Medieval mistake

Print edition : March 28, 2008

As the earth goes around the sun, the sun appears to move against the constellations of the zodiac.-

The story of Indias faulty calendars.

IMAGINE having a faulty wristwatch that ticks slightly faster than it should. You may ignore the small difference it makes, but if it is not set right then after a while the watch may show noon when it is still morning. Then suppose you refuse to correct it and do something absurd, and call morning our noon. The traditional Indian calendars have become just such an absurdity today. They are slowly going out of sync with the seasons by ticking faster than they should and they have already accumulated an alarming gap.

Fifty years ago, a new calendar system was introduced in India called the Indian National Calendar to correct the faulty traditional ones, but we hardly use it; most of us are even blissfully unaware of it. In the meantime, the calendars in use have become more and more out of step with the seasons just like the faulty wristwatch. Today, the time gap stands at roughly 24 days almost a month.

That is why Makara Sankranti, which is actually the day the sun shines overhead on the Tropic of Capricorn (Makara), that is December 22 (the winter solstice), is celebrated in the middle of January. Most of us often wonder about the significance of January and Makara, unaware of the fact that the fault lies with our calendar system, that it cannot keep step with the seasons. It is like looking out at noon and trying to understand why we call it morning because our watch says so.

And it is all because of a mistake made in the medieval times. Moving faster than the seasons, Indian calendars jump ahead by a whole day in roughly 60 years; so they must have accumulated the present gap of 24 days in approximately 1,450 years. The calendars of today came into use circa 5th-6th century C.E. This was the time when the siddhanta (conclusive) system of astronomy was being formulated. There was a lot of debate and discussion at that point of time about a crucial issue, but somehow the prominent astronomers chose to disregard the truth and our calendar system is paying the price for it. The issue was about a discovery made in 2nd century B.C. in Greece, and something that medieval astronomers in India could have easily checked instead of indulging in wordy debates.

What was the crucial issue? And what makes our calendar tick faster than it should? It has to do with the slow motion of the earths axis, which is not very apparent to us but can be detected with careful astronomical observations.

We know that the earths axis is tilted with respect to the plane of its orbit around the sun. We have seasons on earth because of this tilt the sun shines overhead during some parts of the year and it shines obliquely during other times, giving us summer and winter and other seasons in between.

If the length of the seasonal year turns out to be different from the length of the year according to the stars, then the sun sign at spring, for example, will shift over time. The sun used to be against Aries on the spring equinox when the Siddhanta books of astronomy were written and now it goes to that position in May, because the belt of zodiac has moved relative to the orbit of the earth around the sun since then.-

The tilt of the axis is 23.5; and so the latitudes of 23.5 on either side of the equator mark the two extreme points that the sun can shine overhead these are the Tropics of Cancer and Capricorn. The sun shines overhead at these latitudes on June 21 and December 22, and it shines overhead on the equator on two equinox days March 21 and September 22. These are two days when the lengths of day and night are equal. The other markers, the solstice days in June and December either have the shortest or the longest day in the year these are the two extreme days in a year.

As the earth goes around the sun, from the earths point of view the sun completes a circle in the sky, moving against the distant stars. The belt of stars that the sun appears to move against is called the zodiac and is divided into 12 constellations. This is the origin of the different sun signs at different times of the year. For example, the sun shines against the constellation of Pisces during the spring equinox on March 21 now. In other words, if one could somehow see the stars at daytime on that day, one would have seen the sun in that constellation in the sky.

It is natural to take one of these four days two equinoxes and two solstices as the starting point of a year. According to some historians, people of the Indus Valley civilisation took the autumnal equinox (September 22), or the first full moon after it, as their New Year day. A seal from Mohenjodaro has been interpreted by scholars such as Asko Parpola as depicting New Year celebrations. It shows seven ladies, possibly denoting Krittika (Pleiades), and a figure between two branches of a tree, possibly denoting the star Vishakha (shakha meaning branches). During the equinox at that epoch, the sun used to be against the star Vishakha (in Libra, whose symbol, incidentally, is a Balance).

Later, two traditions developed, one with the winter solstice (December 22) and another with the spring equinox (March 21) as the beginning of a new year. When the ancient Vedanga Jyotisha system of astronomy was discarded in favour of a new system a process that took five centuries, from the 1st to the 6th century C.E., to settle down it adopted the spring equinox day as the beginning of a year.

Next, to have a reliable system of calendars, one should be sure about what a year means. If the spring equinox day marks the beginning of every year, a year has to be the time between two consecutive spring equinox days. In fact, experimental methods described in Siddhanta books give a way of measuring this length of time (called a solar or tropical year).

But one can also define a year in terms of the stars rather than seasons (and therefore called the sidereal year). It is the time period between the suns appearance against a star and its coming back to it. If the sun appears at one point in the sky in a zodiac sign, then the time taken for it to come back to the same spot is one sidereal year.

It would have been easy on the astronomers if the lengths of the two years according to seasons and according to distant stars were the same. But they are not, for a simple reason. The motion of the tilted earth around the sun is analogous to that of a spinning top. The axis of the top also rotates although much slower than the spin of the top because of the earths gravity working on the tilted top. In the case of orbiting earth, the gravitational force between the sun and the earth makes the earths axis rotate slowly. Very slowly indeed. It takes about 25,800 years for the axis to complete a cycle. This slow movement is called the precession of the earths axis.

The seasons in the northern hemisphere are shown at different positions of the earths orbit around the sun. On equinox days in spring and autumn, the earths axis is positioned in such a way that the sun shines equally on the two hemispheres. As the tilt of the earths axis slowly changes, the positions in the earths orbit where equinoxes would occur also change. So, the time for seasons also changes. So, the seasonal year is somewhat shorter than the total time elapsed in the orbit, which is defined according to distant stars. It is explained in the picture how the change in the tilt hastens the occurrence of spring. The change shown here is much exaggerated for clarity.-

On equinox days, the day and night boundary on the earth passes exactly through the North and South Poles. In other words, the sun shines equally on the two poles, or on the two hemispheres. By the time the earth comes back to the same position in its orbit when the sun appears against the same star in the sky the axis would have moved to a different direction, and the north-south axis has moved, so it would not be an equinox any longer. The equinox would have occurred about 20 minutes earlier than this.

So the year according to seasons is shorter by 20 minutes than the year according to the distant stars. It is a small difference no doubt, but this amounts to a difference of almost a day in 72 years. (The length of a year adopted in traditional Indian calendars is another three minutes off the correct value, making it jump even faster, and accumulate an extra day in about 60 days.)

Another way of looking at this is that because of the precession of the earths axis, the positions of stars in relation to the earth slowly change with time. Since the axis points towards different spots at different times, what is North Star today would not remain so after thousands of years. In fact, after 14,000 years, the star Vega (Abhijit) that shines almost overhead on summer nights now will become the north star.

The slow shift also makes the zodiac wheel slide in the sky, almost imperceptibly, but which becomes apparent after one or two millennia. This makes the position of the sun on the equinox day shift from one zodiac sign to the next in almost 2,000 years. And this changing background of stars makes the measurement of a year very tricky.

The Greek astronomer Hipparchus discovered this phenomenon in the 2nd century B.C. He recorded the position of the sun on the equinox days when a lunar eclipse occurred around them (on April 21, 146 B.C. and March 21, 135 B.C.), and compared the data with ancient Babylonian records. Later, Ptolemy of Alexandria refined these measurements circa 100 C.E.

Indian astronomers were aware of this discovery even before the new calendar system came into vogue. The Indian tradition listed 27 stars (nakshatras) against which the sun and the moon apparently moved in the sky, and the first star in the list changed from time to time, most probably to take into account the slow slide of the zodiac stars.

In the first millennium B.C., the Vedanga Jyotisha system began the list with Krittika (Pleiades) since the sun on spring equinox then was close to this star. Later, in circa 285 C.E., the Surya Prajapati recorded the list beginning with Ashvini in the constellation Aries (Mesha, the Lamb), since the sun on spring equinox had shifted to this spot by then. (And it has further shifted to Pisces Meena, the Fish at the present epoch.) So, Indian astronomers were probably aware of the gradual shift of stars in the sky, and also the effect it had on the length of year reckoned with respect to seasons.

Yet, there seems to have been a major confusion in the minds of the medieval astronomers. Varahamihira (505-587 C.E.) mentioned the phenomenon (ayana chalana motion of the ayan, year) in his book Brihat-samhita, but he suggested that one should verify it through actual observations. Half a century later, Brahmagupta categorically judged the idea wrong in his book Brahma-sphuta-siddhanta.

Some astronomers thought that the precession did not constitute a cyclic but an oscillatory motion so the shift in the calendar would decrease and increase periodically, and some others thought it was so small that one could ignore it. Much later, in the 10th century C.E., a few astronomers, such as Munjala and Bhaskaracharya, observed the correct shift but by that time our calendar system had become so deeply rooted in the older methods that it was not changed.

As if this was not confusing enough, later astronomers chose to record the positions of the stars in both traditions, with and without the shift due to precession (the sayana and nirayana system), but kept the calendar system rooted in the medieval times. This state of affairs suggests not carelessness but confusion.

The reasons for this confusion are not clear. On the one hand, the methods described in the Siddhanta books for the determination of the length of a year clearly show that medieval astronomers were calculating it according to seasons and not according to the stars. But their measure of a year roughly 365.2588 days was closer to the length of a year according to the stars (365.2564 days) than the seasonal year. The difference between their adopted value and the year according to the stars is about 3 minutes, and about 23 minutes off from the correct value. So it appears that they meant one thing (seasonal year) but measured something else (sidereal year), albeit with a bit of an error.

The Axis OF the earth rotates slowly with a period of 25,800 years. This 'precession of the earth's axis' is analogous to the rotation of a spinning top.-

Why did they stick to the year according to distant stars while setting up the calendar system? Clearly, the reasons have to do with something more than the level of astronomical knowledge in medieval India, which was otherwise sophisticated.

The usual explanation given for the decline in Indian medieval science that the rise of Brahminism after Sankaracharya led to a split of hand and brain and started a paradigm shift away from active experimentation is probably irrelevant here; it was still the heyday of Nalanda and other Buddhist monasteries when the debate was going on, during Brahmaguptas time, for example. (The school of thought in vogue in Nalanda at that time was the Yogachara philosophy, a kind of Kantian idealism, of negating reality; the famous Chinese pilgrim Xuanzang, or Hieun Tsang, came to study it in Nalanda in the early 7th century C.E.)

Another idea, originally of J.D. Bernal, is that the intellectual stimulus vanished once the stimulus of economic progress had dwindled. Historically, when the Siddhanta system was set in place circa 6th century, the political landscape of the subcontinent was changing rapidly. The Gupta empire had ended, and even during the rather peaceful reign of Harshavardhana (590-647 C.E.) several regional authorities from Shashanka in Bengal to Pulakesin and the Pallava kings in the South were striving to assert their power.

Amidst the chaos caused by military adventurism, the medieval trade guilds suffered losses. Some scholars have inferred from the manner Brahmagupta ignored his contemporary scholars in his book (circa 628 C.E.) that Indian mathematics and astronomy had split into various rigid schools of thought by his time. Is the confusion in our calendar due to this growing divergence at this stage? What were the political and economic reasons for this?

Irrespective of the reasons of the original sin in our calendar system, we seem to be stuck with it forever. There are a variety of calendars in use now, but all of them suffer from this generic defect. Some regions States in the north, the east, and Kerala and Tamil Nadu in the south use a solar calendar, in which months are either 30 or 31 days long.

In some other regions Andhra Pradesh, Karnataka, Maharashtra and Gujarat people use a mix of lunar months (of 29.5 days) with a solar calendar.

In the solar calendar, the New Year begins in mid-April, and in the luni-solar calendar it is celebrated on the last new moon (Amavasya) day before the New Year in the solar calendar. So, all these calendars are anchored to the solar calendar, and they are all slowly shifting out of their seasonal contexts because of the precession of the earths axis.

The fact that the length of the year is not an integral number of days it is, to be precise, 365.2422 days, or roughly 365 days, 5 hours, 49 minutes makes the task of any calendar maker hard. How does one take into account the fraction of a day? We could not possibly announce the celebration of New Year at some particular hour one year, and then at a different date and time (being precise about the minutes and seconds); that would usher in a state of permanent chaos.

How is it done elsewhere in the world? First, one defines a year with 365 days, and then inserts appropriate corrections to take care of the missing hours and minutes. In the Gregorian calendar (adopted in the Western world in 1582), the year is taken to be 365.2425 days, and we add an extra day every four years (on the leap year), and then discount a leap year once every century, except after four centuries, so that year 1900, say, is not a leap year but 1600 and 2000 are leap years, and then again have a leap year every 4,000 years (so that year 4000 is a leap year).

All these small nuts and bolts make sure that the calendar keeps the spring equinox on March 21 for at least 20 millennia, after which one will need some extra corrections. Our traditional calendar makers still vouch by the medieval Siddhanta books, which specify 365.2564 days, which is off by about 20 minutes.

The Government of India set up a committee to reform our calendars in 1955 with the renowned physicist Meghnad Saha as its chairman. It surveyed the existing calendars and the methods of corrections adopted in each, and concluded that the Hindu calendar... is a most bewildering production of the human mind and incorporates all the superstitions and half-truths of medieval times.... In spite of these errors, very few have the courage to talk of reform... the beginning of the year is now wrong by nearly twenty-three days, the result of accumulated error of nearly 1,400 years.

The committee went on to lament We are content to allow religious life to be regulated by the encyclopaedia of errors and superstitions which is called the Hindu almanac, and to regard it as a scripture.

The committee recommended that the year should start on March 22 and the first month should be called Chaitra instead of Vaisakh so that the difference between the old dates and the new dates would be approximately 6 (= 30-24) days.

The Indian National Calendar was adopted in 1957 based on its report, and if one followed its recommendations similar to the conventions in the Gregorian calendar then it would stand corrected for several millennia to come.

But this National Calendar is hardly used anywhere outside the confines of the pages of gazettes or broadcasts of All India Radio, while lay people remain blissfully at the mercy of traditional calendar makers.

It is true that people take time to adopt new calendars; the Gregorian calendar took many years before a large number of countries adopted it. England was wary of adopting the recommendations of the Vatican, and finally relented after two centuries (in 1752 A.D.). One could argue that the delay by half a century in India is not too hopeless, but with no debates or discussions taking place, it seems unlikely that Indias traditional calendar makers will change their attitude in the near future.

The medieval hangover of Indian calendars continues, and we deny it the remedy it badly needs.

Biman Nath is an astronomer and a writer. His first novel Nothing is Blue about medieval India will be published by HarperCollins (India) this year.

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