Category Archives: Metric Reform

Metric Wishcraft

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By The Metric Maven

In response to an Op-Ed I wrote promoting the metric system, one commentator stated in opposition to my proposition:

Also saying electricity and gas are measured in improper units then says they should be in gigajoules….kilowatt-hr  and BTUs are amounts of energy just like joules. You can convert BTUs to kWhs and kilowatt hr is metric.  He’s an “engineer” he can convert easily between the two

The internet has provided a place where any immediate thoughtless ejaculation of words can be posted. This concatenation of confabulation was no exception. The specific assertion that caught my attention is his statement that a “kilowatt hr is metric.” Well, I’m afraid I’d have to demur. A kilowatt is metric, and when expressed by this “engineer” in a more fundamental manner is 1000 joules per second. So far, so metric. There is a problem however with multiplying a joule/second by an hour. This will produce joule*hours/second, which is not good dimensional analysis. The base unit for time in the metric system (SI) is the second. An hour is not a metric unit, and multiplying watts by hours immediately disqualifies Kilowatt-hours as a metric expression.

I can only assume that the BTUs were brought up as the units this “commentor” assumed are used for natural gas. My gas bill has the energy of natural gas designated with therms. There is not a BTU to be found. If there were BTUs they would very likely be designated with MMBtu or mmBtu which are one million BTUs. Why the MM or mm?—well Wikipedia—what do you have to say?:

The unit MBtu or mBtu was defined as one thousand BTU, presumably from the Roman numeral system where “M” or “m” stands for one thousand (1,000). This notation is easily confused with the SI mega- (M) prefix, which denotes multiplication by a factor of one million (×106), or with the SI milli- (m) prefix, which denotes division by a factor of one thousand (×10−3). To avoid confusion, many companies and engineers use the notation “MMBtu” or “mmBtu” to represent one million BTU (although, confusingly, MM in Roman numerals would traditionally represent 2,000) and in many contexts this form of notation is deprecated and discouraged in favour of the more modern SI prefixes. Alternatively, the term therm may be used to represent 100,000 (or 105) BTU, and quad for 1015 BTU. Some companies also use BtuE6 in order to reduce confusion between 103 BTU and 106 BTU.[8]

Reduce confusion??? Ok, I think I can summarize that the BTU is a completely ill-defined, readily confusing non-metric unit, which can be expressed in several non-intuitive ways, one of which is therms. There is an interesting metric coincidence that it is often accepted by agreement (in other words we will pretend) that:

In natural gas, by convention 1 MMBtu (1 million BTU) = 1.054615 GJ.[9]

This is close to a Gigajoule. How about we simplify life and use Gigajoules in place of MMBtu? I have shown how simply a utility bill can be expressed with Gigajoules. I realize that the “commenter” is probably so well-off that he need not be bothered with quantifying energy usage, but this “engineer” does, and sees no reason for allowing confusopolies to continue to obscure billing information.

One can also note that his use of a simile: “BTUs are amounts of energy just like joules.”  is not exactly apt. Wikipedia also has this to say:

A BTU is the amount of heat required to raise the temperature of 1 avoirdupois pound of liquid water by 1 degree Fahrenheit at a constant pressure of one atmosphere.[2][3] As with the calorie, several definitions of the BTU exist, because the temperature response of water to heat energy is non-linear. This means that the change in temperature of a water mass caused by adding a certain amount of heat to it will be a function of the water’s initial temperature. Definitions of the BTU based on different water temperatures can therefore vary by up to 0.5%

The BTU is not a well-defined unit for energy, and neither is the calorie, that’s why the joule is used for energy by Engineers, scientists, and persons who want accurate energy bills, and those that have left the 19th century behind.

The “discussions” that occur in comment sections of—well—any blog or posting, have those who assert with great confidence, “information” that sounds right to those who are ill-informed, in an attempt to convince both those reading the assertion and the person making it, to remain so. The length of this blog is testament to this. Note how many words it took to deal with the flawed assertion of but one person. (With apologies to Mark Twain): The most outrageous ignorance that can be propagated will find believers if a man only tells them with all his might. This is what metric proponents encounter constantly.

Postscript:

CNN posted a piece in their “Great American Stories” series entitled Refusing to Give an Inch. The entire story is essentially a celebration of U.S. failure. How is that a Great American Story? The majority of the piece was cribbed from John Bemelmans Marciano’s anti-metric polemic Whatever Happened To the Metric System. A review of this monograph may be found here.

I was contacted by one of the authors by email last February. The story was to be about the controversy over the metric road signs in Arizona.  I sent the reporter links to A Tale of Two Iowans, The Chain Gang, and my response to NIST’s rejection of a We The People Petition to change the U.S. to the metric system. I told the author I was willing to talk at length, at anytime, and that they could find much useful information contained in my blogs.

The video that accompanies the written story is surprising in that a number of people interviewed didn’t seem bothered by the metric road signs. They even seemed to have a fondness for them. One person who recently moved there, soon didn’t notice the difference and seemed fine with the signs. This supports my thesis about The Metric Populist Revolt That Didn’t Happen. Much like the California DOT, that went from metric back to Ye Olde English, the Arizona spokesman speculated about dual-unit signs. He saw that as “the best of all worlds for everyone.” This is simply a way to first give U.S. citizens a way of ignoring the metric designations, and then eventually purging them. See Naughtin’s First Law.

The reason for the replacement of the metric road signs, which look perfectly fine, is they don’t have as much refection at night as desired. I suspect that all of the signs in Arizona must have been changed because of this new specification. Strangely there was no public outcry about the “massive costs” involved with replacing all the Ye Olde English signs. That would have been a perfect time to make all the road signs in Arizona metric. Metric resistance is not about cost, it has no rational basis.

I had hoped for a story with something other than an extended interview with Marciano that contains statements like:

Marciano, however, makes a credible argument for the old way of counting, which is based on everyday things and parts of the body.

“People say the metric system makes sense,” Marciano says, “But in nature we don’t think about dividing things by 10, do we? We think of halves and feet and thirds.”

Acres, for instance, were based on the amount of land a man could plow in a day.

“Throughout history we have measured things by ourselves,” Marciano says. “We are really losing something with metric.”

And another thing: People think the metric system has something to do with science.
It doesn’t, Marciano says, except that it is used in science and every scientist will
probably put forth a convincing argument for why it’s silly not to be metric.

The metric system is very “body friendly.” a long pace is almost exactly a meter (1000 mm). I’ve done this and checked buildings with a laser. The dimensions are remarkably close. The distance between a person’s nose and the tips of their fingers is about a meter. The width of a male hand, Marciano’s hobby horse measurement poster unit, is generally 100 mm. So is the length of many index fingers. The width of a pinky fingernail is about 10 mm.

I have dedicated my life to engineering  and science. Marciano’s statement that the metric system has nothing to do with science is simply at odds with the last two centuries of history. It is like stating that biology has nothing to do with lifeforms. I direct my readers to my essay The Americans Who Defined the Meter. The fact that the Earth is about 40 Megameters (40 000 Km) in circumference, is no simple coincidence. Englishman John Wilkins was tasked by the Royal Society of London to develop a universal measurement system that all scientists could use. When France finally implemented the metric system, it was guided by a number of very famous scientists. It’s science all the way down. The metric system has also been refined to make everyday measurement much easier for everyday people than Ye Olde English. The details are in my blogs.

CNN further informs us that:

…. John Bemelmans Marciano gave up writing the popular “Madeline” children’s books started by his grandfather and last year published “Whatever Happened To The Metric System?”

Marciano says his young editor had no idea the United States had come within millimeters of metrication. The book reveals a fascinating history of how this nation ended up keeping a system in which 16 ounces make a pound, 12 inches make a foot and 3 feet make a yard.

Marciano knows that we never came within a barleycorn of becoming metric. I’ve detailed this, here, and here and it’s tiresome to have metric revisionist history constantly propagated by Marciano and the lazy media. Marciano’s book does not explain what happened to metric system, the book has almost no metric content, and is only a long juvenile paean of schadenfreude directed at the U.S. metric failure. If you want to know why the U.S. is not metric, you will not find the answer in Marciano’s book, you will find it in Hector Vera’s PhD thesis: The Social Life of Measures Metrication in the United States and Mexico, 1798-2004 (September 2011). Worst of all for me was this (forgive me for re-quoting):

There are blogs like “Metric Maven” and even a book on the subject. John Bemelmans Marciano gave up writing the popular “Madeline” children’s books started by his grandfather and last year published “Whatever Happened To The Metric System?”

This, in my view, makes it look like my blog and Marciano’s anti-metric polemic are somehow complimentary or equivalent when they are completely at odds. I guess that it was good that at least I have a link. It would have been nice if this had been an article that does not celebrate a disaster as an American triumph, but I guess no matter what happened, in CNN’s view the lack of the metric system is a “Great American Story.”

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.