The fatal flaw at the root of today’s post is really what might be called “the fundamental myth” about the current property system, namely that the market-contractual role of being the residual claimant in a productive opportunity is treated as a “property right” that is currently owned by some legal party (e.g., the corporation having the contractual role) and that may be bought and sold as well as capitalized into the party’s current valuation.
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.
Development or just poverty reduction?
February 3, 2010 by
Many of the debates about foreign aid and development assistance seem to pivot on different visions of the goal: development or just poverty reduction.
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 […]
The Fatal Flaw in Cost-Benefit Analysis
January 31, 2010 by
In Part I of this commentary on the Sarkozy-Stiglitz Commission on the Measurement of Economic Performance and Social Progress, the focus was on the social engineering perspective underlying the search for such an index. But at the end of that commentary, I noted that the Commission’s discussion of different indices was rather “academic” since there is one dominant index used in governmental decision-making: the monetized gains minus the monetized losses of cost-benefit analysis. A proponent of cost-benefit (CB) analysis would roll up all the Commission’s discussion into the question of the better “costing out” of all the direct and indirect impacts of a social decision.
Obama needs new job creation ideas
January 29, 2010 by
The Obama economics team seems trapped by rather conventional job-creation ideas, e.g., Keynesian pump-priming or tax breaks for small businesses, ideas whose main virtue is that they are better than the opposition’s ideas of more tax breaks for the rich. But there are other ways to increase job creation and entrepreneurship that have been hindered by the size-maximizing tendencies of American corporations.