Expanding The Metric Vocabulary

By The Metric Maven

My Grandfather in Montana read an amazing number of books in his lifetime. Many of them were science and science fiction. He was one of the last of the US blue collar autodidacts.  A spare bedroom contained the books he had finished reading. There was little room to move, and the books were stacked almost from floor to ceiling in open half-high cardboard boxes. This arrangement placed the spines upward, which made the titles easy to read. He often gave books he read to charities, and always was generous with them. I could take any of the books I wanted. There was one exception.   My Grandfather had a very small shelf where he kept his favorites, with which he refused to part, come hell or high water. One I recall was Isaac Asimov’s Only a Trillion. I inherited another, which I believe made it to his 500 mm long literary shrine, it is Mathematics in Everyday Things by William C. Vergara (1923-1994). Vergara was an Electrical Engineer.

I ran across my Grandfather’s fragile paperback copy recently, and began to page through it. The book has short questions and answers. One which attracted my attention is: “Why is the color of incandescent light different than sunlight?” This caught my fancy because electromagnetism (EM) is my specialty, and also because it made me think of James Clerk Maxwell (1831-1879). It was Maxwell who first explained light mathematically, and suggested it be used to scientifically redefine the meter, which it was in 1960. Light is a wave which travels at approximately 300,000 kilometers per second. These waves are often explained with a simple wave diagram—even though they are more complex than this. Below is Figure 43 in Vergara’s book:

Vergara shows the number of wavelengths which pass by a stationary observer in one second. The diagram shows a wavelength of one foot—sigh. The frequency of this wave is 984.25 MHz. Had he chosen 300 mm for a wavelength, this would have produced a value nicely rounded to 1000 MHz for its frequency. The higher the frequency of a wave, the shorter its wavelength. Light waves are usually expressed in wavelengths and not frequency. Vergara then gives a table which details the wavelengths of different frequencies of EM waves:

I suspect some of you are cringing at the way the table describes lengths of different frequencies of light. I’ll get the complete horror over quickly, I will show you the next table, which gives the perceived colors of the rainbow and their wavelengths:

I’m sure by now you are expecting me to chastise Vergara for his sloppy use of the metric system. Clearly you probably expect me to first rewrite the first table using metric prefixes kilometers, millimeters, micrometers, nanometers, picometers and femtometers thus:

Radio, television, communications…….1000 km to 10 mm
Infrared……………………………………………300 µm to 760 nm
Visible Light……………………………………..760 nm to 400 nm
Ultraviolet………………………………………..400 nm to 13 nm
X-Rays……………………………………………10 nm to 10 pm
Gamma rays……………………………………100 pm to 500 fm

And you would be partially right.

One might have tried to spell them all out, as some readers might not be familiar with the prefix symbols.

Radio, television, communications…….1000 kilometers to 10 millimeters
Infrared……………………………………………300 micrometers to 760 nanometers
Visible Light……………………………………..760 nanometers to 400 nanometers
Ultraviolet………………………………………..400 nanometers to 13 nanometers
X-Rays……………………………………………10 nanometers to 10 picometers
Gamma rays……………………………………100 picometers to 500 femtometers

This looks rather clear for a popular audience. Another option is to not use metric prefixes and instead express all the values in meters, multiplied with appropriate engineering notation power of ten exponents. Honestly, I think spelling out the prefixes probably works best for a popular audience—or even an engineering or scientific one. One tends to look at the mantissa (significand) and the exponent is then later noted. This tends to obscure the interpretation of the magnitude of the values presented:

Radio, television, communications…….1000 x 103 to 10 x 10-3   meters
Infrared……………………………………………300 x 10-9 to 760 x 10-9  meters
Visible Light……………………………………..760 x 10-9 to 400 x 10-9  meters
Ultraviolet………………………………………..400 x 10-9 to 13 x 10-9    meters
X-Rays……………………………………………10 x 10-9  to 10 x 10-12    meters
Gamma rays……………………………………100 x 10-12 to 500 x 10-15   meters

The second table with perceived colors and their range of wavelengths, might be better shown in a modern way as:

Color                              Wavelength in nanometers (nm)

Violet…………………………….. 400-420
Blue………………………………. 420-490
Green……………………………..490-570
Yellow……………………………..570-590
Orange……………………………590-650
Red…………………………………650-760

Certainly the tables as originally written are not very clear, or cognitively easy to access, but it’s probably not Vergara’s fault. So why is it that I’m not blaming Vergara for the incredibly poor use of metric prefixes, crazy decimal expressions, and millionths of a centimeter?—and longtime readers know how much I dislike the centimeter. Because Vergara was restricted in his vocabulary of accepted prefixes. The copy of the book I have has a 1959 copyright. In 1959, the prefixes micro, nano, pico, and femto were not officially accepted as SI prefixes. The first three would be adopted in 1960 and femto added in 1964. Americans, fixated on the pseudo-inch British version of the metric system, known as the cgs system, latched onto the centimeter as a replacement inch, whether it was a good idea or not, and shoehorned it in. This remains far too prevalent in the US and is counterproductive.

Even though the prefixes had not been officially accepted, clearly there was some usage of micro by Vergara, but not the best use. On page 270 of his book Vergara has:

We think of one sound being so many times as loud as another, whereas, we would be hard put to say that the former is 43 micromicrowatts per square centimeter more intense than the latter.

Yes, he used micromicro (µµ) as a prefix which is the same as picowatts. Pico had not been accepted just yet either. Electrical engineers of this time period even had a slang term for micromicro, it was mickey mouse. Vergara’s first table of approximate wavelengths even had another option, which I’m glad he did not exercise: the angstrom. An angstrom Å is 10-10 meters, or one ten-billionth of a meter. This completely does not fit with the 1000 or 103 separation of modern metric prefixes, and destroys any logical consistency. Throwing angstroms into the mix has the potential to make the table even worse. Its usage is now discouraged, and I discourage it also.

The refinement of the metric system and its usage is an ongoing project. There were at least three different versions of the metric system at one time, and thankfully they were finally distilled to SI. The metric vocabulary was again increased in 1975, and 1991 when it was needed, but unfortunately the prefix cluster around unity has not been eliminated. The metric system becomes sleeker and sleeker, whereas the medieval Ye Olde English Arbitrary Grouping of Weights and Measurement units used in the US, linger, remain stagnant, and become more and more irrelevant to describe the modern world. There is no microbarleycorn. The use of Olde English units retards the maximum understanding of science by the general US population, which was the very group for whom Mathematics in Everyday Things was targeted. The refusal to adopt the metric system as the sole measurement system in the US, makes the modern world recede into incomprehensibility, and move toward explanations more congruent with magic than with engineering and science.

The Barleycorn Hillbillies

By The Metric Maven

Bulldog Edition

One of the difficult aspects of embracing metric to the fullest extent possible, in the US, by an individual, ok–by individual I mean your humble Metric Maven, is the embarrassment one feels as they experience everyday life in a non-metric country. Each night when I watch the local weather; I see weather maps that have predicted snowfall in inches, which metamorphize into feet. Strangely, the Ye Olde English meteorological changelings never become yards. One could easily use millimeters and have a single unit for rain and snow. Meters for meteorologists would be optional. Given the choice between visualizing 0.2″ and 5 mm, I’ll take the millimeters.

The basis for the current muddle of units in the US goes back to the humble barleycorn. There are three barleycorns to an inch. In other words, the fundamental unit of measurement, the original basis for all the inches, feet, yards, miles and so on is the humble barleycorn. Other countries used the width of a thumb as the “basis” for an inch, but not the Anglo-Saxons. To this day American shoe sizes are derived from the barleycorn. This means that 36 barleycorns equal one foot. Of course the fact that the average length of an actual male human foot is around 10.35 inches (with a 0.47 inch standard deviation) is not a surprise. Behind the relationships between all the archaic units of length used in the US, is a series of shotgun weddings from the past. One of these shotgun weddings was the mile. It was actually a Roman unit that was 5000 feet, but a shotgun wedding with an English furlong produced 5280 feet.

Many wax poetic about the heritage and richness of these forcibly related units. I see nothing poetic at all. I see nothing but the prosaic utterances of Barleycorn Hillbillies. Try for just a moment to imagine you grew up with a smooth continuous measurement system (i.e. SI). 1000 mm is a meter. 1000 meters is a kilometer. The prefixes are shorthand for how many meters are under discussion, or how many times it has been divided—by one thousand. The meter is the only fundamental distance base! The meter is also the product of the best metrological methods available. Suppose this person, who knows only metric, then hears one American woman tell another: “My goodness Alice, my little Johnny grew a foot.”  Now the person from a metric country could be expected to recoil at such a statement. Perhaps the poor boy had grown up near a nuclear waste site, which caused a new appendage to grow. Worst of all, the woman seemed to be proud of it. Imagining further, that this metric person had never heard of a “measurement unit” called a foot, how would it sound after she was told?  My expectation is that to a metric person, it would sound like Johnny’s mother was a member of the most unsophisticated culture on this planet. A foot as a measurement unit?—hilarious and so precious that the Barleycorn Hillbillies would make up such a quaint and absurd fundamental  unit, which is different for every person. This is a ridiculous situation. That’s why I finally have to put my foot down over this issue.

After immersing myself in metric, here is how I’m beginning to react to my fellow citizens describing the world with the dead set of medieval units in everyday use: The units we use are metaphorically similar to zombies from Night of the Living Dead. They are corpses that wander our culture eating our brains. Don’t believe me? How about answering this question: “How many feet in half a mile?” The units just ate your brain. I used a factor of one-half as I’m constantly told that we have a system based on two, a “binary system.” A most annoying fact is that the persons asserting this truism apparently have no concept of how completely incorrect it is. (3 barleycorns = 1 inch, 12 inches = 1 foot, 3 feet = 1 yard, 5 1/2 yards = 1 rod, 40 rods = 1 furlong, 8 furlongs = 1 mile, there is no two anywhere that I can see). So how many meters are in 1/2 kilometer?—why 500 meters of course. I’m sure you’re still working on cyphering that there are 2640 feet in 1/2 mile. Perhaps Jethro Bodine could give you a hand with that. Ok, feet weren’t fair? I didn’t use a unit which is close to a meter?  How about telling me how many yards are in 1/2 mile? I doubt 880 yards immediately rolled off your tongue.

What’s even more fun is that certain American drinking establishments offer “a yard of beer,” or a half-yard if you’re not that thirsty. Yes I know it’s traditionally called a “yard of ale” in the country which provided the sourdough starter for our dead units. Seriously, in the era of cell phones, GPS satellites and such, we are offered a three dimensional volume of beer, which is described as a one dimensional length? I hear rumors that metric countries have a meter of ale, heaven help us, Jethro has arrived in the building.

The real fun begins with a US gallon. The English gallon was defined as the volume of eight pounds of wheat. So we have volume defined in terms of a compressible mass. Don’t forget 7000 wheat grains make a pound. And we all know that four quarts make a gallon, and two pints make a quart, but we often cook with cups. So how many teaspoons are in a cup and how many tablespoons are in a gallon? There are 1000 mL to a liter, and that’s really all you need to use metric. The metric system just seems too modern I guess—like a “cement pond” poured with yards of cement—not ale. When I watch any cooking program, I’m immediately reminded I live in the land of The Barleycorn Hillbillies. It’s both frustrating and embarrassing.

So why did I call the set of units employed in the US as “dead?”  It’s simple, they are. You might not have noticed, but the world has changed a lot since the 17th century. By the end of the 19th century there were about 30 million horses in the US—about one for every four people. Estimates indicate that about one-third of the nations farmland was required to produce horse feed.  Meanwhile in the 21st century, I haven’t needed a horse for transportation or plowing–at all. But the unit used to describe the energy produced by an internal combustion engine, in the land of the Barleycorn Hillbillies, is “horse power.” I am at a loss why we don’t have divisions into “pony power,” “mule power,” and for fine measurement “hamster power.” Power is measured in watts, which is a joule per second, which is of course defined by the metric system (SI).

Years ago, a friend of mine owned a Plymouth Road Runner. It had a 383 cubic inch engine, which probably produced about 415 horsepower. Now I tell you this information because you are certainly intimately familiar with horses, and interact with them on a daily basis?—right?—you don’t? Well then, why would you object to the internal combustion engine described as having 309 kilowatts under the hood? Too modern?—not enough Mr. Ed for you?

The current set of US units are so dead, they cannot describe something that first became useful in the 19th Century, completely transformed the 20th, and is taken for granted in the 21st. Without it there would be no DNA testing, photocopying, cell phones. GPS or other modern creations. It was proudly featured in the 1893 Colombian Exposition, and today essentially everyone in the US has it. It is electricity. No matter how many barleycorns you lay end to end, you will never make it to a standard coulomb, kilowatt, volt or ampere.

The idea of living without electricity is anathema to most, yet because our measurement “system” has been dead for well over 200 years, we cannot use it to describe perhaps the most important physical phenomenon of the last 200 years. So when purchasing a hybrid car like a Prius, should it have two values? Horsepower for the internal combustion engine and watts for the electric motor?  No, The Barleycorn Hillbillies won’t stand for it. Here is the copy I found that describes the Prius, it has “A 1.8-liter four-cylinder engine and electric motor produce a combined total output of 134 horsepower.” In America, it’s a PigFish car. Would it really cause the (metric) Statue of Liberty to collapse if it read that the Prius has: “A 1.8-liter four-cylinder engine and electric motor produce a combined total output of 100 kilowatts.” Strange that 134 horsepower is almost exactly 100 kilowatts, it’s like it had been designed that way! Kilowatts can be used to describe a gasoline engine or an electric motor equally. Australians manage to do it for cars with internal combustion engines:

Australian Car Specifiation for Volvo -- Courtesy of Mike Joy

The lack of metric in the US precludes our citizens from directly describing the modern world. I find it all as backward as describing how well an aircraft can carry cargo using units called broomsticks and kilowitches. Our Ye Olde English units are suited to a pre-industrial and pre-scientific age, not to the current one. We cannot describe and understand the big problems which confront us, if we choose to hide behind meaningless units, and remain Barleycorn Hillbillies. Rather than continue living in the past, we should embrace the measurement system that is constantly being refined and lives, which is the metric system.