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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.
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.
Probability Theory with Superposition Events
June 18, 2020 by
In finite probability theory, events are subsets S⊆U of the outcome set. Subsets can be represented by 1-dimensional column vectors. By extending the representation of events to two dimensional matrices, we can introduce “superposition events.”
From Abstraction in Math to Superposition in QM
January 14, 2017 by
This is a draft paper that makes a perhaps surprising connection between the old Platonic notion of a paradigm-universal like ‘the white thing’ and an indefinite superposition state in quantum mechanics.
Gian-Carlo Rota’s Probability Course: The Guidi Notes
June 13, 2016 by
This is a copy of the Guidi Notes for Gian-Carlo Rota’s Probability course at MIT the last time Rota gave the course. A copy of the Rota-Baclawski text used as course material can also be downloaded here.
Gian-Carlo Rota’s Introduction to Probability and Random Processes
December 1, 2012 by
This is a scanned copy of Gian-Carlo Rota’s and Kenneth Baclawski’s Introduction to Probability and Random Processes manuscript in its 1979 version.
From Partition Logic to Information Theory
February 6, 2010 by
A new logic of partitions has been developed that is dual to ordinary logic when the latter is interpreted as the logic of subsets rather than the logic of propositions. For a finite universe, the logic of subsets gave rise to finite probability theory by assigning to each subset its relative cardinality as a Laplacian probability. The analogous development for the dual logic of partitions gives rise to a notion of logical entropy that is related in a precise manner to Claude Shannon’s entropy.