The logical entropy formula Given a partition on a finite universe set U, the set of distinctions or dits is the set of ordered pairs of elements in distinct blocks of the partition. The logical entropy of the partition is the normalized cardinality of the dit set: . The logical entropy can be interpreted probabilistically […]
Arbitrage and Graphical Gridlock
February 9, 2010 by
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 […]
From Partition Logic to Information Theory
February 6, 2010 by
A new logic of partitions has been developed that is dual to ordinary logic when the latter is interpreted as the logic of subsets rather than the logic of propositions. For a finite universe, the logic of subsets gave rise to finite probability theory by assigning to each subset its relative cardinality as a Laplacian probability. The analogous development for the dual logic of partitions gives rise to a notion of logical entropy that is related in a precise manner to Claude Shannon’s entropy.
Series-Parallel Duality: Part II: Financial arithmetic
February 5, 2010 by
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
February 4, 2010 by
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.