Political Numeracy: Mathematical Perspectives on Our Chaotic Constitution [Hardcover]

Michael I. Meyerson (Author), Michael Meyerson (Author)

Book Description

Publication Date: March 2002

From the impossibility of a perfectly democratic vote to the creation of a model that clarifies affirmative action debates, Michael Meyerson uses mathematics to open a fresh window onto American public life. In accessible terms, this text applies concepts of infinity to the abortion debate; provides an arithmetical justification of the Electoral College; uses topology to understand the shape of American government and Godel's incompleteness theorem to shed light on metaconstitutional problems. The text discusses how mathematics is not about reducing life to numbers and black-and-white solutions but instead offers a mind-expanding perspective on the complexities of the world.

Editorial Reviews

Amazon.com Review

There's more math in the Constitution than most people realize, from legislative majorities to congressional apportionment to what Michael Meyerson calls "the ugliest number in the Constitution"--the Founders' treatment of each slave as "three-fifths" of a person for the purposes of representation and taxation. Political Numeracy is a delightfully offbeat book, bursting with ideas that will appeal to the sort of person who had trouble deciding whether to major in math or political science: "Our federalist system can be seen as a kind of fractal structure," observes the author at one point. Meyerson, a law professor at the University of Baltimore, writes accessibly; it does not require a prior knowledge of fractals to follow his prose. Indeed, he even appreciates the severe limits of math: "It is utterly incapable of making the sorts of judgments and interpretations that lie at the heart of the Constitution." At the same time, he uses math to illuminate our understanding of that document. His discussion of the electoral college, for instance, shows why the result of the 2000 presidential election, in which the winning candidate won fewer popular votes than his opponent, should not be considered anti-majoritarian. Political Numeracy will appeal to fans of The Armchair Economist by Steven E. Landsburg and other readers who like to look at old topics from new perspectives. --John Miller

From Publishers Weekly

University of Baltimore law professor Meyerson shows how a wide range of mathematical subjects, from Euclid's ancient axiomatic method to recent developments in chaos theory, can throw light on the Constitution and how the Supreme Court interprets it. Though he sometimes delves into fairly sophisticated math game theory, transfinite arithmetic, G”del's Incompleteness Theorem his sharp focus on essential insights should put all readers at ease. For example, he demonstrates how the comparison of infinite numbers illuminates different precious values the author's life may be of "infinite value" to him, for example, and yet his children's lives are more valuable. Calculations are rare and only involve simple arithmetic. By disavowing claims that a focus on math can replace other perspectives, Meyerson highlights the valuable insights his methods can provide. His use of proportional analysis as a way of evaluating affirmative action is fascinating not because he suggests an ultimate solution, but because the mathematical approach "infuses analysis with an awareness of the inevitable imperfections of one's own position." Such an awareness might encourage more reasoned debate. Some of Meyerson's topics voting systems, reapportionment have long been studied mathematically, but most get a novel treatment (for example, "our federalist system can be seen as a kind of fractal structure"). Particularly intriguing is the argument, based on chaos theory, which asserts that the nation is on a "very different constitutional path" than Madison and Hamilton would have ever imagined. Meyerson's insights vary in profundity, but all serve to stimulate awareness of a potentially rich new perspective. Illus.
Copyright 2002 Cahners Business Information, Inc.

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Product Details

• Hardcover: 256 pages
• Publisher: W. W. Norton & Company; 1 edition (March 2002)
• Language: English
• ISBN-10: 0393041727
• ISBN-13: 978-0393041729
• Product Dimensions: 8.5 x 5.8 x 1.1 inches
• Shipping Weight: 1.1 pounds
• Average Customer Review: 3.8 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #2,062,182 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

2 of 2 people found the following review helpful:

5.0 out of 5 stars Great Book, August 29, 2002

By A Customer

This review is from: Political Numeracy: Mathematical Perspectives on Our Chaotic Constitution (Hardcover)

I found myself talking about mathematical concepts and social issues with my mother after reading this book. It was so accessible and well-written that she and I had a great conversation about the concept of "infinity" and the abortion debate. Go figure. The book is creatively conceived, engaging, and passionately even-handed. Its a must read for anyone wanting an enlightening overview of our system of government, brought to life and made real by using some of the great historical and current social debates as a framework. Hard to describe. You must read it to understand. Great book.

7 of 10 people found the following review helpful:

2.0 out of 5 stars Rather obvious, July 14, 2003

By 

T. Patrick Sullivan (Germantown, TN United States) - See all my reviews
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This review is from: Political Numeracy: Mathematical Perspectives on Our Chaotic Constitution (Paperback)

Meyerson tries in this book to bring some of the ideas of mathematics into the law. Not just many, but most, legal issues would benefit from this infusion (some simple probabilistic reasoning would bring clarity to a lot of shrill debates, especially those surrounding malpractice insurance and the medical field), but he doesn't seem up to the task. His grasp of the mathematics is competent, but his comparisons to policy don't really use the mathematics at his disposal. I'm thinking in particular of his chapter on topology and his chapter on Euclidean and non-Euclidean geometries. In the former case, he makes some obvious comments about "stretching and adapting" the constitution while maintaining its initial structure. True, this is part of what topology is about, but to bring it up hardly illustrates anything novel about the constitution. In the latter case, his only political conclusions are that we need to recognize the fallibility of initial axioms. In both of these cases, he hasn't really showed us what is mathematical about politics but that mathematics and politics both share broad characteristics such as a concern with change, conflict, clear reasoning, etc. But this can be said about almost every academic discpline. I think that any bright HS student could throw together some similarly superficial comparisons between biology and politics or physics and politics or sports and politics.

Of course, I very much enjoyed his chapter on self-referential problems with the constitution, because I thought it was funny and interesting. However, the interesting part was not the application of mathematics in politics but the discussion of odd situations that can arise in politics. (He correctly argues that Godel's result yields no substantial conclusions for politics. Then why talk about it in a book on politics? Its only value is as a metaphor, and a weak one at that.)

On a side note, I know this isn't a forum, but the pedant in me must correct the previous reviewer. If we define a function, f(x)=(x^2-1)/(x-1), then f(x) is defined only when x is not equal to 1. In that case f(1) is undefined (because f(1)=0/0), and it makes no sense to cancel the common factors (x-1). Or to put it another way, this cancellation is only valid when x is not equal to 1. Otherwise, we would be cancelling a factor zero from the numerator and denominator (and no number except 0 has 0 as a factor). To put it yet another way, suppose we want to say that f(x) is equivalent to (x+1), as the previous reviewer does. If we do this, we must remember that we reached this result only by assuming we could cancel (x-1) from the numerator and denominator. Again this cancellation is only valid when x is not 1. Therefore, f(x)=(x+1) only when x is not equal to 1. Sorry, but I couldn't stand the thought of someone out there being misled on this point.

2 of 3 people found the following review helpful:

3.0 out of 5 stars The Delights and Limits of a Whirlwind Tour, March 22, 2003

By 

J. Gellman - See all my reviews
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This review is from: Political Numeracy: Mathematical Perspectives on Our Chaotic Constitution (Paperback)

The exploration of a dozen or so mathematical topics in Meyerson's Political Numeracy leaves one with feelings much like having toured for the first time ten European cities in two weeks: the new sites are a delight to behold, but the day-to-day context (here the relationship between mathematical concepts and Constitutional ones) slips away as your tour guide quickly repacks for the next leg of the journey.

The speed of Mr. Meyerson's survey may account for two mathematical lapses. First, there is the awkward statement that "Bush received more than 150,000 fewer popular votes than Al Gore." (pp. 54-55) Although published in 2002, this statement seems frozen in the first half of November 2000, before Gore's popular vote plurality over Bush was finalized at 537,000 votes.

Second, in discussing the theory of limits, the book recounts an interesting experience of David Berlinski, recalled in his book, A Tour of the Calculus, in which a function, (x squared -1) divided by (x-1), gets closer and closer to its limit (where x=1), but never reaches that limit because the resulting fraction, zero divided by zero, is impossible, leaving a limit that is as unattainable as God. (pp. 209-210) This is an evocative story, but it fails to disclose an identity of factors that turn what seems a quadratic function into a simple, linear one that, contrary to Berlinski, has no limit. As (x squared - 1) is the product of (x+1) and (x-1), then the function described by Berlinski and by Meyerson is actually equivalent to (x+1), once identical factors (x-1) in both parts of the fraction are eliminated. Viewed in that way, this function involves no division and has no limit. A simple alteration, e.g. (x squared -2) divided by (x-1), could have conveyed the same story without relying on a function whose simplification would remove any limits.

One additional mathematical topic worthy of a future edition: the theory of statistical sampling, in the context of the debates over the relative accuracy of direct counts and sampling for purposes of the Census required every ten years by the Constitution.