Navaratna Rajaram

Above: Movement of seasons (symbolic image)

Since linguists who have dominated Vedic studies for over a century do not use quantitative methods, being unfamiliar with mathematics. Hence they tried to apply techniques borrowed from linguistics, resulting in absurd conclusions, like Vedas and their language being foreign impositions dating to 1200 BCE or so when we have demonstrably Vedic architectural remains in Indian archaeology more than a thousand years older. They have tried to separate them by claiming archaeological remains as the result of the depredations of the invading Aryans, a mythical people.
But it was not long before the field began to attract competent scientists including mathematicians like A. Seidenberg, B.B. Datta and N.S. Rajaram. This has been discussed in detail in the book Vedic Aryans and the Origins of Civilizations by Rajaram and Frawley, which brought to the fore the importance of Vedic Mathematics of the Sulbasutras for the first time.
(Not to be confused with the work Vedic Mathematics by Swami Bharati Krishna Tirtha, which is a modern work and not part of the Vedic literature.)
The following article by Dr. Koenraad Elst summarizes some of its principal findings in a highly readable form.


Dating the Rg-Veda by Dr. Koenraad Elst
(Edited by N.S. Rajaram)
The determination of the age in which Vedic literature started and flourished has its consequences for history. The oldest text, the Rg-Veda, is full of precise references to places and natural phenomena in what are now Punjab and Haryana, and was unmistakably composed in that part of India. The date at which it was composed is a firm terminus ante quem for the presence of the Vedic Aryans into India. They may have come from abroad or they may have been fully native, but by the time of the Rg-Veda, they were certainly Indians without memory of a foreign homeland.

In a rather shoddy way, Friedrich Max Muller launched the hypothesis that the Rg-Veda had to be dated to about 1200 BC, and even though he later retracted it, that arbitrary guess has become the orthodoxy.  It is forgotten too often that in his own day, other scholars rejected this extremely late date on a variety of grounds. Maurice Winternitz based his estimate on purely philological considerations: “We cannot explain the development of the whole of this great literature if we assume as late a date as round about 1200 BC or 1500 BC as its starting-point.  Isn’t it refreshing to find how logical and unprejudiced the early researchers were? You cannot credibly cram the complicated linguistic, cultural and philosophical developments which are in evidence in Vedic literature, into just a few centuries.

But since this argument of plausibility can always be countered with the argument that unlikely developments are not strictly impossible, we need a firmer basis to decide this chronological question. The most explicit chronology would be provided by astronomical markers of time.

Ancient Hindu astronomy hits Biblical superstition

One of the earliest estimates of the date of the Vedas was at once among the most scientific. In 1790, the Scottish mathematician John Playfair demonstrated that the starting-date of the astronomical observations recorded in the tables still in use among Hindu astrologers (of which three copies had reached Europe between 1687 and 1787) had to be 4300 BCE. His proposal was dismissed as absurd by some, but it was not refuted by any scientist.

Playfair’s judicious use of astronomy was countered by John Bentley with a Scriptural argument which we now must consider invalid. In 1825, Bentley objected: “By his [= Playfair’s] attempt to uphold the antiquity of Hindu books against absolute facts [as in the Bible], he thereby supports all those horrid abuses and impositions found in them, under the pretended sanction of antiquity.

Nay, his aim goes still deeper, for by the same means he endeavors to overturn the Mosaic account, and sap the very foundation of our religion: for if we are to believe in the antiquity of Hindu books, as he would wish us, then the Mosaic account is all a fable, or a fiction. [Which it is, editor]

Bentley did not object to astronomy per se, in so far as it could be helpful in showing up the falsehood of Brahminical scriptures. However, it did precisely the reverse. Falsehood in this context could have meant that the Brahmins falsely claimed high antiquity for their texts by presenting as ancient astronomical observations recorded in Scripture what were in fact back-calculations from a much later age. But Playfair showed that this was impossible.

Back-calculation of planetary positions is a highly complex affair requiring knowledge of a number of physical laws, universal constants and actual measurements of densities, diameters and distances. [Especially then when there were no computers. Even today it is not always easy, NSR]
Though Brahminical astronomy was remarkably sophisticated for its time, it could only back-calculate planetary position of the presumed Vedic age with an inaccuracy margin of at least several degrees of arc. With our modern knowledge, it is possible to determine what the actual positions were, and what the results of back-calculations with the Brahminical formulae would have been, e.g.:

“Aldebaran was therefore 40′ before the point of the vernal equinox, according to the Indian astronomy, in the year 3102 before Christ. (…) [Modern astronomy] gives the longitude of that star 13′ from the vernal equinox, at the time of the Calyougham, agreeing, within 53′, with the determination of the Indian astronomy. This agreement is the more remarkable, that the ancient sages , by their own rules for computing the motion of the fixed stars, could not have assigned this place to Aldebaran for the beginning of Calyougham, had they calculated it from a modern observation. For as they make the motion of the fixed stars too great by more than 3” annually, if they had calculated backward from 1491, they would have placed the fixed stars less advanced by 4or 5 degrees, at their ancient epoch, than they have actually done. So, it turns out that the data given by the sages corresponded not with the results deduced from their formulae, but with the actual positions observed, and this, according to Playfair, for nine different astronomical parameters. This is a bit much to explain away as coincidence or sheer luck.

Ancient observation, modern confirmation

That Hindu astronomical lore about ancient times cannot be based on later back-calculation, was also argued by Playfair’s contemporary, the French astronomer Jean-Sylvain Bailly: “the motions of the stars calculated by the Hindus before some 4500 years vary not even a single minute from the [modern] tables of Cassini and Meyer. The Indian tables give the same annual variation of the moon as that discovered by Tycho Brahe — a variation unknown to the school of Alexandria and also to the Arabs.

Prof. N.S. Rajaram, a mathematician who has worked for NASA, comments: “fabricating astronomical data going back thousands of years calls for knowledge of Newton’s Law of Gravitation and the ability to solve differential equations. Failing this advanced knowledge, the data in the ancient records must be based on actual observation. Ergo, the Sanskrit-speaking Vedic seers were present in person to record astronomical observations and preserve them for a full 6,000 years: “The observations on which the astronomy of India is founded, were made more than three thousand years before the Christian era. (…) Two other elements of this astronomy, the equation of the sun’s centre and the obliquity of the ecliptic (…) seem to point to a period still more remote, and to fix the origin of this astronomy 1000 or 1200 years earlier, that is, 4300 years before the Christian era.

All this at least on the assumption that Playfair’s, Bailly’s and Rajaram’s claims about the Hindu astronomical tables are correct. Disputants may start by proving them factually wrong, but should not enter the dispute arena without a refutation of the astronomers’ assertions. It is something of a scandal that Playfair’s and Bailly’s findings have been lying around for two hundred years while linguists and indologists were publishing speculations on Vedic chronology in stark disregard for the contribution of astronomy. [and mathematics, and archaeology as well.]

2.3. The start of Kali-Yuga
Hindu tradition makes mention of the conjunction of the “seven planets” (Saturn, Jupiter, Mars, Venus, Mercury, sun and moon) and Ketu (southern lunar node, the northern node/Rahu being by definition in the opposite location) near the fixed star Revati (Zeta Piscium) on 18 February 3102 BC. This date, at which Krishna is supposed to have breathed his last, is conventionally the start of the so-called Kali-Yuga, the “age of strife”, the low point in a declining sequence of four ages. However, modern scholars have claimed that the Kali-Yuga system of time-reckoning was a much younger invention, not attested before the 6th century AD.

Against this modernist opinion, Bailly and Playfair had already shown that the position of the moon (the fastest-moving “planet”, hence the hardest to back-calculate with precision) at the beginning of Kali-Yuga, 18 February 3102, as given by Hindu tradition, was accurate to 37′.9 Either the Brahmins had made an incredibly lucky guess, or they had recorded an actual observation on Kali Yuga day itself.

Mathematician Richard L. Thompson claims that in Indian literature and inscriptions, there are a number of datelines expressed in Kali-Yuga which are older than the Christian era (and a fortiori older than the 6th century AD).More importantly, Thompson argues that the Jyotisha-shastras (treatises on astronomy and, increasingly, astrology, starting in the 14th century BC with the Vedanga Jyotisha as per its own astronomical data, but mostly from the first millennium AD) are correct in mentioning this remarkable conjunction on that exact day, for there was indeed a conjunction of sun, moon, Mercury, Venus, Mars, Jupiter, Saturn, Ketu and Revati.

True, the conjunction was not spectacularly exact, having an orb of 37’ between the two most extreme planetary positions. But that exactly supports the hypothesis of an actual observation as opposed to a back-calculation. Indeed, if the Hindu astronomers were able to calculate this position after a lapse of many centuries (when the Jyotisha-Shastra was written), it is unclear what reason they would have had for picking out that particular conjunction. Surely, such conjunctions are spectacular to those who witness one, and hence worth recording if observed. But they are not that exceptional when considered over millennia: even closer conjunctions of all visible planets do occur (most recently on 5 February 1962).11 If the Hindu astronomers had simply been going over their astronomical tables looking for an exceptional conjunction, they could have found more spectacular ones than the one on 18 February 3102 BC.

The precession of the equinox The slowest hand on the clock (see above)
The truly strong evidence for a high chronology of the Vedas is the Vedic information about the position of the equinox. The phenomenon of the “precession of the equinoxes” takes the ecliptical constellations (also known as the sidereal Zodiac, i.e. those constellations through which the sun passes)12 slowly past the vernal equinox point, i.e. the intersection of ecliptic and equator, rising due East on the horizon. The whole tour is made in about 25,791 years, the longest cycle manageable for naked-eye observers. If data about the precession are properly recorded, they provide the best and often the only clue to an absolute chronology for ancient events.

The very fact the ancient sages were aware of the phenomenon of the precession (See Gods, Sages and Kings by David Frawley)  indicates they had been observing the skies for thousands of years.

If we can read the Vedic and post-Vedic indications properly, they mention constellations on the equinox points which were there from 4,000 BC for the Rg-Veda (Orion, as already pointed out by B.G. Tilak, see above) through around 3100 BC for the Atharva-Veda and the core Mahabharata (Aldebaran) down to 2,300 BC for the Sutras and the Shatapatha Brahmana (Pleiades).

Other references to the constellational position of the solstices or of solar and lunar positions at the beginning of the monsoon confirm this chronology. Thus, the Kaushitaki Brahmana puts the winter solstice at the new moon of the sidereal month of Magha (i.e. the Mahashivaratri festival), which now falls 70 days later: this points to a date in the first half of the 3rd millennium BC. The same precessional movement of the twelve months of the Hindu calendar (which are tied to the constellations) vis-a-vis the meterological seasons, is what allowed Hermann Jacobi (left)to fix the date of the Rg-Veda to the 5th-4th millennium BC.15 Indeed, the regular references to the full moon’s position in a constellation at the time of the beginning of the monsoon, which nearly coincides with the summer solstice, provide a secure and unambiguous chronology through the millennial Vedic literature.

Chronological conundrum: Kalidasa’s date

It is not only the Vedic age which is moved a number of centuries deeper into the past, when comparing the astronomical indications with the conventional chronology. Even the Gupta age (and implicitly the earlier ages of the Buddha, the Mauryas etc.) could be affected. Indeed, the famous playwright and poet Kalidasa, supposed to have worked at the Gupta court in about 400 AD, wrote that the monsoon rains started at the start of the sidereal month of Ashadha; this timing of the monsoon was accurate in the last centuries BC.16 This implicit astronomy-based chronology of Kalidasa, about 5 centuries higher than the conventional one, tallies well with the traditional “high” chronology of the Buddha, whom Chinese Buddhist tradition dates to ca. 1100 BC, and the implicit Puranic chronology even to ca. 1700 BC.

Some difficulties
These indications about the precessional phases may be unreliable insofar as their exact meaning is not unambiguous. To say that a constellation “never swerves from the East” (as is said of the Pleiades in the Shatapatha Brahmana 2:1:2:3) seems to mean that it contains the spring equinox, implying that it is on the equator, which intersects the horizon due East. But this might seem insufficiently explicit for the modern reader who is used to a precise and separate technical terminology for such matters. But then, the modern reader will have to accept that technical terminology in Vedic days mostly consisted in fixed metaphorical uses of common terms. This is not all that primitive, for the same thing will be found when the etymology of modern technical terms is analyzed, e.g. a telescope is a Greek “far-seer”, oxygen is “acid-producer”, a cylinder is a “roller”. The only difference is that we can use the vocabulary of foreign classical languages to borrow from, while Sanskrit was its known classical reservoir of specialized terminology.

Another factor of uncertainty is that the equinox moves very slowly (1degree in nearly 71 years), so that any inexactness in the Vedic indications and any ambiguity in the constellations’ boundaries makes a difference of centuries. This occasional inexactness might possibly be enough to neutralize the above shift in Kalidasa’s date — but not to account for a shift of millennia (each millennium corresponding to about 14 degrees of arc) needed to move the Vedic age from the pre-Harappan to the post-Harappan period, from 4000 BC as calculated by the astronomers to 1200 BC as surmised by Friedrich Max Muller.

On the other hand, it is encouraging to note that the astronomical evidence is entirely free of contradictions. There would be a real problem if the astronomical indications had put the Upanishads earlier than the Rg-Veda, or Kalidasa earlier than the Brahmanas, but that is not the case: the astronomical evidence is consistent. Inconsistency would prove the predictable objection of AIT defenders that these astronomical references are but poetical fabulation without any scientific contents. However, the facts are just the opposite. To the extent that there are astronomical indications in the Vedas, these form a consistent set of data detailing an absolute chronology for Vedic literature in full agreement with the known relative chronology of the different texts of this literature. This way, they completely contradict the hypothesis that the Vedas were composed after an invasion in about 1500 BC. Not one of the dozens of astronomical data in Vedic literature confirms the AIT chronology. (This is extraordinary. So their are unsupported by any material evidence– astronomy or archaeology.) As already shown in my earlier post Genes of Time, it is contradicted by data from natural history and population genetics.

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