Metric’s furlong

No, metrology isn’t math, but let’s not let that stop us.

The International System of Units, or SI, justifiably prides itself on being easier and more logical than Imperial units (in which 12 inches are a foot, 3 feet are a yard, 5.5 yards are a rod, 4 rods are a chain, 10 chains are a furlong, and 8 furlongs are a mile). But have you ever looked closely at SI prefixes? I’ve used SI units most of my life but the prefixes hecto-, deka-, and deci- rarely, which is part of why I didn’t know the prefix for deka- until I came across it today. Here are the prefixes:

Factor Name Symbol |Factor Name Symbol
1024 yotta Y |10-1 deci d
1021 zetta Z |10-2 centi c
1018 exa E |10-3 milli m
1015 peta P |10-6 micro µ
1012 tera T |10-9 nano n
109 giga G |10-12 pico p
106 mega M |10-15 femto f
103 kilo k |10-18 atto a
102 hecto h |10-21 zepto z
101 deka da |10-24 yocto y

If you take a look at the first and last, they’re for the factors 10^{24} and 10^{-24}, a complementary pair one might say, and the names “yotta” and “yocto” are related, and the symbols are an uppercase and lowercase Y respectively. Similarly zetta, Z, and zepto, z. Nice pattern. Be a shame if something happened to it.

So next we have exa, E, and atto, a. Wait, what happened?

Well, at least we have the pattern that the large prefixes are uppercase and the small ones are lowercase. That holds strictly true, except that the division between “large” and “small” isn’t in the middle of the system, between 10^1 and 10^{-1}; it’s between 10^6 and 10^3. There’s two more pairs of prefixes using upper/lowercase versions of the same letter: peta (10^{15}) and pico (10^{-12}), which are not complementary factors, and mega (10^{6}) and milli (10^{-3}), likewise. Chaos!

Every prefix is a single Roman letter.

Well, except for micro, which is Greek, µ.

And except for deka, which is two letters, da. No wonder no one likes you, deka.

Well, logically, there shouldn’t even be a deka, or hecto, deci, or centi, since they’re the only prefixes not corresponding to a power of 1000, but look, that’s a feature, not a bug, okay?

Imperial has furlongs, and it has teaspoons, tablespoons, ounces, cups, pints, quarts, gallons, here’s good luck to the half barrel, and so on, and it’s a mess which SI avoids with factors of 10 and prefixes. Except the prefixes are a mess. Can we start over? Is it too late to start over? It is, isn’t it?

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