Abraham Seidenberg
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Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician.
Quotes[edit]
- However, Seidenberg was told by the Indologists that these Sutras, or any Vedic text for that matter, were definitely written later than 1700 BC. But mathematical data cannot be manipulated just like that, and Seidenberg remained convinced of his case:
“Whatever the difficulty there may be [concerning chronology], it is small in comparison with the difficulty of deriving the Vedic ritual application of the theorem from Babylonia. (The reverse derivation is easy)… the application involves geometric algebra, and there is no evidence of geometric algebra from Babylonia. And the geometry of Babylonia is already secondary whereas in India it is primary.” [To satisfy the indologists, he said that the Shulba Sutra had conserved an older tradition, and that it is from this one that the Babylonians had learned their mathematics:] “Hence we do not hesitate to place the Vedic (…) rituals, or more exactly, rituals exactly like them, far back of 1700 BC. (…) elements of geometry found in Egypt and Babylonia stem from a ritual system of the kind described in the Sulvasutras.”- Seidenberg: “The ritual origin of geometry”, Archive for History of Exact Sciences, 1962, p. 488-527, specifically p-515, quoted by N.S. Rajaram and D. Frawley: Vedic Aryans’ and the Origins of Civilization, WH Press, Québec 1995, p-85. Seidenberg: “The ritual origin of geometry”, Archive for History of Exact Scieces, 1962, p.515, quoted by N.S. Rajaram and D. Frawley: Vedic ‘Aryans’ and the Origins of Civilization, p.85. , quoted in Elst, Koenraad (1999). Update on the Aryan invasion debate New Delhi: Aditya Prakashan.
- "By examining the evidence in the Shatapatha Brahmana, we now know that Indian geometry predates Greek geometry by centuries. 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! Two aspects of the 'Pythagoras' theorem are described in the Vedic literature. One aspect is purely algebraic that presents numbers a, b, c for which the sum of the squares of the first two equals the square of the third. The second is the geometric, according to which the sum of the areas of two square areas of different size is equal to another square. The Babylonians knew the algebraic aspect of this theorem as early as 1700 BCE, but they did not seem to know the geometric aspect. The Shatapatha Brahmana, which precedes the age of Pythagoras, knows both aspects. Therefore, the Indians could not have learnt it from the Old-Babylonians or the Greeks, who claim to have rediscovered the result only with Pythagoras. India is thus the cradle of the knowledge of geometry and mathematics."
- In his work, The origin of mathematics, Archive for History of Exact Sciences. vol. 18, 301-342, Abraham Seidenberg : attributed at [1]
About[edit]
- As N.S. Rajaram has rightly observed, Seidenberg traces Babylonian mathematics and astronomy to Indian models. He suggests the Kassite dynasty (18th-16th century) as the channel of transmission, as the Kassite language has an Indo-Aryan substrate. This is eminently reasonable. Thus, Babylonian astronomy divided the ecliptic in 18, yet by the first millennium it had adopted a division in 12, the same as existed in Vedic culture, where a nightly division into 28 lunar houses was complemented by a daily division of the ecliptic in 12 half-seasons (Madhu, Madhava etc.), and where the rishi Dirghatamas introduced the first-ever division of the circle into 12 and 360. Till today, the division into 360 is explained in textbooks as a Babylonian invention, but the earliest mention is Indian.
