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.

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.

The Metric System and Innumeracy

By The Metric Maven

Bulldog Edition

Many years ago, while attending a conference promoting science and scientific skepticism, I unexpectedly found myself interviewed by a reporter for a print newspaper. Her countenance revealed she did not either like the fact she had been given this assignment, or that she really didn’t care for the people there gathered. With a slight amount of impatience she asked me just why it was important to be skeptical. I replied with a question: “Suppose I told you that 350 million Americans purchased a car last year. Should you believe me?”  The woman looked at me with a slight amount of alarm and said “well, it depends on who said it.” I told her that was exactly the wrong answer for a scientific skeptic. She challenged me to explain what I meant. “Well,” I said “How many people are there in the United States?” She paused, and thought and thought. I finally said “About 315 million. [I changed both numbers to reflect today’s population estimate] “Did more than every person in the US including children all purchase a new car last year?” Her facial expression and statement appeared to indicate both “oh, that’s common sense, and you’re just being a smart-ass.” Obviously that exchange was never included in her newspaper article.

Not long before this conversation, I had read discussions about innumeracy  in an essay by Douglas Hofstater and in the book Innumeracy by John Allen Paulos. While I do not recall the particular information in either person’s works, I do recall some points they made which have remained with me. One of the most important was, know how many people are in the US, in your state, in your town. This will allow you to evaluate statements and assertions for numerical reasonableness. What these authors impressed upon me was that innumeracy starts with counting, and the ability to judge magnitudes of numbers, and to relate them with other important numbers. A person who does this can often find themselves on the wrong end of an emotional outburst. Innumeracy is something most people ignore and it is not seen as embarrassing—like illiteracy is—until innumeracy is revealed. People who cannot read are so ashamed they hide it. Often they cannot often admit they have a problem, and begin dealing with it. Innumeracy is assumed to not even exist in the minds of most people, so when it is revealed, the reaction can be visceral.

When I was taking Driver’s Education many moons ago, I heard the statement: “Most accidents occur within 25 miles of your house.” I immediately pointed out that most of us seldom drive further from our residences than that over the majority of our lives. I was told in no uncertain terms that most people thought accidents occurred on long car trips. “Why would they think that?” I thought. To this day I’m not certain why people would. But I do suspect it’s a form of innumeracy.

I often hear people who are interviewed about an accident or other common occurrence on television say with certainty: “it happened about 250 ft that way” or “the creek is about 200 yards over there.”  I have my deepest doubts that if one measured them, that the distances would be anywhere close to the distances quoted. One way to make a bad innumeracy problem worse, is to proliferate and use units that have no logical relationship. If I asked the person who had just given me the 250 ft estimate to guess that value in yards, I’ll bet it would take some cyphering.

While the metric system cannot by itself solve innumeracy, it can help to reduce it because of its continuous spectrum of overlapping prefix magnitudes. If a person said “it happened about 250 meters away” shifting to kilometers would be easy: 0.25 Kilometers, and it would be easy to realize this is also 250,000 millimeters away. It could all be done in one’s head. Metric has a logical overlapping continuum of values which are designated with standard prefixes. One does not have the strange numerical discontinuities of three barleycorns to an inch, twelve inches to a foot, three feet to a yard and five thousand two hundred and eighty feet in a mile. The Ye Olde English units used in the US only serve to preserve innumeracy in the same way that Roman Numerals preserved the inability to multiply and divide effectively until the advent of Arabic Numerals.

I have explained in an earlier blog how the use of Metric Ton or Tonne by members of the press obfuscates a person’s ability to relate the magnitudes of quantities reported by the media. The metric prefixes (without the prefix cluster about unity) allow for quick comparisons of magnitudes when they are used. Micro, milli, kilo, mega, giga, tera and peta, these should all be known and understood instantaneously to a numerate public. They are magnitude bins that one can immediately use to sort sizes and compare them. They form a measurement continuum with a simple relationship (i.e. 1000). How many people populate the US today? 315 MegaPersons. In 1900 it was 76 MegaPersons  In 1800 it was 5.6 MegaPersons. The first official census was in 1790 and totaled 3.9 MegaPersons. We can see that from 1790 to 1990 we went from 3.9 MegaPersons to 249 MegaPersons. How much bigger is a 250 MegaByte computer disk drive when compared to a 4 MegaByte? It’s quite a difference isn’t it.

So what about the top ten countries for population? How many people do they have?

China 1354 MegaPersons (or 1.35 GigaPersons)
India   1210 MegaPersons (or 1.21 GigaPersons)
US    315  MegaPersons
Indonesia 237 MegaPersons
Brazil 193 MegaPersons
Pakistan 183 MegaPersons
Nigeria  171 MegaPersons
Bangladesh 153 MegaPersons
Russia 143 MegaPersons
Japan 127 MegaPersons

The world’s total population is 6950 MegaPersons (or 6.95 GigaPersons)

If we include the Tiny Two:

Liberia 3.5 MegaPersons
Myanmar  39 MegaPersons

This gives us 358 MegaPersons who are not in metric countries and 6593 MegaPersons who are. Now remember, 6.593 GigaPersons is 6,593 MegaPersons and 6,593,000 KiloPersons or 6,593,000,000 Persons.

For people in the US we could make this world population clearer for them by starting with 6,950,000,000 inch-persons which is 579,400,000 foot-persons and 193,133,000 yard-persons or 1,316,000 mile-persons for comparison. I’m just making sure my fellow Americans can understand the values after the onslaught of the completely incomprehensible metric prefixes I used. I’m sorry I didn’t start with Barleycorns, but my understanding is we use the inch as our base now—well actually 25.4 mm since the Anglo-Saxon compromise of 1959.

One argument made by anti-metric people is that changing to metric would be “cost prohibitive.”  Well, let’s do some estimates which relate to the costs of not going metric. The Australian construction industry has saved about 10-15% on building costs since their switchover in the 1970s when compared to using Imperial. Suppose for a moment, we pretend that John Shafroth was able in 1905 to convert over just our US building industry to metric (with millimeters). Well that’s about 100 years ago. In recent years construction is about 5% of GDP. We can add up the GDP (in today’s dollars) over each year for the last 100 years and take 0.5 percent of it (10% savings of the 5% construction of the GDP [or 0.005]). That’s clearly a large waste of money we’ve tolerated over a century, in just one sector. The total GDP from 1905 to 2000 is about 25,000,000 Trillion dollars total so we are talking about 125,000 Trillion dollars of wasted construction value in the US. Do these numbers just seem too large to be correct?  Well how about just using last year’s estimates for GDP which is 13.67 Trillion dollars. Let’s just use 13.5 Trillion and take 0.5% (0.005) which is 0.0675 Trillion or 67.5 billion dollars wasted, just last year! And these losses are only for one sector of the economy which does not use metric. And, as we all know, 50 billion here, and 50 billion there, and pretty soon we’re talking real money. Knowing that we have around 300 million people in the US, it therefore costs every person about 225 dollars each year. Wouldn’t it be better to not have that expense and save the money instead.

Anti-metric people in Australia offered their own estimates to show the public that switching to metric was simply out of the question, because it cost too much. In Metrication In Australia  it is related that:

Opponents of metrication sometimes claimed that its cost in Australia was $2 500 000 000. This amount was first suggested in 1973 and had not been amended by 1982. It was clearly an estimate not based on facts, and in view of the difficulty the Board had in obtaining reliable figures, it seemed highly unlikely that a less well equipped organization could have been more successful in this regard.

Even assuming, for a moment, this cost to be accurate, it represented $179 per person or $18 per person per year for ten years which was a small enough cost compared with the benefits which resulted from metric conversion.

Dear Abby Column from 1977 (click to enlarge)

So even using the numbers offered by the anti-metric people in Australia, which I suspect were, considering their view, hysterically padded, the costs for one-year for a metric conversion would have been $180 per person. This is a one time cost. In the US, just for construction alone, this would be amortized in one year, and from that point on  it would all be savings. In ten years each person in the US would save $2,250 – $180 (using the value produced from the out-of-the-rear-end anti-metric Australian estimate) or $2070. I still see anti-metric people in the US just state with authority on threads that “metric conversion would cost too much money” and believe the discussion is over. It is—if you are innumerate and truth depends on who makes a claim. Every time metrication has occurred in a rational manner, it has saved money for the country which has implemented metric. You can count on it.