THE NOTHING THAT IS

Part history, part philosophy, with some story problems thrown in for good measure: a wandering tale of the origins and uses of the number zero. Remember learning the Roman numerals in grade school? Kaplan is quick to point out that their system of counting used different letters for 1, 5, 10, 100 (I, V, X, C). This leads to problems when you want to represent the very large, millions or billions. A number system that uses place as an indicator of size was clearly needed, but this creates a need for a placeholder. Otherwise, 207 would be indistinguishable from 27, and chaos would ensue. Kaplan opens with a history of counting systems even more confusing than the Roman, Sumerians counting in base 60 or the Buddha counting by hundreds. Kaplan proposes several theories about the origin of the shape of the zero. Is it the impression left on a sand-covered counting board by the removal of a stone, signifying a placeholder with nothing in it? Or is it perhaps the crescent shape of a writing stylus pressed twice into the clay? Was zero “discovered” by more than one culture independently? From the origins of zero we discover what zero represented for different cultures. To the Mayans, zero was an angry god, periodically represented by a human who would be beaten to death. On the mathematics side, we learn how zero is used in algebra (solving quadratic equations), calculus (maxima and minima occur where the slope of a function is zero), physics (conservation laws), and set theory (generating the integers from the empty set). Finally, the author discusses the larger meaning of nothing. Perhaps it is “the salaryman of Japanese society” or more generally “anonymity, mirroring our fear of making no difference to others.” Full of ideas but going nowhere in particular, which is perhaps what the author intended all along. (First printing of 40,000; author tour)