Could India's "Failed" Monsoon Have Been Predicted by the Right Calendar?
by C. K. Raju

From the following forthcoming book sponsored by The Infinity Foundation:
Kâla: Traditional Indian Views of Time in Relation to the Western and the Scientific

Agriculture traditionally was the mainstay of the Indian economy, and still remains vital to the Indian economy. Accordingly, a method of timekeeping in the form of a good calendar remains a critical technology in India. Traditional calendar-making techniques, calibrated over centuries, therefore, deserve serious consideration and evaluation, and should not be rejected in a cavalier manner.

Consider the current situation. This year the monsoon did not arrive for so long that there was a sever water crisis, and the government declared the state to be severely drought affected. Eventually the monsoon has arrived, after nearly a month of delay, and in Bhopal at least, the deficit has been wiped out, with floods in nearby rivers. (It is still raining heavily, but water is still being supplied only on alternate days!)

The question is this: was the monsoon delayed? or is the calendar wrong?

The background to this question is as follows. The traditional Indian calendar uses the sidereal year, while the Julian and Gregorian calendar use the tropical year. The sidereal year is defined as the time period in which the sun returns to the same position with respect to the stars, while the tropical year is defined as the time between two successive vernal equinoxes. The sidereal year involves the motion of the earth relative to the stars, and is MORE than 365.25 days (365.256363 days, approximately), while the tropical year involves the motion of the sun relative to the earth, and is LESS than 365.25 days (365.24219 days approximately, at the present epoch). The difference between the two types of years is approximately 20 minutes per year (1223 s), which can become substantial
over long periods. The difference is attributed to the precession of the equinoxes: the axis of the earth is thought to precess like a top, so that it points to different points in the sky at different times along a cycle of some 26,000 years (i.e., Polaris was not the north-star a few thousand years ago, and will not be the north star a few thousand years from now).

The Julian calendar was based on the tropical year or the equinoctial cycle; so is its corrected version-the Gregorian calendar (which is the calendar in current use).

The Gregorian calendar reform committee tried to consult Indian calendrical sources, as I have pointed out elsewhere-in connection with the transmission of the differential calculus from India to Europe. Christoph Clavius was the head of the Gregorian calendar reform committee, and just prior to the Gregorian calendar reform of 1582, Claviuis' student, Matteo Ricci, was in India, in Cochin, searching for Indian calendrical manuals, after having been appropriately trained for this purpose. (I have a photocopy of Ricci's original handwritten letter. I don't know if they actually made any use of these Indian manuals and books for the Gregorian calendar reform.)

The Gregorian calendar reform itself was initiated because the Julian calendar fixed the length of the year very crudely, in my opinion just because the Romans were not adept with fractions. Because of the error in the second decimal place (the Julian calendar took the year to be exactly 365.25 days) the Julian calendar slipped by about a day in a century, and had, by 1500s, slipped 10 days out of phase in the 1200 years since the Council of Nicaea fixed the date of Easter/vernal equinox. The Gregorian calendar reform corrected that (by advancing the calendar by 10 days, and, e.g., by making every 100th year not a leap year etc. to get a more accurate
figure for the fractional part of the length of the tropical year.) This correction of the calendar was needed for the very practical purpose of fixing latitude from observation of solar altitude at noon. (Navigation was, then, extremely important for Europe, which was then way behind the Indians and Arabs.) However, it became a religious issue and Protestants opposed the papal bull. The reformed calendar was eventually accepted in Britain and in USA (then a British colony) only in 1752, by advancing the calendar by 11
days and implementing the rest of Clavius' recommendations.

Though neither calendar has changed in the last 500 years, perceptions have. Therefore, ironically, after independence, the Indian calendar reform committee adopted the Gregorian calendar without much ado! In its report, the Indian calendar reform committee, dominated by M. N. Saha (and N. C. Lahiri), simply stated that it is obvious that seasons depend on the tropical year. "For calendarical purpose [sic], it is unmeaning to use the sidereal year...as then the dates would not correspond to seasons. The use of the tropical year is enjoined by the Hindu astronomical treatises like the Surya Siddhânta and the Panca Siddhântikâ. But these passages have been misunderstood, and Indian calendar makers have been using the sidereal year with a somewhat wrong length since the fifth century AD."

If that is so, then the traditional Indian calendar ought to have slipped out of phase by around 21 days over the last 1500 years. (Also, I don't see the part about "misunderstanding", since Aryabhata, prior to Varaha Mihîra and the Panca Siddhântikâ, unambiguously advocates the sidereal year.)

But how is it obvious that one must use the tropical year? While it is true that physically the sun is the main source of energy, one does not merely want to determine the hot and cold seasons-for the key feature of the calendar in India relates to the monsoons, which are the mainstay for agriculture. The monsoons depend upon the wind regime.

The wing regime or global circulation is not, however, decided solely by the position of the sun. Hot air rises at the equator, but it doesn't descend at the poles. Because of the so-called Coriolis force, due to the earth's rotation, the air is deflected and descends before the horse-latitudes.

The monsoons, thus, depend also upon the Coriolis force. The Coriolis force is an inertial force. The only possible inertial frame being a frame fixed relative to the distant stars, the Coriolis force hence relates to the sidereal motion of the earth. Thus it might be that the monsoons relate also to the sidereal year.

At any rate, the monsoons have arrived on time according to the Indian calendar, since Rakhi too was "very late" this time, and the current month is still Srâvana. (The calendar we are talking about was calibrated for Ujjain, about 150 km from Bhopal.) The monsoons, however, are delayed by a month according to the Gregorian calendar: or, to put it differently, the Gregorian calendar has given the time of the monsoons in a grossly incorrect way. If the monsoons depend only on the tropical year, then, because of the
difference between the tropical and the sidereal year, it is the Indian calendar that ought to have been out of phase by three weeks (around 21 days).

Admittedly, the argument sketched above is no more than a conjecture at this stage, but a whole lot of research involves chasing such conjectures, when we see that something does not "fit". Such conjectures, however, first need to be articulated, and my aim would be only to articulate this conjecture. Actually solving the Navier-Stokes equations over a long period to ascertain what the periodicity of the monsoon depends upon is a supercomputing problem (still a "grand challenge problem" according to NASA). In the absence of an actual solution, the assertion that the monsoons should have a simple periodicity depending upon the tropical year is also not particularly credible, but is merely an article of belief. However, since this belief is held by many in authority, there should be at least some prima facie evidence to support such a study, which asserts that the opposite belief might be the case. At any rate, one cannot consider as "obvious" that the seasons depend only on the tropical year, and that the traditional Indian calendar is hence wrong. Maybe this is so, but there is nothing obvious about it, and a study at least is needed.

There could, of course, be other reasons why sidereal time was used in Indian astronomy. The rotation of the earth varies less than the apparent motion of the sun around the earth, so that the sidereal day provides a better method of timekeeping. It is also a more convenient method of timekeeping: for stellar transits are easy to observe, etc.

It will be necessary, of course, also to summarise-if not sort out-the whole vexatious issue of the precession of equinoxes vs libration: whether or not the precession of the equinoxes is actually taken into account in the Indian astronomical literature.