Alex's Adventures in Numberland - Alex Bellos [45]
The festival gets under way only when the local holy man, the Shankaracharya of Puri, stands in front of the crowds and blesses them. The Shankaracharya is one of Hinduism’s most important sages, the head of a monastic order that dates back more than a thousand years. He was also the reason I had travelled to Puri. As well as being a spiritual leader, the Shankaracharya is a published mathematician. I was also a pilgrim in search of enlightenment.
Right away in India, I noticed something unfamiliar about their use of numbers. In my hotel reception I picked up a copy of The Times of India. With the paper’s corners flapping from gusts of competing metal fans, the front-page headline caught my eye:
5 crore more Indians
than govt thought
Crore is the Indian-English word for ten million, so the article was saying that India had just discovered 50 million citizens it never knew it had – a number roughly comparable to the population of England. It was startling that a country could overlook such a large number, even if it represented less than 5 percent of the overall population. Yet I was more puzzled by the word crore. Indian English has different words for high numbers than British or American English. For example, the word ‘million’ is not used. A million is instead expressed as ten lakh, where lakh is 100,000. Since ‘million’ is unheard of in India, the Oscar-winning film Slumdog Millionaire was released there as Slumdog Crorepati. A very rich person is someone who has a crore of dollars or rupees, not a million of them. The table of Indian equivalents for British/American number words is as follows:
Note that above a thousand, Indians introduce a comma after every two digits, while in the rest of the world the convention is every three.
The use of lakh and crore is a legacy of the mathematics of ancient India. The words come from the Hindi lakh and karod, which in turn came from the Sanskrit words for those numbers, laksh and koti. In ancient India coining words for large numbers was a scientific and religious preoccupation. For example, in the Lalitavistara Sutra, a Sanskrit text that dates from the beginning of the fourth century at the latest, the Buddha is challenged to express numbers higher than a hundred koti. He replies:
One hundred koti are called an ayuta, a hundred ayuta make a niyuta, a hundred niyuta make a kankara, a hundred kankara make a vivara, a hundred vivara are a kshobhya, a hundred kshobhya make a vivaha, a hundred vivaha make a utsanga, a hundred utsanga make a bahula, a hundred bahula make a nâgabala, a hundred nâgabala make a titilambha, a hundred titilambha make a vyavasthânaprajñapati, a hundred vyavasthânaprajñapati make a hetuhila, a hundred hetuhila make a karahu, a hundred karahu make a hetvindriya, a hundred hetvindriya make a samâptalambha, a hundred samâptalambha make a gananâgati, a hundred gananâgati make a niravadya, a hundred niravadya make a mudrâbala, a hundred mudrâbala make a sarvabala, a hundred sarvabala make a visamjñagati, a hundred visamjñagati make a sarvajña, a hundred sarvajña make a vibhutangamâ, a hundred vibhutangamâ make a tallakshana.
Just as in contemporary India, the Buddha went up the list in multiples of a hundred. Since a koti is ten million, the value of a tallakshana is ten million multiplied by a hundred 23 times, which works out as 10 followed by 52 zeros, or 1053. This is a phenomenally large number, so large, in fact, that if you measure the entire universe from end to end in metres, and then square that number, you are roughly around 1053.
But Buddha didn’t stop there. He was just warming up. He explained that he had described only the tallakshana counting system, and above it there was another one, the dhvajâgravati