''The 21st century will begin Jan. 1, 2001.'' That simple sentence, admitting no dispute, comes straight from the World Almanac and Book of Facts.

The Royal Greenwich Observatory agrees. So do the U.S. Naval Observatory, the Encyclopaedia Brittanica and Webster's Third International Dictionary, among others. And so do I.The starting date of the 21st century - and the third millennium - should not even be questioned.

The issue was settled to the satisfaction of everyone who could count straight a century ago, when Pope Leo XIII, Czar Nicholas II, President Charles William Eliot of Harvard and The New York Times all agreed that the 20th would begin with 1901.

Curiously, Kaiser Wilhelm and President Seelye of Smith College disagreed with them, and today there are millions, maybe billions, of misguided earthlings in that camp, thinking that the upcoming Big Day is Jan. 1, 2000.

The Savoy Hotel in London and the Rainbow Room in New York are already booked for millennial merry-making as the calendar flips from Dec. 31, 1999, to Jan. 1, 2000.

The self-anointed Millennium Society plans celebrations at midnight in each of the 24 time zones, and the biggest of all at the Great Pyramid of Cheops outside Cairo.

Yielding to no one, New York City aims to attract a million revelers to Times Square for the magic moment, as if all of Asia, Europe and Africa had not passed that point hours before.

They will all be a year too soon. Putting it simply, for the 20th century to end with 1999, the first century would have had to end with 99 and, to make it 100 years, it would have begun with the year zero. But there was no year zero.

Indeed, the keepers of the calendar in ancient Rome did not even have a numeral for zero. There was no dispute about the end of the 1st century, because people had no idea that another century was about to begin. Centuries as we count them now were unknown.

The dating of years ''before Christ'' and ''anno Domini'' was not conceived until the 6th century, when Pope John I commissioned the monk Dionysius Exiguus, or Dennis the Little, to develop a system for setting the date of Easter.

At the time, the calendar was dated from the reign of the Emperor Diocletian, a fierce persecutor of the early Christians. So Dionysius switched the base to the date of Christ's birth.

Later historians established that Christ was born a few years earlier than Dionysius thought - in 5 or 6 B.C. rather than A.D. 1. That being so, the 21st century has already begun.

But that argument persuades neither the purists like me who insist on 2001 nor the odometer-fixated who want to see 1999 turn to 2000.

Robert Bartley, editor of The Wall Street Journal, said in a recent column that 2000 vs. 2001 is all wrong anyhow. By his reckoning, the 19th century began when Wellington bested Napoleon in 1815, the 20th began with the outbreak of war in 1914 and the 21st began when the Berlin Wall collapsed in 1989. At the least, Mr. Bartley bolsters the view that this whole business is rather arbitrary.

Michael Barkun, a scholar at Syracuse University's Maxwell School of Communications, offers as good a reason as any for believing that 2000 is the year to celebrate.

He calls it ''the unconscious tyranny that the decimal system exercises over our minds,'' our quasi-magical assumption ''that round numbers have a certain significance.''

Neal H. Ewing offered a practical reason in a letter to the editor of The New York Times on July 20, 1899:

''The centurial figures are the symbol, and the only symbol, of the centuries. The initial figure 18 (remember, he was writing in 1899) is time's standard which the earth carries while it makes 100 trips around the sun. Then a new standard 19 is put up. Shall we wait now a whole year for 1901 at the behest of those who calculate by counting balls on an abacus?''

The debate in The Times went on for months. In an editorial on Dec. 8, 1899, Times editors pronounced themselves ''much disturbed'' by news the Kaiser had declared that the new century was about to begin.

In a second scolding a few days later, it said he ''must stand in solitary grandeur as the only man of any prominence who cannot count up to one hundred.''

In still another editorial, The Times made its position absolutely clear: ''Beyond question, '1899' means the one thousand eight hundred and ninety-ninth year of the Christian era, and the next to last year of the nineteenth century.''

The literary digest, in its final issue of 1899, joined the ranks for 1901. ''If there was a year 0,'' it asked, ''why not a century 000? Perhaps there are only 399 society leaders in the 400! Perhaps we should begin counting our ages one year later, making each of us a year younger!''

It concluded with ''one disquieting thought - that in a hundred years it will all be forgotten, and some 'letter to the editor' will start the whole whirl going again.''

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