Anirudh Kanisetti is a public historian. He is the author of ‘Lords of Earth and Sea: A History of the Chola Empire’ and the award-winning ‘Lords of the Deccan’. We enjoy Mr Kanisetti’s pieces because he is not only skilled at using history to give us learnings from the past but also at using history as a warning – a warning that people & cultures who turn inwards and become conservative eventually fall behind in the global race to develop & refine ideas and intellects. This superb column from Mr Kanisetti in The Print is worth reading in full because it fulfils all of these functions.
The first thing that we learn from this piece is how remarkably clever ancient India’s mathematicians – with the prodigious Aryabhatta at the helm – were. They were absorbing concepts created elsewhere in the world (with the ancient Greeks & Arabs being their major intellectual influences) and, at the same time, leading the world in mathematical thought:
“The earliest recorded Indian mathematics, then, comes from the Vedas. Historian David Pingree studied them in his Jyotiḥśāstra: Astral and Mathematical Literature. Vedic priests constructed elaborate altars of mud-brick, in the shape of hawks, herons, chariots and so on. In order to maintain consistent designs, they used geometrical formulae, recorded in the Sulbasutras, appendices of the Yajur Veda dating to c. 500 BCE. From this early period, Indians developed a fascination with trigonometry, including what came to be known as the Pythagorean theorem.
In the centuries after, the trajectory of Indian mathematics is somewhat unclear. Around the 4th century BCE, Jains were developing an expansive cosmology, with vast distances and eras of time. Mathematician George Gheverghese Joseph, in The Crest of the Peacock: Non-European Roots of Mathematics, provides some examples. “A rajju is the distance traveled by a god in six months if he covers 1,00,000 yojanas (a million kilometres) in each blink of his eyes; a palya is the time it will take to empty a cubic vessel of side one yojana filled with the wool of newborn lambs if one strand is removed every century.” This led Jains to develop advanced concepts of infinity: infinite in one or two directions, in area, in time, in space. Europeans, writes Joseph, only came round to this idea in the late 1800s.
By the turn of the first millennium CE, the subcontinent’s connections to global trade grew denser — a phenomenon we’ve examined many times in Thinking Medieval. As Indian textiles, spices, animals and other exotica went to the Mediterranean, mathematical and astronomical ideas flowed in the other direction. Sanskrit learning branched out from liturgy into new disciplines, like politics and aesthetics; the earliest Puranas were also compiled, addressing topics of mythology, ritual, history, and cosmology.
Sanskrit scientific writings took on a heterogeneous character. Puranic authors insisted that the Earth was a flat disc surrounded by oceans, supported by elephants, turtles and serpents; the planets, stars, Sun and Moon were held to revolve in wheels above. But another set of authors, composing treatises called Siddhantas, absorbed Mediterranean conceptions such as a spherical Earth and elliptical orbits. However, the basis for calculations and geometry was rooted in Indian techniques. This rich exchange is visible in the work of then 23-year-old prodigy Aryabhata in his Aryabhatiya, completed in 499 CE. According to Joseph, the Aryabhatiya introduces the sine and versine (1-cosine) functions, as well as methods for solving quadratic equations. Wielding these techniques, Aryabhata made extremely accurate calculations of the value of pi, of longitude and the position of planets over time.”
Then we learn that our Sanskrit scholars became inward looking convinced that they had it all figured out. Thus began our decline. Mr Kanisetti writes:
“Over the next centuries, Sanskrit writers further developed their knowledge of trigonometry, calendrical calculations, and arithmetic. However, there were two major challenges. As Sanskrit was seen as the language of divinity, the main current of Sanskrit knowledge tended to be conservative, resistant to new developments. And rather than developing ideas based on observations, there was a tendency to emphasise theory over observation and experimentation. Arabs, in the 8th and 9th centuries CE, were able to break new ground in optics, hydraulics, and astronomy, both by translating Indian ideas and verifying claims with observations. In India, meanwhile, as late as the 12th century, Siddhanta writers such as Bhaskara II were still rejecting Puranic notions that eclipses were caused by the demon Rahu. Prof Pingree, in his 1978 paper ‘Indian Astronomy’, argues that medieval Indian astronomers often miscalculated eclipses, and found that despite the confident statements of some Sanskrit treatises, their tables of planetary and star positions could contain errors. There are also precious few descriptions of measuring equipment, such as astrolabes.
How could both innovation and stagnation, dogma and genius, coexist in the same literary tradition? Firstly, to be “learned” by medieval standards was to have an encyclopaedic command of texts, wielding rhetorical, linguistic and logical tools to defend a metaphysical viewpoint taught by one’s guru. Mathematical truths were developed out of curiosity, or for better calculations. But the idea of scientific innovation for its own sake, to profitably harness natural principles, did not exist as it does today.
The bigger limiting factor on Sanskrit was that it required years of specialised study. This could only happen at elite institutions with endowments of food and capital, such as Brahmin Agraharam settlements or Buddhist mahaviharas. Needless to say, these institutions tended to be open only to elite men, even if they came from distant countries. Though many male-authored Sanskrit texts pay lip service to female and “lower” caste devotees, barely a handful of actual texts authored by these groups survive across Sanskrit’s millennia-long history. They made their own advancements, though poorly recorded. Even as the Sanskrit astronomical tradition floundered, as attested by Arab travellers in the 12th century CE, the star-charts of illiterate South Indian seafarers were the most accurate in the world.”
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