Familiarity versus Simplicity

By The Metric Maven

Bulldog Edition

Sometimes the advantage of simplicity is obvious. I recall a time when a person at a  grocery store check-out counter entered the price of each item using mechanical buttons on a cash register, then used their palm to press a large flat beige metal key which would enter the transaction into it. Later, laser scanners that could read universal product codes (UPC) were introduced. The items just glided across a glass window, and with a beep, each item price was registered. The person at the register went from using some arithmetic skills to none.  In other cases, where one has to rethink an intellectual method, no matter how much simpler it might be, people often cling to the familiar with great tenacity. If they run into a new method, they often will try to impose the old manner upon it, which only makes the new method much more complicated.

I thought of this when I was reading an old folio on the metric system. It is called The Metric System of Weights and Measures and was written by J. Pickering Putnam in 1877. The book was published by the American Metric Bureau. They describe themselves thus:

There is an amazing color chart included in the book which completely illustrates my point about simplicity versus familiarity. The entire chart is reproduced below so that you can enlarge it, but I will address parts of it using cropped sections.

Metric Chart (1877) click to enlarge

Here is the illustration of metric volumes from the chart:

Volume Examples (1877) click to enlarge

When the modern metric system is used, generally volumes are described using milliliters and liters. One can introduce the archaic prefix cluster around unity and have centiliters, deciliters and so on, but they are impractical and generally understood to be nothing but a complicating factor. First let’s look at the volumes offered in the chart. It shows 1/2, 1/5, 1/10, 1/20, 1/50 and 1/100 fractions of a liter as suggested volumes. These are 500 mL, 200 mL, 100 mL, 50 mL and 10 mL volumes. When written in a modern manner, they are all nice whole numbers which can be immediately compared; but that’s not what was suggested by the pro-metric American Metric Bureau chart. It expresses liters in the common vernacular of the day—fractions, which do not provide an instant recognition of relative magnitude. The nineteenth century was still a place with an almost uncountable number of measurement units–so this would probably seem like a simplification.

The chart has also suggested names for each quantity below one-half liter. They are the Double Deciliter (200 mL), Deciliter (100 mL), Demi-Deciliter (50 mL), Double Centiliter (20 mL) and Centiliter (10 mL). Amazingly, my nemesis, the cubic centimeter, is also expressed as 1000 cubic millimeters and correctly asserted to be equal to 1 milliliter. It is shown that one milliliter of water weights one gram, but we note that milliliters are not used at all in the “parade of illustrated volumes.” What this demonstrates, is that the ubiquitous way pre-metric weights and measures were used, was unconsciously foisted on the much simpler metric system. They were imposed without a technical justification, but instead relied on an unspoken common usage justification. It reminds me of a section of the TV version of The Hitchhiker’s Guide to The Galaxy where a hair dresser is given a pair of sticks to make fire, and constructs  a faux-scissors from them. They were feckless for producing fire, but they seemed like a rational path to him, based upon his experience and education as a hair dresser. He is only able to think in terms of what he knows, what is familiar.

The fact that 10 cubic centimeters is 10 milliliters, which is also 1 centiliter, and when filled with water is a dekagram is never seen in modern metric usage, but is given in the chart. Generally we don’t use a k in deca either. The multiple equivalences is related to the idea that somehow we need lots of weights and measures, because we have always had lots of weights and measures, such as: a firkin, a hogshead, a kilderkin, a chaldron, a pottle, a gill etc. It is a nineteenth century reflexive belief that we need many measurement monickers. It is familiarity over simplicity.

Mass Values (1877) click to enlarge

When looking at the “parade of grams” they appear to use a capital G with a typeface that looks like a C, which may be an archaic Latin usage. In this case they actually use integer values of 1, 2, 5, 10, 20, 50, 100 and 200 grams; but at the last moment they resort to 1/2K for 500 grams, and 1K for 1000 grams. Yes, they use a capital K with which I agree, but modern usage “style” forbids it. Each quantity again gets its own name: 1 gram, double gram, demi dekagram, 1 dekagram, double dekagram, demi hektogram, double hektogram, and demi kilogram. This time I did not put the integer values next to the names. How did you do at identifying the values from their names? I’m sure the names were completely opaque. The modern nomenclature is much simpler. Remember, this chart was published by a group that was promoting metric, they were trying to help. They were trying to illustrate the simplicity of  “The New System.” This fact serves to imply how complicated are the old weights and measures, by comparison.

click to enlarge

For length they offer a four decimeter rule, which I guess is supposed to be a sort of metric foot size of rule. It is marked in decimeters with black and light brown patches which show centimeters, but no millimeters. It does identify that a Half-meter = 5 decimeters = 50 centimeters = 500 millimeters. They also offer a “Double Decimeter” length rule which is divided into centimeters and millimeters.

click to enlarge

In my view, these are all artifacts from the era when the metric system was created, but it was not understood how it might best be used. Clearly the chart did not need fractions for the volume, milliliters would have been fine with a reminder that 1000 mL is a liter. None of the names for each volume division are needed, and are not currently used. This probably seemed to make sense in an era where every commercial quantity might have its own measurement unit.  The grams could all have been shown as integers, and again there is no need to name each multiplication of a gram as shown. When illustrating volume, they started with the liter, and subdivided it with fractions. In the case of the gram, they started with it and used integer multiples. In modern use mL and grams make the most sense. We know that 500 mL of water is 500 grams, and the integer values match. The American Metric Bureau’s suggested use of the metric system in the 19th century offered familiarity, but not simplicity. The use of Naughtin’s Laws allows one to make metric the simplest and most intuitive measurement system so far devised. There is however one particularly egregious archaic metric holdout which still haunts our world.

Recently my long-time friend Ollie came upon myself conversing about metric with a few other persons at a table. Ollie has a background in Geology and Paleontology. She related that I should be very happy because at her Paleontology meetings all measurements are metric. I sighed and said “yeah, but I bet they do them all in centimeters.” She began to protest that using millimeters produced numbers that are “too big.” I reached into my pocket and obtained a mm only metric tape measure, extended it, and asked her to find the centimeters on it. She studied it carefully, and was clearly surprised and a bit confused that it existed.

Ollie was getting over a cold and was concerned that I might get it because she handled the tape measure. She ran to a rest room to clean it off. When she returned others asked her what she was doing:

Ollie: “I was washing it off so he would not catch my cold”

Maven: “No she wasn’t.”

Ollie: “Yes I was!”

Maven: “No, she was hiding in the bathroom measuring items with the tape measure and enamored at the simplicity of millimeters compared with centimeters. She just doesn’t want to confess it.”

Fortunately I came to no bodily harm. Ollie changed the subject before I could complete the explanation I had for her. I will now offer it here. Ollie had stated that 31.7 centimeters is easier to state than 317 millimeters. I want you to note how many symbols are used to write each number. There are four symbols in the centimeter expression, that is three numbers and a decimal point. In the case of using millimeters you have three symbols, and no decimal point. This clearly requires less typing or writing when using mm rather than cm. Your mind stops to note the decimal point, but sees the integer as a “packet.”

How do they compare linguistically?  Thirty-one-point-seven centimeters is eight syllables. Three-seventeen millimeters is six syllables. Wait! I might hear you protest, you cheated and did not use hundreds!  Ok. Three-hundred-seventeen millimeters is nine, so it took one more syllable using the hundred designation. Well, that way it is barely longer. I have no studies which compare the linguistic efficiency, but for the most part I think it’s pretty close whether one relates cm or mm values linguistically.

This form of argument was also enlisted against the use of metric pre-fixes, and the metric system in general in centuries past. It was stated the units had too many syllables. Yard or meter, kilometer or mile, micron or micrometer, it’s the same complaint. Actual understanding of measurement quantities is sacrificed on an imaginary altar to some innumerate linguistic deity. The same argument could be made about English in general. Suppose I say “I have a group of books” Why do I need an s? Why can’t I say “I have a group of book.”  The word group clearly tells me there are more than one book–it’s just extra! The great advantage of having the extra prose in a language is that it offers more and redundant information. This provides clarity.  A millimeter, milliliter, and milligram all tell us the division of the base unit is by one-thousand with three syllables. This one syllable shorter than one-thousandth of a meter. One can also directly write down the numerical values from the prose.

As I have said before, the centimeter is but a pseudo inch which is maintained for no good reason and complicates the measurements made by ordinary citizens. It is the hold-out on the 1877 metric chart which has not been exorcised. The centimeter needs to be banished to where-ever the decimeter, decameter and hectometer were exiled over the years. We can get along without them just fine, and with greater ease of use. Is a milliliter and a gram too small of a unit to use?—I never hear that argument. Would you miss the centigram or the centiliter if they were never again used? Then why would you miss the centimeter?—what makes it so special? Reject it! Choose simplicity over familiarity.

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

Related essays:

Doubling Down

Longhairs

Metamorphosis and Millimeters

Postscript:

The following conversation is from the BBC series Sherlock, “The Sign of Three” shown on Masterpiece Mystery! in the US and aired on 2014-01-26:

Sherlock: “Two Uh..beers please”

Bartender: “Pints?”

Sherlock produces two 500 mL graduated cylinders.

Sherlock: “Four-Hundred-forty-three point five milliliters.”

Apparently only the metric system is accurate enough to provide the perfect amount of beer for the famous detective and his partner Dr. Watson: 443.5 mL.

19 thoughts on “Familiarity versus Simplicity”

1. If the centimeter were purely an inch substitute, then they would only be used by English-speaking nations who have only recently metricated, or are still in the middle of metricating. This is demonstrably not true as French, Germans, and citizens of most long-metric nations use the centimeter for human height and clothing sizes. Since the whole point of the SI is internationally accepted and understood measurement, Americans must understand the centimeter whether or not you approve of their using it.

I would like to offer a softer rule for your consideration:
*If integer centimeter resolution is appropriate to the subject, centimeters may be used.
*If the subject demands decimal subdivision of the centimeter, millimeters should be used.

When you count symbols, you should not only count the numbers and decimals but also the unit symbols. Thus 31.7 cm is 6 symbols, 7 if you count the space. No naked numbers! There is one exception, not really approved in the SI Brochure, but widely used in engineering practice. A note on the drawing may designate that all numbers are in millimeters unless other wise noted, in which case 317 would be acceptable and understood to be 317 mm.

A few other random observations:
*”deca” is British spelling, “deka” is the preferred American spelling for the prefix (NIST SP 330). However, everyone agrees on the modern hecto spelling, not hekto as used in the illustration. Note that all preferred American spellings (meter, liter, deka) were established by 1877 (and are in the Metric Act of 1866).

*American labeling law (FPLA and UPLR) requires liters or milliliters for volume, deciliters and centiliters are not allowed. Therefore Americans tend not to use them. Other countries may require them, however, and again, Americans need to understand them. The 750 mL bottle of wine is 75 cL in the EU and UK. I sometimes watch a program called New Scandinavian Cooking on PBS and recipes frequently use centiliters and deciliters rather than milliliters. To be properly educated in the SI and able to understand prevalent international usage, Americans must be able to understand and process your much-hated prefixes, which should merely be “less loved.”

• I fail to see how another article that says the inch is an ambiguous unit says anything about the large number of metric countries that use the centimeter, at least for certain thing.

If you want to understand anything those people say, you have to know how the centimeter fits between the millimeter and meter. In the same vein, it is difficult to understand the standard definition of a liter if you don’t what a decimeter is. These prefixes have to be taught (but should not be overemphasized, certainly not to the exclusion of millimeters).

• Well, thanks for that — I think. You’ve reminded me of the different ways my high school teachers seemed to regard the “prefix cluster around unity.” Math teachers ignored it for the most part, while for English teachers it was an irresistible opportunity to display classical language pedantry. This seemed harmless enough at the time, even if it didn’t have much other justification, but nothing in contemporary metrication discussion seems to generate more heat than light than linguistic, orthographic — even typographic — minutia.

You may want to take another look at the link the Maven gave you, because there’s a graphic showing various “Inches of the World,” or at least Europe, wherein you may note references to many non-English-speaking cities and nations, which apparently had some form of inch, including the countries you named. Excuse some non-random counter-observations:

No one is suggesting the centimeter should be dropped down the memory hole, any more than the inch. But there is a point here, that no one seems to have been perspicacious enough to catch. The U.S. is now set to run dead-last in metrication, presuming it ever does cross the finish line. But if there are penalties for being last, there are also dangers in being first. That countries that metricated early retain features of former, less systematized, metric systems, is not surprising. So, if we have to be last, we might at least still make an effort to get it right. One obvious way to get things right, is to encourage further systemization of the prefixes. In doing so, we can hardly claim to be innovators, since the Australians have already come very close to doing this, but it would be something.

Centimeters, like inches, obviously must be taught if children are to be able to read books published in the last century. But that doesn’t mean they need to spend endless time trying to determine when the centimeter is “appropriate.” The classic example is, once again, Australian house building: the millimeter has been demonstrated to be entirely appropriate for all aspects of construction, from kitchen cabinetry, where millimeter tolerances are necessary, to rough concrete work, where even centimeter tolerances may be optimistic. Our advocacy is actually for something far “softer” than your own rule: by all means teach the kids that centimeters are out there, but then please let them off the hook: ”Yes, you need to know what a centimeter is, but you’ll never be marked down for giving an answer in millimeters. You can build a house in millimeters, kids.” And for all official, commercial, and industrial usages — as distinguished from colloquial — the centimeter can be deprecated as unnecessary.

The notion of “implied precision,” so often used as the justification for keeping the centimeter hanging around, is actually dangerous, even in non-engineering contexts. It is also ad hoc rationalization: I don’t think I’ve ever heard anyone demand the decimeter should be kept because there are times when centimeters are too small.

What I have heard is that we can’t possibly give up the decimeter because the liter depends on it. Even Kevin Wilks makes this bizarre claim in Metrication in Australia. It’s not true: the liter can as easily be described as a cube 100 millimeters on a side, or even as a “milli-cubic meter.” Either definition would be as comprehensible to non-scientists and non-engineers, and neither would entail the recalibration of any instrument. But neither is really necessary: the notion that the decimeter is suitable for everyday household use, because it holds a kind of quill-pen-and-parchment place in the statute books, is only more rationalization.

We are aware that the centiliter is used in alcoholic contexts. I’ve devoted considerable time to researching the issue at my local wine and liquor megamart, since this really is very odd. My conclusion is that wine sold in the U.S. is labeled in liters and milliliters, regardless of country of origin, but I have seen bottles in which “75cL” is molded into the glass at the base. These seem to be from certain French and Italian vintners, and my suspicion is that these just happen to be buying their bottles from a glassmaker whose molds carry that inscription. I’ve also seen UK products in this line online which carry a very odd dual labeling: 75cL / 750mL. And the International Bartenders Association is notorious for specifying cocktails in centiliters.

The unexamined logic — if that’s the word I’m looking for — may be that bartending has its own traditional measures, as various and ill-defined as the inch. That the centiliter should crop up here, and almost nowhere else, suggests something is going on very similar to the centimeter as a pseudo-inch. A case could be made that the centiliter is functioning here as a pseudo-pony, a pseudo-jigger, or a pseudo-shot. This would reinforce the Maven’s contentions, rather than refuting them.

• We shouldn’t teach children either centimetre or millimetres, but metres and the prefixes and allow them to scale numbers with the appropriate prefix so the number falls withing a sensible number of digits without a plethora of decimal dust.

Teaching centimetres and millimetres, etc as independent units is akin to teaching them feet, inches, yards, etc.

This is why the break with bad USC habits persists.

• Actually, I would say that the Metric Maven has repeatedly advocated throwing centimeters down the metric hole, a position I disagree with.

I am NOT advocating that they be supreme and replace millimeters.

I can agree with your remark “”Yes, you need to know what a centimeter is, but you’ll never be marked down for giving an answer in millimeters.” Millimeters are always acceptable, at least to 99 999 mm, maybe further, and are widely used “naked” in engineering in this way. However, I am ALSO saying integer centimeters (labelled) may be acceptable in certain contexts.

I am not insisting they must be used, although I am insisting an individual properly educated in the SI should understand them when they are used. I am also NOT advocating that certain industries must abandon them (when only integer centimeters are used).

Another position that bears on this is the liter/cubic decimeter. I don’t really agree, but some argue only the cubic decimeter should be used, not the liter, or that the liter should be used only for fluid volumes, the cubic decimeter for dry volumes. The SAE advocates that volumes of luggage compartments be given in cubic decimeters, but no one follows this advice, manufacturers use liters. Again, everyone should at least understand they are two words for the same thing.

The SI is defined by the SI Brochure, and where it allows options, I don’t think it is appropriate for the rest of us to say one option is required and the other forbidden. It is OK for a nation to say one is preferred and the other acceptable.

• Sadly, also the kilometer is often used as a pseudo-mile: for example, the average distance between the Earth and the Sun, i.e. the AU, is almost always defined as about 150 million kilometers, rather than 150 Gm (gigameters), as it should be if SI were used correctly, with its formidable prefixes.

So, also this not going above the kilometer for measuring distances is yet another example of a “customary” – or “lazy” – use of the SI.

One of the few fields where the “big” prefixes are used in everyday life is with computers: e.g., hard disk capacities, now in the “tera era”.

There’s still a long way to go before SI will become really mainstream and used as it really should, thus…

2. A 443.5 mL beer? What a daft size. I wonder if this is an accidental Americanism by the BBC as it is 15.00 US fl oz or 15.61 Imp. fl oz to reasonable rounding.

3. In any science exercise I was a part of in school, and now in my professional life as a pharmacist, I used, and use, ONLY milliliters to subdivide the liter. It is both a matter of convenience to the healthcare worker and a matter of patient safety that only one decimal fractional unit is used. It’s all in the integer. Integers are just simpler to work with.

My Australian friend Mike Joy introduced me to room diagrams in which the millimeter is assumed to be the submultiple of the meter, so each room in the drawing was marked, for example, “10,000 x 4,000″ or 11,000 by 8,000.” Want meters? One can simply “see” where the deciimal point belongs. Utter simplicity of use.

4. Must point out one minor mistake that would not make your English teacher/s proud. It should be “altar,” not “alter,” I believe, in the next to last paragraph. Glad to see the post by Paul Trusten, I ,too, am a member of the U.S. Metric Assoc. I agree fully with him about both the safety, simplicity and convenience in medicine to use one factor. In medic training in the U.S. Army and later on in both hospital and field experiences, this point was demonstrated many times. I also used it in my work in civilian hospitals as both a lab technician and even more so later as a pharmacy technician. Looking forward to your future posts Maven.

• Thanks Woodie, a spell checker is not a content checker. I re-learn that often.

5. From webmd.com regarding blood sugar levels for diabetics: “At present, the diagnosis of diabetes or prediabetes is based in an arbitrary cut-off point for a normal blood sugar level. A normal sugar level is currently considered to be less than 100 mg/dL when fasting and less than 140 mg/dL two hours after eating. But in most healthy people, sugar levels are even lower.” I guess they figure it is easier to do mg/dL rather than mg/10cL or mg/100mL or even g/L. Diabetics and doctors seem to be ok with it.

Deci isn’t used in as many places, but is used. Centimeters are often used in the medical industry. A visit to a non Australian country would reveal that centi measures are quite common. The countries I’ve visited (South Korea, Japan, Malaysia, Philippines, Thailand) use the centimeter as a standard unit of measure along with kilometers, meters and of course millimeters. Apparently they accepted it as part of the metric system and nobody told them that the centi was an evil thing. If you’re really opposed to all things centi, you can send all your centidollars my way. 😉

• BTW, up until 20-30 years ago, it was mg/100mL, with mg/dL now the common standard.

• Thank you David. I didn’t know. All I know is what my presently diabetic family and friends report. I was unaware of previous measures.
Be well.

• Actually, the international standard for measuring blood glucose levels is mmol/l, with mg/dl as yet another US throwback, albeit a metric one.

6. Maven, you may find this article to be familiar with what you are discussing.

The advantages attributed to metric usage can only be truly realised when customary habits are removed from metric practice.

Your war against the centimetre is based on the flawed assumption that the centimetre is a unit. It isn’t. The centimetre, millimetre, kilometre, etc are not units, the metre is. Unlike previous measurement unit collections, SI is radically different. SI is structured on a coherent and consistent set of units and a set of scaling prefixes. When we don’t recognise this we are trapped into thinking each prefixed unit is in itself a unit, then we are thinking customary, not SI.

The function of the BIPM is to construct, maintain and lend legitimacy to the SI. It is not there to tell users what prefix works best for them. That is either an individual choice or the decision of an industry. This is something you need to come to grips with.

In the world of engineering the prefix milli used with the unit metre is the perfect choice. You are correct in this aspect that centi would not work and must be avoided. The entire engineering discipline is in agreement with this.

But neither you nor I should force the prefix milli in applications, such as clothes sizes or personal heights if centi is perfectly useful. That doesn’t imply that clothes should be made using the centi prefix as clothes manufacturing is an industry and in manufacturing the milli prefix is the most useful and wise.

The key factor here is that the BIPM, the guardians of SI only have the job of assuring the units and prefixes available are defined and supported, but it is the user who determines the proper combinations of units and prefixes based on their experiences.

I hope this makes the situation clear to you.

• Nope, the “war” on the centimeter is driven by one thing only, something much less arcane: unabashed laziness. We see this as having positive survival value for the species — at least in this instance: it saves energy for running from predators.

Suppose you need a widget. You go online, and find a couple of widget manufacturers. Company A lists its product line in a table from 175 to 360 millimeters in diameter. Company B offers widgets ranging from 17.8 to 48 centimeters. Which company makes bigger widgets? Smaller? Congratulations, I’m sure you got the right answers, but to get them you had to perform unit conversions. That is, you had to apply factors other than unity, either mentally, on paper, or with calculator. Not only is this extra work, it’s extra opportunity for error.

The “flawed assumption that the centimetre is a unit”???? Excuse me, but what you are calling flawed assumption, we see as accepted definition. That centimeters are scaled from a base unit, does not diminish their “unithood,” any more than in the case of the millimeter and the kilometer — and you may have noticed that we really like those. To deny the centimeter its common appellation of unit seems to go well beyond your usual linguistic captiousness, and well beyond our dislike for the thing. It sounds downright dangerous. It would imply that 1.0 m was a length, while 100 cm was a dimensionless number.

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