Take It With 64.798 91 Milligrams of Salt

Grains-of-SaltBy The Metric Maven

Bulldog Edition

I have often made a point that a pound of feathers weighs more than a pound of gold, and that an ounce of feathers weighs less than an ounce of gold. This is because A troy pound is equal to 0.822 857 1 avoirdupois pounds. Feathers are weighed in avoirdupois pounds and gold is measured with troy when using medieval units. The Troy pound is divided into 12 ounces and the avoirdupois pound is divided into 16 ounces.

At one time I made the incorrect assumption that because the troy pound is defined as 5760 grains and the avoirdupois pound is 7000 that the value of a troy grain and avoirdupois grain were different. To my surprise, the common weight definition for pounds in Ye Olde English is the grain. The same grain is used to define the 5760 grains of a troy pound and the 7000 grains of an avoirdupois pound.

Recently I was watching an episode of the 1960’s mini-series The Prisoner. A discussion took place concerning how much of a drug had been given to the main character and what should be done when the effects were not as predicted:

Number 86: “I gave him eight grains of mitol. Suspicion, doubt, these are factors of aggression. The drug should preclude all such reactions.”

Number 2: “….go to him now repeat the dose.”

Number 86: “Now? But sixteen grains of mitol is quite impossible.”

Number-86The values are all in grains. What struck me as I thought about this exchange is the concern that some literary Lilliputians have that our clichés will suffer at the hands of a metric switch-over. The one phrase I don’t recall being discussed in this context is: “you better take that with a grain of salt.” It means that one should view a statement with some skepticism. The origin of the phrase is a bit apocryphal and is possibly from a Latin phrase. I realized that I had never interpreted the phrase “properly” until I saw that old episode of The Prisoner. The invention of the microscope around 1610 or so soon allowed humans to look at individual “grains” of salt. These grains vary, but a reasonable estimate is about 60 micrograms per salt crystal “grain.” I always took the meaning of taking something with a grain of salt as adding in an infinitesimal amount of salt to make it more palatable. When I thought of the phrase I thought of the microscopic salt crystals of NaCl and not the approximately 1000 of them that make up the Ye Olde English unit called the grain. when I think of a grain of sand I don’t think of 64.798 91 milligrams of sand, I think of a single particle of sand, which is on the order of 15 milligrams.

The grain as a unit is so unfamiliar to Americans as to be intellectually invisible. One has to remind people that some aspirin in the US are also labeled in grains, and if one asked how many grains are in an ounce they would not realize that it is 473.5 grains for an avoirdupois ounce and 480 in a troy ounce. The grain is as devoid of meaning for the average person as is a coomb.

The grain was defined in 1572 long before our modern notion of mass was developed. The pound was not uniquely defined as a mass or a force, and because of its pre-scientific heritage it continues to act as a barrier to a scientific understanding of our world by the average person, and often educated engineers and scientists. When we stand on a bathroom scale and read off the value in pounds, it is often assumed to be a mass. But the word pound is used interchangeably for weight or the force gravity exerted on the mass of the object. We in the US still say pounds per square inch when discussing pressure, which in terms of mass does not seem to make any sense. An object with mass is a three dimensional object and not a two dimensional area. Using the identical name pound for pound-mass and pound-force traps citizens in the US into a medieval view of the world. It also traps engineers and scientists.

Recently I was watching an episode of the highly enjoyable program Impossible Engineering. It dealt with the design of the World’s Biggest Cruise Ship. In the program Physicist Dr. Andrew Steele sets out to demonstrate the amount of drag or opposing force that different hull shapes of boats produce, as first mathematically expressed by engineer William Froude (1810-1879) in the 19th century. Dr. Steele attached a spring scale using rope to each example and then described the amount of force (hydrodynamic drag) they each exert. The value is read from the scale in Kilograms (mass) and not in newtons (force). Dr. Steele is British, which produces a sort of double irony. When a person is conditioned to see pounds as both mass and force, it is a short step for an average person, or a PhD, to substitute Kilograms for newtons and blur the modern distinction. The retention of medieval units brings along their pre-scientific baggage in a world where the public understanding of science is of existential importance.

When you see scientific explanations on popular television programs, remember to take them with a grain of salt.

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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.

Metric Parochialism

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Saddle Mountain — Wikimedia Commons

By The Metric Maven

I’ve noted from time to time reader comments that go something like this: “clearly The Metric Maven’s never lived in a metric country, or he would understand the importance of centimeters.” This of course ignores the fact that Pat Naughtin lived in a metric country and was the person who (along with Sven) first brought me to a realization about centimeters and other kludgy uses of the metric system. It also appears to confirm the proverbial idea of the provincial American in the minds of non-Americans.

What was most amusing for me as I read this criticism, was the knowledge that I had, in fact, lived in a metric country as a boy. I had resided in Mexico. The first metric surprise met us as we crossed from Laredo, Texas into Nuevo Laredo Mexico; it was the road signs. They were all in Kilometers. As we headed down the open road with the sun setting in a burned orange pastel sky, the large reflective road signs only told us how many km it was to Monterrey–no miles–no mas. In those days no American car had a speedometer with graduations in Kilometers, only miles. As we were having a family discussion about this, and whether we were currently speeding or not, it was suddenly realized that a second set of small numbers existed on the speedometer of our Volkswagen Beetle. They were graduations in in km/hr. In a microsecond, the small numbers which had gone almost unnoticed for so long became of paramount importance. We had the Rosetta Stone for travel in Mexico, because of the Germans. Had we been in a provincial American car, life would have been much more complicated.

I looked over at the illuminated dial of the speedometer and realized that we were just above 100 Km/hr, so a good guess at an average rate of speed would be about 100. The distance to Monterrey was about 234 Kilometers, which I realized immediately was around 2.3 hours. It really struck me what an amazing coincidence that was–and how simple.

The metric system continued to surprise me now and then in Mexico. The first time we stopped for gas, the amount of gasoline registered on the pump was far more rapid than I expected. I puzzled for a moment, then it hit me. It’s selling us gasoline in liters. One morning a delightful young woman who made my acquaintance at the American school greeted me. I mentioned it had been very hot and seemed even hotter today. She agreed and stated:

“Yes, very hot, I heard it’s going be almost 40 degrees today!”

My mind screeched to a halt. I babbled in astonishment “Forty degrees?”

She restated her assertion “Yes, 40 degrees.” with a bit of impatience with my confusion and a countenance that insinuated I might be a bit dense.

Suddenly the realization hit me: “Oh, oh, you’re talking metric?” With this revelation, I could see the surprise on her face that I seemed clueless about something so prosaic as the weather, melt into recognition. We were now speaking the same measurement language. An American in Mexico would even have a hard time discussing the weather it appeared.

I have a vague memory of a science magazine I bought there, but a clear one that the magazine had a length which it compared with a test tube’s length—in millimeters.

Life in Mexico for the next few months proved interesting. There were many unfamiliar foods like potato chips with chili and lemon or the section a large white plant of some type with seasoning, but one could almost always get a hamburger anywhere. A woman who was helping my mother with our apartment made what she called azucar tortillas or “sugar tortillas.” They were a pre-teen epicurean delight, and an almost perfect complement to a bottle of Coca-Cola. When the time came to leave Mexico, I asked for the recipe. I had a translator friend present to help with the documentation. Then a stumbling block appeared, the cooking was all done in metric and they had no idea how to change it to American measurement. Once again I was foiled by the lack of metric use in the US. That was the last time I ever had azucar tortillas. I looked on the web as I wrote this, and to my astonishment, I found a recipe for Sugar Tortillas. I made a batch and they are exactly as I recall. The irony is not lost on me that the recipe is in Ye Olde English and I had to convert it back to metric.

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Sugar Tortillas — Back from Ye Olde English Oblivion

The strange assumption (in my view) made by commentators who live in other countries is that they have perfected their use of the metric system, and I should submit to their usage. I have instead come to the conclusion that many metric countries could use metric reform. This leads me to a statement by John Bemelmens Marciano (JBM). In his metric challenged book, Whatever Happened to The Metric System, he complains about the complications of metric measures:

I moved to Rome in 2000 and spent most of my time learning Italian. In order to make dinner, I also had to learn to talk metric, as nearly everything in the market is bought by the etto, which is short for ettogrammo, or hectogram. But measures are a lot harder to learn than most foreign vocabulary. Whereas a casa is the same thing as a house and a macchina precisely a car, an etto is about halfway between three ounces and a quarter of a pound. Our standards—feet, pounds, quarts, degrees—are nouns, which we conceive as something concrete. To think of them as anything different takes a serious taxing of the brain. (page 5)

The exclusive use of grams allows one to use integers for everyday values of mass. A hectogram is 100 grams. This is the mass of a hamburger that I make on a regular basis. I go to my meat market and ask for 0.45 pounds and when I get home it’s very close to 200 grams. I measure and make two 100 gram burgers (give or take a couple grams). When one looks at the masses offered in a British supermarket, they are in grams or Kilograms alone. There are no decagrams or hectograms. The British—who are still not completely metric—clearly saw the simplicity of grams with integer values and don’t bother with the prefix cluster around unity. I suspect that because the UK waited so long to become metric, that when they did, the British were more thoughtful about its implementation. Countries like France (1795) and Italy (1861) transitioned without the 20/20 hindsight that Australia would utilize a century or so later. In my essay Familiarity Versus Simplicity we see a 19th century American pro-metric organization pushing for an amazing amount of unit proliferation within the metric system in 1877. I’ve had many discussions about the implementation of the metric system in the US and as we are essentially the last, we should do our best to implement it in the most streamlined fashion possible.

Hector-Grams

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JBM lived in Italy and found the adjustment to the language easier than coping with their weights and measures. He complains that:

Americans in Europe are constantly being called upon to defend their country against all sorts of attacks. Why do you Americans think you should be different? Why can’t you admit when someone else’s way is better? Europeans find our system of measurement a perfect example of our stubborn stupidity. Why on earth do we insist on keeping such a nonsensical, archaic system of measures when there is another system that makes perfect sense and is used by the entire rest of the world?

In answer to such questions, I at times acted like Wolfe’s “good little colonial,” but I did think that Europeans do certain things better than Americans. In my heart of hearts, however, I never believed that one of them was the metric system.” (page 5-6)

JBM then managed to write an entire book with metric in its title without bothering to learn anything about the metric system. If he had he might have questioned the usage, not the system.

I had an odd encounter a couple of years back at an engineering meeting. The device we were building was to be for a European country. Strangely they used a Canadian company as a supervisory contractor, and I found myself across a table from three engineers who were all from separate European countries. We were going over the specifications and the measured performance of the device when one of the foreign engineers had had about enough. He was tired of seeing inches, foot-pounds and all of the Ye Olde English that permeated the US engineering work. He pointed out that the European country who had funded this project specified it to be exclusively in metric. The other U.S. engineers (working for another company) began an attempt to defend the incredible amount of pigfish introduced into this “metric only” design. The European engineers would have none of it. One began to castigate the US for not converting to the metric system, and the US engineers in particular for fighting it.

The engineers in the room took note that I had remained quiet throughout the brouhaha—which they realized was a bit of an anomaly. The lead European engineer queried me for my thoughts. I took a breath and said (as best as I can recall):

I completely and totally agree with you. The US should have become metric years ago. It is an embarrassment that we have not. If I had my way we would change TOMORROW. However the use of metric by metric countries is often kludgey and poorly implemented. You have several of your specifications in centimeters, this is poor practice. The Australians use millimeters for building construction and never need a decimal point. If we are using millimeters with a decimal point, you know it’s engineering precision. There are many other effective ways to present metric data and specifications that I would be glad to discuss afterward.

One US engineer in the room actually gasped when he heard the Australians build their houses with all metric in millimeters. This was before I found out that the UK also uses millimeters. After one US engineer thought about it he said: “sweet!” The European engineers across from me had a look of surprise and seemed uncertain what to say. The US engineer in charge of all the specifications began removing centimeters with decimal points and changing them all to integer millimeters. Indeed when we needed a decimal point with millimeters, it was for precision parts. I also insisted on changing values like 0.012 millimeters to 12 micrometers. US engineering drawings with metric dimensions are generally in millimeters.

JBM could not offer a statement like mine to the Italians, because he knew nothing about the elegant use of the metric system. After he wrote a book, ostensibly about the metric system, one might expect that he would know enough about it to realize the poor usage he described. It was not like this information was hidden. I was writing my blog at that time. Pat Naughtin’s videos, missives and newsletters were and are on the web. At a certain point, this sort of ignorance by an author who proclaims to know enough about the metric system to author an anti-metric polemic speaks for itself. One can remain provincial even if they have traveled extensively, and be worldly even if they have never ventured outside of their city.