Close Enough for American Work

Rose-QuartzBy The Metric Maven

Metric Day Edition

Recently my Significant Other (SO) requested that I take her to a rock and mineral shop. She had driven past it many times, but never stopped. There were all manner of minerals and small fossils. The displays were all very interesting and it seemed I would be destined to look, but not to make a purchase. Then, I noticed the tools section. There was a common inch ruler with a centimeter scale on its opposite edge. Yet another sad testament to metric “practice” in the US. Nothing unexpected there. To my surprise there was also a small dual-scale caliper with þe olde English and metric, but it had fractional inches on one side and millimeters on the other. I was quite surprised and for $7.50 I could not resist purchasing it. Here is a photo:

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Inexpensive Calipers (click to enlarge)

My SO, who had requested we visit, did not make a purchase, but I did. When I arrived at the cash register, an older man with a beard was waiting. I commented on the millimeter scale on the calipers and that it did not have centimeters. The man did not miss a beat and said “We have to have them, all the precious stones are measured in millimeters.”

I looked at the calipers with more care and noticed a lower scale.

Then I said: “Oh my goodness, look at this, it has a vernier scale on the metric side.”

The cashier had no idea what a vernier scale is. I did my best to explain it from memory. I also told him that in my opinion, the creation of the vernier scale was a very important development in the history of engineering and science. I recalled that I had learned to use a vernier scale when using a micrometer during my time working as an offset pressman. It was in Daniel J. Boorstein’s book The Discoverers (pg 400) that I first ran into a historical discussion of the vernier scale. The scale was created by French Mathematician Pierre Vernier (1580–1637) and bears his name.

A U.S. Quarter Dollar coin has a diameter of 24.26 millimeters. I placed a current 25 cent coin into the calipers to measure it. The scale is shown below:

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Vernier measurement of a US quarter Dollar (click to enlarge)

The first line of the vernier scale indicates the measured length is between 24 and 25 millimeters. We next look for the vernier line that matches up best with the upper scale. The three is probably the closest to the best alignment and so we could estimate that the diameter is about 24.3 mm. This deviation is only 0.04 mm (40 um) from the design value. This is a very close estimate for such a roughly fabricated device.

Let’s look at upper inch scale. Oh, my, there is no vernier scale. It would appear that because it is graduated in fractions, a vernier scale was not added. The smallest fractional division appears to be in sixteenths of an inch or 0.0625 inch. When converted to a useful metric unit, 1/16″ is 1.588 mm. It also appears that it would be rather easy to confuse the smallest division with 1/8″ rather than 1/16″ and this would complicate the inch measurement considerably. The mark half-way between zero and 1/2 has about the same downward length as 1/8. This is not the “standard” way that U.S. rulers are marked. Below is an example with the first inch divided down to 1/32″ and the second inch down to 1/16″.

Fractional-DivisionsIf you want to know why the divisions are different for the first inch, I invite you to read my blog The Design of Everyday Rulers. This odd set of graduations caused me to wonder if the calipers had been manufactured in a metric country by a person who is not familiar with our complex þe olde English practices. That the word meter is employed, with an er rather than an re, makes one suspicious that an American was behind this muddled design. Clearly the calipers makes measurements in millimeters and not meters. Why use the word meters rather than millimeters or metric?

Assuming we have figured out the inch fractions on the caliper, we see about 15/16″ and “a little more.” How much more is this? Well, because we do not have a vernier scale, we have to estimate the value by eye.  It looks like it maybe about 1/10th of a 1/16″ space if I have to guess—which I do. So what is 1/10th of 1/16″ to divide fractions we invert and multiply as I was told as a youth. We end up with 10/16 — that can’t be right. Oh wait we need to divide 1/16 into 10 parts or 1/16 divided by 10/1. When we invert and multiply now we get 1/160. Now we need a common denominator to add the fractions and obtain a final value. We multiply the top and bottom of 15/16″ by 10 and have 150/160. We now can add 150/160 + 1/160 to get 151/160 inches. Now we can make this fraction a decimal and get 0.94375 inches or, when converted to millimeters, it becomes 23.97 mm which we can compare with the vernier value of 24.3 mm directly. Even after all of that work and estimating, the vernier scale with millimeters is more accurate, and DEFINITELY simpler to read.

Today we have mechanical dial calipers, and also calipers with electronic readouts; but a vernier scale with millimeters is still an accurate and simple way to measure length. This example also illustrates the inaccurate and complicated way we in the US measure with fractional inches. We have not even bothered to decimalize the inch on our common everyday rulers. I have a proposal, let’s just switch-over to the metric system directly, and skip a kludge like decimal inches for the streamlined system that uses millimeters.

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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.

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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

Click to enlarge

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.