Category Archives: Metric Education

Who Says!?

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Isaac.Asimov01
Isaac Asimov

By The Metric Maven

Isaac Asimov Edition

One Sunday, I was attending my weekly coffee klatch, when one of the participants asked: “Who besides you thinks millimeters should be used instead of centimeters?” I was rather surprised at the question, even though I’m the resident metric advocate. I blurted out “Well, Isaac Asimov does for one, so does the U.S. metric building code, the late Pat Naughtin did, and so did Herbert Arthur Klein in his book The Science of Measurement.” The person who asked the question has a solid scientific background, and what surprised me about the question was the appeal to authority. I have found it very puzzling that when I explain the situation, people do not seem to absorb its meaning, or don’t really think about the simplified symbolic expression.

First, lets start with authority. In his 1983 book The Measure of The Universe, Isaac Asimov has this to say about the centi prefix:

The prefix “centi” (SEN-tih), symbolized as “c,” represents a hundredth of a basic unit, from the Latin “centum” meaning “hundred.” A “centimetre,” therefore, is a hundredth of a metre. The prefix is not commonly used, except in “centimetre,” and its use is falling off even there.

Isaac Asimov has this to say about the milli prefix:

The prefix “milli” (MIL-ih), from the Latin “mille,” meaning “thousand,” is symbolized as “m,” just as “metre” is. A millimetre is therefore symbolized as “mm.” Increasingly “milli-” is replacing “centi-” and “deci-” in use. We are approaching the point where 1 centimetre will routinely be referred to as 10 millimetres, and 1 decimetre as 100 millimetres. This is even more true where these prefixes are used for any basic measure other than “metre.”

There it is, documented with sans serif typeface, Isaac Asimov asserting the utility of the milli prefix over the centi prefix. Asimov also had this to say in his essay “Read Out Your Good Book In Verse” in his 1984 book X Stands for Unknown:

Light wavelengths have traditionally been given in “Angstrom Units,” named in 1905 for the Swedish physicist Anders Jonas Ångström (1814-74), who first used them in 1868. An Angstrom unit is one ten-billionth of a meter, or 1 x 10−10 meters.

Nowadays, however, it is considered bad form to use Angstrom units because they disrupt the regularity of the metric system. It is considered preferable now to use different prefixes for every three orders of  magnitude, with “nano” the accepted prefix for a billionth (10−9) of a unit.

In other words, a “nanometer” is 10−9 meters, so that one nanometer equals 10 Angstrom units. If a particular light wave has a wavelength of 5,000 Angstrom units, it also has a wavelength of 500 nanometers, and it is the latter that should be used.

Again Asimov asserts the importance of using metric prefixes with separations of three orders of magnitude.

Nine years earlier in 1974, Herbert Arthur Klein, in his book The Science of Measurement, wrote this about the metric prefixes:

HAK-Prefixes

Herbert Klein sees the atavistic magnifying prefixes deka, hecto, and myria as unnecessary and implies that separations by 1000 are best. He sees only milli as a reducing prefix in good standing, and again argues for reduction by factors of 1000.

Pat Naughtin spent considerable time exploring why millimeters worked so much better than centimeters when implemented in industry. When millimeters were used, the metric transition was quick and almost painless. The introduction of centimeters would delay metric adoption almost indefinitely. He wrote a long discussion of this in 2008 and pleaded for people to use millimeters.

Long time readers know that when the issue was explained to me, and I used millimeters and millimeter instruments in my own engineering work (sans centimeters); I became convinced that the centi prefix, and centimeters are considerable intellectual barriers to metric adoption in the U.S..

After I understood the problem with centimeters, it seemed obvious to use millimeters, but as Isaac Asimov states in his 1971 book The Stars in Their Courses:

One of the pitfalls to communication lies in that little phrase “It’s obvious!” What is obvious to A, alas, is by no means obvious to B and is downright ridiculous to C.

I’m going to do my best to return to my unexamined world view and try to explain the epiphany that struck me at Mach III+. Below is an image from a newspaper film box, probably from the 1970s. The film size is in inches, and it is converted to metric in centimeters.

Newspaper-Film-1970s

The film size is 45.7 x 58.4 centimeters. The number of symbols used is four for each linear dimension. In the everyday world, a measurement with only the precision of a centimeter, is generally too coarse to be of any practical use. The odds that one will measure to an even centimeter are rather low, and so almost all common measures in our world require an unnecessary decimal point and a value for a tenth of a centimeter.

But a tenth of a centimeter is a millimeter. This implies that everyday measurement is generally useful only to a millimeter value. When 45.7 cm and 58.4 cm are written in millimeters, only three symbols are required to express the very same value of length: 457 mm x 584 mm. The mind does not need to stop and perceive the location of a decimal point and parse the decimal number. The number of symbols used is reduced from four to three.

The objection often offered is that one only has to move the decimal point to change from millimeters to centimeters! Pat Naughtin pointed out that often people who work on construction are less familiar with manipulating numbers than scientifically trained professionals. Asking them to slither a decimal point along in any calculations they might do, will only introduce an opportunity for error. In the case of centimeters, the error can be very large because of the unit size chosen.

But, indeed, the proof of the pudding is in the eating, and so it is with the millimeter and the metric system. Pat Naughtin has an extensive discussion (50 pages) about millimeters versus centimeters. His original observation was an empirical one: Industries that used the millimeter had quick and smooth metric transitions, those that chose the centimeter are still in turmoil to this day. Why is this the case? It was analysis after-the-fact that offered clues.

Naughtin makes this observation:

Talking or arguing with people who have not done any measuring with the metric system is quite pointless. But as soon as they experience the simplicity of the metric system for themselves they will then convince themselves that it is the better

Sven had lobbied for the use of millimeters, but it was only when I had all-millimeter rulers and instruments, that I realized their utility, and adopted millimeters exclusively.

I continue to have people who are from “metric countries,” who, with an air of sanctimoniousness say “I’ve never had a problem with centimeters. I use them all the time.” They don’t seem to realize I could just as easily say I’ve used inches (feet, yards, rods, miles) here in the U.S. and I’ve never had a problem. Or stating that “I can use Roman numerals, and have for years,” with the implication that your mind is obviously too small and dim to handle them. Not that they are in fact awkward. It took about 1000 years for people to realize there was a problem with Roman Numerals. They never saw a problem because the were immersed with them.  These denizens of “metric countries,” have an antique metric system usage, that is contemporary with Þe Olde English, and they are fine with the retention of familiarity over simplicity. There is no examination or self-reflection, just a thoughtless assertion. References are offered, reasons explained, and the response appears to be reactionary truthiness, rather than thoughtful introspection.

Certainly Isaac Asimov has demonstrated that he is trustworthy, but I’m sure he would also indicate that a person should never take his word alone. It is always best to understand an idea directly. The question should not be who says?! but why.

Related essays:

Building a Metric Shed

Metamorphosis and Millimeters

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

John and the Argot-nauts

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By The Metric Maven

Bulldog Edition

You’re eighteen hands at the shoulder

— Heavy Horses by Jethro Tull

Thurston

John Bemelmans Marciano (JBM) often laments what might be lost aesthetically if we were to switch to the metric system. In  his ill-titled book Whatever Happened To The Metric System? he discusses his “family business”:

Our family business was horses, Like any insular community, the horse world comes with its own specialized vocabulary, but it is  particular in preserving so many dialectical relics. Riding pants are called “britches,” an old variant of “breeches,” a fashion that began to disappear when it became a symbol of aristocrats during the French Revolution. …

***

The terminology of horses also includes a couple of otherwise obsolete but once widely used measures, the furlong and the hand. Races under a mile are held in furlongs, of which there are eight to a mile, while the height of horses is measured in four inch hands. The cutoff between a horse and a pony comes at 14.2 hands (which is not fourteen and two tenths but fourteen and a half) as measured to the withers. These terms are the only ones used; to call a six-furlong race three quarters of a mile would sound odd, and to say a pony has to be four feet ten inches tall or shorter absolutely ridiculous.

For me, the hand and furlong were measures that meant something, and I could visualize them in a way I couldn’t a kilometer or anything else metric, save liters of soda. Not that I thought much about the metric system after I finished school. At least not until I had to.

It is interesting that when JBM mentions a metric measure to which he can relate, in this case the liter, it is a metric measure that is ubiquitous in the U.S.. He then divulges that for him, the height of horses only has meaning when presented in hands, and again is a unit with which he is personally familiar, but is arcane to the majority of the U.S. public.

The measurement of horses using hands involves entry into the world of the sport of kings, which most of us plebeians have not experienced. A childhood friend had a considerable number of horses, and we would ride them during the Summer for short periods. He showed me how to saddle a horse, and make sure the girth used was held tight until the horse exhaled, or the saddle could slip. I do not recall him mentioning horse heights in hands. Of course this was a common Midwestern farm, and he was not breeding horses for races run in furlongs. There were horses on my cousin Ralph’s farm, and I don’t recall him once describing their height in hands. It was not as if I had not been around horses through my teenage years, I had. It is possible the height of horses in hands was mentioned, but I did not take notice.

The use of the hand to measure horses is rather esoteric. A “hand” is standardized to four inches. According to Wikipedia, the hand is used in Australia, Canada, the Republic of Ireland, the UK and the United States to measure horses. Apparently, only when the international inch was finally adopted, could the hand become a standard size. In other words it was not until the international inch was defined in terms of the metric system that this unit of kings had a single agreed-upon value. Despite the alleged “naturalness” of hands, elsewhere in the world horses are measured in metric units.

There are a number of websites that explain how to measure your horse in hands. JBM brought up the fact that the height above which a pony becomes a horse is 14.2 hands. The value 14.2 in hands is 14 hands with what appears to be a decimal point. It is NOT a decimal point, but is instead a separator between two types of units. The two units are hands and inches, and this linear quantity is written as hands.inches. But wait! there are only four inches to a hand, so the number after the separator point is never four or above. One hand is four inches or 1.0 and two and one half hands are 2.2, so obviously 14.3 hands is 59 inches. According to one source, one can also add a fraction of an inch at the end. One can have a horse that is 14.2 1/2 HH where the HH stands for Hands High, or just H for hands, or in other cases hh and h lower case. So we have a measurement notation that uses what is generally interpreted as a decimal separator or radix instead as a units separator with the option of fractions tacked on at the end? This is the numerical wonder that JBM insists on preserving?!

Decimal notation never adds any of these complications. It is also standard throughout the world. The left side of the decimal point has each place multiplied by ten. We recognize 123. as 1 x 100 + 2 x 10 + 3 x 1. On the right hand side the downward decrease by ten continues without discontinuity. The number .456 is 4/10 + 5/100 + 6/1000. The total number 123.456 has but one rule of interpretation and attaches to it only one type of unit.

Perhaps I’m reading too much into John Bemelmans Marciano’s embracing of the hand as a meaningful unit. Perhaps it is only a unit created so that he can segregate himself from other tribal groups. The way the hand unit is used appears to be a numerical form of argot. Wikipedia defines argot as:

An argot is a secret language used by various groups—e.g. schoolmates, outlaws, colleagues, among many others—to prevent outsiders from understanding their conversations.

The purpose of an argot is not to facilitate communication, but to restrict it to an “in group.” A classic example would be the CB radio argot of the 1970s in which truck driver’s referred to a Volkswagen Beetle as a “pregnant rollerskate.” One reason for the implementation of the metric system was to eliminate argot, and the graft that accompanies it, with a universally understood measurement system.

Eye-Hand

John Bemelmans Marciano sees the metric system as inhuman and sterile, he celebrates his equine argot as something with a deep rich meaning. JBM believes he should be left alone to pursue his furtive world of aristocratic-hipster measures. His constant eagerness to tie the metric system to the horrors of the French Revolution, and his insistence on patrician equine argot, points toward a desire to simply preserve elitism. In his book, Marciano seems to say: “I’m just like Neal Cassady,  but I see the world like Thurston Howell III.” With JBM, it is the dog that does not bark (measured in hands?) that is most interesting. That metaphorical dog is John Wilkins, the Englishman who first proposed the system part of the metric system. The ad nauseum guilt by association of the metric system with the French Revolution that JBM uses in his book, appears to be but a polemic device. Without it, JBM’s rickety “thesis” of the origins of the metric system during the French Revolution could not support itself for an attosecond. There is the Sport of Kings, and measurements designed for the common person, and they will remain segregated!

For just one moment, let’s look at the hand’s relation to metric quantities. A hand is four international inches or 101.6 millimeters. So one could create a “metric hand” that is exactly 100 millimeters. The value of 14 hands would be 1400 mm, and with another half of a metric hand we obtain 50 mm or 1450 mm. This is the height at which a horse and pony have their demarcation. It’s really simple to use millimeters, take the number of hands multiplied by 100 mm, or just add two zeros. Therefore 10 hands is a meter, 12 hands is 1200 mm. Marciano’s central argument that metric is not “natural” and “For me, the hand and furlong were measures that meant something, and I could visualize them in a way I couldn’t a kilometer or anything else metric” is ridiculous. Marciano shows an epic lack of familiarity with the metric system, despite finding a way to write a book with metric system in its title.  JBM does not notice that the hand can be seen as a “stealth metric measure,” which is almost exactly commensurate with a direct value in millimeters! Apparently millimeters are quite natural.

We see that 14 and one-half metric hands is 1450 mm. If one told JBM that Big Jake, the world’s tallest horse, is 2102 mm, could he not immediately realize that Big Jake is essentially 21 hands tall! Is JBM’s real desire to preserve the hand as elitist equestrian demarcation? Preserving metrological argot promotes separation of the U.S. from a measurement system that has been embraced by 95% of the world’s population. Not one country has expressed interest in returning to pre-metric measures after converting to metric. When the entire world agrees on one measurement system, it reduces the opportunity for fraud. In my view, JBM’s celebration of the hand, is nothing but an elitist “bitch-slap” of ordinary humanity.

Related essays:

Bonfire of The Vanity Units

Whatever Happened to the Metric System?

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.