The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality–that is described mathematically by partitions. Our sense-making strategy is implemented by developing the mathematics of partitions at the connected conceptual levels of sets and vector spaces. Set concepts are transported to (complex) vector spaces to yield the mathematical machinery of full QM, and the complex vector space concepts of full QM are transported to the set-like vector spaces over ℤ₂ to yield the rather fulsome pedagogical model of quantum mechanics over sets or QM/sets.
Three Themes about the Mondragon cooperatives
January 1, 2014 by
This is a preprint of a paper developing three themes, capital structure, active learning, and spinoffs, with special attention to the Mondragon cooperatives.
Introduction to Partition Logic
January 1, 2014 by
This is an introductory treatment of partition logic which also shows the extension to logical information theory and the possible killer application to quantum mechanics.
On Property Theory
November 25, 2013 by
This paper is an introduction to property theory including the invisible hand mechanism which handles the initiation and termination of property rights in an on-going private property market economy. The Fundamental Theorem is that when Hume’s conditions of no involuntary transfers and no breached contracts are fulfilled, then the Lockean principle of people getting the fruits of their labor, i.e., imputing legal responsibility in accordance with de facto responsibility is satisfied. The major application is to the current system of a private property market economy based on the renting of persons, i.e., the employment contract.
This is a reprint of the paper in the Journal of Economic Issues in Sept. 2014.
Introduction to Logical Entropy
November 24, 2013 by
This paper, a reprint from the International Journal of Semantic Computing, introduces the logical notion of entropy based on the newly developed logic of partitions that is mathematically dual to the usual Boolean logic of subsets (aka “propositional logic”), and compares it to the usual Shannon entropy.
Quantum mechanics over sets
October 24, 2013 by
This paper gives a toy model of quantum mechanics over the field 2, where the vectors can be interpreted as subsets of a universe set, and hence the name: “Quantum mechanics over sets.” It gives the “logic” of QM in the old-fashioned sense of the essential logic of a theory pared down to operations on sets (vectors over 2). This includes the simplest logical treatment of the double-slit experiment, Bell’s Theorem, the probability calculus based on Born’s Rule, and much else (all restated in the context of sets).
Determination through universals
May 28, 2013 by
Semiadjunctions (essentially a formulation of a universal mapping property using hets) turn out to be the appropriate concept for applications of category theory in the life sciences.
Making Enterprises and Markets Responsible
March 26, 2013 by
This is a paper written to further Richard Cornuelle’s abiding vision of a more responsible economy and posted here to invite comment. The basic idea is revisit the whole idea of a market economy dominated by absentee-owned and publicly traded corporations (“Wall Street Capitalism”) that disconnect companies (“the Mother of all disconnects”) from the natural desires of the people working in the companies to improve their communities.
Information as distinctions
January 23, 2013 by
This paper is sub-titled “New Foundations for Information Theory” since it is based on the logical notion of entropy from the logic of partitions. The basic logical idea is that of “distinctions.” Logical entropy is normalized counting measure of the set of distinctions of a partition, and Shannon entropy is the number of binary partitions needed, on average, to make the same distinctions of the partition.