The Vedanga Jyotish, India’s most ancient extant scientific text(dated to about 1400 BCE), spells out the notion of calendar, seasons, equinoxes and solstices, and discusses the 27 nakshatras or lunar mansions; a little later, the Shulba Sutras describe elaborate geometrical constructions of Vedic fire altars, spell out the so-called ‘Pythagorean theorem’ and yields precise values for the squre roots of 2 or 3. The Vaisheshika Sutrras indulge in bold speculations on time,space and the concept of atoms. The daring speculations of Buddhist and Jain mathematicians follow : the Jain cosmology, for instance, involved a time  scale of 2588(that is, 2 multiplied by itself 587 times!) and was at ease with the notion of infinity.

Because many ancient texts disappeared, important gaps remain in our understanding of the transition towards the Siddhantic period – the golden era of Indian mathematics and astronomy, from the fifth century CE.(A siddhanta is a conclusion, and by extension, a technical treatise.) A simple way to gauge the creativity of those times is to list a few achievements of the celebrated Aryabhatta, born in 476 CE, who in face ushered in Siddhantic School. Most of his contributions come to us from his Aryabhatiya, a concise, sometimes cryptic, text of 121 verses, which yields, among other advances

  • A proposed value of pi equal to 62832/20000 or 3.1416(correct to the fourth decimal), and a surprisingly perceptive explanation that is value is only ‘approximate’;
  • An ingenious method for the extraction of square and cube roots;
  • A succinct and precise table of sines(or jyaa), in the form of just two lines of coded syllables giving sine values of angles up to 90 degrees(in twelve increments of 3 degree 45 minutes), with all values correct upto three or four significant figures
  • A statement that the earth is a sphere with a diameter of 1,050 yojanas, which comes fairly close to the actual figure;
  • A prescient assertion that the earth’s rotation is what cases the fixed star’s to move.
  • Observations of the planets’ orbits, recorded with ‘astonishning precision’, in words of the French scholar Roger Billard, who did an advanced statistical study of Aryabhata’s table, proving it to be correct based on actual observations;
  • Remarkable accurate estimates for the sidereal day and year

Aryabhata also worked out a conceptual framework of yugas –the concept of yugas, and pulsating, ceaselessly destroyed, and re-created again. ‘Time is without beginning or end’, said Aryabhata.

An American cosmologist, noted the following regarding the yugas – a concept that leads to the value of day of Brahma to be 4.32 billion years, regarded by scientist, as equal to age of the earth.

“The Hindu religion is the only one of the world’s great faiths dedicated to the idea that the Cosmos, itself undergoes an immense, indeed an infinite, number of deaths, and rebirths. It is the only religion in which the time scales correspond, to that of scientific cosmology…..

…..A millennium before Europeans, were willing to divest themselves of the Biblical idea that the world was a few thousand years old, the Mayans were thinking of millions and the Indians of the billions….”

Such is India’s native framework, a worldview that dislikes limits, since the inner Reality can essentially have none. For Aryabhata, the ultimate objective of astronomy appears to have been spiritual: ‘One attains the supreme Brahman after piercing through the orbits of the planets and stars.’ The physical and the spiritual infinites could only be the same…



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