Origins of Vedic Science, Part 2
BY: DR. SUBHASH C. KAK
Jan 3, BATON ROUGE, LOUISIANA (SUN)
Geometry and Mathematics
Seidenberg, by examining the evidence in the Shatapatha Brahmana, showed that Indian geometry predates Greek geometry by centuries. Seidenberg argues that the birth of geometry and mathematics had a ritual origin. For example, the earth was represented by a circular altar and the heavens were represented by a square altar and the ritual consisted of converting the circle into a square of an identical area. There we see the beginnings of geometry!
In his famous paper on the origin of mathematics, Seidenberg (1978) concluded: "Old-Babylonia [1700 BC] got the theorem of Pythagoras from India, or both Old-Babylonia and India got it from a third source. Now the Sanskrit scholars do not give me a date so far back as 1700 B.C. Therefore I postulate a pre-Old-Babylonian (i.e., pre-1700 B.C.) source of the kind of geometric rituals we see preserved in the Sulvasutras, or at least for the mathematics involved in these rituals."
That was before archaeological finds disproved the earlier assumption of a break in Indian civilization in the second millennium B.C.E.; it was this assumption of the Sanskritists that led Seidenberg to postulate a third earlier source. Now with our new knowledge, Seidenberg’s conclusion of India being the source of the geometric and mathematical knowledge of the ancient world fits in with the currently understood chronology of texts.
Using hitherto neglected texts related to ritual and the Vedic indices, an astronomy of the third millennium B.C.E. has been discovered (Kak 1994a; 1995a,b). Here the altars symbolized different parts of the year. In one ritual, pebbles were placed around the altars for the earth, the atmosphere, and the sky. The number of these pebbles were 21, 78, and 261, respectively. These numbers add up to the 360 days of the year. There were other features related to the design of the altars which suggested that the ritualists were aware that the length of the year was between 365 and 366 days.
The organization of the Vedic books was also according to an astronomical code. To give just one simple example, the total number of verses in all the Vedas is 20,358 which equals 261 x 78, a product of the sky and atmosphere numbers. The Vedic ritual followed the seasons, hence the importance of astronomy.
The second millennium text, Vedanga Jyotisha, went beyond the earlier calendrical astronomy to develop a theory for the mean motions of the sun and the moon. This marked the beginnings of the application of mathematics to the motions of the heavenly bodies.
The Vedic planetary model is given in the Figure above. The sun was taken to be midway in the skies. A considerable amount of Vedic wisdom regarding the struggle between the demons and the gods is also a model for understanding the motions of Venus and Mars.
The famous pastime of Lord Vamanadev's three strides measuring th e universe becomes more interesting when we note that early texts equate Vishnu and Mercury. The pastime is also used as a model to celebrate the first measurement of the period of Mercury (Kak 1996a), since these periods equal the number assigned in altar ritual to the heavens. Other arguments suggest that the Vedic people knew the periods of the five classical planets.
Cryptological analysis has revealed that the Brahmi script of the Mauryan times evolved out of the third millennium Sarasvati (Indus) script. The Sarasvati script was perhaps the first true alphabetic script. The worship of Sarasvati as the goddess of learning remembers the development of writing on the banks of the Sarasvati River. It also appears that the symbol for zero was derived from the fish sign that stood for "ten" in Brahmi and this occurred around 50 B.C.E.-50 C.E. (Kak 1994b).
Barend van Nooten (1993) has shown that binary numbers were known at the time of Pingala’s Chhandahshastra. Pingala, who lived around the early first century B.C.E., used binary numbers to classify Vedic meters. The knowledge of binary numbers indicates a deep understanding of arithmetic. A binary representation requires the use of only two symbols, rather than the ten required in the usual decimal representation, and it has now become the basis of information storage in terms of sequences of 0's and 1's in modern day computers.