The Nothing That Is: A Natural History of Zero

Book review 2010.04

Author: Robert Kaplan

A summary of this book from chapter 15: “We have come to know zero intimately in its mathematical, physical and psychological embodiments. It remains elusive.”

After reading three really enjoyable novels, I decided a change of pace was in order. This is one of those books that’s been on my shelf for some time. It’s a recent work, as academic treatises go, from 1999, and purports to be a historical look at the role of zero in mathematics since the dawn of time.

You see, ancient peoples didn’t have zero in their math because they were, as Kaplan describes it so well, only using numbers to represent heaps of things and exchanges of goods and monies. They weren’t doing any fancy theoretical maths.

The first section of this book explores that history and how the concept of zero evolved in math and in philosophy. It turns out that our beloved null spent time as the representation of the evil absence – the void; and at other times as the embodiment of brahman and God - all that is.

My reaction to this book is conflicted. Kaplan is an entertaining writer and a master of the food metaphor. His explanations and mathematical examples are clear and concise. And there isn’t too much math; I didn’t walk away from the book at any time feeling like I had bombed his test. Overall, I enjoyed the exploration.

Should any of you care to borrow the book, you can expect short examinations of the mathematics of Greece, India, and the Middle East, all of whom intermingled their ideas, creating a wonderful melting pot of mathematic theory. He also addresses the Mayans, who developed their science in isolation.

The author naturally makes his way to the Middle Ages where mathematics really evolved into our modern forms. He doesn’t dwell on any period or place overly much, and only discussed my heroes Descartes and Leibniz in passing. (I admit that I sneered when he referred to Leibniz as the “co-founder” of the calculus. While I’m glad everyone plays nicely together for the love of the craft, I’m just an armchair mathematician, so I can pick a favorite, and for me, it’s my man Gottfried.)

What I had trouble with was his philosophical meanderings, especially in the latter part of the book. After covering the role of zero in mathematics and philosophy, which was the real meat of the book and done very well, Kaplan branches out to explore zero's roles in the physical world and psychology. And that got boring pretty quick. Still, I couldn’t stop reading because I was in the home stretch and as I said, Kaplan is a skilled writer. He kept the math/philosophy/psychology geek in me entertained in his winter wonderland enough to shovel my way through that unending snowfall that is the last quadrant of the book.

If you like mathematics or philosophy as much as I do, it’s worth a read. I certainly learned some stuff and enjoyed the ride. But for the other 98% of you, don’t bother.

While I’m on the topic, I’ll point you to two other excellent books for your math fix. First, for a wonderful read on the history of math and philosophy in the Middle Ages, check out Descartes’ Secret Notebook by Amir D. Aczel. I read this book last year and enjoyed every minute of it. It was more dry than Kaplan, but had a very strong historical essay bent. And of course, covered my favorites in detail: Descartes, Leibniz, Galileo, and a bunch of others.

Next, for a fun way to brush up on your basic math and math theory, please do yourself a favor and read The Number Devil by Hans Magnus Enzensberger (I own that one and would be glad to loan it to you.)

And now I’ll leave you with my favorite line from this book: “Pause a moment to savor the bouquet of so absurd a situation.”