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.


Popped Secret

By The Metric Maven

Bulldog Edition

Popcorn is a very New World food. It is amazing that in ideal conditions the kernels of unpopped popcorn can be stored almost indefinitely. Corn was first domesticated in Mexico about 9000 years ago. As a young boy, I recall a friend showing me a popcorn pan with a hand-crank on the lid. We were watching an old movie and he wanted to make something special. My friend placed oil into the pan and heated it, he then tossed in a measured amount of popping corn. Normally, at that point one would  immediately put the lid on to keep from being splashed if it started popping immediately. He next tossed in some sugar. The handle was part of a wire sweeper that could push the corn around. This was done until the popcorn had finished popping, and for the first time I had popcorn with a sugar coating. At that age it seemed exotic. At that point in my life I gave no thought to how much extra energy was imparted by the introduction of sugar. The agitator was a nice addition. Generally when popping popcorn in a pan one would need to continuously shake the pan forward and backward to keep the popcorn from burning. Popping popcorn at home was an acquired skill. Popcorn balls (generally colored in some fashion) were often handed out at Halloween in my small town as a treat. The largest documented popcorn ball is 2.4 meters in diameter, 7.5 meters in circumference, with a mass of 1549 Kilograms (well over a Megagram). Popcorn was also strung on thread to decorate Christmas trees during the winter holiday season.

In China and Korea a sealed cast-iron canister with popcorn inside is used like a rotisserie  over a fire.  When a pressure gauge on the container reaches a threshold value, the canister is taken from the flame, a canvas sack placed over the top and the seal broken. With a large boom, the popcorn explodes all at once. It is then poured into the canvas bag.

The first popcorn was popped by hand (sometimes over an open fire), and  was later automated with steam powered mechanisms designed in the late 19th century. This new popcorn popper was introduced at the 1893 Colombian Exposition. When I was a boy we purchased sealed plastic bags of popcorn kernels with Jolly Time printed onto the transparent film. The big change in popcorn preparation came when General Mills obtained the first patent for bagged microwave popcorn in 1981. This made popping popcorn much more convenient and a surge in popcorn consumption followed. People also ceased to see popcorn kernels any longer as they now come in an opaque bag.

Microwave popcorn allows one to eat popcorn with a very consistent serving size in terms of mass and volume. This consistency would be great for those who are trying to monitor their food energy intake. When I first attempted to determine the energy content of popcorn I was very surprised at the low value. The serving size per bag is about 3 and the serving size is 1 cup popped or three cups. This works out to 90 Calories (377 KJ). My significant other (SO) immediately doubted this value. It had to be higher. In recent years it has been emphasized that we should go back to Olde English only nutrition labels. One can see this from the nutrition labels that Ye Olde English is still Kyng. Here is the nutrition label for Pop Secret’s Homestyle Microwave Popcorn:


So if the servings per bag is about three, and the serving size is two tablespoons unpopped, then it would be a total of 3*150 Calories or 450 Calories (1884 KJ). The fact that the serving size is given as 2 tablespoons unpopped and 1 cup popped seems to indicate an equivalence. So which is it? Ninety Calories per bag or 450 Calories per bag? This difference is a factor of five! The range given on the web for a single bag of Pop Secret Homestyle was from around 400-500 Calories or so. When I looked at the bag after popping, and used my 100 mm wide hand to measure it, the bag appeared to be somewhere around two liters in volume, but I had no idea how many cups that might be. I could immediately estimate the value in metric, but could not do the same with Ye Olde English.  My SO and myself then conducted an experiment, we popped a bag and measured it with a one cup measure. It turned out to be somewhere from about 10-12 cups of popped popcorn. It would seem that each bag contains about 6 tablespoons of unpopped popcorn, and 15 cups when popped, but the nutrition label does not say that.

When converted to metric the clarity has not increased much:

Nutrition Facts
Serving Size  15 mL unpopped  237 mL popped

Amount            15 mL     237 mL
Per Serving      Unpopped   Popped

Calories           150        30

So 15 mL of popcorn becomes about half of a 500 mL bottle of soda or water. Does that make sense or not? I was able to estimate the volume of a popped bag at about two liters or 2000 mL.  Given about 200 mL per serving 2 liters would be about ten servings or 300 Calories. Clearly the value would not be 90 Calories.

In my view this label has been designed to confuse. Who eats unpopped popcorn? Who even sees the unpopped popcorn in a sealed opaque paper bag? How would you estimate the unpopped amount when you can’t even see it! One would immediately look  at the label assume 3 cups per bag at 30 Calories per cup and compute 90 Calories total. There have been moves to go back to Ye Olde English from metric for US nutrition labels to make them more “understandable.” The Pop Secret label is unclear in metric and even more inaccessible in Ye Olde English. It could have been written:

Nutrition Facts

Calories per bag: 450

Servings per bag: 3

Calories per serving 150.

Calories per cup 30

Volume of bag: approximately 2500 mL

The nutrition label as it is originally formatted appears to be designed to mislead consumers into believing that microwave popcorn contains far less calories than it does. This in turn causes the person to consume more calories and hence more product while blowing their estimated food energy intake.

Profiting from measurement confusion and misinterpretation is often thought to be a thing of the past. It is clearly not—and never has been. I have a measuring scoop provided inside my laundry detergent box which has a volume twice that recommended for each wash. It has a line halfway up its side which is the recommended volume. People don’t notice the transparent line, or read the tiny instructions, and generally fill the scoop up to the top, using twice the recommended amount of soap. People who see the importance of implementing the metric system, and the teaching of basic numeracy as fringe issues in the United States, are but ignorant marks for our modern industrialized hucksters.


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.