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.
Talk Slides about European ESOP
April 4, 2024 by
These are slides from a talk about the European ESOP (Employee Stock Ownership Plan) developed by the Institute for Economic Democracy in Ljubljana, Slovenia.
Worker Cooperatives and other so-called “Cooperatives”
March 30, 2024 by
Most cooperative organizations today do not exemplify any cooperative activity; non-worker cooperatives do not represent any cooperative activity of the members since the only joint activity of the organization is carried out by employees. The idea that cooperatives are democratically governed does not apply to non-worker cooperatives (based on the employment relation) since the members are not choosing the managers or governors of their own activity but of the activity of the people working in the cooperative.
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.
Heteromorphic Approach to Adjunctions
January 18, 2024 by
Saunders Mac Lane famously remarked that “Bourbaki just missed” formulating adjoints in a 1948 appendix (written no doubt by Pierre Samuel) to an early draft of Algebre–which then had to wait until Daniel Kan’s 1958 paper on adjoint functors. But Mac Lane was using the orthodox treatment of adjoints that only contemplates the object-to-object morphisms […]
The Born Rule is a feature of Superposition
October 20, 2023 by
The Born Rule arises naturally out of the mathematics of probability theory enriched by superposition events. It does not need any more-exotic or physics-based explanation. No physics was used in the making of this paper. The Born Rule is just a feature of the mathematics of superposition.
Kaldor-Hicks Petitio Principii Fallacy
October 4, 2023 by
This paper shows that implicit assumptions about the numeraire good in the Kaldor–Hicks efficiency–equity analysis involve a ‘‘same-yardstick’’ fallacy (a fallacy pointed out by Paul Samuelson in another context), a special case of the Petitio Pricipii fallacy.
The new partitional approach to (literally) interpreting quantum mechanics
May 1, 2023 by
This paper presents a new `partitional’ approach to understanding or interpreting standard quantum mechanics (QM). The thesis is that the mathematics (not the physics) of QM is the Hilbert space version of the math of partitions on a set and, conversely, the math of partitions is a skeletonized set level version of the math of QM.
“Follow the Math” Preprint
February 26, 2023 by
The slogan “Follow the money” means that finding the source of an organization’s or person’s money may reveal their true nature. In a similar sense, we use the slogan “Follow the math!” to mean that finding “where the mathematics of QM comes from” reveals a good deal about the key concepts and machinery of the theory.