This is an essay in what might be called “mathematical metaphysics.” There is a fundamental duality that runs through mathematics and the natural sciences, from logic to biology.
A Basic Duality in the Exact Sciences: Application to QM
May 12, 2024 by
This approach to interpreting quantum mechanics is not another jury-rigged or ad-hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences.
A Pedagogical Model of Quantum Mechanics Over Sets
April 9, 2024 by
The new approach to quantum mechanics (QM) is that the mathematics of QM is the linearization of the mathematics of partitions (or equivalence relations) on a set. This paper develops those ideas using vector spaces over the field Z2 = {0.1} as a pedagogical or toy model of (finite-dimensional, non-relativistic) QM.
New Logic & New Approach to QM
March 17, 2024 by
The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM.
4Open: Special Issue: Intro. to Logical Entropy
January 14, 2022 by
4Open is a relatively new open access interdisciplinary journal (voluntary APCs) covering the 4 fields of mathematics, physics, chemistry, and biology-medicine. A special issue on Logical Entropy was sponsored and edited by Giovanni Manfredi, the Research Director of the CNRS Strasbourg. My paper is the introduction to the volume.