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Monday, July 23, 2018

It’s nothing

The zero has aged gracefully, but the history of mathematics is more or less unchanged

By: Editorial | Published: September 16, 2017 1:16:50 am
Bakhshali manuscript, history of mathematics, zero, Brahmagupta, ancient history mathematics,  arithmetic algorithms The zero has aged gracefully, but the history of mathematics is more or less unchanged

The age of the Bakhshali manuscript, a mathematics text discovered in 1881 near Peshawar, has been hotly debated by scholars for about a century, on the basis of textual analysis and radiocarbon dating. Now, the radiocarbon accelerator at Oxford has coaxed it into revealing its age, which is 500 years more than estimated. But the analysis has also revealed a fresh problem — the pages date from three periods across almost eight centuries. Savants can now happily spend the next hundred years worrying about how they found their way into a single volume.

What effect does this have on the history of mathematics? Zero. The Bakhshali manuscript focuses on arithmetic algorithms, and the practical problems it sets suggest that it was used by traders on the Silk Route, rather than scholars. Its importance lies in the copious use of zero as a placeholder. The device was widely prevalent across the ancient world, from South America to China, and survives as the decimal point which descended, via India and Arabia, from the Babylonian placeholder zero. It was not restricted to decimal systems, either. The Babylonians used base-60 for astronomical calculations, which survives in the telling of time — 60 seconds make a minute, and 60 minutes make an hour. India’s contribution was to extrapolate from zero as a placeholder to zero as a number. It made it possible to contemplate the void mathematically. It also birthed the wiliest gremlin of computer programming, division by zero, which freezes systems.

The Bakhshali manuscript is not primarily associated with zero as a number, a revolutionary idea first used by Brahmagupta in 628 CE. But he did not claim credit for it, and it could have predated him. In ancient history, there is rarely a final verdict on anything, and open questions are always preferable to dubious certainties.

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