By Dr. Hossein B. Zadeh

London, EnglandForget about the millennium time-bomb. I've got a problem with the calendar TODAY. Last year, my birthday was on the 27th January, and so will it be next year. However, this year it fell on the 26th. Why, oh, why?

The short answer is this: 1996 was a year too early to be a leap year. For the long answer, read on...

The (Western) calendar is drifting away form its 'natural' course. Pope Gregory XIII did manage to make a long-delayed correction in the calendar in 1582, but he also laid down a system which is simple enough to follow but has little correspondence with the natural calendar. The cosmos would not obey His Holiness's decrees.

My birthday is first and foremost recorded in a calendar which follows the natural course of the movement of the earth around the sun. The calendar was initially set up by the renowned Iranian poet, philosopher and mathematician Omar Khayyam in the 11th century AD. Soon after, it was forgotten for a long time and then revised and put in use as the official calendar of Iran early this century.

The two calendars are both solar and have the same length of 365 days in normal years and 366 days in leap years. The leap years in both calendars used to come once every four years; and as long as most Iranians can remember, these were so close to each other that the distance between the two extra (leap) days in the two calendars been less than three weeks - from the 29th of February to the last day of the Iranian year March 20th. (The Iranian calendar closely reflects the structure of astrological zodiac signs. More on this later.)

The year1996 was a leap year. Customarily, Iranians used to have the corresponding Iranian year of 1374 as a leap year too - but it was not to be. As a result, the Iranian New Year's Day for 1375 (first day of Aries) fell on the March 20th instead of the usual 21st. Consequently, the corresponding days of the two calendars will be different (for some years) from what they used to be in recent past. And the next time the two leap years correspond closely to each other, as they did for the last 30 years or so, will be in the Gregorian year of 2096 and the Iranian year of 1474 (and yet again it will soon be followed by another distortion four years later in the year 2100! -- see details later).

The reason is both complicated and fascinating. But before going into that, let us have a look at the Iranian calendar -- known as Jalaali [1]-- and appreciate some of its unique features.

The Jalaali calendar is more ``natural'' than the Gregorian calendar. It starts with the natural cycle of the year, the first day of spring (for the northern hemisphere). As such, it has no national, regional or religious significance [2]. It is truly universal. Every season is associated with three full months of the year. So no confusion arises about which day of the year, for example, the season begins. The first six months all have 31 days and the second six months all have 30 days in leap years, with the last month having 29 days in non-leap years.

Compare these with the Gregorian calendar. There, you will find no easy correspondence between the start and end of months and seasons, nor between the natural and calendar years. The months have arbitrary length of seven 31 days, four 30 days and one 28/29 days interleaved irregularly. It took only a Roman dictator like Augustus to increase the days of the month of August by one day just because July, the previous month named after his predecessor Julius Caesar, had 31 days in it! Luckily, for Iranians, in spite of being ruled by a stream of dictators who occasionally fancied playing with calendars (the last failed attempt was by the shah in the mid 1970s who added 1180 years to the base date to link his reign to ancient Persians), the Jalaali calendar has remained almost intact.

Add to the above features, the fact that the Jalaali year follows closely the movement of the earth (round the sun). A natural solar year is neither 365 days nor 366. It is something like 365 days, 5 hours and 49 minutes. While for Westerners, the new year begins at midnight, for Iranians there is an exact time (to the seconds) worked out by astronomers who specify the beginning of the new year. This is the exact time of the vernal equinox [3].

However, for the purposes of the calendar, a day (of 24 hours) can either belong to the past year (say, the last day of Esfand) or the new year (1st of Farvardin). So what Iranians do is simply this: if the exact moment of vernal equinox is before midday (Tehran time), they regard the same day as the New Year's Day (1st Farvardin/Arie's). Otherwise, the New Year begins on the following day. This has made the Jalaali calendar year much more accurate than the Gregorian one.

Now, because the natural year is approximately 365 days and 6 hours, it means that approximately every four years we have an extra day in the year - hence the leap years. But the year's length is about 11 minutes shorter than that. So, over the years, these 11 minutes added together affect the cycle of the leap years. For instance, while four years ago the vernal equinox occurred just after midday (Tehran time), and so the following day was New Year's Day, for the current year it happened before midday, and so the same day, and not the following day, was regarded as New Year's Day. As a result, the leap year has been pushed to this year. This happens once every 33 years, when the differences of 11 minutes add up to approximately 360 minutes -- equal to 6 hours. That is enough to cause an extra non-leap year every 33 years.

That is how the Jalaali calendar system is organized: In this calendar, usually, eight years out of every 33 years are leap years. The leap years are those with a remainder (after dividing by 33) of 1, 5, 9, 13, 17, 22, 26, and 30. For instance, 1375, the current year, divided by 33 leaves 22 as the remainder, and so is a leap year. Moreover, the above figures show that there has been a five-year span (instead of the usual four years) between this leap year and the previous one. The last time the same thing happened was between the leap years of 1337 and 1342 (Gregorian years 1958-59 and 1963-64, respectively).

Now, let's look at how the Gregorian calendar deals with these anomalies. Here, things have been made much simpler. The leap years have been fixed for every four years -- except for the years which are divisible by 100 but not by 400. So, the year 2000 will be a leap year (as it is divisible by 400) but not, say, 2100. In this way, the calendar has managed to compensate for the shortfall of 11 minutes per year over a span of 400 years. A clever way but not consistent with the actual size of a natural year. Moreover, while the Jalaali calendar is self-correcting, the Gregorian system deviates still further from the natural year over a longer period of time. But that will be far after the millennium time-bomb is defused...

Footnotes[1] Named after Jalaal-ol-Din Malek-shaah-e Saljuqi by Omar Khayyam who re-worked it in late fifth century hejri.

[2] The years' count is based on a historical religious event ({hejrat}). But that's a different story. Gregorian calendar is based on religion for both its base date and start of the year.

[3] A solar calendar year begins at the point when the sun appears to cross the equator from the southern hemisphere to the northern hemisphere as viewed from the centre of the earth.

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