Who invented calculus?

On the occasion of India and Pakistan's birthday, Isaac Newton's credentials are questioned, and the green revolution gets a new facelift.

Topics: Globalization, How the World Works, India, Pakistan,

The Partition of India occurred at midnight, Aug. 15, 1947. Pakistan, however, celebrates Independence Day on Aug. 14, while India’s Independence Day is Aug. 15.

For eloquent meditations on the 60th anniversary of independence for both countries, I recommend British historian William Dalrymple, author of the fabulous “The Last Mughal,” writing in The Guardian on the topic of Pakistan, and Nobel Prize winning economist and philosopher Amartya Sen, writing on India for Forbes.

But neither man, unfortunately, takes this opportunity to ponder whether South Asians discovered calculus 250 years before Isaac Newton and then transmitted their knowledge to the West by way of Jesuit missionaries. The Indian blogosphere has been quite chuffed at the news, announced by researchers at the Universities of Manchester and Exeter, that a group of Malayali scholars known as the “Kerala School” “identified the ‘infinite series’ — one of the basic components of calculus — in about 1350.”

Some are less enthused. At least one blogger, who styles himself as “Angry in the Great White North,” pooh-poohed the announcement, declaring that “the real issue, of course, is slapping down the evils of Western cultural imperialism!”

Hey, it’s India’s Independence Day, marking the anniversary of that happy day when the ancient civilization finally emerged from under the boot of Western imperialism. Cut ‘em some slack. I say, Hurrah for the Kerala School, whether or not Newton stood on their shoulders, or anyone else’s.

Some seven centuries closer to the present comes another tidbit of news that is worth pondering as India celebrates. India’s National Council of Applied Economic Research has published “India Policy Forum 2006-2007″ — a collection of research articles examining “India’s reforms and economic transition.” (Thanks to BioPact for the tip.) One essay title, “Whether Economic Growth Reduces Fertility,” caught my eye, and I managed to dig up a draft version of the paper originally presenting the data by Brown and Yale economists Andrew D. Foster and Mark R. Rosenzweig.



The authors analyze a wealth of data from rural India from 1971 to 1999 in an attempt to parse out exactly what factors have influenced the steady decrease in reproductive fertility in Indian families. They find that the two most significant factors are an increase in agricultural productivity and rising wages for women.

A demographic revolution now appears to have at least in part resulted from, rather than just accompanied, the green revolution.

In summary, our results suggest that the process of economic growth has had a major impact on fertility in India over the last two decades and that, given sustained economic growth that continues to raise wages and increase returns to human capital, the fall in fertility in India will persist for the foreseeable future.

India’s Green Revolution has been criticized by those who wonder if an agricultural model reliant on large inputs of fertilizers and pesticides is environmentally sustainable over the long run. But if in the short run these spikes in agricultural productivity contribute to population stabilization, then we have a nifty paradox: a (possibly) unsustainable agricultural model contributing to (possibly) sustainable population levels.

The Green Revolution, along with other economic changes that were likely in part responsive to the increased growth and occupational diversification made possible by the overall expansion in agricultural productivity, also expanded worker productivity and thus led to an expansion in labor demand. The resulting rise in wages, not only made child-rearing more expensive but shifted the nature of women’s activities both within and outside the household. As a result patterns emerge that look much like a fundamental change in women’s autonomy that leads to fertility change.

Happy sixtieth birthday, India.

Andrew Leonard

Andrew Leonard is a staff writer at Salon. On Twitter, @koxinga21.

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