Naughtin’s Laws

On 2011-07-16 advocates of U.S. metrication lost one of their greatest friends: Pat Naughtin, of Metrication Matters. In his untiring efforts to introduce the metric system to Americans, not as something to be feared but as an amazing benefit, he should be counted among the nation’s greatest unappreciated friends.
Pat Naughtin was an expert in the psychology of measurement. He was, as he was quick to point out, not at all the right person to consult on the purely technical aspects of measurement, such as the calibration of scientific instruments. Instead, he was fascinated by questions of why people measure in certain ways, why these are often awkward and counterproductive, why people often resist adopting better ways, and how they can be helped over such mental hurdles.
It is a field in which there are very few, if any, other experts. In fact, although he was far too modest to make such a claim, it is hard to think of him as not having invented the field. And it is an important field. The Australian conversion to the metric system was probably the most successful national metrication ever accomplished: every industry involved, all work essentially completed within a single decade, the 1970s, and all done without any of the social disruption and mental anguish which Americans have been taught to fear by our political classes. That this was done so easily was in large part the result of attention to details and methods which Pat studied and promoted so effectively.
Pat was not the kind of person to formulate anything so pretentious as a set of precepts named after himself. But it is impossible to read through the written material he left behind, and listen to his recorded presentations, without noticing that certain simple and elegant principles occur throughout. Here at the Metric Maven, we will be exploring these, in detail and diverse ways. Since they will be referenced often, it seems good to give them names at the start, and summarize them in a single, prominent place. And since Pat was, whether he would claim them as his own or not, at least their most effective contemporary advocate, it also seems fitting to name them in memory of a fine and generous gentleman. Here then, we propose Naughtin’s Laws.
Naughtin’s 1st Law: Dual-Scale Instruments are Evil
Don’t let the word instrument put you off: a ruler, a measuring cup, and a kitchen scale, are all instruments. One might suppose that a dual-scale ruler, inches down one edge and centimeters down the other, would be an excellent teaching device to accustom a non-metric user to metric measurement. In fact, it has the opposite effect: as long as the familiar scale is within the user’s field of vision, the unfamiliar scale might as well be invisible. To make matters worse, what most Americans think of as the centimeter edge of a ruler is almost always a millimeter scale numbered as though it were a centimeter scale. This is just sad.
Currently, this is a hard rule to apply consistently in the U.S., because well-designed purely metric measures are almost impossible to find. This is particularly the case in kitchen measures. One can find measuring spoons with metric markings, but these are usually smaller than the imperial markings, and the numbers make it clear that the metric markings are an afterthought. A tablespoon, for example, may carry the secondary legend of “15 mL,” or even “14.7 mL,” as though recipes regularly called for such awkward amounts. Kitchen scales are almost always dual-scale devices, but at least the better ones today “remember” the scale last used when activated. There may, however, be some so poorly designed that they always “wake up” in their imperial mode and have to be reset every time. The Metric Maven strongly supports recycling such nightmares at your nearest electronics recycling center.
Naughtin’s 2nd Law: Prefer Measures Without Decimals
Decimals are wonderful. If given the choice of using decimals or fractions, what sane person beyond grade school would not prefer decimals? You can look at two decimal numbers, and immediately tell which is larger, something impossible to do with fractions of mixed denominators. But if both fractions and decimals can be avoided, why not do so?
One rather startling fact about the Australian metric conversion is that nearly all of their industries opted for the millimeter as their preferred unit of measure, including the construction industry. The plans for Australian houses are drawn up in millimeters. Why use something as small as a millimeter to design something as large as a house? Because decimal numbers are eliminated from the blueprints. Which means that the guy on the job site running the radial arm saw never has to deal with anything but whole numbers. Which means that he makes fewer mistakes. Which means that waste is greatly reduced.
Naughtin’s 3rd Law: Don’t Change Measures in Midstream
To give the simplest possible example, if you start out measuring things in millimeters, don’t feel obligated to switch to meters just because you find a few objects that go past the 1000 mark on the tape. Zeros are a good thing. They are your friends: you do not need to swap prefixes and shift decimals just to avoid zeros.
The most common wine bottle today is 750 milliliters. What then should we call a bottle exactly twice that size? For a number of reasons, including the fact that it would make the columns in the shopkeeper’s inventory spreadsheet more readable, because it saves the customer from the mental effort of shifting a decimal, and because it precludes the need for a decimal at all (see 2nd Law, above), the Metric Maven strongly advocates 1500 milliliter wine bottles (and responsible consumption). Wine bottles in this size, however, are usually labeled 1.5 liters. Wine shop advertisements may flip-flop between liters and milliliters, decimals and whole numbers. This is not, for once, a matter of U.S. metric obstructionism, but a matter of worldwide metric obtuseness. Even metric countries could do metric better.
It’s also possible to find examples of switching measures within a single measurement. In the strange phenomenon of “unpacking,” a single number may be broken into two or more numbers, or more than one prefix may be applied to one number, and the author may actually believe this makes things clearer. The deprecated metric prefixes around unity (see 4th Law, below) encourage this error: “125 mL” may become “one deciliter, and two centiliters, and five milliliters.” This sort of awkwardness may be acceptable in non-metric cookbooks (“now add one cup and two ounces…”) but it’s unnecessary in metric.
Naughtin’s 4th Law: No Centimeters!
Actually, no centi-anything. Also, no deci-anything, no deca-anything, and no hecto-anything. But the centimeter is far-and-away the most common violation of this rule, and the only one most of us ever hear much of, so it gives its name to the law. The system of metric prefixes is, ultimately, a fantastically useful device. But the inventors did go a bit crazy by placing a tight cluster of prefixes around the number one. There are metric prefixes for tens and tenths (deca and deci) and hundreds and hundredths (hecto and centi). These should be forgotten. They convey much less information to the mind than an extra zero. Quick, which is more: 1 mL or 1 cL? Yes, I’m sure you got the right answer, but I’ll bet there was a moment of thought. Which is more: 1 mL or 10 mL? Now wasn’t that easier?
Drop these four prefixes, and there are only two remaining that non-technical people will ever have to deal with commonly: kilo for thousands, and milli for thousandths. Conversions between measurements become almost unnecessary, and on the rare occasions when they do crop up, there is one and only one conversion factor to remember: 1000.
These four laws, or rules or precepts if you prefer, can be taken as a kind of style manual in embryo for metric usage. As with any language or tool, the metric system can be used well or poorly. Pat Naughtin promoted metric usages designed to simplify rather than complicate, communicate rather than obfuscate, encourage rather than daunt the well-disposed, and persuade rather than alienate the ill-disposed.
Thank you, Mr. Naughtin.

7 thoughts on “Naughtin’s Laws

  1. Pingback: The Metric Populist Revolt That Didn’t Happen | The Metric Maven

  2. Pingback: Making The Milligrade | The Metric Maven

  3. The idea of the 4th law has also struck my mind. I believe that the centi, deci, deka and hecto prefixes appeared as a fix for the cubic meter dilemma. If you use only 1000 based prefixed, you will wound up with some rather unusable amounts. Start with 1 mm^3, which is 1 µl, then you have 1 m^3, which is 1 Kl, followed by 1 Km^3, which is equal to 1 Tl. The jumps are just to large, thus the centi-deci-deka-hecto muddle. But if you remove the litre out of the picture, and use these prefixes, it works. 1 mm^3, 1 cm^3, and so on and so forth. It seems that the litre and these prefixes were invented to address the cubic metre dilemma individually, but they were both inserted into the metric system. I think that these prefixes add to much resolution, steps of a thousand is just perfect, 1 millilitre, 1 litre and 1 kilolitre. But then you wound up with 2 units for volume, the cubic metre and the litre, which counteracts the whole principle of the metric system. And then what do you do with square metre; 1 kilohectare, 1 kilotare or hectohectare?

    • Marten,

      Your points are well received. The “cubic centimeter” was used to define the “milliliter?!” This sounds like an absurd idea on the face of it. A centi prefix quantity is used to define a milli prefix quantity? What sense does that make? What I have been suggesting to educators, is to define the milliliter as a cube with 10 millimeter long sides, and eschew the centimeter in the definition. The way the system is setup, it appears we cannot escape a prefix discontinuity somewhere. We might as well use a 10 millimeter cube for 1 mL, which allows for the simplification (elimination if possible) of the “prefix cluster around unity” (i.e. centi-deci-deka-hecto prefixes). The non sequitur is absorbed in the definition and only appears again after careful examination of other unit relationships. Indeed a 1 mm cube is still one microliter, which has the same mismatched prefix problem, but a milliliter is the more common volume used by ordinary people, Engineers, chemists and so on around the world, so we should try to kludge it there in my view. It is possibly because of an irrational desire early on, to keep a unit which was near the magnitude of the various inches then in use, that the centimeter was defined. In my view, it was a bad idea which has slowed metric adoption in some industries. The cgs system existed, but eventually SI was adopted instead. It is only through discussions like this we might find simpler and better ways to use and express SI. Thanks for the comment

      The Metric Maven

    • It is possible to argue this in the opposite direction, but it still supports your point. Instead of the milliliter being a cubic centimeter, I was taught that the liter was a volume one tenth of a meter on a side: a cubic decimeter, in other words. In a way, this was a good teaching device: it made it possible to envision a liter easily. But teachers spent way too much time on such conversions, and this left the kids with the impression that these deci- / deca- games were common in real world measurement, when in fact they are never used. I used to think it was preferable to describe a glass of water as two deciliters, rather than 200 mL. It took me a ridiculously long time to realize this was only making a simple thing obscure. I wonder now if it wasn’t English teachers, rather than math teachers, who were more infatuated by metric prefixes: since these derive from a classical language, they may be more attractive to the linguistic- rather than the number-oriented.

      The liter is a little odd in that it is a named volume in a system that technically doesn’t need one. Once you define a unit of length, like the meter, you have by extension an area measure, the square meter; and a volume measure, the cubic meter. But as you point out, this leads to a volume that is inconveniently large for many purposes, and so we prefer the liter, which is one thousandth of that. If the makers of the system had been perfectly logical, they might have seen they could assign a name to the cubic meter, and then use prefixes to derive more comfortable units. What we call a liter might have been a milliliter. It is as though the word contains an implicit conversion factor. But in common practice this causes no problems, even if scientists and engineers need to keep it in mind for certain conversions. And when such questions arise, the factor is always 1000.

      You mentioned the hectare. I’ve just realized that while the metric system has a named unit for a small volume, the liter, it has no similarly named unit for a small area. I think this is true of the imperial “system” as well: there is a ridiculous number of volume measures, but it isn’t until you get to the acre, and land measurement, that anyone apparently felt the need for a named area measure. The more I learn about the hectare, the less i like it. The prefix hecto- seems to have melted into the word, but because it’s an area measure, the implied factor is 10,000 rather than 100. Among other awkwardness, this means that the square meter was actually considered to be a “centiare” at one time. And a kilohectare implies a factor of 10^7. My fervent recommendation is to use square meters for house lots to city blocks, square kilometers for counties to continents — and try to forget the hectare ever existed. Apparently, it isn’t even an official unit.

      • In 1922, a pro metric group quoted from The United States Military “Metric” Manual set of units in their book World Metric Standardization. Along with meter, liter, and gram it also had the Are which it claimed was the normalized metric unit of area. The do not say what size the are is other than unity. The Encyclopeadia Britannica online defines it as:

        are, basic unit of area in the metric system, equal to 100 square metres and the equivalent of 0.0247 acre. Its multiple, the hectare (equal to 100 ares), is the principal unit of land measurement for most of the world.

        As Sven rightly points out, why on earth didn’t we just have the unit of area as one square meter? We could have a kiloare as 1000 square meters and go from there. The introduction of hectare only seems to complicate and de-simplify metric. From my standpoint, it’s another example of why we need to demphasize and possibly eliminate the “prefix cluster around unity.” One square meter is the basis of the A series papers (i.e. A0), why not also for metric in general?

        It also struck a chord with me that linguistic teachers might me more enamored with the prefixes than math and science teachers. Looking back, that was my personal experience.

        The Metric Maven

  4. As a Professional Metrologist having had my start in the U.S Navy, Your website has interested me on many levels. All of my working standards are derived from the “SI” units. Metric is standard practice all over the world, until you get to the United States. (I have to do conversions on a daily basis… My head hurts just thinking about it.)
    The problem with the metric system is the discrimination at both large and small measurement increments outside of the meter. Size jumps too much for most people (Americans’) to feel comfortable. As an example we have 3 feet or a yard to describe the same length as a meter, because of this I feel that this is about the practical applications in the way we deal with describing everyday objects to each other. If I have a fish that is 2 feet long we get a mental picture of it immediately. That same fish is (approx.) 61 centimeters, thus making the same description sound much bigger… Just a fish tale…
    We can call any distance or length any name we want then, describe it. Have a reliable easy method of reproducing it. The issue is how well does it work in relating to the natural world around us. Individuals in power have been creating this type of system since mankind began trying to describe things to others.

    Cheers – with a pint in hand.

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