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ByA customeron August 29, 2002

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.

ByT. Patrick Sullivanon July 14, 2003

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.

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.

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ByS. Chessareon November 13, 2005

It's a great way for even a non-math person to understand how math really does underpin most of reality, including our political system. The book is difficult to describe without reading it, but is a great read for anyone interested in politics or even history. The author's extensive use of historical documentation and quotations is also extremely cool--clearly a ton of research went into this book.

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ByJ. Gellmanon March 22, 2003

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.

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.

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