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By Root 792 0

can. After all, they are watching the clockwork of the heavens—a clockwork that does not hiccup on leap years or reset itself every time humans decide to change the calendar. Thus the astronomers decided to ignore human calendars altogether. They don’t measure time in years since the birth of Christ. They count days since January 1, 4713 BC, a pretty-much arbitrary date that the scholar Joseph Scaliger chose in 1583. His Julian Date (named after his father, Julius, rather than Julius Caesar) became the standard way to refer to astronomical events, because it avoided all the weirdness caused by calendars that were constantly under construction. (The system has since been modified slightly. Modified Julian Date is simply the Julian Date less 2,400,000 days and 12 hours, putting the zero hour at midnight on November 17,1858. Again, a more or less arbitrary date.) Perhaps astronomers will refuse to celebrate 51542 Modified Julian Date, and the Jews will ignore 23 Tevet, 5760 (anno Mundi), and the Muslims will forget about 23 Ramadan, 1420 (anno Hejirae). On second thought, probably not. They will all know that it is December 31, 1999 (anno Domini), and there is something very special about the year 2000.

It’s hard to say just why, but we humans love nice, round numbers with lots of zeros. How many of us remember being a child and going for a ride in a car that was about to top the 20,000-mile mark? Everybody in the car waits, silently, as 19,999.9 slowly creeps forward…and then, with a click, 20,000! All the children cheer.

December 31, 1999, is the evening when the great odometer in the sky clicks ahead.

The Zeroth Number

Waclaw Sierpinski, the great Polish mathematician…was worried that he’d lost one piece of his luggage. “No, dear!” said his wife. “All six pieces are here.” “That can’t be true,” said Sierpinski, “I’ve counted them several times: zero, one, two, three, four, five.”

—JOHN CONWAY AND RICHARD GUY, THE BOOK OF NUMBERS

It may seem bizarre to suggest that Dionysius and Bede made a mistake when they forgot to include zero in their calendar. After all, children count “one, two, three,” not “zero, one, two.” Except for the Mayans, nobody else had a year zero or started a month with day zero. It seems unnatural. On the other hand, when you count backward, it is second nature.

Ten. Nine. Eight. Seven. Six. Five. Four. Three. Two. One. Liftoff.

The space shuttle always waits for zero before it blasts into the air. An important event happens at the zero hour, not the one hour. When you drive toward the site where a bomb went off, you’re approaching ground zero.

If you look carefully enough, you will see that people usually do start counting with zero. A stopwatch starts ticking from 0:00.00 and only reaches 0:01.00 after a second has elapsed. A car’s odometer comes from the factory set at 00000, though by the time the dealer’s done tooling around town, it’s probably got a few more miles on it. The military’s day officially begins at 0000 hours. But count aloud and you always start with “one,” unless you’re a mathematician or a computer programmer.* It has to do with order.

When we are dealing with the counting numbers—1, 2, 3, and so on—it is easy to rank them in order. One is the first counting number, two is the second counting number, and three is the third. We don’t have to worry about mixing up the value of the number—its cardinality—with the order in which it arrives—its ordinality—since they are essentially the same thing. For years, this was the state of affairs, and everybody was happy. But as zero came into the fold, the neat relationship between a number’s cardinality and its ordinality was ruined. The numbers went 0, 1, 2, 3: zero came first, one was second in line, and two was in third place. No longer were cardinality and ordinality interchangable. This is the root of the calendar problem.

The first hour of the day starts at zero seconds past midnight; the second hour starts at 1 AM, and the third hour starts at 2 AM. Though we count with the ordinals (first, second, third), we mark time