Brahmagupta · Mathematics
Brahmagupta’s astronomy - a spherical earth that draws heavy things toward it, planetary and eclipse computation by geometry - set against his stubborn conservatism: he rejected Aryabhata’s rotating earth and, on scriptural authority, defended the demon Rahu as the cause of eclipses. A study in brilliance bounded by orthodoxy.
It is easy to forget, celebrating Brahmagupta’s zero and his equations, that the Brahmasphutasiddhanta is first and foremost a work of astronomy. Its twenty-four chapters are largely devoted to the motions of the sun, moon, and planets, to eclipses, risings and settings, and to the geometry of the celestial sphere; the dazzling mathematics is embedded there to serve the sky. Brahmagupta wrote as the leading astronomer of Ujjain, then India’s great centre of astronomical learning, in a mature tradition (the siddhanta tradition) that already took for granted a spherical earth sitting at the centre of a spherical cosmos. His task was to compute the heavens accurately - to predict where a planet would be, when an eclipse would fall - and his arithmetic and algebra were the instruments of that computation.
Brahmagupta’s picture of the earth combines a strikingly modern element with a strikingly conservative one. The modern element: the earth is a sphere, hanging in space, and it draws heavy things toward itself - which is why people stand upright everywhere on its curved surface and do not fall off the ‘bottom,’ and why dropped objects fall toward the centre. This is a genuine anticipation of the idea of attraction, of gravity as a property of the earth. The conservative element: Brahmagupta insisted the earth is motionless. He used his own attraction intuition as a weapon against Aryabhata’s rotation, reasoning that a spinning earth would shed its contents. So the same man who glimpsed gravity used that glimpse to argue, wrongly, for a fixed earth. His physics was ingenious and his conclusion mistaken - a reminder that a true premise, pushed with confidence, can still lead to a false result.
How could the same man compute eclipses by shadow-geometry and also insist a demon causes them? The answer lies in the layered world Brahmagupta inhabited. For the practical work of prediction - when an eclipse will occur, how deep it will be - he used the correct model: the moon and the earth’s shadow, handled with real geometry, the nodes of the moon’s orbit still bearing the names Rahu and Ketu as a computational convenience. But for the cause, in the register of doctrine, he deferred to scripture and the beliefs of the people, and rebuked those who let the shadow-explanation displace the demon. He seems to have held both: the geometry for calculating, the demon for orthodoxy. To modern eyes this looks like a contradiction; to Brahmagupta it may have looked like keeping the peace between exact science and sacred authority - with authority given the last word.
This is the opening of the lesson. The rest — the dialogue, the primary source, and the recall — is in the app.
You learned that Brahmagupta’s Brahmasphutasiddhanta is chiefly an astronomy treatise; that he held the earth to be a sphere that draws heavy things toward it (an early attraction idea); that he rejected Aryabhata’s rotating earth; and that, despite computing eclipses geometrically, he defended the demon Rahu on scrip…
Leads to Aryabhata.
Begin this lesson →epoché — a humanities education that remembers you.