This old essay deals with a connection between a relatively recent (1940s and 1950s) field of mathematics, category theory, and a hitherto vague notion of philosophical logic usually associated with Plato, the self-predicative universal or concrete universal.
Introduction to Series-Parallel Duality
December 11, 2012 by
This is an introduction to the mathematics of series-parallel duality which shows many unexpected applications.
Mathematics of Real Estate Appraisal
December 11, 2012 by
This paper on the math of real estate appraisal is my most downloaded paper on the SSRN site! Hence I might as well make it available here too. It is a long discourse on the mathematics of compounding and discounting.
Mathematics of Double Entry Bookkeeping
December 11, 2012 by
This is a scan of the first publication in a mathematics journal of the mathematical treatment of double-entry bookkeeping using the group of differences construction.
Double Entry Multidimensional Accounting
December 11, 2012 by
This is a scan of the first journal publication of the mathematical formulation and generalization to vectors of double-entry bookkeeping.
Arbitrage Theory
December 11, 2012 by
This a reprint of an applied math paper connecting the notion of arbitrage and the Lagrange multipliers of mathematical economics. The paper has a simple application showing that a circular gear train (all in the same plane) with an odd number of gears is rigid (cannot move) like the graphic to the left.
Ellerman-Rota Mathematics Paper
December 7, 2012 by
This was my only math paper co-authored with Gian-Carlo Rota who in many respects was my mentor in mathematics. It reduced my Erdos number from infinity to 3.
Generalized-Ultraproducts
December 7, 2012 by
Published version of my 1971 PhD dissertation in mathematics.
Intellectual Trespassing as a Way of Life: Essays in Philosophy, Economics, and Mathematics
December 3, 2012 by
Dramatic changes or revolutions in a field of science are often made by outsiders or ‘trespassers,’ who are not limited by the established, ‘expert’ approaches. Each essay in this diverse collection shows the fruits of intellectual trespassing and poaching among fields such as economics, Kantian ethics, Platonic philosophy, category theory, double-entry accounting, arbitrage, algebraic logic, series-parallel duality, and financial arithmetic.
Economics, Accounting, and Property Theory
December 1, 2012 by
This is my first book. In order to develop a mathematical model of the stocks and flows of property inside a firm, I first had to give a math model of the usual double-entry accounting for the stocks and flows of the scalar value, and then generalize it to vectors of property rights.