Système International Prefixes: Part 1

The Système International d’unités, commonly known in English as the SI units, is a version of the metric system that, in addition to a carefully specified set of measurement units, contains a list of defined prefixes to specify multiples and fractions of its basic units. This set of prefixes has grown eccentrically over the years.

Title page of Instruction sur Les Mesures
The metric system arrives, 1795

The origin of the SI system is with the Republican metric system of France, which was passed into law on April 7, 1795. It was called metric because it was based around an entirely new unit of length measurement, the metre (in American English, the meter), which derived its name from the Greek metron,  “measure”. The metre was originally defined as being 1/40,000,000th part of the circumference of the Earth. (If you speak French, you’ll see that “deduced from the size of the Earth” was prominently displayed on the title page of the original description of this new metric system, which I’ve reproduced above.)

The metre was subdivided using prefixes into decimetres, centimetres and millimetres, designating a tenth, hundredth and thousandth part of a metre, respectively. Multiples of the metre were the decametre, hectometre, kilometre and myriametre, indicating tenfold, hundredfold, thousandfold and ten-thousandfold multiples, respectively. This approach was adopted only after considerable discussion—there was a body of opinion that the prefixes would cause confusion, and that it would be better to adopt a completely different name for each order of magnitude. But the prefix system was simply too flexible to be discarded—once in place, it could be applied intuitively to any and all units of measurement.

The classical prefixes seem to have been chosen with some care—all the fractions are Latin, all the multiples are Greek. It’s a pleasing approach, but (as I’ll describe later) it didn’t last.

Deci- comes from Latin decimus, “tenth”, the origin of our word decimal, “pertaining to tenths”; and also decimate—originally, to kill every tenth person of a group, a punishment used by the Roman army. It has since taken on a more extreme meaning, implying that the group has been nearly wiped out. Decimus is also the origin of the word dime, originally meaning a tenth part of something, and now attached to the American coin valued at a tenth of a dollar.

Centi- is from Latin centum, “hundred”, which gives us the name of another coin— the cent. A lot of currencies use cents, and usually they are equivalent to a hundredth of some larger denomination. Per cent means “in every hundred”, but its origin is slightly obscure. It may come from Italian per cento or French pour cent, both meaning “for a hundred”; what it doesn’t come from is per centum, which is only pseudo-Latin. To centuple is to multiply a hundredfold. A century is a hundred years or (about) a hundred roman soldiers, the latter being commanded by a centurion. And, speaking of the Roman army again, centesimation was milder than decimation—only one in a hundred was punished or killed. There may also have been an intermediate level, vigesimation, involving the punishment of one in twenty, but it seems to be poorly attested.

If you live a hundred years you are a centenarian, and you celebrate a centenary. If something is divided into a hundred units, it is centigrade, like the temperature scale. If it has a hundred feet (or just looks like it might possibly have a hundred feet) it is a centipede. And if it has a hundred eyes it is centoculated—a word that seems only ever to have been used with reference to the mythical and ever-watchful giant, Argus Panoptes.

Milli- is from Latin mille, “thousand”, which gives us millennium, a thousand years. According to some interpretations of the Book of Revelation, the Millennium is a thousand-year period in which Jesus Christ will return to reign on Earth. A millenarian subscribes to that belief, which is called millenarianism. It has been suggested that there was an outbreak of millenarianism at the approach of the year AD 1000, with many people anticipating that the Millennium would begin after the end of the first millennium of the Christian calendar—but the evidence of that seems to be patchy and debatable. It did, however, lead to a shift in association for the word millenarian—there were various sorts of panic and anxiety associated with the arrival of the year 2000, and they were all referred to as being millenarian, whether or not they had any Christian underpinning.

Something with a thousand feet (or that just looks like it might have a thousand feet) is a millipede. If it is very spotty, maybe even having a thousand spots, it is millipunctate. A milleme is another coin—it was a thousandth part of the old Egyptian pound. To millecuplate is to multiply a thousandfold, but it’s an awkward and ugly word, which has deservedly fallen into disuse. Mille-feuille is a multilayered pastry—its French name means “a thousand leaves”. A millesm is a thousandth part, a mille-millesm is a millionth part, and millimillenary denotes accuracy to one part in a million.

A milliard is a thousand million—or at least it used to be, back in the days when the British used the word billion to denote a million million. But French mathematicians started using the word billion for a thousand million, the Americans followed suit, and the old British usage has been steadily driven towards extinction, taking the word milliard with it.

So much for the Latin fractional prefixes. In my next post about words, I’ll write about the Greek multiplicative prefixes. And in the one after that, I’ll write about how the system expanded in later years.

To close here, I’ll offer one example of the flexibility of the prefix system when applied to new units of measurement. I’ve previously discussed the science fiction and fantasy writer Poul Anderson. In his novel Fire Time (1974) he introduced a standard measure of female beauty—the millihelen, defined as enough beauty to launch a single ship.

Note: In annoying sychronicity, a letter-writer to the current edition (23 April 2016) of New Scientist has just told the story of the millihelen, albeit without giving Anderson due credit.
Update (May 14, 2016): Oh-ho. Turns out Anderson didn’t originate the joke. New Scientist have now unearthed a discussion of the millihelen on their own letters page, dating back almost fifty years: 27 November 1958, p.1400.

4 thoughts on “Système International Prefixes: Part 1”

  1. “he introduced a standard measure of female beauty—the millihelen, defined as enough beauty to launch a single ship.”

    Shouldn’t the standard be referred to as a “Helen” with the millihelen a subdivision?

    God, the story of Hector and Parris still cheeses me off. Especially versions that downplay Parris’ guilt in getting his older brother killed and bringing about the destruction of his own city-state and dynasty due to lack of self discipline.

    1. Well, it would have been a pretty poor joke without the “milli” part.

      But there’s good precedent for standards based on subdivisions or multiples—both the old c.g.s. and the current SI system have standards that aren’t base units—the centimetre and the kilogram, respectively.

  2. Hi, as it is I am native French speaker, albeit Belgian, and in France and Belgium, we say milliard for thousand millions, and billion for a million millions. The first times we meet billion in English are always a bit of a shock…

  3. French seems to have a chequered history with billion, at least according to the Oxford English Dictionary.
    Their narrative says that the word was introduced in French in the sixteenth century, meaning a million million, and then adopted into English with that meaning by the end of the seventeenth century. The usage was then changed by “French arithmeticians”, to mean a thousand million, and the Americans followed suit, while the British retained the older meaning, “to which France reverted in 1948”. (I don’t know the significance of that very specific date.)
    So presumably French milliard went in and out of use according to the current meaning of billion in French.

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