Hiding at the heart of the US Constitution is an invidious number: the fraction three-fifths. This was the worth placed on slaves, compared with free men. The so-called “three-fifths compromise” declared that each state should count slaves as three-fifths of a person for purposes of taxation and representation. Such is the power of numbers within the political sphere, as described by Michael Meyerson, professor of law at the University of Baltimore.

Meyerson starts from the premise (itself a quintessentially mathematical gesture) that principles of mathematics underlie the legal framework which informs much American political life, from the Constitution to affirmative action. While this seems at first blush an unpromising point of departure, Meyerson is following in a great tradition of mathematical interdisciplinary literature, including Morris Kline’s Mathematics and Western Culture and John Allen Paulos’s A Mathematician Reads the Newspaper, both of which  Meyerson acknowledges in his preface. Here, Meyerson stresses the role which aesthetics plays in mathematics, quoting with approval the mathematician David Hilbert’s reaction on hearing that a promising student had rejected a mathematical career for that of a poet: “Good - he did not have enough imagination to be a mathematician.”

The word “chaotic” in the subtitle is used in its mathematical sense: an unstable feedback system in which changes to initial conditions can lead to wild shifts in outcomes. This is the butterfly effect: the flapping of a butterfly’s wings in Asia can lead to a tornado over America.  Meyerson plausibly argues that insights from chaos theory can be fruitfully applied to constitutional interpretation, since the US constitution is itself a dynamic system driven by feedback (in this case, previous Supreme Court rulings). Meyerson’s historical survey demonstrates that legislators and judges explicitly appealed to mathematical forms of proof in order to ground their judgements in certainly; chaos shows that if the judgements on which subsequent rulings rely are themselves flawed, injustice will proliferate throughout the system. In a similar vein, Meyerson introduces other mathematical concepts, such as that of a “limit”, “game” or “equality” and teases out the political ramifications of the analogy, so that equality leads to a discussion about affirmative action, vetoes and discrimination, for example.  The section on how to devise equitable voting systems is particularly illuminating in the wake of the 2000 election, when a margin of just 537 votes separated the 6m strong electorate in Florida.

While his material is drawn from US political life, the thrust of his argument is equally applicable to the UK. By drawing a parallel with the concept of “political literacy”, Meyerson reminds us that the ability to think with and about numbers is an essential part of our duty as active citizens, and is just as important to a healthy political process as is our ability to reason with words. Meyerson stretches his point when argues that the type of logical reasoning (the syllogism) which underpins the Constitution is mathematical in nature: one could just as easily argue that it is mathematics which is governed by logic, rather than the other way round. But that is a minor quibble in a work which surveys the twin landscapes of numerical and political discourse with clear-sighted authority, and casts new light on the relationship between them.