Doubling Down

Double-MeasureBy The Metric Maven

Bulldog Edition

When I lived in Mexico as a boy, it was pointed out by my peers, that rather than drink the more expensive Coke or Pepsi, one should buy a less expensive Cola they called Doblay Cola. I became used to  the pronunciation as Dob-lay and expected it was a Mexican product. Years later I was in the US and saw a bottle of Dob-lay Cola, but suddenly I realized it was actually called Double Cola, and is from the US. When I was surrounded with Spanish, I saw words as all being pronounced as they would be within that environment. The modern bottle of Double Cola shown on the upper left has the marketing copy: “Double Measure Double Pleasure.” In light of the information that follows, it struck me as rather prescient. Recently Amy Young brought an interesting web page to my attention, and again I was faced with an English-French version of what I had experienced with Double Cola.

The university web page has an English translation of the original 1795 metric decree in France. There are a number of declarations about measures, and they are mostly what I would expect, but it offered extra context. It is interesting that the millimeter does not appear to be mentioned, but not exactly shocking.  What did surprise me was item number eight:

8. In weights and measures of volume, each of the decimal measures of these two types shall have its double and  its half, in order to give every desirable facility to the sale of divers items; therefore,  there shall be double liter and demiliter, double hectogram and demihectogram, and so on with the others.

Suddenly, the origin of the incredible name proliferation found in a chart made by the American Metric Association in the 19th Century revealed itself. In my essay Familiarity Versus Simplicity I diagnosed the inclusion of the double gram, demi dekagram, dekagram, double dekagram, demi hectogram, hectogram, double hectogram, demi kilogram and kilogram as a vestigial inclusion of pre-metric thinking. I suspected it had been ad-hoc and was very suspicious that it was introduced by Americans. It had not occurred to me that double in English and double’ in French would both mean well—double or twice an amount. I then realized that double and demi were introduced as concatenation prefixes of sorts. This is not unlike the Ye Olde English prefixes used with metric, like one billion Kilometers or one million Kilometers. The prefix demi (in the linguistic sense) is from Latin dimidium or “divided in half,” via Old French and Middle English, it became demi.

Why on Earth was it so important to include a prefix that is a factor of two rather than ten at the time? We have 3 barleycorns to an inch, but often the inch is divided into halves, quarters, eighths and sixteenths. When moving upward using linear measure it’s 12 inches to a foot, 3 feet to a yard and so on. The interest in doubling and halving is not presented for linear measure in the early metric system. There is no double meter or demimeter offered in the 19th century chart. The value of masses and volumes are given double and half values in this metric chart. Why? Probably because it is fairly easy to use a beam scale to halve flour or sugar or beer or whatever. This binary approach would match our Ye Olde English measures right? Well—not exactly.

Isaac Asimov in his work Realm of Measure has this to say:


Binary relationships quickly breakdown in Ye Olde English linear measure, volume and weight. The Troy pound has 12 ounces and the Avoirdupois pound has 16 ounces. Those who claim our Ye Olde English measures are consistent and binary are simply wrong. What is interesting is that the first draft of the metric system had provisions for doubling and halving values. I can only speculate at this point that this inclusion was an attempt to encompass a binary set of measures as a kind of reform of earlier measures that might have been more useful if they had strictly stayed with doubling and halving. This reform was developed at a time before modern scales with analog or digital readouts. When continuous reading scales were introduced, the idea of using a balance scale for everyday measures was moot. There was little reason to use the double or demi designations. I discuss the importance of the creation of a measurement continuum in my essay The Count Only Counts—He Does Not Measure. Modern measurement instruments are more than likely the reason that binary measures began to vanish. When one was no longer chained to binary quantities, it opened up a world where any measure for a product could be realized. Just look at any set of supermarket shelves.

Section 6 of the document calls for the prefix cluster around unity and the myriameter:

6. One-tenth of a meter shall be called a decimeter; and one one-hundredth thereof, a centimeter.

A measure equal to ten meters shall be called a decameter, which furnishes a very convenient measure for surveying.

Hectometer shall signify the length of 100 meters.

Finally, kilometer and myriameter shall be the lengths of 1,000 and 10,000 meters, and shall designate principally the distances of roads.

The incredibly useful millimeter is not listed in the document. The liter is defined and is asserted to be for both dry and liquid measure, as it is to this day.

The original formulation of the metric system as presented in this document illustrates how far we have come in simplifying and thereby  increasing the utility of this ubiquitous system of measures—well ubiquitous outside of the United States.

Related essay:

Familiarity versus Simplicity


The Metric Maven has published a new book titled The Dimensions of The Cosmos. It examines the basic quantities of the world from yocto to Yotta with a mixture of scientific anecdotes and may be purchased here.


3 thoughts on “Doubling Down

  1. I still ponder whether fractional math is somewhat easier on our brains. I asked Nerida Ellerton (a math professor at ISU and also a physicist). She told me, “One of the times my students actually questioned me on this. Because they had, they said, ‘But our ruler has measurements in one-fourth of an inch, one-half an inch, and so on. You can’t mix that with decimals.’ Because I told them they have to calculate it using decimals. Two-point-five inches, not two-and-a-half inches. So, it depends. If you were using a calculator, for example, it’s very much easier to use two-point-five, put it in. If you were doing a quick mental calculation, like two-and-a-half times four, you may well say, oh, two times four is eight, four one-halves is two, and you’ve got ten. It would depend what you’re calculating…” Witold Kula mentions in “Men and Measures”(1986) how we can change the quantity we’re buying (handy when coins were hard to come by and maybe not in many denominations) or we pay a different price (easier when we have decimal currency and many denominations). But I still think of fabric in inches and fractions of a yard, perhaps because that’s how I learned it and sewing stores sell it in those units, probably to balance the labor of cutting. I’m still undecided about the issue.

  2. Sounds like some one was trying to emulate the binary mess of English measure – creating a binary exponential scale of measure. (Most likely this was created by people with only two fingers?) The range of this included everything from a ‘mouthful’ to ‘tun’.

    It is an example of positive feedback – because the old system was understood this way – there was pressure to bend the decimal system into something similar. (Good thing it failed).

    I once had a landlord that taught Physical Therapy at KU (back in 1985). He had a requirement to pass he called the ‘ruler test’. With hard questions like which is bigger 3/8″ or 3/4″. One had to pass this test to pass his course – he said the university changed his grades to retain students – after which he just gave everyone A’s,

    My point is that not everyone learns fractions ( and many of these mathematically illiterate end up with so-called ‘degrees’). Doing simple fraction math is beyond a large part of the general population – which of course leads to bad decisions, poor price discovery of the market place etc.

    Avoiding fractions should be a wind at the back of using metric. Yet on the other hand, if someone does not ‘get’ fractions, they are not likely to understand exponents either.

  3. Not only the demi and double units not introduced by Americans, but, in fact, are absent from the Metric Act of 1866. I’m not sure if we didn’t sign up to them, or they had already gone out of vogue. The original tables in the Metric Act of 1866 do include things like the stere (1 m³) and the obsolete prefix myria (10 000).

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