Brahmagupta's chapter of faults, the gist

Brahmagupta's chapter of faults

In the year 628 an Indian astronomer gave a whole chapter of his book to listing another astronomer's mistakes, in verse, and finished by saying the man knew nothing about any of his three subjects.

This is the short way in. The essay has the working, the sources and the sky.

The insult names mathematics, timekeeping and the sphere as the three things his opponent does not understand. Those are the titles of the opponent's own chapters. Thirty-seven years later the same critic opened a new book by calling that same opponent "master".

In 628 an astronomer called Brahmagupta finished a large book of astronomy in Sanskrit, all of it written in verse. He was 30, and he worked in a town in what is now Rajasthan. The eleventh chapter of that book examines everybody else's astronomy, and the tables of contents give it a second name: the chapter of fault-finding.

Most of the faults belong to one man. Aryabhata had written his own short book in 499 and had been dead for over a century.

The chapter has a rhythm. Quote the line you object to, say "that is not so", give your reason, move on.

Some of the objections are good. Brahmagupta argues that if you get the size of the earth wrong, then the correction for how far east or west of a reference line you are is wrong, and then the moment a lunar day ends is wrong, and then your eclipse timing is wrong. That is a real argument about one bad number at the bottom of a system. He also notices that two books carrying Aryabhata's name disagree about the number of days in one great cycle, a puzzle scholars have still not closed.

Some of the objections are simply mistaken, and later Indian editors said so in print.

The angriest ones are not about arithmetic at all. Aryabhata had cut the great cycle of world-ages into four equal parts where tradition cut it unequally. He had said the earth spins. He had explained eclipses by shadows. On eclipses, Brahmagupta attacks something Aryabhata never wrote: Aryabhata described the shadow and simply did not mention Rahu, the being that older accounts blame for eclipses.

Brahmagupta's own book credits Rahu with eclipses in one chapter and computes them from shadows in others. Four hundred years later the scholar al-Biruni read both, noticed, and said the man must have known better.

Arguing like this was normal. These treatises had a formal slot for refuting rivals. What was not normal is the closing insult.

Words decoded

Brahmagupta: an Indian astronomer and mathematician, born 598, who wrote the book this essay is about
Aryabhata: the astronomer he attacks, whose own book is dated 499
Brahmasphutasiddhanta (ब्रह्मस्फुटसिद्धान्त): Brahmagupta's big book of 628, 24 chapters of astronomy and mathematics
verse: these books were written as numbered two-line stanzas, so they could be memorised and copied accurately
chapter of fault-finding: the eleventh chapter, given over to finding errors in earlier astronomers
yuga (युग): a very long cycle of world-ages that these books use for counting time
tithi (तिथि): a lunar day, the unit an Indian calendar actually runs on
Rahu (राहु): in older accounts, the being who swallows the sun or the moon during an eclipse
smriti (स्मृति): received tradition, the body of remembered teaching a writer was expected not to contradict
al-Biruni: a scholar from Central Asia who studied Indian science around 1030 and wrote a book about it
Khandakhadyaka (खण्डखाद्यक): Brahmagupta's short practical handbook of 665, written when he was 67
Prithudaka: the commentator whose line-by-line explanation of Brahmagupta's book keeps taking Aryabhata's side

Why anyone should careFields that look settled from outside were argued over from inside, sometimes rudely, and the arguments were kept rather than tidied away. An objection that follows a wrong number through a system is doing science; a line saying your opponent knows nothing is doing something else, and telling the two apart is a skill worth having.

Read it properly, 8 min Brahmagupta's chapter of faults