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.

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Related essays:

The Design of Everyday Rulers

Stickin’ it to Yardsticks

The American “Metric Ruler”

America’s Fractional Mind

The New Traditionalists

New-TraditionalistBy The Metric Maven

Bulldog Edition

One of the great legacies of Pat Naughtin, in  my opinion, is his willingness to examine traditional usage of the metric system, and suggest improvements. Before I encountered his writings and lectures, I had been inculcated with the idea that when one crosses a prefix boundary, there should be an abrupt transition to the next prefix. If my last data point was 900 meters, and the next data point is 1200 meters, then one should write down 1.2 km instead of 1200 meters. I believed that this rule had been carefully considered by academics at my university, who were much wiser than myself.  Their other admonition, no concatenated prefixes, no micromicro or kilomega, made good sense and so I thoughtlessly swallowed their prescribed use of the metric system whole. Over the next couple of decades of my career, this metric dogma had become fixed. Because I mostly used inches, pounds and such at my place of employment, metric was just an internal abstract concern. My theoretical work was computed in pidgin metric, but the final number would be expressed in Ye Olde English representation. Pat Naughtin encouraged me to question my basic assumptions about metric usage. My consulting work gave me the opportunity to embrace metric exclusively. I was then able to try out Naughtin’s suggestions and develop my own thoughts. It was liberating.

From the beginning of my blog, I have made a considerable number of metric proposals. Some are ideas that would require government coordination to achieve, others could be adopted by individuals. Here is a list:

Some of these suggestions were met with minor brouhaha’s. Often BIPM documentation was cited, chapter and verse, and displeasure expressed. I continue to use these, and seldom do readers make much of a fuss these days. These have become so comfortable, they’re invisible to me.  So it came as a bit of a surprise when I read this from a metric advocate[1]:

“Don’t use centimeters!” “Use only the millimeter!” go the cries from would-be metric purists over which scale of reference to use in a particular measurement situation. Add to these screeds those who would adhere to “units” that find their definitions in metric terms such as “the” Angstrom and “the” micron, and one has a customary system within the SI. This is not the plan envisioned by the architects of the international measurement system. SI units were meant to thrive on newfound logic, not newfound tradition.

The word purist is defined by the Merriam Webster Dictionary as:

a person who has very strong ideas about what is correct or acceptable and who usually opposes changes to traditional methods and practices

This definition applies to someone who opposes change. Eleven examples of suggested change are summarized in the bullet points above. I’m clearly on the side of change. One of the proposals is to eliminate the use of centi. In my view, to argue for the use of centimeters, in the light of the millimeters proven usefulness, is to be a slavish follower of tradition.  A person advocating nothing but the status quo is a purist, but a better term might be New Traditionalist. The archives of the association this New Traditionalist represents, document the anti-utility of centimeters. This hard earned realization has apparently been sacrificed on an altar of tradition and amnesia. The centimeter is back.  Strangely, New Traditionalists do not call for the use of earlier traditional metric quantities, such as the myriameter (10 000 meters), or the double deciliter, demi-deciliter, double centiliter, double gram, demi dekagram, double dekagram, demi hectogram, and so on. A myriameter is based on ten, just like the centimeter, why don’t we need a myriameter?

At least he agrees with me that the angstrom and micron should be banished—I think. The prose is rather opaque. I guess he is saying that people like myself are trying to create a replacement tradition without any rational basis behind it? I have explained my reasons for the proposed changes in considerable detail. I’ve provided links in the bullet points above to blogs that explain my rationals.

Only a New Traditionalist, would defend a “…plan envisioned by the architects of the international measurement system” that includes the use of tonne with SI. First, tonne is easily confused with the Ye Olde English ton (long or short) because it is a homophone (i.e both ton and tonne have the same pronunciation). Second, the use of a metric prefix with tonne, is obfuscating. For example, the use of Kilotonnes undermines numerical comprehension. When one encounters 39.37  Kilotonnes, and then wants to actually use this value in a metric computation, it must be first be recognized that a tonne is a Megagram. Then we apply the Kilo prefix to obtain KiloMegagram. This violates the BIPM commandment “thou shalt not concatenate prefixes,” but is accepted for use with SI? This is the plan envisioned by the architects of SI?—based on logic?

The simplicity of the metric system is buried when one has to decode an “accepted” metric expression. For example, the number of grams in 4.7 Gigagrams is straightforward, it is 4.7 x 109 grams, the number of grams in 4.7 Kilotonnes is not. New Traditionalists apparently are fine with the idea that the tonne is not part of SI, but is accepted for use with SI. It is ignored that when tonne is used with metric prefixes, it automatically violates the rule against concatenating prefixes. This is a practice the New Traditionalists apparently embrace with exaltation as part of “..the plan envisioned by the architects of of the international measurement system.” The lack of rational usage one finds with the implementation of the tonne in SI is epic. The dead weight of tradition is obvious when the tonne is logically examined. It appears New Traditionalists want to save SI from improvement and clarity. Tonne is clearly “a customary system within the SI”, but there is no objection from the New Traditionalists.

It is further stated:

However, there is a certain amount of facility that one, both as a user of decimal arithmetic and also eventually as an SI citizen, develops in placing the decimal point.

The fraction or multiple of the base unit should be selected by the eye and the mind, and not by heraldic prescription.

I guess the first statement is simply a claim that it is easier to use decimals when one uses decimals? If one doesn’t need to use decimals at all, isn’t that easier?—and in the case of millimeters for everyday work—empirically demonstrated to decrease errors?  This does not seem apparent to New Traditionalists. I find this blind spot as baffling as those who don’t see how much easier decimals are to use than fractions. Everyday people have the choice of using the side of a ruler with decimals, or a side with fractions. People in the U.S. continue to use the ruler side with fractions instead of the side with decimals.  I’m sure New Traditionalists find the fact that people don’t seem to see this obvious decimal simplicity, and use the decimal/centimeter side of a US ruler, as confounding as I find the New Traditionalists not realizing that integers are simpler than decimals, and therefore millimeters are the obvious choice.

Centimeters seem to have become a kind of fetish for The New Traditionalists. Curiously, there seems to be no fetish for centigrams dekagrams or centiliters. No chemist, or average person argues that we need to use centiliters with decimals instead of milliliters alone for volume, or centigrams dekagrams with decimals in place of grams. Why would we complicate metric length by using centimeters with decimals, when millimeters perform the same simplifying function as milliliters and grams? The choice of milliliters allows for the use of whole numbers when dealing with volume, as does the use of grams for mass. Millimeters should be an obvious choice, but for New Traditionalists, they seem to be as un-obvious as decimals are for the users of Ye Olde English fractions.

Decimal representation is absolutely essential to my engineering work, and when needed, nothing better exists. But for everyday use, it should be clear to any average person that using whole numbers on a millimeter scale is much easier than using whole numbers combined with a fraction involving 1/2, 1/4, 1/8 or 1/16. A millimeter ruler automatically has a precision of 1/25th of an inch!—and it’s much simpler to use! I don’t see how any of my metric usage suggestions are a form of medieval “heraldic prescription,” that might have been produced at an SCA meeting. As longtime readers know, I’m very much against Ye Olde English.

The New Traditionalist further states:

It is not expected that humankind will memorize the entire list [of prefixes] and be prepared to refer to it mentally when challenged to select a frame of reference.

Humankind faces a considerable number of challenges that require as much numeracy as possible—if we are to confront them rationally. Global Warming is an existential threat. The late Pat Naughtin demonstrated that with well selected metric prefixes, quantities relevant to understanding global warming, can be readily understood in relation to one another and evaluated by anyone.

Currently sea level is rising about 3-4 millimeters per year. Since 1880, tide gauge records show there has been a 200 millimeter cumulative increase in sea level. The total amount of water in the Earth’s ocean is about 1386 Exaliters. The area of the Earth’s ocean is about 335 square Megameters. With these values, we can compute an average ocean depth of about 4.14 Km. The 335 Mm2 area of the global ocean has increased its depth by 200 mm. If we multiply the total area of the ocean by the increased depth due to global warming, we arrive at the total increase in the ocean’s volume. This works out to an additional volume of about 67 Petaliters over the last century. The total amount of fresh water on Earth is about 109 Petaliters. The majority of the water entering the oceans is from melted ice. This water is drinkable; but when it is mixed with the ocean it becomes unfit for human consumption. There is not enough fresh water to dilute the ocean enough to make it drinkable. I made this point in my essay To Infinity….and Beyond. The additional amount of fresh water lost to our salt water ocean each year is about 670 Teraliters. This is drinkable water lost to humanity because of global warming. The amount of drinkable water on Earth is already critical. A minute amount of this increase in sea level is from the warming of the oceans, but with these values, and metric numeracy, one can readily estimate important quantities. The loss of naturally stored drinkable water each year is clearly an important quantity.

In this country, we readily make up songs to recall the names of all the 50 states. It would seem to me that developing a song, and teaching all 16 metric prefixes, from grade school through high school, is not asking much. Each prefix could have the size of an object in the song for reference. In my view this would be a much more worthwhile exercise than using a song to learn the names of the first 44 Presidents of the U.S. We can all recite our abc’s, and their are only 26 of them. Sixteen metric prefixes should not be a problem. I cannot see why New Traditionalists would excuse our populace from naming and committing to memory, all the metric prefixes, and understand their relationships. The issues we face as humans are more and more intertwined with science and engineering. The more directly a populace can understand quantities involving peak oil and energy or water resources and global warming, the better chance we have of making informed decisions. Rather than passively deferring these decisions to others, who may have conflicts of interest, people need to be informed. Promoting an ignorance of large metric prefixes, is truly the purview of New Traditionalists. Exclusively using only the prefixes that existed before the microscope and telescope were invented, only preserves the limited intellectual scope found within the mind of the 17th century, when we are confronted with 21st century problems.

When I look at the metric system, I see possibilities for improvement and streamlining. I argue for my position as rationally as possible. New Traditionalists embrace stasis and the apotheosis of current BIPM rulings. When people in the U.S. started using the capital letter L for liter when writing milliliters (mL), I’m sure there were New Traditionalists who were against this altered usage worldwide. Eventually the improved clarity of the new symbolism was realized and accepted. Reflexively defending the status quo, when better options have been proposed, is defending tradition and thoughtless obedience. It is the opposite of scientific discourse, it is theological discourse.

[1] Metric Today Volume 50 Number 5 September/October 2015 Page 3.

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