Saturday, March 16, 2013

The Nothing That Is: A Natural History of Zero by Robert Kaplan

Source of book: borrowed from the library
Date originally published on Facebook: December 3, 2010.

I am republishing my early Facebook reviews on my blog. This book was fascinating. Definitely one of my favorite books in the sciences and mathematics category.

The title for this book comes from Wallace Stevens’ poem, The Snow Man.

One must have a mind of winter
To regard the frost and the boughs
Of the pine-trees crusted with snow;

And have been cold a long time
To behold the junipers shagged with ice,
The spruces rough in the distant glitter

Of the January sun; and not to think
Of any misery in the sound of the wind,
In the sound of a few leaves,

Which is the sound of the land
Full of the same wind
That is blowing in the same bare place

For the listener, who listens in the snow,
And, nothing himself, beholds
Nothing that is not there and the nothing that is.

I quote the whole poem because I like it, not that it is central to the book. Except for the last line.

In order that there be no confusion, I want to clarify that this book is written by Robert Kaplan the mathematics professor and author; not Robert S. Kaplan, of Harvard Business School, also a professor and author; or Robert D. Kaplan, of The Atlantic Monthly; or even Bob Kaplan, former Canadian MP. Since all except for the last have been published recently, it is easy to get mixed up.

Robert Kaplan teaches an interesting variety of subjects. Math, of course, but also several languages including Sanskrit. He also has taught “Inspired Guessing”, which sounds intriguing. This book is mostly about math and the history thereof, but also about the intersection of math and philosophy.

The Nothing that Is looks at the history of the concept of zero. For anyone who has attempted to multiply using Roman numerals, it is clear that zero was a revolutionary change in mathematics. The use of a placeholder simplified notation, certainly, but it also opened up new worlds of calculation.

I am not a mathematician like several in my family and in my wife’s family. I did fine in high school, but never went beyond trigonometry and coordinate geometry. It would have been fun to take calculus, but I never was able to fit it in. That said, I still remember my algebra and plane geometry pretty well. Thus, with this limited scope of knowledge, I was happy that I made it through 150 pages before my head got spun. I’m thinking I should take a look at calculus sometime, but I probably need someone to walk me through it until I get a “eureka” moment.

This book could have been boring, but wasn’t, largely because Kaplan writes with both skill and enthusiasm. Kaplan uses his broad knowledge of literature and philosophy to connect the math with the era and its ideas and prejudices. His discussion of the Mayans alone was worth the time spent.

I do not intend to reiterate the substance of this book, as I could, at best, make a pale imitation. Zero’s story is fascinating whether you liked math or not, and Kaplan tells it well.

In addition to the history, Kaplan spends some time discussing philosophy. After all, numbers (other than counting numbers used for specific things) are an abstract construction. We define them, and manipulate them using rules that are as much invented as discovered. Despite this, as we have built ever more complex systems of calculation, we have discovered that they in fact represent the nature of the world. The development of calculus enabled every science dealing with curves from engineering to astronomy. If the math can be used to predict the actual world, how in fact are they related? Kaplan has no axe to grind here, and doesn’t tip his hand as to his own philosophy. Instead, he examines through both math and philosophy how both attempt to approach and define truth.

I suspect the book may seem simplistic for a true math scholar, but for a dabbler like me, it was both entertaining and thought provoking. Unless you hate math, history and philosophy (in which case I pity you), give this book a read.

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