This post describes the duality between the usual (series) addition and the dual parallel addition. This duality is normally considered in electrical circuit theory and combinatorics, but it has a much wider applications. In Part I of this post, the focus is on developing series-parallel dual formulas—in contrast to the usual focus on formulas using only the series sum.
The Math of Double-Entry Bookkeeping: Part I (scalars)
February 3, 2010 by
Double-entry bookkeeping illustrates one of the most astonishing examples of intellectual insulation between disciplines—the very opposite of intellectual trespassing.
The Math of Double-Entry Bookkeeping: Part II (vectors)
February 3, 2010 by
Although double-entry bookkeeping (DEB) has been used in the business world for 5 centuries, the mathematical formulation of the double entry method is almost completely unknown. The correct mathematical formulation allows the generalization from the value scalars of ordinary DEB to multi-dimensional accounting using vectors–which is the topic of this post.
The implication operation on partitions
February 2, 2010 by
Partitions and equivalence relations In a 2001 commemorative volume for my mathematical mentor, Gian-Carlo Rota, three of his associates noted that “the only operations on the family of equivalence relations fully studied, understood and deployed are the binary join and meet operations.” This note defines the apparently new operation of implication for partitions, an operation […]
From propositional logic to subset logic to partition logic
February 1, 2010 by
From propositional logic to subset logic This note outlines the following sequence of ideas. First, ordinary propositional logic is reinterpreted as the logic of subsets of a universe set U, with the propositional case being isomorphic to the special case of U = 1. Then the category-theoretic duality between subsets of a set and partitions […]
Straight-line and Hoskold Capitalization in Real Estate Appraisal
March 24, 2000 by
Here is the paper you have been waiting for: Ellerman, David. 1994. “New Results on the Straight Line & Hoskold Methods of Capitalization.” Real Property Perspectives, no. July: 29–36, 80–81.