8.3 Mb | 240 Pages
A symbol for what is not there, an emptiness that increases any number it's added to, an
inexhaustible and indispensable paradox. As we enter the year 2000, zero is once again
making its presence felt. Nothing itself, it makes possible a myriad of calculations.
Indeed, without zero mathematics as we know it would not exist. And without mathematics
our understanding of the universe would be vastly impoverished. But where did this
nothing, this hollow circle, come from? Who created it? And what, exactly, does it mean?
Robert Kaplan's The Nothing That Is: A Natural History of Zero begins as a mystery story,
taking us back to Sumerian times, and then to Greece and India, piecing together the way
the idea of a symbol for nothing evolved. Kaplan shows us just how handicapped our
ancestors were in trying to figure large sums without the aid of the zero. (Try
multiplying CLXIV by XXIV). Remarkably, even the Greeks, mathematically brilliant as they
were, didn't have a zero--or did they? We follow the trail to the East where, a millennium
or two ago, Indian mathematicians took another crucial step. By treating zero for the
first time like any other number, instead of a unique symbol, they allowed huge new leaps
forward in computation, and also in our understanding of how mathematics itself works. In
the Middle Ages, this mathematical knowledge swept across western Europe via Arab traders.
At first it was called "dangerous Saracen magic" and considered the Devil's work, but it
wasn't long before merchants and bankers saw how handy this magic was, and used it to
develop tools like double-entry bookkeeping. Zero quickly became an essential part of
increasingly sophisticated equations, and with the invention of calculus, one could say it
was a linchpin of the scientific revolution. And now even deeper layers of this thing that
is nothing are coming to light: our computers speak only in zeros and ones, and modern
mathematics shows that zero alone can be made to generate everything. Robert Kaplan serves
up all this history with immense zest and humor; his writing is full of anecdotes and
asides, and quotations from Shakespeare to Wallace Stevens extend the book's context far
beyond the scope of scientific specialists. For Kaplan, the history of zero is a lens for
looking not only into the evolution of mathematics but into very nature of human thought.
He points out how the history of mathematics is a process of recursive abstraction: how
once a symbol is created to represent an idea, that symbol itself gives rise to new
operations that in turn lead to new ideas. The beauty of mathematics is that even though
we invent it, we seem to be discovering something that already exists. The joy of that
discovery shines from Kaplan's pages, as he ranges from Archimedes to Einstein, making
fascinating connections between mathematical insights from every age and culture. A tour
de force of science history, The Nothing That Is takes us through the hollow circle that
leads to infinity.
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