A tale of two calendars

C. K. Raju

Albukhary International University
Alor Setar, Kedah, Malaysia

ckr@ckraju.net


The Christian (Gregorian) calendar presents many difficulties. Just to state any date one must recite the superstitious belief in AD and BC which recitation is offensive for non-Christians, and involves a historical falsehood. (The “zero” point of the calendar was fixed only in the 6th c. CE in relation to the date of Easter.) It is a thoroughly unscientific calendar since its months are in total disarray with the lengths of some (such as July with 31 days) set to suit the vanity of Roman dictators, Presumably due to the persistent arithmetical incompetence of early Europeans, all months in that calendar have got completely disconnected from the natural lunar cycle. As for the length of the tropical year on which that calendar is based, the Julian calendar adopted the incorrect figure of 365 ¼ days, which was hopelessly wrong even by the standards of the 5th c. This wrong figure was adopted just because the Greek (Attic) and Roman numerals were too primitive even to articulate the precise fractions needed to state the correct length of the year.1


The Gregorian reform (which borrowed from Indian astronomy texts,2 despite the papal bull), corrected the error in the Julian calendar by about 1 day in 133 years. Note that, a complex system of leaps years was used since, even in the 16th c., the adopted length of the tropical year could still not be stated in decimal fractions as 365.2425 since decimal notation (for whole numbers) was introduced in Europe only a few years later, by Stevin, and Clavius had just introduced fractions into the Jesuit syllabus.3 Overtly, the Gregorian reform was solely for the purposes of Christian ritual, and corrected the earlier slip in the date of Easter, by one day in a century. Such a correction may not be appropriate for other secular purposes, since the length of each year still remains wrong by a small amount: so, this is like accepting a watch which runs slow on the grounds that this is acceptable since the watch is reset every month.


However, this calendar, which propagates superstition and historical untruth, and is unscientific and inaccurate is the only calendar that most Western educated people learn. Western education not only sidelines other cultures, it implants the deepest suspicion of anything non-Christian. Accordingly, the Western educated elite in India rarely know much about the traditional Indian calendar (most cannot even name the months on it), and they regard the Christian calendar as secular and universal!


By way of comparison, I will consider only the traditional Indian calendar, though it has many aspects in common with the Islamic calendar and the Chinese calendar (made by Buddhists).4 The Indian calendar certainly has a concept of civil day (sawan din), and the idea of day number was in extensive use in India from where the notion of present-day notion of Julian day-number derives (without acknowledgment, as usual). However, the Indian calendar is not a Robinson Crusoe calendar, like the Gregorian calendar, based on the civil day alone. The concept of tithi allows months to be handled systematically. A tithi is defined as the duration in which the observed angular distance between sun and moon increases by 12o. Consequently, every month always has exactly 30 tithi-s, though there is no 1-1 correspondence between tithis- and civil days. Further, since the solar and lunar cycles are incommensurable, there is naturally a need for intercalary months (adhik mas) to reconcile the two. As for accuracy, the 5th c. Arybhata's figure for the duration of the sidereal year5 was off by a small amount only in the third place after the decimal point. The traditional Indian calendar ought to be preferred over the Christian calendar, at least in India, on these grounds alone: that it is an accurate and scientific calendar, which avoids superstition and historical untruths. However, there is rather more to the matter.


The Indian economy is still heavily dependent on agriculture, which is mostly monsoon driven. The Christian calendar has no concept of a rainy season, while the Indian calendar has a concept of the rainy months of Sawan and Bhadon, known to every Indian child through the culture. This calendar should, therefore, have been adopted after independence. However, post-independence, the Indian calendar reform committee,6 headed by Meghnad Saha, declared that the use of the sidereal year by the Indian calendar was “obviously” an error. With all my respect for Saha and his textbook on heat and thermodynamics, one can say with greater justification that this “obviously erroneous” declaration was the consequence of Western mind wash. The tropical year decides the heat balance, and summer and winter seasons do depend on that. However, the heat balance alone does not decide the rainy season or the moisture balance. That is decided by the wind regime. That is the critical issue in the Indian case, since it is the wind regime which decides the monsoons.


Hot air rises at the equator but it does not settle down at the poles. It is deflected at the horse latitudes due to Coriolis force. The Coriolis force is an inertial force due to the rotation of the earth. The only known inertial frame is one that is fixed relative to the distant (fixed) stars. (On orthodox Newtonian physics, this dependence of inertial forces on distant stars is deemed not to need any explanation.) That is, the sidereal year is important for the wind regime, hence the monsoon.7


Apart from this, since tidal forces vary as the inverse cube of the distance, the lunar tidal forces are stronger than the solar one's. Tidal effects in the atmosphere are obviously huge compared to tidal effects on the sea, and such tides may affect the monsoon. That is, lunar motion is also important for the wind regime. It is conceivable that the two effects (inertial and tidal forces) might combine to affect the monsoon in a chaotic way as happens when there is an adhik sawan on the traditional calendar. Incidentally, this was precisely the case in 2004 when the monsoon was “delayed” (on the Gregorian calendar, but not the traditional Indian calendar) by almost a month.8


Empirically speaking, if the calendar reform committee had been right, and the wrong year (sidereal instead of tropical) was being used, the current Indian calendar should have been off by a month. Instead, the rains have been delayed on the Gregorian calendar, somewhat persistently over the last decade, leading to repeated dire anticipations of drought, and crop failure due to mistiming of agricultural operations.9 Further, there is the evidence of commonsense. In the case of the navigational instruments of the Lakshadweep islanders, Britishers like James Prinseps reached foolish conclusions because, wallowing in their racist sense of superiority, they ignored the elementary fact that the islanders had successfully navigated to small islands for centuries.10 Likewise, it was the persistently successful practice of agriculture which made India into such an incredibly wealthy country that Europeans were ready to die like flies (and did) for a bit of the loot. Agricultural success required a good calendar which could tell the monsoons accurately. It is one thing that our Marxist historians too use AD and BC as if they were secular terms; it is quite another that they have neglected even the means of production and their relation to the historical development of science in India.11


Of course, what is needed is a causal rather than a statistical account; I have expressed this opinion earlier,12 and I still abide by it. Anyway, the scientific approach is that between two theories, one should choose the better one, and the traditional Indian calendar is clearly better at predicting the monsoon than the simple-minded belief that the monsoon comes on a fixed day on the Christian calendar. A statistical average is no proof of that, and at least a comparison with alternative theories is needed.


Against this background it is curious how this unscientific belief is preserved by the academic systems developed in the West with a view to preserve church superstitions. The stock first tactic is to denounce the critic (any critic) of the West as a chauvinist of some sort. This tactic can be used by any ignoramus, since all substantive criticism is avoided, so no knowledge of the subject is needed. The second tactic is that of censorship: there are enough editors of journal and newspaper to ensure that any support for anything traditional is not published, at least not in “reputed” journals, for publication is today the other test of science. Serious reasons for editorial rejection are never provided, for the objective of censorship is to suppress debate not to encourage it.13 The third tactic is to shift the onus of proof. The demand is that the existing beliefs, howsoever absurd, must be disproved. (The related trick here is the indefinite sharpening of the standards of proof, as I have discussed elsewhere in the case of false claims about Copernicus.14) The fourth tactic is resource deprivation, using the three grounds above. Starting from 2003, I have repeatedly pointed out the above simple argument to the government and to the Department of Science and Technology, and suggested that an investigation is in order. Though the Indian government has spent hundreds (more probably thousands) of crores on drought relief in the past decade, it refuses to even consider spending even 0.0001% of that amount to fund an investigation. Presumably they are afraid of the truth. As a general rule, the DST readily funds projects which imitate the West, and does not bother even to respond to other proposals (in the absence of political pressure), for, like science journalists, they believe science is the practice of imitating the West.


Ironically, the inability to provide a causal account (or good model) of the monsoon is freely admitted by NASA and science journalists (and newspapers have space for this admission). The slightest application of the mind would have, however, shown the absurdity of admitting that monsoons are hard to predict while hanging on to the belief that it is “obvious” that the monsoons have a simple periodicity on the tropical year.


Scientifically speaking, the proper starting point should be a theory of monsoons, as already incorporated in the Indian calendar which has worked well down the ages. Specifically, the starting point ought not to be an apologetic desire to maintain colonial status quo. If science is not mindless belief in the West, the traditional Indian calendar must continue to be used till one has a demonstrably better theory of the monsoons. This would probably save the lives of millions of Indian farmers. Improvements, of course, are always possible, and there is a clearly discernible improvement in the trigonometric values related to Indian traditional calendar from the 5th to the 16th c., with their accuracy going up from (sexagesimal) minutes to seconds and thirds (9 decimal places).



1C. K. Raju, Is Science Western in Origin? Multiversity, Penang, and Daanish Books, Delhi, 2009.

2Matteo Ricci,.tetter to Petri Maffei on 1 Dec 1581. Goa 38 I, ff 129r–30v, corrected and reproduced in Documenta Indica, XII, 472-477 (p. 474). Ricci was a pet student of Clavius, the author of the Gregorian reform. In this letter from Cochin, he states that he was looking for “an intelligent Brahmin or an honest Moor” to tell him about Indian methods of timekeeping. These methods of timekeeping were in Indian astronomy texts, which were translated and imported bringing also the calculus to Europe.

3Christoph Clavius, ca. 1575 “A method of promoting mathematical studies in the schools of the society”, Document No. 34 in E. C. Phillips, “The proposals of Father Christopher Clavius, SJ, for improving the teaching of mathematics”, Bull. Amer. Assoc. Jesuit Scientists (Eastern Section), 18 (1941) (No. 4) pp. 203–206.

4C. K. Raju, “Interactions between India, Western and Central Asia, and China in Mathematics and Astronomy,” in : A. Rahman (ed) Interactions between India, Western and Central Asia, and China, PHISPC, and Oxford Univ. Press, New Delhi, 2002, pp. 227–254.

5Aryabhatıya of Aryabhata, ed. and trans. K. S. Shukla and K. V. Sarma, INSA, New Delhi, 1976.

6Govt of India, Report of the Calendar Reform Committee, CSIR, New Delhi, 1955, p. 158. The quote occurs in part C of the report on the “The History of the Calendar. . . ”, by M. N. Saha and N. C. Lahiri, published as a separate volume, under that title by CSIR, p. 158.

7Cultural Foundations of Mathematics: the Nature of Mathematical Proof and the Transmission of Calculus from India to Europe in the 16th c. CE (Pearson Longman, 2007), chp. 4, Box 4.2, pp. 208-212. http://ckraju.net/papers/Calendar-from-Cultural-Foundations-of-Mathematics.pdf.

8C. K. Raju, Cultural Foundations of Mathematics, cited above, box 4.1.See link above.

9The related newspaper clippings are archived in the extract from class notes on "Calculus without Limits" at http://ckraju.net/papers/Monsoon-pages-from-calclnm.pdf.

10C. K. Raju, “Navigation: Kamal or Rapalagai”,. Chp. 5 in Cultural Foundations of Mathematics, cited above.

11“Cultural Foundations of Mathematics”, Ghadar Jari Hai, 2(1), 2007, pp. 26-29. http://ckraju.net/papers/GJH-book-review.pdf.

12C. K. Raju, Cultural Foundations of Mathematics, cited above.

13Recently, however, some newspapers have provided space.. See my article, “National Year of Mathematics”, Millennium Post, 19 May 2012,at http://www.millenniumpost.in/NewsContent.aspx?NID=2227, and subsequent related articles on mathematics education at http://millenniumpost.in/OpinionList.aspx?AID=90. The mass circulation Dainik Bhaskar also carried related articles in Hindi, e.g.,. "किस 'गणित' का उत्सव?”, दैनिक भास्कर, 10 April 2012. http://www.bhaskar.com/article/ABH-what-mathematics-of-the-party-3104218.html. . See also the article by Sandhya Jain, “Stars, not sun, predict monsoon accurately” Pioneer, 17 July 2012. http://www.dailypioneer.com/columnists/item/52007-stars-not-sun-predict-monsoons-accurately.html. .

14For more on varying standards of proof, see Cultural Foundations of Mathematics, cited above, and Is Science Western in Origin? also cited earlier.