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Zero: Sometimes Nothing Is Something

May 16, 2008
What's in a number? In the case of the number zero, quite a bit. The story of this humblest of numbers - after all, it stands for nothing - is so interesting that in recent years several journalists have written popular books tracing its history. Friendships have been ended, philosophical battles engaged in, heretics excommunicated, and battleships sunk - all because of zero.

As Charles Seife points out in one of the best of these books, Zero: The Biography Of A Dangerous Idea, the concept of zero was developed by Babylonian mathematicians. Earlier peoples had no idea of the concept of zero, and no use for it. The most ancient civilizations seem to have used no numbers except "one", "two", and "many". But the Babylonians used the abacus - a sort of ancient computer in which pebbles are arranged into different columns to keep track of amounts - to figure large numbers.

"Adding numbers on an abacus," Seife writes, "is as simple as moving the stones up and down. Stones in different columns have different values, and by manipulating them a skilled user can add large numbers with great speed."

The problem arose when it came time to write those numbers down. If you look at an abacus, you can tell whether one pebble means 1 or 10 because of which column it's in. The Babylonian system for writing numbers was based on the abacus' there was a single symbol that stood in for the pebble - but there was no way to represent which column that "pebble" belonged in, so that 1, 10 or 1000 looked identical when written down. (They all looked like "pebble". So, to keep these numbers from appearing identical to each other, the Babylonians developed another symbol to indicate which column in the abacus the "pebble" belonged to. That way, you could tell whether you were looking at one, 60, or 600 - this new symbol told you, in effect, how many zeros to place after the number.

Simple enough. But Greek mathematicians - whose work influenced the way the subject was taught for centuries afterward _refused to adopt this Babylonian practice, even though doing so would have simplified many of their calculations enormously. After all, the Greek approach to math was highly philosophical. They couldn't simply accept the zero as a sort of placeholder symbol, but they had to analyze its properties and notice its behavior when combined with other numbers.

Zero doesn't behave like other numbers. If you add it to any other number, the first number remains unchanged; the same is true of subtracting zero. Multiplying and dividing by zero are equally dicey. Zero violates laws of logic followed by every other number; it seems to call the entire number system into question. For thinkers as rationalistic as the Greeks, this was unacceptable. Aristotle firmly rejected the idea, and his influence on subsequent Christian metaphysics was such that zero went unused in the West for hundreds of years.

Finally, Muslim mathematicians'influenced by Hindu mathematics, which did accept the idea of zero - revived the concept in the West; they ignited a controversy over Aristotle's ideas in general which led to church councils, heresy trials and a great deal of spilled ink (if not blood). Ever since, philosophers and mathematicians have been attracted and repelled by the idea of zero. Henri Bergson, a once-dominant French thinker of the early twentieth century, theorized that the ability to imagine a negative quality the absence of something was among the skills that separated humans from animals; and writer Thomas Pynchon built his massively influential novel Gravity's Rainbow (1973) around the paradox of the fact that certain equations seem to go beyond the zero (as the book's first section is titled).

More recently, zero caused plentiful mischief because of its effect on certain kinds of computer codes. Seife recounts the story of the USS Yorktown, an American missile cruiser that ran aground after the engineers who installed its new engine-control software failed to remove a zero that was supposed to be removed from the code. And we all still remember the madness that attended New Year's Eve 1999 - when millions waited to see whether old computer mainframes, which hadn't been programmed to handle the existence of a year 2000, would malfunction, causing according to the gloomiest forecastsweapons malfunctions, bank wipeouts, powergrid failures, and general darkness upon the face of the earth.

Thankfully, a massive code-cleanup effort in the couple of years preceding 2000 prevented the Western world from falling into exactly the chaos that, for the Greek mathematicians, had seemed to lurk in this little, misbehaving number.
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