
Modern physics possesses extraordinarily powerful formal structures, but the existence of a successful formalism does not by itself settle what that formalism means. This essay proposes an interpretive program in which the Lie bracket is read as a generative relation and the Jacobi identity as a higher-order regulatory condition. On this interpretation, the familiar passage from binary relation to Jacobi coherence may be understood as the mathematical trace of a more general movement from two-sided differentiation toward a coherent whole. A previous proof-of-concept formulation of general relativity, in which extrinsic gravitation was modeled as a homeostatic coupling between CPT-symmetric spacetime manifolds, provides one possible spacetime realization of this idea, but may not be the most economical foundation for it. The deeper structure is already present in the pre-geometric formalism of Lie algebra. Quantum mechanics then supplies a further point of contact: noncommuting observables are constrained by uncertainty relations whose lower bound is directly related to their commutator. This does not prove a philosophical theory of attention, but it permits an interpretive extension in which different modes of attending to relational structure have different formal consequences. Iain McGilchrist’s distinction between narrow and broad attention provides a useful interdisciplinary vocabulary for this extension, without implying an identity between quantum mechanics and his account of cognition. The resulting proposal is neither a replacement for mathematical physics nor an attempt to derive metaphysics from equations. It is an argument for an interpretive meta-science in which formal mathematics establishes relational constraints while interdisciplinary inquiry asks what kind of organization those constraints may express.
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