Setting a date for destiny

Owen Gingerich takes time out to consider the measures of mankind.

No reader of the daily press can miss the fact that a new millennium is approaching. The ubiquitous Y2K computer bug and the rollover from 19 to 20 will make 2000 a year to be remembered. But will it be the first year of the new millennium or the last of the old? Clearly curiosity about the history of the calendar is on the rise. Among the early and useful arrivals of the anticipated throng of explanatory texts are E. G. Richards's Mapping Time , a thorough-going reference work that only the most dedicated will find enjoyable leisure reading, and David Ewing Duncan's Calendar , an engaging but occasionally unreliable romp through the calendrical history of western civilisation.

Richards's interest in the calendar began with an endeavour to write computer algorithms that could convert from one calendar to another: from Gregorian to Egyptian, to Persian, to Baha'i, to Islamic, to Jewish, to Mayan, etc. As his project blossomed, he explored the varieties of number systems, the complex cycles and calendars of India and the Maya, the intricacies of Easter calculation and the origin of the seven-day week. The results are documented here in astonishing and sometimes mind-numbing detail.

We learn, for example, of Joseph Scaliger's Julian cycle of 7,980 years, the longest associated with the western calendars, and how it is dwarfed by the Chinese chi of 31,920 years, the Indian mahayuga of 4,320,000 years, and the Mayan hablatun of over a billion years. Here, too, are the palaeolithic moon phases, inscribed some 30,000 years ago on a bone plaque from the Dordogne Valley, and the festivals of Beltane and Imbolg in a hypothetical Bronze Age year of 16 "months".

Duncan's relatively compact narrative focuses more narrowly on the road to our present calendar. Delightfully written, its small vignettes bring to life the ancient Alexandrian library, the steamy affair of Caesar and Cleopatra, the brilliance of Charlemagne's court, the journey of a 13th-century squire's son to Oxford, the horrors of the Black Death and the battle over Gregory XIII's calendar reform.

Most primitive societies began with a lunar calendar of about a dozen "moonths" per year. The problem with calendar-making rests on the fact that neither the number of months nor the number of days comes out even in a seasonal year. There are approximately 365.25 days in a year, and it was a radical triumph on Julius Caesar's part to ignore the moon and to establish a purely solar calendar with an extra day every four years. But this scheme creates one too many leap days every 133 years, making the year on average a little too long.

As a result of the slightly too long Julian year, over the centuries the calendar drifted with respect to the seasons. By dropping ten days in October of 1582, the Gregorian reform brought the vernal equinox back as it was at the time of the Council of Nicea in AD325. At the same time, it solved the problem of a year that was 11 minutes too long by omitting three leap days every four centuries compared with the Julian calendar. 1700, 1800, and 1900 were not leap years, but 2000 will be. In 1582, insular Britain and its colonies showed solidarity with the Protestants of northern Europe by rejecting such a papal invention; their continental neighbours for the most part abandoned resistance in 1700, when the lack of a Gregorian leap day would have placed the old and new calendars out of step by 11 days. Eventually commercial interests forced England to join the European common calendar in 1752, by omitting 11 days in September. Today, in terms of nearly universal acceptance, the Gregorian calendar is the most successful.

Meanwhile, the moon continues to play a critical role not only in the Jewish and Islamic calendars, but in the calculation of Easter as well. The Islamic calendar solves the incommensurability problem by ignoring the solar year; its months march through the seasons in a cycle of nearly 33 years. In contrast, the Jewish calendar adds an extra "intercalary" month every two or three years, or more precisely, seven in each 19 years, a period called the Metonic cycle after an ancient Greek astronomer who proposed a calendar reform based on this discovery.

The date of Easter has its roots in the Jewish lunar calendar; the Council of Nicea proposed that Easter should fall on the first Sunday after the first full moon after the vernal equinox, which they took arbitrarily as March 21. This is the reason that the Gregorian reform took out precisely the number of days to make the vernal equinox again fall on March 21, as it had done at the time of the Council of Nicea. The difficult part of the Gregorian reform involved not the pattern of leap days or the assumed time of the vernal equinox but the lunar tables for finding Easter. Duncan's account clearly explains how the Gregorian calendar gradually won worldwide usage, but for all its detail it is Richards's description that will give you more answers than you have questions for.

Neither book comes down clearly on the question of whether the next millennium begins on January 1 2000 or January 1 2001, but the background for an answer can be teased out of the dense array of information presented here. One element is the notion of regnal periods, that is, dating an era according to the year of a ruler's reign. The ancient, traditional method of recording regnal periods always began by assigning year one to the first full year of each kingship -J there was no need in the lists for a zero because one royal regime followed another and no one counted backwards.

The present AD system began with the work of Dionysius Exiguus, a Roman monk of the 6th century. He wrestled with the problem of Easter determination, the dates of which danced back and forth within the Julian calendar in a repeat pattern of 532 years. (This number is the product of the 19-year Metonic cycle that provides the basis of the solar-lunar congruity, the seven days of the week, and the four-year pattern of leap years.) One method of keeping track of the years in Dionysius's day reckoned the years from the reign of the 3rd-century Roman emperor Diocletian, the "Era of Martyrs". Dionysius had a 95-year Easter table (that is, five Metonic cycles) constructed by Cyril, bishop of Alexandria, which ended on Diocletian 247. Dionysius saw that on the following year there was a tabular coincidence of both the vernal equinox and a new moon, a propitious time to start an Easter cycle. Thus, Dionysius started his new 95-year table where the old left off - Diocletian 248.

Working backwards, Dionysius saw that a complete 532-year cycle ending on Diocletian 247 would have started very close to the time of Christ's birth. Dionysius did not know in precisely which year Jesus was born, but according to Richards, he assumed that the nativity took place on Christmas day in the first year of this cycle. Following the regnal system, Dionysius took the second year of the Easter cycle, the first full year of Jesus's life, as AD1. (This made Diocletian 248 equivalent to AD532.) Dionysius felt that it was inappropriate for Christians to measure their years from an emperor who was a notorious persecutor of their forebears, the implication being that the regnal era based on the long Easter cycle could serve better; and within a few centuries, the Dionysian era became the chronology of choice.

It did not take scholars too many centuries to realise that Jesus was born not one but a few years before AD1. Nevertheless, the numeration has stuck. The third millennium on this system begins on January 1 2001. Because Dionysius erred, the millennial anniversary in effect marks a non-event. However, January 1 2000 marks two millennia from the beginning of the year in which Dionysius probably thought that Jesus was born. So why not celebrate twice?

Owen Gingerich is professor of astronomy and the history of science, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts.