On the Aesthetics of Number Names

What we call things matters, and on a more fundamental level than you might realize.

I came across the following Numberphile video through NPR’s Robert Krulwich (H/T Andrew Sullivan).  While I vaguely recall references to a larger value for a billion when I was really small, I share Krulwich’s slight amazement at how prevalent the long system of numbers is outside of the U.S.  (Canadian readers, especially those in Quebec, feel free to snicker politely to yourselves.)  In brief, the differences between countries over measures are of a kind with the differences over numbers.  (While the video doesn’t address this, the differences apply to the really small numbers as well as the really large.)

Putting aside the cultural subtext (of which the perceived decline of the U.K. is but one part), there are competing models of logic involved here.  Or, if you’re not math(s) centered, competing models of aesthetics.  The video describes the perspective from the long system as to why the short system is ‘illogical’ and one could determine rationales for why the reverse is the case (changing names with each comma in a number is more orderly than changing with every second comma, is more consistent with SI measurements).  But there is, at least to my eyes, a certain arbitrary quality to all of these descriptions.  This isn’t a bad thing, but I think it goes against a notion of there being a universally logical rationale for one system over the other.

Since most numbers with lots of zeros are usually discussed in terms of standard notation (a number multiplied by a power of ten), this discussion is perhaps as academic as the periodic attempts to establish tau (equal to twice pi) as the constant that matters for calculations involving circles.  But with the numbers comparisons, it may say more about the mathematicians behind the positions than the positions themselves.

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