When does the new millennium begin-in 2000 or in 2001? The people (and their governments) have voted with their chequebooks for the former. Travel bookings are brisk for the end of 1999. Favourite destinations include the pyramids, the Taj Mahal, the Ngorongoro Crater in Tanzania and Machu Picchu in Peru. Civic leaders in Nazareth are building 2,000 new hotel rooms in anticipation of the crush. Islands located a hair's breadth west of the International Date Line are vying to be the first to usher in the millennium-and for the dollars accompanying it-despite the fact that it will be hurricane season.
Yet the idea that centuries begin in years ending in 01, not 00, has been agreed by historians, newspaper editors, calendarists and other arbiters of culture for at least three centuries. This opinion is not dispassionately held. The Times wrote on 26th December 1799: "The present century will not terminate till 1st January 1801... We shall not pursue this question further... It is a silly, childish discussion and only exposes the want of brains of those who maintain a contrary opinion to that we have stated." Those afflicted with a "want of brains" included Goethe, Schiller and Victor Hugo, all of whom made the error of defending 1800 as the beginning of the 19th century. In the US the New York Times, the Washington Post, Scientific American and the Nation put editorial weight behind 1901 as the first year of the 20th century. The New York Times has weighed in for 2001 to start the 21st century. I have not found one US publication which has broken ranks, although Science News went astray in 1986 when it stated in an obituary that Admiral Hyman Rickover, whose birthday was 27th January 1900, had been born in the first year of the century.
The Old Royal Observatory in Greenwich, London, the internationally recognised authority on timekeeping and self-proclaimed last word on calendrics, proclaims 1st January 2001 as the start of the new era. (Timekeeping is defined as the "measurement of fractions of a day," whereas calendrics is "the reckoning of time over extended periods.") The US has no official calendar and no legally prescribed method for numbering years. In general, though, the US uses the Gregorian calendar, established by an Act of Parliament in 1751 as the official calendar of England. This Act also applied to the American colonies, but that obligation was cancelled by the revolutionary war. You could run a US company according to the Mayan 584-day Venutian calendar (based on Venus years) without fear of prosecution, although not without practical difficulties.
Despite this calendrical freedom two US government agencies, for reasons best known to themselves, have taken a stand on the beginning of the next millennium. Both the National Institute of Standards and Technology and the Library of Congress have declared 2001 the first year of the 21st century.
Every proponent of 2001 puts forward the same argument. Although the idea that a century begins on the year 00 may stem from an intuitive logic, it betrays the public's lack of mathematical sophistication. The first AD year was 1. Because there was no AD 0, one cannot begin the 2nd century with AD 100, because that would leave only 99 years in the first century. The 2nd century must begin with 101, the 3rd with 201, and so on. The crux of the 2000 versus 2001 debate is the controversial nature of the number zero. The issue touches on history, number theory, religion, politics and economics-all of it coloured by western chauvinism.
in the late 5th century AD, Pope Gelasius brought over Dionysius Exiguus, a Scythian monk whom he knew from Constantinople, to translate documents in the papal archive. A few decades later, working under Pope John I, Dionysius translated the Easter tables drawn up by Saint Theophilus, of the Church of Alexandria, from Greek into Latin. Easter is Christendom's most important movable feast. Its date is one of the most difficult to calculate. Dionysius was using the Alexandrian method to calculate his own Easter tables when the thought struck him that he was living in the 525th year since the birth of Christ. The monk saw the opportunity to dispense with the old numbering system-Anno Diocletian, which started with the reign of emperor Diocletian, an infamous persecutor of Christians. He began his new era with Anno Domini 1-which he calculated as the year of Jesus's birth-and never looked back.
Dionysius has been accused of two blunders-or a blunder and a half. He was wrong about Jesus's birth date (now set at 4 BC). Dionysius's other "blunder" was that he began with AD 1 rather than AD 0. The Scythian monk was simply a product of his times: the Romans had no zero in their cumbersome numbering system. In our modern base-ten system, zeroes abound: in 10, 20, 100, 1,000 and so on. To declare that a culture had no zero seems absurd. But the Romans in AD 525 had only Roman numerals: X (10), XX (20), C (100), M (1,000) and so on. There was no Roman numeral for zero. Making the year of Jesus's birth 0 would have solved many problems, but it is mathematically acceptable to begin a series with 1-or 2, or 3, or any number-as long you are consistent and no numbers are skipped.
The AD system was not an immediate success. Pope John died a year later, and anti-Greek sentiment in Rome swept Dionysius out of office. The AD system languished for 200 years until the Venerable Bede-the Northumbrian Anglo-Saxon monk-picked up Dionysius's calendar in his classic work, the Ecclesiastical History of the English People, completed in 731. The AD system spread when the Emperor Charlemagne adopted it for dating acts of government throughout Europe.
Bede made a blunder of his own. Attempting to improve upon Dionysius's system, he invented the BC system to extend backwards into times before Jesus's birth. Like Dionysius, Bede was hampered by the lack of a zero. He added 1 BC immediately before AD 1. This makes no more sense than counting backwards from 2001 directly to 1999, skipping 2000. The result is a year numbering system with a year missing in the middle, a mathematical oddity which has endured for more than 12 centuries.
Because Dionysius and Bede skipped a number, we must either acknowledge the mistake and correct it-or extend it into the next millennium by beginning centuries in the 01 year. Experts have chosen the latter, but have drawn a veil over the mathematical shortcomings of western culture in the first millennium AD. (Although neither Dionysius nor Bede had zero, the Indians and the Mayans had been using it since the 1st century.)
Their defensive argument, that we do not need a year 0, takes two forms. First, no one ever referred to a year 0 while living in that year. But no one ever knowingly lived in 1 BC either. In fact, AD 1 was not labelled as such until AD 524. Numbering schemes often take effect after the fact. Who can say what the year 1997 will be labelled when the calendar is revised by the Church of Scientology in the next century? The second claim is that zero is not a real number-that people just do not count with it. It can be skipped with impunity. The Library of Congress states categorically: "There has never been a system of recording reigns, dynasties or eras that did not designate its first year as the year 1."
Anthony Aveni, professor of astronomy and anthropology at Colgate University in the US, disagrees-the Mayans began each month with a day 0. "We have a parochial view," he says. "We're caught up with the Graeco-Roman ways of doing things. It's in our nature not to think of nothingness." The Babylonian kings called the first year of a reign the accession year. The following year was year 1. Even in mediaeval England reigns did not always begin with year 1. Sometimes the second year was 1, sometimes the accession year was 1; sometimes year 1 did not begin until the king had done something big. For some this could take a long time.
Astronomers have solved this problem by revising Bede's numbers to make room for a year 0. In 1740 Jacques Cassini, the French astronomer, replaced BC-AD with a minus-plus system in which 0 replaces 1 BC, -1 replaces BC 2 and so on. All the AD years remained the same. Cassini also declared that centuries begin on the 00 year. He had little choice. Consider Halley's Comet, which passes every 75 years. The comet cannot accommodate Bede's sloppy maths or the preferences of the Library of Congress by truncating its orbit and losing a year as it crosses the BC-AD interface.
Not all calendars replicate astronomical cycles, but those which we have followed in the west have all purported to mirror the rhythm of the heavens. The calendar we use today was created by Julius Caesar, modified shortly thereafter by Augustus and modified again by Pope Gregory XIII in the 16th century. This was an attempt to solve the problem of Julius Caesar's leap years. Caesar had instituted a leap year every four years, too many over the long term because the solar year does not have exactly 365.25 days. By the 16th century the calendar was ten days out of sync with the earth's orbit around the sun. Pope Gregory authorised that ten days be excised from the year 1582-5th October to 14th October-and decreed that leap days should not be added in centennial years not divisible by 400. (Thus, 1600 and 2000 are leap years; 1700, 1800 and 1900 are not.) Not all countries agreed immediately. England did not drop the extra days until 1752. George Washington, born under the Julian calendar but still an English citizen when the Gregorian calendar was adopted, ended up with two birthdays.
The Gregorian reform was the last straw for some astronomers. "What are we supposed to say?" Anthony Aveni asks: "There was no sky for ten days?" Many do not use Cassini's minus-plus system, favouring the earlier Julian day calendar developed by Joseph Justus Scaliger in 1583. This begins counting time in 4713 BC and gives each day a new number; years are irrelevant. The Julian day calendar is, Aveni says, "a perfect system for reckoning the time from, say, one perihelion of Halley's Comet to the next. I don't have to worry about leap years." At present we are close to 2.5m Julian days.
Still, the Library of Congress insists that our calendar is based on sound "simple arithmetic." It asserts-in spite of the Mayans and the Babylonian and English kings-that no one counts with zero. But Rob Navias, a shuttle-launch commentator for Nasa, assured me that no rocket or spaceship, in the US or abroad, has ever blasted off on the count of one. Manned or unmanned, they blast off at zero. In the US the zero serves as a crossover point between the staff at Cape Canaveral, in Florida, in charge of launches, and those at the Johnson Space Center, in Houston, in charge of actual flights.
Michael Jordan-Reilly, of the Otis Elevator Company, told me that his firm will number floors in whatever manner its customers request. In the US the ground floor is usually counted as one. But Europeans begin with zero. There is a certain logic to this. The first floor is one flight up. The eighth floor is eight flights up-not seven flights as in the US.
But is zero a real integer, a counting number, or just a vertical line on a timeline? I called the mathematics department at the Massachusetts Institute of Technology to find out the proper way to count and whether zero is a real number. Counting is not MIT's forte: no one in the department would comment. As for zero, an administrator said: "Our people are interested in numbers invented after 1972."
Tobias Dantzig wrote the classic cultural history of numbers, Number: The Language of Science (1930). "In the history of culture," he wrote, "the discovery of zero will always stand out as one of the greatest single achievements of the human race." Zero marked a "turning point" in maths, science and industry. Dantzig also noted that zero was invented not in Europe but in India, in the early centuries after Jesus. Negative numbers followed soon thereafter. The Mayans invented zero in the new world at about the same time. Europe did not accept zero as a number until the 12th or 13th century, which hampered European mathematics for centuries. Without zero and negative numbers, Ren? Descartes could not have developed analytic geometry and the familiar diagram with x and y axes. Without analytic geometry we would not have the work of Newton, Leibniz, Euler or the Bernoulis. And the inability of the Greeks to conceive of the void as a number, let alone endow the void with a symbol, hampered western physics, too, for more than 1,000 years. The pre-Socratic Greek philosopher Democritus of Abdera had the idea of a void: "Nothing exists except atoms and empty space; everything else is opinion." Plato disagreed and Democritus's particle physics was abandoned in the west until the Renaissance.
The Old Royal Observatory (ORO) at Greenwich insists that there was no year 0 and that the millennium begins in 2001. Although it is the arbiter of timekeeping, the ORO has little authority in the area of calendrics. Kristen Lippincott, director of the Millennium Project at the Old Royal Observatory-from whose geographic co-ordinates Greenwich Mean Time is measured-insists that the ORO is an authority. But in settling on 2001 and renouncing zero, the ORO has broken with its past and with geography. One of the ORO's most illustrious directors was Nevil Maskelyne (1732-1811), an astronomer royal, who stated that a century begins on the 00 year. The Old Royal Observatory sits astride the prime meridian, also known as zero-not 1-longitude.
Lippincott argues that the ORO's stand on when the day-and thus the century-begins is based on international law. According to the International Meridian Conference of 1884, the universal day does not legally begin until it is "mean midnight at the cross hairs of the airy transit circle in the Old Royal Observatory." Let us accept the legal definition: the millennium begins at midnight on 31st December 2000 at Greenwich. Now imagine yourself vacationing in Tonga, near the International Date Line, where it is 12 hours earlier than it is in Greenwich, on the night of 31st December 2000. At the stroke of midnight your digital watch turns from 31st December 1999 to 1st January 2000. Happy New Year! Happy New Millennium! Well, no. Because it is still noon on 31st December in Greenwich, the millennium has not yet started. Legally it is still yesterday. And it will remain yesterday until noon Tonga time, all evidence to the contrary. In all 12 time zones east of Greenwich, midnight will come sooner than at the ORO, but it will stay yesterday until midnight GMT. On the US's east coast, five hours behind Greenwich, the new millennium will start at 7pm. Those people who celebrate midnight in Times Square will be five hours late. Californians must celebrate the new millennium at 4pm, while stuck in rush hour traffic.
So can we celebrate 2000 without fear of censure from the ORO? Certainly-with the necessary cash. The ORO has set up an office in Greenwich, Connecticut, to sign up corporate sponsors for the observatory. Stephanie Record, its US representative, says she is looking for Fortune 500 companies doing business with Britain to become sponsors. In exchange for a fee they will be able to display a "Greenwich Meridian 2000" logo. Greenwich 2000? Not 2001? "We're loosening up the dogma," Record says. "Our purpose is to draw sponsors. Frankly, the year 2000 appeals to more people." The ORO plans to hold a year-long celebration in 2000, culminating with New Year's Eve on 31st December, to usher in the real new millennium for its corporate sponsors. Some may get to ride Concorde, celebrating midnight over Greenwich, England, then jetting to the US to celebrate midnight again over Greenwich, Connecticut, five hours later. (But wait: does the millennium not start at 7pm US east coast time?)
last winter i was pulling out of a car park in Hadley, Massachusetts, when the odometer of my 13-year-old BMW turned from 99,999 miles to 100,000. I pointed this out to my ten-year-old son, who sat beside me. He was thrilled. About a mile down the road, I tried an experiment. Yelling and bouncing up and down with as much excitement as I could muster, I shouted, "Look! 100,001!" My son hardly looked up. "What's your point?" he inquired.
Think how history might have changed had the Venerable Bede driven a BMW. Bede achieved one of the great near-misses in mathematics. By counting years "before Christ," in effect he became the western inventor of negative numbers. Had he made the logical next step and invented zero, he could have forestalled our current calendrical problems and accelerated western thought by several centuries.
He could also have made a profound contribution to Christianity. The word zero is derived from the Indian sunya. Sunyata is a Buddhist concept: it means emptiness, the void, the mother of all existence from which everything is born and into which everything must return. Zero was no less profound for the Mayans. In Mayan hieroglyphics archaeologists have found a flowerlike symbol, which they believe stands for zero. Zero was a flower. All life grew out of it.
Bede could have created a zero for the 0th year of the Christian era, with a symbol which represented not only zero but also the man he considered to be the son of God. In our everyday calculations and reckonings all of us-Christians, Jews, Muslims, Buddhists, atheists-would have been continually confronted by Jesus.
