On Time and Calendar: The Millennium

Once an expatriate Indian accosted an English gentleman in a London street and inquired, "Excuse me, Sir, what is time?" Unaware of the nuances of the English language, the inquirer expected the Englishman to tell him the time of the day. However, the Englishman, steeped in Formalism, interpreted the question in a literal sense. Puzzled, he looked at the questioner for a few seconds and then replied, rather gravely, "Well, that is a very deep, philosophical question." Leaving aside the comic aspect of the situation, it must be admitted that time is indeed a very intricate concept.

While one facet of human consciousness is the awareness of time, the meaning of the word, time, cannot be distilled into a neat verbal definition. Time seems to flow or pass, or else people seem to advance through it. But the nature of this passage or advance appears to be mysterious; it in fact transcends human understanding. Further, did time have a beginning or does it have an end? According to cosmologists, the universe is expanding with the galaxies receding from one another, and the universe as it is known originated in a primeval explosion, called the Big Bang, at a date of the order of 15x109 years ago. This could be regarded as the beginning of time. There is no unanimity among scientists as to whether time will ever come to an end. In revealed religions, such as Islam, Christianity and Judaism, the Day of Judgment marks the end of time.

Although defining time presents formidable problems, measuring it in terms of days, months, and years, is a relatively simple matter. Even primitive societies measured time in these units in order to regulate their civil life and religious observances. The device, known as a calendar, by which time is divided into convenient units to meet society's needs continues to play a vital role in the modern world also. The basic unit of computation in a calendar is a day, measured from midnight to midnight in the West. In the East, however, the day is often measured from dusk to dusk, or from dawn to dawn. The seven-day week owes its origin partly to the Babylonian belief in the sacredness of the number 7, and partly to the importance of Sabbath in Jewish life.

The month (moon) is based on the lunation, that period in which the moon completes a cycle of its phases, from New Moon to New Moon. This is called the synodic month. This period lasts approximately 29days, and most early calendars were, essentially, collections of months - a collection of 12 consecutive synodic months forming a year (lunar).

The duration of the lunar year is 354 (29X12) days, while the mean solar year, the period taken by the earth to make a complete revolution round the sun is 365 days. To be more precise, one synodic month amounts to 29.53059 days, whereas the solar year (the mean tropical year) amounts to 365.242199 (almost 365) days. Consequently, a calendar based on lunar month is not suitable for determining the seasons which are a solar, not a lunar, phenomenon. To make matters worse, there is no simple relationship between the two numbers. 29and 365, and neither is composed of a complete number of days. Hence, in order to compile a calendar that keeps in step with the moon's phases or with the seasons it is necessary to insert days at intervals; such additions are known as intercalations.

The Julian calendar introduced by Julius Caesar in 46 BC achieved this objective to a large extent. This is a solar calendar, and the length of the solar year is taken as 365days. Further, 11 months out of 12, into which a year is divided, have either 30 or 31 days and the remaining month of February contains 28 days in common (365-day) years, and 29 days in every fourth year (a leap year, of 366 days). The intercalation of a "a leap day" every fourth year was intended to maintain correspondence between the calendar and the seasons. However, the solar year comprises precisely 365 days 5 hours 48 minutes and 46 seconds, slightly less than 365days, resulting in an error of 11 minutes 14 seconds per year. This error amounts to about 8 days in 1000 years.

By the middle of the 16th century the Julian calendar became increasingly out of phase with seasons. At this stage, Pope Gregory XIII effected some refinements in the Julian calendar to correct the error that had accumulated. The Gregorian calendar stipulates that no century year is a leap year unless it is exactly divisible by 400. A further refinement, the designation of years exactly divisible by 4000 as common (not leap) years, will keep the Gregorian calendar accurate to within one day in 20000 years. Mathematically speaking, these successive refinements constitute what is called an iterative process. The Gregorian calendar is the one that is almost universally used today.

The Muslim Era (Hegira), a lunar calendar, introduced by Hazrat Omar (PBUH), the second caliph, dates from 16 July 622 AD, when the Holy Prophet (PBUH) emigrated from Makkah to Madinah Since lunar calendar falls short of the solar calendar by about 11 days, the current Muslim Era is 1420 AH, not 1377 AH (1999-622), the Muslim Era advancing one year almost every 32 solar years.

Although the Julian calendar, as a means of grouping days into months and year, was codified by Julius Caesar, the system of actually numbering the consecutive years with reference to some important event was started much later. The Christian Era, now in vogue throughout the world, was devised by D Exiguus, an Italian monk, in 525 AD. Christ's birth was taken as the point of reference, and years were reckoned as either AD (Anno Domini, "in the year of the Lord") or BC (Before Christ). There was no AD 0; the year before AD 1 was BC 1. This omission, or aberration as the mathematician would call it, is attributable to the fact that the digit, 0, was not known to the West until the 13th century. Zero (0) was invented in the Indian subcontinent and the West came to know about it through the Arabs much later. It is interesting to note that the Roman numerals (I, V, X, L, C, D, M), which the venerable monk presumably used, do not contain any symbol for 0. Equally interesting is the fact that the digits - 0, 1, 2,..., 9 - that we use everyday are known as Arabic numerals. This omission led to a "conflict" between history and science, or more precisely, between history and mathematics.

In mathematics, the point of reference, or the origin as it is normally called, is always assigned the value 0. Other quantities, counted in relation to this origin, either increase or decrease depending on which side of the origin the quantity lies. There cannot be any break in time as it flows continuously. One cannot jump from - 1 to + 1 without passing through 0. To put it another way, there must be 0 on the time axis between - 1 and + 1. That is, in the present context, there must be AD 0 between BC 1 and AD 1. For a scientist, this is an immutable principle; it cannot be trifled with. Any departure from this will result in inconsistencies and contradictions. Since it is not possible, at this stage, to have AD 0, the mathematician would treat AD 1 as the origin, at least notionally, and then terminate the first millennium on 31 December 999 in order not to duplicate the same error over and over again. The first millennium will then span a period of 999 years only, but the second and the succeeding millennia will remain immune from the "virus" of misplaced origin. That is, each of them will cover a period of 1000 years, as it should.

What is more important, this convention will obviate many complications that would ensue from the omission of AD 0. It is, as if, the mathematician has preempted the occurrence of a serious problem similar to Y2K bug that we were about to face. The convention might appear rather esoteric, and cause a little unease. But the fact remains that we are not free to use numbers in a way that contravenes the very principles on which they are based. The number system is, after all, a theoretical framework with its rigid laws and bye-laws. Hence the second millennium which commenced on 1st January 1000 AD expires on 31 December 1999. However, from the standpoint of a historian, the second millennium begins in 1001 AD, and the third in 2001. In this tug of war between history and science, science and mathematics have prevailed. The requirement of the number system itself has predicated this.

Understandably, the approach of the Third Millennium generated a great deal of excitement and expectations all around the globe. Apart from the fact that a millennium, like a century, is a convenient unit of time, it has no special significance - physical, religious, or otherwise. It has no magical attribute, either for good or for evil. A day and a year have physical significance in that they are both caused by the movement of the earth. A millennium, on the other hand, is just a creation of the human mind. Let us treat it as such, and disabuse ourselves of fancy myths concerning the millennia.

The author is a former Professor of Statistics at Dhaka University.