The Man of Numbers

November 22, 2011

Every schoolchild in America is taught to read Roman numerals, but I’ve never understood why. Computation with Romans isn’t taught (wow, would that ever make math unpopular!). So what does “numeral recognition” achieve? As far as I was concerned, the only benefit I ever derived from Romans was the ability to read the year a movie or TV show was first produced when the credits rolled.

Given my flip view of Roman numerals, I was utterly blown away to learn from Keith Devlin‘s slim new book of mathematical history (subtitled Fibonacci’s Arithmetic Revolution) that the transition from Roman to Hindu-Arabic numerals began only recently (the latter appeared in Europe after 1200 C.E. and it took a couple of centuries before they had clearly carried the day), that it was instigated by the writings of a single man, a certain Leonardo of Pisa (who many of us recognize more readily as “Fibonacci”), and was driven by commercial interests.

It turns out that Leonardo did far more than describe a new way to represent numbers, he also described how to perform all manner of calculations with them, which he illustrated through hundreds of practical problems (some of which schoolchildren will still recognize!). We know very little about Leonardo, but we can guess that he learned the new system as an adolescent assisting his merchant father in northern Africa and his writings appeared at just the right time, neatly dovetailing with the expanding activities of Italian traders. The new Hindu-Arabic numerals made computation far more convenient, and once one could compute conveniently, one could begin to solve all sorts of problems like currency exchanges, interest on loans, and dividing profits among unequal investors, that had been difficult or nearly impossible under the Roman numeral system.

But there’s so much more I would like to know. The Italian traders were the ‘globalizers’ of their day, dominating trade across the Mediterranean. These innovations in trade and math appeared just before the Black Death would wipe out a vast portion of Europe’s population. How did trade and arithmetic survive? Would our global information network survive a modern health/environmental catastrophe?

On a personal level, what compelled Leonardo to write his methods down? He wasn’t the inventor of Hindu-Arabic numerals or the inventor of the arithmetic procedures that they permitted, and much of what he wrote had already been written down in Arabic and spread throughout that culture. What made him (besides his young age) receptive to these ideas, and what made him decide to organize them so comprehensively?

And, more generally, what determines when an idea will take root and flourish?

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