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The New Traditionalists

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By 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.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.

The Count Only Counts — He Does Not Measure

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By The Metric Maven

Bulldog Edition

In many television programs about mathematics that involve weights and measures, one is often taken to an open air market. The presenter will immediately seize upon the utility of numbers which have numerous divisors. The number twelve will be immediately enlisted. If one has a dozen eggs, then it can be divided up by 1, 2, 3, 4, 6 and 12. Often they move on to describe the amazing number of ways that 60 may be divided: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60, which is why one has clocks with 60 seconds in a minute, and 60 minutes in an hour. One can imagine oranges, apples, pears and such all being sold in integer groups. Often it has been my experience that a person can purchase any of these fruits in any number they wish.

When one considers purchasing walnuts, they are small enough that counting them out begins to tax one’s time. It is still possible, but selling them in 60 walnut quantities takes time to count out. It also takes time for the purchaser to count them out, and make certain that all 60 walnuts are in a given bag.

Wheat is a commodity that like oranges, eggs and walnuts, exists in integer units, but the individual grains are so small that the amount of time needed to count out 7000 of them, which was the definition of a pound, is prohibitive. Do my seven thousand wheat grains each have the same mass as those used to define a “grain“? Counting out seven-thousand grains definitely takes a lot of time, and checking each one against a “standard” grain would be untenable. Of course, one could count out 7000 wheat grains and then use a balance to compare a bag with 7000 grains to one which you are pouring into a second sack. When the balance is level, a naive consumer might assume that the two bags contain exactly the same number of grains. Who is going to take the time to count?

On closer examination, one knows that the reference bag has 7000 grains, but because of the variation in the masses of individual grains, perhaps because they came from a location far away in a country with different growing conditions, the new bag might contain more than 7000 grains, they are just smaller, and each possess less mass. This is the beginning of the idea of measurement, versus the notion of counting. People seem to realize that the same amount of “stuff” is in each bag if they balance, even if the individual grain count does not match. The question is, who’s bag of 7000 grains should be the one used by everyone as a standard?  This is where the modern notion of measurement begins to appear.

One can’t be certain that the number of grains in all the bags are equal to the seven-thousand in the “standard” bag, but instinctively people seem satisfied that the same “amount” of wheat has been meted out.

Illustration of Hooke’s Law (Wikimedia Commons)

Robert Hooke (1635-1703) was the first to note that the length of a spring, within limits, is directly proportional to the force of an object which hangs from it. We can take our 7000 wheat grains, hang them from a spring which obeys “Hooke’s Law” and use the length the spring stretches, using our standard, as a known “calibrated” point. In the case of a spring we could put a pointer on the spring, and then place a mark at zero, when no grains are being measured, and a mark at 7000 wheat grains. A graduated scale can be placed behind the pointer. The location of the pointer is no longer restricted to single units of grain, it can point to an infinite number of locations along the scale distance from zero to seven thousand wheat grains. The divisions on the scale can be subdivided at will to produce more and more precision. We have stopped counting, and have begun to measure.

Sylvester and Bird Seed

We can define seven-thousand wheat grains in terms of an indirect abstract quantity, not attached to a specific concrete item, such as cloth, grain or wood. This proxy quantity of “general stuff” we call an avoirdupois pound. The pound can in turn be used as a reference amount for a measurement of the quantity of any substance, corn, wheat, fish, bird seed or whatever. A person can fabricate a metal object which deflects the measurement pointer by the same amount as the wheat grains which make up a pound so that we can have a more stable, reproducible, and reliable standard.  A second check can be accomplished by using a balance to make certain the two objects, the grains of wheat and the piece of metal, have the same amount of “stuff” in them. We call this abstract amount of stuff “mass” these days. So now we have created a one-pound mass for a standard, and we can measure commodities to as much of an exactness as we can produce graduations for the pointer to point at, and resolution for our eyes to read.

Once again, it is a problem to decide whose bag of wheat grains is used to determine which piece of metal is considered a pound. The history of weights and measures is generally a history of fraud and deceit. The definition of a standard value of mass, was not very standard, and variations could be used to cheat when trading. Below is a table of all the competing standards for a pound that I could locate:

They vary from 316.61 grams to 560 grams.

So what do we do?  Well, John Wilkins (1614-1672) originally defined his unit of mass, which would later be known as the Kilogram, as a cube of water with sides which are one-tenth of of his base unit. This base unit, with a different definition, would later be known as the meter. In other words, a cube of water with 100 mm sides is the original mass standard for the metric system. A cube of pure water, at a given temperature, made sense, but again, temperature could affect this definition. The temperature of water’s maximum density was chosen as a calibration point. When the value of this mass was determined by the French, during the development of the metric system, it was preserved in a more practical way, as an equivalent mass of platinum-iridium alloy. The relative of this agreed-upon mass is the International Prototype Kilogram (IPK).

The point of measurement, versus counting, is that it produces a continuum of available measurement values, and this value is independent of integer, or discreet values of poppy seeds, wheat seeds, barleycorns, bird seed or anything else. Once one has an agreed upon unit of mass, such as the Kilogram, it may be indefinitely subdivided. An easy way for humans to subdivide this base value, is by using 1000’s. The measured value is found on a continuum of available values, which can be further divided if needed. This is not counting by any stretch of the imagination. It is measurement. The argument for a choice of a numerical base which has lots of divisors is of no import when you have a continuum of possible measurement values.

So is the idea of using numbers which have lots of divisors irrelevant to the metric system? No, they are only irrelevant to metric system measurement. When metric units are chosen such that the amount of precision needed for everyday work is slightly smaller than required, integer values again become important. What I mean by this can be illustrated with metric housing construction in Australia and the UK. In order to make the description of lengths easy, we choose a unit length which in all practical circumstances will always be an integer. The unit chosen for construction is the millimeter. The millimeter is small enough that one never needs to use a decimal point in everyday construction. We have chosen to go back to integers (simple whole “counting” numbers). This is converting measures back to countable “atoms” of measure.

We use our modern measurement system to define a small length value, the millimeter, which is solidly known, rather than using a pre-metric small unit which varies—like a wheat or barlycorn grain. When we use this small unit to produce integers, we can use convenient values which indeed have lots of factors for division. In the case of metric construction, the value chosen is 600 millimeters for stud spacing. Its factors are:  1 2 3 4 5 6 8 10 12 15 20 24 25 30 40 50 60 75 100 120 150 200 300 and 600. What we are doing is not exactly measurement when we construct a house, it is equating multiples of integer values with multiples of a measured integer value, which is a different exercise. When we do this, it makes perfect sense to choose lots of divisors. With millimeters we have “atomized” the values on the construction drawings we are using to guide us. If we want to add in features, such as a window, not originally present on the drawing, or when initially creating a drawing, chances are that we will be able to divide the newly inserted distance easily. This is because of the conscious choice to use small units which can remain integers. We are not measuring in this case, we are back to counting.

Of course as we spent more time measuring our world, we discovered that it is actually discontinuous when it comes to fundamental values of mass. John Dalton (1766-1824) realized and demonstrated that the world is made of atoms. Each individual atom has a defined mass, but the same type of atom can have a range of masses. For instance, tin has atoms that are all chemically tin, but possess ten different mass values. These different mass variations of chemically identical atoms are called isotopes.  Tin has ten isotopes, cesium has thirty nine!

Silicon Sphere — The Commonwealth and Industrial Research Organization of Australia (CSIRO) — cc (creative commons)

One of the candidates to replace the current Kilogram standard, which is still an artifact from the nineteenth century, is the silicon sphere. This is a sphere of silicon atoms that will contain a known number of them. If a person knows the mass of each atom in the sphere, and their total number, it can be used to define a mass. In strange way, this procedure is similar to using 7000 wheat grains, but in this case we know that if an atom of silicon is of the same isotope as all the others in the sphere, it possesses a mass which is identical to all the other silicon atoms present. One of the largest difficulties for the team which is attempting to make a silicon sphere Kilogram mass standard, is making certain that all the silicon atoms present within the sphere are of the same isotope. Silicon 28 is the chosen isotope the silicon sphere team will use to create a new Kilogram standard—after counting all the atoms of course.  We are counting an integer number of atoms, so that we can develop more accurate continuous set of measurement values, just as was done in the past with wheat grains. These values, which are continuous subdivisions of mass when compared with the discreet values of the atoms in the standard, may be used for the measurement of values which are smaller than the silicon atoms used.  But remember, counting is not measuring.

If you liked this essay and wish to support the work of The Metric Maven, please visit his Patreon Page and contribute. Also purchase his books about the metric system:

The first book is titled: Our Crumbling Invisible Infrastructure. It is a succinct set of essays  that explain why the absence of the metric system in the US is detrimental to our personal heath and our economy. These essays are separately available for free on my website,  but the book has them all in one place in print. The book may be purchased from Amazon here.


The second book is titled The Dimensions of the Cosmos. It takes the metric prefixes from yotta to Yocto and uses each metric prefix to describe a metric world. The book has a considerable number of color images to compliment the prose. It has been receiving good reviews. I think would be a great reference for US science teachers. It has a considerable number of scientific factoids and anecdotes that I believe would be of considerable educational use. It is available from Amazon here.


The third book is called Death By A Thousand Cuts, A Secret History of the Metric System in The United States. This monograph explains how we have been unable to legally deal with weights and measures in the United States from George Washington, to our current day. This book is also available on Amazon here.