Who Says!?


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-PrefixesHerbert 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-1970sThe 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.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page

Related essays:

Building a Metric Shed

Metamorphosis and Millimeters

Dual Unit On One Unit

Groucho_Marx-portraitBy The Metric Maven

There are proverbial questions that seem abundantly obvious as they appear to contain the answer within the question itself. These questions are sometimes offered as jokes. For instance, Groucho Marx would ask contestants  on You Bet Your life questions like: “Who’s buried in Grant’s Tomb?” Despite the obvious nature of the question, the answer is “no one is buried in Grant’s Tomb.” Both Grant and his wife are in sarcophagi above ground and not buried at all. While the question seemed obvious,  there was an unexpected subtlety to the answer.

Recently I was looking at site statistics for themetricmaven.com and came across the list of the top twenty search strings which ushered people to the website. I have the first 15 included below:

Notice that millimeter ruler, and mm ruler are number one and two. Number nine is “how to read mm tape measure.” To a lot of metric proponents this may seem as oddly obvious a question as such as: “how long did the Hundred Years War last?” But in the US, the design of rulers make this far less than a conceptual slam dunk. For instance here is a ruler that was photographed for a project in Nuts and Volts, an electronics magazine:

Ruler-Jams-cm-mm-and explainsThe metric side is in millimeters it appears, but the graduations are chosen to split the digits with a virtual decimal point to create integer centimeters, virtual decimal centimeters, centimeters with millimeters or integer millimeters. It is hard to make out, but there is a handy set of printed instructions which appear to read:

To read length in centimeters omit the final zero after the index line. To read length in millimeters include the final zero.

This may seem like a rather redundant and perhaps even intelligence insulting set of instructions. But in the US, unfamiliarity with the metric system is so ubiquitous, that poorly marked centimeter/millimeter rulers, which have only mm labeled on them, cause confusion between centimeters and millimeters. I’ve written about this in my essay The American Metric Ruler.

I wondered who had manufactured this ruler and so I wrote to Nuts and Volts and the contributing editor. I did not receive a reply. The ruler seemed strangely familiar and then it struck me, it’s some variation of a Starrett ruler. I have a 1000 mm Starrett ruler. On its front side it has inches and millimeters in the same way as the ruler shown above, but no instructions. When I looked at the back side of the ruler, it appears to be a millimeter only metric ruler from 0 to 1000 mm. It also has the instructions for use on it:

Starrett-Ruler-1000mmThis is a Starrett Aluminum Meter Stick No. MS-2. It has 33 conversions written below the millimeter only scale, so it is clearly aimed at US users.

I find it quite an oddity that we have metric rulers which are dual scale like this one from a previous post:

Honest-RulerThis ruler is one of the very few that identifies that both units are on the same ruler. Rather than just choose millimeters and make this ruler a single unit ruler, we have dual unit rulers in the US. Starrett tries to cut the baby in half by placing an index line so that both units are defined on the same ruler, a sort of dual-unit on one unit ruler.

The visceral clutching onto the centimeter, which is far too large for any ordinary precision work, is exasperating. As I’ve pointed out, some rulers put the centimeter into perspective by having a centimeter side and a millimeter side. Here is what the centimeter side of a ruler like this looks like:

Dual-Scale-Metric-Ruler-cm-Side-300x202In the US the centimeter is treated as just another version of an inch, but it is not. The inch is divided using fractions which are not of identical numerical scale (i.e. they cannot be directly added like integers) but are theoretically the same unit. The centimeter is a unit that is too large for use by itself, and so in the US one immediately uses decimals; but this is equivalent to the same integer number in millimeters, with the addition of an extra unnecessary symbol—a decimal point. One can decimalize centimeters in an attempt to preserve something like Þe Olde English inch, using centimeters and decimals, which are analogous to inches and fractions, or one can choose a unit which is simple for everyday use—millimeters. No instructions needed. The irony for me is that I was constantly told in grade school to choose the “right unit” when I was schooled in medieval units, such as the inch, foot, yard and mile; but metric is so esoteric in the US, that it seems nonsensical to my fellow citizens to use millimeters alone and to mark rulers with them. With this much confusion and dogma inculcated into everyone, it should not be surprising that Americans would need instructions on how to read a millimeter ruler, as they so seldom ever see one.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page

Related essays:

The Design of Everyday Rulers

Stickin’ it to Yardsticks

The American “Metric Ruler”

America’s Fractional Mind