Zero: The Biography of a Dangerous Idea

by Charles Seife

Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity.

In the history of culture the discovery of zero will always stand out as one of the greatest single achievements of the human race.

(The words calculate, calculus, and calcium all come from the Latin word for pebble: calculus.)

Mayans had a zero in their counting system, so they did the obvious thing: they started numbering days with the number zero.

A Roman soldier saw the bedraggled 75-year-old and demanded that Archimedes follow him. Archimedes refused, since his mathematical proof was not yet finished. The enraged soldier cut him down. Thus died the greatest mind in the ancient world, slaughtered needlessly by the Romans. Killing Archimedes was one of the biggest Roman contributions to mathematics.

Though we count with the ordinals (first, second, third), we mark time with the cardinals (0, 1, 2).

To Pascal, this seemingly bizarre behavior proved that it wasn’t an abhorrence of the vacuum that drove the mercury up the tube. It was the weight of the atmosphere pressing down on the mercury exposed in the pan that makes the fluid shoot up the column.

Infinity and zero are simply opposite poles on the Riemann sphere,

This is the definition of the infinite: it is something that can stay the same size even when you subtract from it.