Monday, July 30, 2012

I ask for nothing - Columns

Consider Calvino, a civil contractor in ancient Rome. He’s tasked with constructing one of the famous Roman roads that crisscrosses the empire. Having surveyed the landscape, he works out that he needs 4,679 cut stones for the next stretch. At the Roman quarries, each of those will set him back 83 sestertii. So, Calvino has to calculate how much he must bill Rome.

Today, you and I might pull out a calculator, punch in those numbers, multiply them and read off the answer—388,357 sestertii, as it happens. But spare a thought for Calvino, saddled with using ludicrous Roman numbers. He would have had to multiply, by hand, the numbers LXXXIII (that’s 83) and MMMMDCLXXIX (4,679). I have no idea how they did such calculation in Rome—though they must have, they built plenty of roads and other trappings of civilization—but I imagine Calvino thinking: LXXXIII x !!@#$AB%@#, that’s more like it!

Here was a number system that had symbols for certain numbers and rules for how they joined forces to create new numbers: in that sense no different from the number system you use today. But among other issues, this system produced labels for numbers that gave Romans no immediate sense of how big those numbers are. For example, LXXXIII is 83, but the much shorter MM is 2,000. And compare MM with XX, which is 20, or II, which is 2.

Luckily for the world, the Roman empire withered away, as did its rather bizarre system of numbers. (Though it still finds inexplicable use with overhyped sports extravaganzas, like Super Bowl MIX, or their teams, like Kings XI Punjab).
But even more luckily, Indian mathematicians came up with nothing.