Zero: The Biography of a Dangerous Idea

by Charles Seife

Cultures girded themselves against zero, and philosophies crumbled under its influence, for zero is different from the other numbers. It provides a glimpse of the ineffable and the infinite.

This is why it has been feared and hated—and outlawed.

history of the paradoxes posed by an innocent-looking number,

Zero is powerful because it is infinity’s

The biggest questions in science and religion are about nothingness and eternity, the void and the infinite, zero and infinity.

Underneath every revolution lay a zero—and an infinity.

Yet through all its history, despite the rejection and the exile, zero has always defeated those who opposed it.

Humanity could never force zero to fit its philosophies. Instead, zero shaped humanity’s view of the universe—and of God.

The story of zero is an ancient one. Its roots stretch back to the dawn of mathematics,

before the first civilization,

before humans could read ...

for ancient peoples zero was a foreign—and fr...

zero not only evoked images of a primal void, it also had dangerous mathematical properties. Within zero there is the power...

beginnings of mathematical thought were found in the des...

civilizations functioned perfectly well for millennia before its discovery.

zero was so abhorrent to some cultures that they chose to live without it.

30,000-year-old wolf bone with a series of notches carved into it.

but it is pretty clear that early humans were counting something.

However, Gog preferred to count in groups of five rather than four, and people all over the world shared Gog’s preference.

“fiving” to describe the process of tallying.

Germanic protolanguages that English came from, and thus those people used a base-10 number system.

However, none of these systems had a name for zero. The concept simply did not exist.

You never need to keep track of zero sheep or tally your zero children. Instead of “We

Zero just never came up.

And like most other civilizations Egypt did not have—or need—a zero.

problems millennia later. The Egyptians’ innovation of the solar calendar was a breakthrough, but they made an even more important mark on history: the invention of the art of geometry. Even without a zero, the Egyptians had quickly become masters of mathematics.

geometry was born. These

zero was nowhere to be found within Egypt.

They never progressed beyond measuring volumes and counting days and hours. Mathematics

Greeks were different; they embraced the abstract and the philosophical, and brought mathematics to its highest point in ancient times. Yet it was not the Greeks who discovered zero. Zero came from the East, not the West.

Greek system would need only two symbols: π for 80, and ζ for 7.

That title was held by another Eastern invention: the Babylonian style of counting. And thanks to this system, zero finally appeared in the East,

Babylonian system seems perverse. For one thing the system is sexagesimal—based on the number 60. This is an odd-looking choice, especially since most human societies chose 5, 10, or 20 as their base number.

Greek system was based on letters and the Egyptian system was based on pictures.

It was the Bronze Age equivalent of computer code.

the abacus relies upon sliding stones to keep track of amounts. (The words calculate, calculus, and calcium all come from the Latin word for pebble: calculus.)

Zero was the solution to the problem. By around 300 BC the Babylonians had started using two slanted wedges, , to represent an empty space, an empty column on the abacus.

Though zero was useful, it was only a placeholder.

nothing. Zero was a digit, not a number. It had no value.

zero as a nonnumber even though we all know that zero has a numerical value of its own, using the digit 0 as a placeholder without connecting it to the number zero.

One seems like the appropriate place to start counting, but doing so forces us to put zero in an unnatural place.

We saw what happened when you multiply a number by zero: the number line is destroyed.

Division by zero should be the opposite of multiplying by zero.

It should undo the destruction of the number line. Unfortunately, this is...

Strange things also happen when we look at 1/0 in a different way. Multiplication by zero should undo division by zero, so 1/0 × 0

should equal 1.

There is no such number that, when multiplied by zero, yields one—at least no...

if you wantonly divide by zero, you can destroy the entire foundation of ...

Dividing by zero once—just one time—allows you to prove, mathematically, anything...

Multiplying by zero collapses the number line. But dividing by zero destroys the entire framework of mathematics.