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Summary: A history of a difficult idea we take for granted
Review: This is the sort of book I like to take with me on a long airplane trip. It's easy to read in the airport, or the plane, it's small, it's paperback, and it's got enough intellectual validity to it that I don't feel like I'm vegetating or wasting my time.Before reading this book, pay close attention to the subtitle: "A natural history of zero." That's important in understanding what this book is about. I hadn't looked closely enough when I picked it up. I'd expected it to be more along the lines of Paul J. Nahin's book "An imaginary tale: the story of root -1." A quick flip through the book was enough to show it didn't have Nahin's load of equations, but still, I was expecting more of a math book than a history book. This is mostly a history book. It contains several different chapters that describe how ancient people first came to conceptualize the concept of zero, or nothing. This idea was wrapped up in many different cultural/religious customs/superstitions/traditions that resulted in some cultures embracing the idea, while others shunned it and only accepted it later. Often, those who rejected, and then accepted the notion of zero did so out of shear practicality because of the numerical utility of the concept in keeping track of the sale and distribution of goods. Often this was accompanied by the gradual reinterpretation of religious notions. This process of accepting zero as a number was often an evolutionary one. As Kaplan says: "despite its power to extend the empire of numbers, we have yet to see zero treated as a number itself. It evolved from a punctuation mark and long kept its supernumerary character - no more a number than a comma is a letter." This is an excellent book for anyone who might take our system of numbers and counting for granted. Kaplan includes several examples of ancient counting systems - without zero - and shows how painfully difficult those systems were for solving even simple problems. For example, "Roman-style counting confused the issue, since there was no year zero between 1 BC and 1 AD; hence millennialists had to reckon then - as they do now - with the difficulty that years ending in zero were the last of their decade, century, or millennium, not the first of the next..." The book isn't just history. There are lots of practical and interesting discussions about zero as they apply to mathematics, too. There are some fun and interesting graphical examples pertaining to concepts from calculus toward the books end. Not exactly light reading, and not too heavy, either. But definitely interesting reading, I very much enjoyed this book, and recommend it enthusiastically.
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