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## A Basic Duality in the Exact Sciences: Application to QM

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

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

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

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

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

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

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.