Pearls of Wisdom
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Whilst making love a necklace broke
A row of pearls mislaid
One sixth fell to the floor
One fifth upon the bed
The young woman saved one third of them
One tenth were caught by her lover
If six pearls remained upon the string
How many pearls were there altogether?
What a charming problem we have here! If our modern schoolteachers had set us exercises involving birds, bees and strings of pearls, we could all have been string theorists and winners of the Fields Medal — the mathematician's equivalent of the Nobel. But I remember having to endure the dreariest practical problems. Boring arithmetic involving municipal water flowing into and leaking out of overhead tanks. Having to figure out how many men it takes to dig a ditch or raise a wall, and how much faster these unremarkable feats could be accomplished by hiring more men. And how much they should be paid. No mention of women at all, though the urbanisation wave had just started when I was in school and India was being built mainly by women labourers.
What a difference eight centuries and the shadow of colonialism have made. The problem of the love-torn pearls is from Lilavati, an introduction to arithmetic and geometry, the first volume of Bhaskaracharya's Siddhanta Shiromani. It was probably composed in the mid-12th century in Ujjain where Bhaskara, then in his 30s, served as chief astronomer at India's leading observatory. His Ujjain was the Greenwich of the early medieval world — the prime meridian, zero degrees, ran through the city's observatory.
Numbed to mathematics by the prosaic practicalities of ditches, walls and tanks, the colonial contagion spread across the subcontinent by industrious, neo-industrial Britain, I cannot possibly answer Bhaskara's pearl-strewn verse riddle. But following Douglas Adams, a Briton I admire, I hazard that it's 42. Since The Hitchhiker's Guide to the Galaxy declares 42 to be a multivalent number expressing the meaning of life, the universe and everything, it ought to cover all eventualities. No?
Bhaskara's problem is quoted from HT Colebrooke's translation from the Sanskrit Lilavati, with notes by Haran Chandra Banerji, published in 1892 and still available in print from Asian Educational Services (Delhi and Chennai). But the first English translation dates from 1816. Executed by John Taylor, a doctor with the East India Company in Bombay, it is available from Google Books, scanned from a copy at the Bodleian in Oxford. Taylor is not as poetic as Colebrooke but he offers a
50-page introduction explaining the peculiarities of Indian computing and an appendix with illuminating observations on 19th century Indian pedagogy, which appears to have been much more practical and humane than our present school system. His version is not only beautiful, it can also help young readers get a perfect math score in school.
Lilavati's opening verse is absolutely stunning. It enumerates the gradation of numbers known in Bhaskara's India, less than a century after the Norman Conquest. The biggest number is parardha — one lakh billion. Halfway into the text, Bhaskara grudgingly concedes that pi is 22/7, but for circles of the celestial dimensions that astronomers deal with, he suggests a more accurate ratio: 3927/1250.
But let us return to pearls, which are incalculably more beautiful than numbers and ratios, and to the Persian translation of Lilavati, commissioned by Akbar in 1587 and executed by Faizi, Abul Fazl's brother. Faizi reveals that Lilavati was Bhaskara's daughter. Her father cast her horoscope — all Indian astronomers and mathematicians were astrologers first — and found that she was destined to be unmarried and childless. Determined to cheat fate, Bhaskara ascertained an auspicious moment for her to marry. He closeted Lilavati and her intended with "the hour cup in a vessel of water… in order that when the cup should subside in the water, those two precious jewels should be united." (Taylor's translation from Persian.) But "the girl, from a curiosity natural to children, looked into the cup to observe the water coming in the hole, when by chance a pearl separated from her bridal dress, fell into the cup and rolling down to the hole, stopped the influx of water."
The auspicious moment passed unnoticed and the devastated Bhaskaracharya told his daughter: "I shall write a book in your name that shall remain till the end of time, for a good name is a second life." And so Lilavati, mathematics at play and a luminous pearl of a Sanskrit poem, lives on in our midst. firstname.lastname@example.org
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