NEWTON’S UNIVERSE HAS often been likened to divinely designed clockwork by those who wish to hymn its harmonious operation. Unfortunately, it is a clock that keeps pretty lousy time.

Consider the units of time we use today. Some of them are arbitrary. Why does a day have twenty-four hours? That would seem to be a legacy of the twelve signs of the zodiac. Why does a week consist of seven days? Because people used to believe there were seven planets, including the sun and the moon.

But other units of time are not so arbitrary. They depend on (roughly) circular, hence cyclical, motions. A day corresponds to the period it takes for the Earth to complete one rotation on its axis. A month is (more or less) the time the moon requires to circle the Earth. And a year is (again, more or less) the time it takes the Earth to make one revolution around the sun.

Now here is what’s vexing: None of these "natural" intervals is a nice, clean multiple of any of the others. One "synodic" month–the time between successive full moons–equals 29 days, 12 hours, 44 minutes, and 2.9 seconds. Twelve such months add up to 354.357 days–well short of a year, which currently equals 365.242199 days.

It gets worse. Why is a year important to us? Because it represents one complete cycle of the seasons, which are crucial for agriculture and transportation, not to mention for knowing when to plan marriages and worship the gods. Annoyingly, though, a complete cycle of the seasons takes about twenty minutes less than one complete revolution of the Earth around the sun. That is because of a wobble in the Earth’s axis caused by gravitational tugs from the sun and moon on our planet’s less than perfectly spherical shape.

Small wonder, then, that humankind’s efforts to come up with a workable calendar should be a millennia-long series of miscalculations and blunders. (Among the many books that have been written on this history, two recent ones are particularly engrossing: "Mapping Time: The Calendar and Its History," by E.G. Richards [Oxford], and "Calendar: Humanity’s Epic Struggle to Determine a True and Accurate Year," by David Ewing Duncan [Bard].) Take the archaic Roman calendar. It consisted of twelve synodic months, which meant that it ran eleven days fast against the solar year–a discrepancy that, if uncorrected, would result in a flipping of the summer and winter solstices every sixteen years. The Roman college of priests was only too happy to tamper with it by intercalating extra days or months every so often, when, say, they wanted to keep favored consuls in office longer or manipulate public finances for personal gain.

By the time Julius Caesar came along, the calendar had veered way off the solar year. Following the advice of Egyptian astronomers, Julius fixed things by extending the year an extraordinary eighty days in 46 b.c.–which consequently became known as the ultimus annus confusionis. He also rejiggered the months so that they no longer corresponded to the phases of the moon and added an extra day to the calendar every fourth year to help keep it in sync with the seasons.

Thanks to these improvements, calendrical time came to be taken for granted as an objective, almost God-given thing. But there was still a problem. The Julian calendar consisted of 365.25 days, whereas the solar year was some eleven minutes shorter. Thus, by the sixteenth century the official year was out of whack with the seasons again, by ten days. That might not have seemed so bad for practical purposes, but it was something of a religious scandal, for it meant that Christians were celebrating the resurrection of Jesus on the wrong day. So in 1582 Pope Gregory XIII issued a bull jumping the calendar forward by ten days and canceling leap years at the beginning of centuries not divisible by four hundred. (Thus, 1900 was not a leap year, but 2000 will be.)

As pope, Gregory had, after all, inherited from Caesar the title pontifex maximus, and thus the guardianship of the calendar. Non-Catholics, however, did not see it that way. There were riots in Protestant Germany, where people accused the "Roman Antichrist" of trying to steal ten days of their life. Catholics countered by adducing a nut tree in Gorizia, Italy, that had obeyed the papal reform by blossoming ten days early.

Britain reluctantly adopted the Gregorian calendar 170 years after the papal reform, by which time eleven days had to be skipped; to great popular consternation, the interval from September 3 to 13, 1752, vanished by parliamentary decree. Orthodox Russia resisted until after the Bolsheviks seized power, which is why the October Revolution is today commemorated, if at all, in November.

The Gregorian calendar is remarkably accurate, running only twenty-six seconds faster than the solar year; the error will not amount to a full day until around the fiftieth century, if anyone’s still here to notice. Nonetheless, a lively Internet debate continues over what additional improvements ought to be made as we approach the turn of the millennium.

That milestone, of course, is pure social construction. For one thing, base 10 is arbitrary. For another, Jesus–whether or not you consider him your Lord–was born circa 4 b.c. Besides, as pedants everywhere know, the Anno Domini system is off by a year because Dionysius Exiguus, who came up with it in the sixth century, neglected to include the year 0 a.d. And who can blame him? Zero had not yet been invented.