### The Volokh Conspiracy

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# Something's rotten in base-20 numbering systems!

Here's what I learned earlier this week.

You may be familiar with the French numbering system, which has a base-20 aspect for certain numbers (apparently of Celtic origin). The numbers between 60 and 100 go: sixty, sixty-one, sixty-two, …, sixty-nine, sixty-ten, sixty-eleven, …, sixty-nineteen, four-twenties, four-twenties-one, four-twenties-two, …, four-twenties-nine, four-twenties-ten, four-twenties-eleven, …, four-twenties-nineteen, one hundred. (Don't like it? Go to Belgium or Switzerland, where you can be spared some of these excesses and just say "septante", etc.)

You may also be familiar with the numbering system in languages like German, where the units are placed before the tens, as in "four-and-twenty".

German (like some other languages, including some other Germanic languages and also Russian) also follows a rule for time-telling where "half six" refers to 5:30, i.e., halfway to six.

Well, let me propose a new numbering system, to combine the best elements of all these.

- 60 and 80, we'll call "three times twenty" and "four times twenty". For simplicity, we'll shorten these to "threet" and "fourt".
- 50, 70, and 90, we'll call "2½ times twenty", "3½ times twenty", and "4½ times twenty". But instead of 2½, 3½, and 4½, we'll call them "half three", "half four", and "half five". So 50, 70, and 90 will be "half-three times twenty", "half-four times twenty", and "half-five times twenty", or, for simplicity: "half-threet", "half-fourt", and "half-fivet".
- Then we'll put the units before the tens, so "73" would be "three-and-seventy", that is, "three-and-3½-times-twenty", or "three-and-half-four-times-twenty", or "three-and-half-fourt" for short. For simplicity, we'll omit the hyphens, so for "73" we'll write "threeandhalffourt".

Do you like this numbering system? It turns out that this numbering system is exactly the one they use in Danish. I am not exaggerating.

By the way, I have an extra idea, where we can combine this with subtractive notation, as in Roman numerals and Latin numbering more generally, where (especially in the Middle Ages) you could read "18" and "19" as "two-from-twenty" and "one-from-twenty".

- Thus, a number like "68" would be "two-from-seventy", or "two-from-3½-times-twenty", or "two-from-half-four-times-twenty", or "two-from-half-fourt". Hey Danes, you can use this idea for free!

Unrelatedly, how about "half/quarter past/till" notation for centuries? For "1875", we can say "quarter to 1900". I like the idea of saying something in French like "Je suis venu aux Etats-Unis en deux mille moins le quart." Yes, this might be ambiguous (does "quarter to 2000" mean 1500, 1750, or 1975?), so for greater clarity we can say "vingt-cents" instead of "deux mille".

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