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.
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.
The Logical Theory of Canonical Maps
July 11, 2020 by
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and functions.
New Light on the Objective Indefiniteness or Literal Interpretation of QM
December 17, 2018 by
This paper shows how the mathematics of QM is the math of indefiniteness and thus, literally and realistically interpreted, it describes an objectively indefinite reality at the quantum level. In particular, the mathematics of wave propagation is shown to also be the math of the evolution of indefinite states that does not change the degree of indistinctness between states. This corrects the historical wrong turn of seeing QM as “wave mechanics” rather than the mechanics of particles with indefinite/definite properties.
Talk: Hamming distance in classical and quantum logical information theory
January 12, 2018 by
This is a set of slides from a talk on introducing the Hamming distance into classical logical information theory and then developing the quantum logical notion of Hamming distance–which turns out to equal a standard notion of distance in quantum information theory, the Hilbert-Schmidt distance.
Talk: New Foundations for Quantum Information Theory
November 28, 2017 by
These are the slides for a talk given at the 6th International Conference on New Frontiers in Physics on Crete in August 2017.
Talk: New Foundations for Information Theory
November 28, 2017 by
These are the slides for a number of talks on logical information theory as providing new foundations for information theory.
Logical Information Theory: New Foundations for Information Theory
September 17, 2017 by
There is a new theory of information based on logic. The definition of Shannon entropy as well as the notions on joint, conditional, and mutual entropy as defined by Shannon can all be derived by a uniform transformation from the corresponding formulas of logical information theory.
Logical Entropy: Introduction to Classical and Quantum Logical Information Theory
July 15, 2017 by
Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences, and distinguishability, and is formalized as the distinctions of a partition (a pair of points distinguished by the partition). This paper is an introduction to the quantum version of logical information theory.
The Existence-Information Duality
October 30, 2015 by
The development of the logic of partitions (dual to the usual Boolean logic of subsets) and logical information theory bring out a fundamental duality between existence (e.g., elements of a subset) and information (e.g., distinctions of a partition). This leads in a more meta-physical vein to two different conceptions of reality, one of which provides the realistic interpretation of quantum mechanics.