The arbitrage-free law (or Kirchhoff’s voltage law) Recently I emailed a friend to complain when his organization used this 3 gear image as their logo. What was my complaint? Read on. The basic idea of arbitrage is to “get something for nothing” by trading commodities or currencies around some circle ending up with more than […]

## Series-Parallel Duality: Part II: Financial arithmetic

In financial arithmetic and in the appraisal literature, it has been noticed that the basic formulas occur in pairs, one being the reciprocal of the other. This Part II of the series-parallel duality post shows that these reciprocal formulas are an example of the SP duality normally associated with electrical circuit theory.

## Series-Parallel Duality: Part I: Combating Series Chauvinism

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)

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)

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.