A tale of two calendars

C. K. Raju

Albukhary International University
Alor Setar, Kedah Darul Aman, 05200 Malaysia


The Christian calendar presents many difficulties. Just to state any date one must recite AD and BC. This is offensive for non-Christians, for it involves saying Anno Domini or “in the year of our Lord”, and BC or “before our Saviour”, thus admitting to Christian beliefs in Jesus as Lord and Saviour. Imagine that US school children are asked to recite “in the year of our Lord Rama” and “before our Saviour Rama” every time they state a date. There would undoubtedly be howls of protest about the Hindu religious bias. So, why should a Christian religious bias be taught to school children elsewhere? More specifically, why should the state help propagate this religious bias in a secular country like India, or in any country unwilling to teach a Christian religious bias to all its people.

Further, the AD-BC superstition encourages a historical falsehood—the belief that the zero point of the calendar is somehow related to the birth of Jesus and the origin of Christianity. The myth of Jesus relates to pre-Christian mystery stories,1 and there is no corresponding historical figure, and no historical evidence for his existence. Christianity probably originated in the 2nd c. CE in relation to dawn of the “new age” of Pisces. In the first century of the “Christian Era”, there is no evidence for Christianity. The Roman historian Flavius writing around the end of the 1st c. CE is unaware of Christians, as is Pliny a few decades later.2 In actual fact, the “zero” point of the Christian calendar was fixed only in the 6th c. CE in relation to calculations of the date of Easter, by Dionysus Exiguus in 536. It has no relation whatsoever to any historical event.

Further, that calendar is a thoroughly unscientific one, since its months are in total disarray. The Greek inability to reconcile the lunar and solar cycles had already led to a clumsy system in which 7 months of 30 days “alternated” with 5 months of 31 days. Subsequently the length of July was increased to 31 days to honour Julius Caesar for his attempts to end the earlier prevailing chaos in the Greek calendar, thus undoing his attempt! Not to be outdone, his successor Augustus demanded the same privilege, so August too has 31 days. Both days were stolen ad hoc from February which is reduced to 28 days (and 29 in the leap year, to add to the confusion). The net result is that months, originally intended to mark the natural lunar cycle, have got so completely disconnected from it, in the Christian calendar that it is impossible to ever re-connect the two until that calendar is abandoned.

Now, the Roman calendar derived from that of the early Greeks, who, in turn, copied their calendar from the Egyptians, as Herodotus informs us. Given that all sorts of imaginary achievements are chauvinistically attributed to “Greeks” by Christian and racist historians, it is important to understand why both Greeks and Romans were unable to link the lunar cycle to the month. This happened because of their arithmetical incompetence (and consequent incapacity to do any science). Indeed, even the solar cycle could not be properly linked to the length of the year on the best efforts of Greeks and Romans: the reformed Julian calendar set the length of the (tropical) year to the wrong figure of 365¼ days. I emphasize that this figure was hopelessly wrong even by contemporary standards: the 5th c. CE Aryabhata gives a length of the (sidereal) year an order of magnitude better, as does the 3rd c. Surya Siddhanta.

We should understand the exact reasons for this error in the Julian calendar: the Greek (Attic) and Roman numerals are so primitive they do not have any systematic notation for fractions. One never finds ¼ written as, say, I/IV in Roman numerals! (Would the I in the numerator cancel with the I in the denominator?!) Because Greeks and Romans lacked the ability to work with precise fractions, hence, they were unable even to state the precise fraction needed for the correct length of the year,3 as was done by Aryabhata. Romans could manage only a few simple fractions like ¼ which were parts of 12. Hence, they used that to describe the length of the year.4 This Western difficulty with fractions persisted in all of Europe until the 11th c., and in most of Europe (barring Florentine merchants) until the 16th c. when the Indian arithmetic of “algorismus” finally won over the primitive Greek and Roman arithmetic of abacus5 a victory depicted on the cover of Apianus' book.

The Gregorian reform of 1582 (which borrowed from Indian astronomy texts,6 despite the papal bull), corrected the error in the Julian calendar by about 1 day in 133 years. Note that, a complex system of leap years was used for this correction, just to avoid fractions. This shows that even in the 16th c., the adopted length of the tropical year could not be readily stated in precise decimal fractions as 365.2425 (the figure used in the Gregorian reform). Indeed, the decimal notation (for whole numbers) was introduced in Europe only a few years later, by Stevin (ca. 1587) and Clavius had just introduced the study of fractions into the Jesuit mathematics syllabus (ca. 1572).7

Why was the Gregorian reform carried out? I have argued that it was covertly motivated by the practical need to determine latitude at sea (which needed a correct date for the equinox). Determining latitude was then a major problem then being faced by European sailors. However, overtly, the Gregorian reform was done solely for the purposes of Christian ritual, to correct the earlier slip in the date of Easter. So much confusion then prevailed about this matter in Europe that the Protestant countries did not accept the reform until 170 years later, in 1752. (This indicates the state of astronomy then prevailing in Europe.) Because the inability to state precise fractions persisted into the 16th c., the Gregorian reform only corrected the average length of the year (averaged over a century) and is not appropriate for other secular purposes, since the length of each year remains wrong by a small amount. Hence, the equinox still does not come on a fixed day of the calendar.

Nevertheless, this calendar, which propagates (a) religious bias, (b) historical untruth, and is (c) unscientific and (d) inaccurate is the only calendar that most Western educated people learn. Western education not only sidelines other cultures, it works hard to implant the deepest suspicion of anything non-Western, and to exclude it from the minds of those it “educates”. This happens because Western education was designed to produce missionaries.8 Accordingly, the Western educated elite in India rarely know much about the traditional Indian calendar (typically they cannot even name the months on it). Worse, somewhat foolishly, they regard the Christian calendar as secular and universal! Indeed, I was taught in my childhood that the two secular festivals of independent India (Independence day and Republic day) were hence fixed on the Gregorian calendar (and I believed it then)!

What is the alternative? I will consider only the traditional Indian calendar, though it has many aspects in common with the Iranian and Arabic calendars and the Chinese calendar (made by Buddhists from India).9 The Indian calendar certainly has a concept of civil day (sawan din), and the idea of “day number” (ahargana) was extensively used in India. It is from there that what is today called “Julian” day-number derives and is used for present-day scientific purposes. (The concept was copied by Scaliger without acknowledgment, and, as usual, historians can always supplement that with a further false claim of “independent rediscovery”.)

However, the Indian calendar is not a Robinson Crusoe calendar, like the Gregorian calendar, based on counting civil days 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. Naturally, there is no 1-1 correspondence between tithis- and civil days, but the mathematical relation between the two is worked out in all Indian calendrical texts. Further, since the solar and lunar cycles are incommensurable, there is naturally a need for both intercalary tithi-s (both plus and minus) and months (adhik mas) to reconcile the two incommensurate cycles. As for accuracy, the 5th c. Arybhata's figure for the duration of the sidereal year10 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: namely that it is (a) an accurate and (b) scientific calendar, which avoids (c) superstition and (d) historical untruths.

However, there is rather more to the matter. The Christian concern with the calendar was primarily ritualistic—for the purpose of fixing the date of the then-most-important Christian festival of Easter. In contrast, the Indian calendar had and has a very important practical aspect. The Indian economy is still heavily dependent on agriculture, which is mostly monsoon-driven. Hence, the successful practice of agriculture in India requires an ability to identify the rainy season. The Gregorian calendar has no concept of a rainy season. On the other hand, the Indian calendar not only has a concept of the rainy months of Sawan and Bhadon, this is known to every Indian child (including the “illiterate”) through the culture. Knowledge of the monsoon remains critical to farming activities even today.

Inability to correctly identify the rainy season leads to crop failure. To demonstrate very clearly, I have put up newspaper clippings from the last decade on my website. These headlines concern the “delayed monsoon”, a phenomenon which happened repeatedly over the last decade. At least “delayed monsoon” is how it is expressed in English, referring to the Gregorian calendar. In actual fact, the monsoon came on time on the Indian calendar, and was delayed only on the Gregorian calendar. This “delay” led to crop failure due to mistiming of agricultural operations.11 (Like doctors who go by the advice of medical representatives, the peasants now go by the “marketing advice” of seed retailers, who understand only the Gregorian calendar.) It was naively (and wrongly) assumed that the monsoon has a simple periodicity based on the tropical year used by that calendar.

For its practical importance for agriculture too, the Indian calendar ought, therefore, to have been adopted after independence.

However, post-independence, the Indian calendar reform committee,12 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. Sadly, the calendar reform committee remained completely silent on the question of the monsoons. Though most Indian festivals are linked to agricultural activities, our calendar reform committee remained oblivious to the possible use of the calendar for agriculture. The obvious reason for this sort of blindness is that at that time the Indian elite had succumbed to the educational propaganda that everything Western was superior.

Instead of spouting hot air, the calendar reform committee should perhaps have paid more attention to its dynamics! 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.13

Further, the motion of the moon may also be important for the wind regime, hence the monsoon. This relates to tidal forces. Since (on Newtonian physics) 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 wind regime, hence the monsoon. But the effect of lunar motion on the wind regime seems not to have been studied by present-day scientists.

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.14

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, as already pointed out.15

We don't have to go by a ten year sample: for there is the evidence of commonsense. Recall how, in the case of the navigational instruments of the Lakshadweep islanders, Britishers like James Prinseps reached foolish conclusions. Thus, while wallowing in their racist sense of superiority, they ignored the elementary fact that the islanders had successfully navigated to small islands for centuries.16 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. In India, 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.17

Of course, what is needed is a causal rather than a statistical account; I have expressed this opinion earlier,18 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.

Against this background it is curious how this unscientific belief is preserved by the academic systems, which 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 easily published, at least not in “reputed” journals, for publication is today the other test of science (as it was of theology). Serious reasons for editorial rejection are never provided, for the objective of censorship is to suppress debate not to encourage it.19

The third tactic is to shift the onus of proof. The demand is made that the existing beliefs, howsoever absurd, must be disproved. This is convenient, because 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.20 That is, this amounts to a demand that Westerners must be convinced, regardless of their bias. That is rather like asking one to convince a fundamentalist Christian.

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 (DST), India, and suggested that an investigation is in order. Though the Indian government has spent hundreds (more probably thousands) of crores on drought relief (due to falsely “delayed monsoons” in the past decade), it refuses to even consider spending even 0.0001% of that amount to fund an investigation. 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. 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. But that is how the DST functions: without application of the mind.

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. The starting point ought not to be an apologetic desire to maintain colonial status quo. If science is not mindless imitation of the West, the traditional Indian calendar must continue to be used till such time 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. This was always accepted in India, 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).

1This is clear from the way early church representatives referred to these as the devil's parody. Justin Martyr, First Apology, chp. 21, “Analogies to the History of Christ”, http://www.earlychristianwritings.com/text/justinmartyr-firstapology.html. (From A. Roberts & J. Donaldson, ed. “Justin Martyr”, Ante-Nicene Fathers, vol. 1, T&T Clark, Edinburgh, 1980.)

2In response to these questions about evidence, first raised by non-Christians, like Porphyry, in the 4th c., a clumsily forged passage (the “testimonium Flavium”) was added into Flavius' account later! However, the need to use forged (or even suspect) passages as historical proof only underlines the absence of any real evidence for the mythical Jesus or for the existence of Christianity in the 1st c. CE. Such forgeries were commonly used by the church which, for example, obtained the Vatican by using a forged document (Donatio Constantini). The church introduced many forgeries even in the Bible, which made it so different from the original that to destroy the evidence of forgery, the Portuguese burnt all the oldest (Aramaic) Bibles in India in 1599 at the Synod of Udayamperoor (Diamper). With the same motive of suppressing or destroying evidence, the 8-volume work of Isaac Newton, investigating the systematic changes in the Bible, is still suppressed.C. K,. Raju, “Newton's secret”, in: The Eleven Pictures of Time, Sage, 2003.

3C. K. Raju, Is Science Western in Origin? Multiversity, Penang, and Daanish Books, Delhi, 2009.

4The tall claims about Ptolemy are manifest by the fact that the “official” version of the Almagest states the length of the year as 1 day in 300 less than 365¼ days, but even that figure never found its way in the Roman calendar, demonstrating that the text was inaccessible to Roman calendar reformers of the 5th c., like Hilarius.

5C. K. Raju, “Math wars and the epistemic divide in mathematics”, chp. 9 in Cultural Foundations of Mathematics, Pearson Longman, 2007. Earlier version available online at http://www.hbcse.tifr.res.in/episteme/episteme-1/allabs/rajuabs.pdf.

6Matteo 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.

7Christoph 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.

8C. K. Raju, Decolonising our universities: Time for a change”, GlobalHigherEd blog, http://globalhighered.wordpress.com/2011/09/11/decolonising-our-universities-time-for-change/

9C. 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.

10Aryabhatıya of Aryabhata, ed. and trans. K. S. Shukla and K. V. Sarma, INSA, New Delhi, 1976.

11The 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.

12Govt 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.

13Cultural 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.

14C. K. Raju, Cultural Foundations of Mathematics, cited above, box 4.1.See link above.

15The 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.

16C. K. Raju, “Navigation: Kamal or Rapalagai”,. Chp. 5 in Cultural Foundations of Mathematics, cited above.

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

18C. K. Raju, Cultural Foundations of Mathematics, cited above.

19Recently, 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. .

20For more on varying standards of proof, see Cultural Foundations of Mathematics, cited above, and Is Science Western in Origin? also cited earlier.