Category Archives: International Standards

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.

The Nylon Curtain (Made Elsewhere)

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By The Metric Maven

Bulldog Edition

My friend Pierre has an uncanny ability to come across unusual measurement use in the US. Apparently he had taken an interest in ballistic nylon and had done some research.  Recently he sent me this bit of prose after asking me rhetorically if I had heard of  a denier:

But I’m right here to help. Denier is an entirely metric measurement that means:
1 |dəˈni(ə)r, ˈdenyər|a unit of weight by which the fineness of silk, rayon, or nylon yarn is measured, equal to the weight in grams of 9,000 meters of the yarn and often used to describe the thickness of hosiery: 840 denier nylon.

Tell me that’s not a random way to measure your pantyhose and backpack fabric. Grams/meter or threads/inch isn’t enough for you? It has to be 9000 meters worth of yarn thickness or weight? Nobody knows which.

So, where’d the 9000 come from? I’m thinking the Euros came up with this when they
ran out of polyester sheep.  Can they really make 9000 meter long yarn? Why not just 1 meter’s worth?

I recalled that a number of times Pat Naughtin mentioned the textile industry as one which seems to be incorrigible when it comes to converting to metric. Naughtin pointed to their attempt to embrace the centimeter as a contributing cause of delay. After I did some reading, I suspected it was centimeters and a desire for the use of archaic insider speak which acts as a barrier to entering the textile trade.

When I looked up denier on Wikipedia I found an amazing entry:

Denier /ˈdɛnjər/ or den is a unit of measure for the linear mass density of fibers. It is defined as the mass in grams per 9000 meters.[1] The denier is based on a natural reference—i.e., a single strand of silk is approximately one denier. A 9000-meter strand of silk weighs about one gram. The term denier comes from the French denier, a coin of small value (worth 1⁄12 of a sou). Applied to yarn, a denier was held to be equal in weight to 1⁄24 of an ounce. The term microdenier is used to describe filaments that weigh less than one gram per 9000 meters.

My mind almost had a momentary black-out when it contemplated the smoothly inserted euphemism: “The denier is based on a natural reference.” Well, so is the foot, it’s very natural, and also ill-purposed for providing a measurement standard. The use of a single strand of silk (apparently from a standard silkworm) which is 9000 meters (9 Km) long, that weighs “nearly” one gram, as an industrial standard is just so 17th century. This is a “standard from nature” which makes about as much sense as using three barleycorns to an inch.

This absurdity caused me to think about Samuel S. Dale, who was Fredrick Halsey’s partner in anti-metric mischief early in the twentieth century. Halsey wrote the “book” The Metric Fallacy in 1904, but it is actually two monographs bound into one. The second monograph is The Metric Failure, written by textile enthusiast Samuel Dale. I had not read Dale’s half of their anti-metric tome, but it now seemed high time to do so.

When reading Dale’s work it reminds one of numerology, where, given enough numbers, one can construct any scenario against the metric system one wants. Dale admits that the US has four different ways that it numbers yarn, and that a single method would be desirable, but he makes clear that replacing them with a metric method would be absurd:

Evidently the fabric to which they referred was spun from such stuff as dreams are made of, woven on the loom of imagination and designed to cover the nakedness of the metric and not of the human system. (pg 146)

Yes, within Dale’s flourish you can clearly hear the echoing of John Quincy Adams’ castigations of “the metric” from some seventy years earlier. The measures of the metric system are inhuman and antiseptic! The statement is almost a vestigial cry against creeping heliocentrism seeping into our culture. Dale sees the icy hand of the government forcing at least 1 000 000 textile workers to attend night school to learn the metric system. He further warns: “…that our textile weights and measures can be eradicated only by exterminating all who use them and by destroying all our textile records.” (pg 165)

Dale finally explains the basis of measurement for textiles: “In manufacturing textiles the ratio between weight and length or area takes the place of cubic measurements.” He goes on to explain:

In textile manufacturing measurements are employed for weight, distance and area only, and those for distance are in turn limited by reason of the elimination of all measurements of thickness. The volume and thickness of textile materials, finished and in process of manufacturing, are indicated by the ratio between weight and length. The bulk of cloth, for example, is expressed, not in cubic inches, but in either the weight per yard of a given width or in the number of yards per pound.

Dale explains that if cotton is spun so that one pound has a length of 840 yards, the count is 1, and if it weights one pound and has a length of 1680 yards it is number 2. This is the English standard for measuring cotton yarn. He explains that if 16 000 yards of silk weigh one ounce (he does not indicate troy or avoirdupois) its length is No. 1. If two threads of silk are side by side and weigh two ounces when 16 000 yards long they are No. 2. I will spare you the explanation of Hanks of different lengths, and the 300 yard system. In my view these examples do not provide evidence for the simplicity of traditional textile “measurements.”

Finally we encounter Dale’s discussion of the deneir:

The modern silk industry was first established in France and Italy, and their various systems of numbering silk yarn were adopted and became so firmly rooted long before the birth of the metric system that they have resisted all attempts to change them and are to-day the world’s standards for what is known as raw silk. These systems of numbering were based upon the weight in deniers of 9,600 aunes of silk, the denier being a coin weighing 24 Paris grains.

Dale explains that 400 aunes is equivalent to 476 meters. A Paris grain is 53.11 mg. So the length of 9600 aunes in metric is 11 424 meters and the mass would be  1.2746 grams. Now if we divide to get the length needed for one gram we have 8962.53 meters. This is a good approximation to 9000 meters for a gram. The exact mass expected  for 9000 meters in this situation is 1.004 180 grams, which is probably close enough to one gram for even the exacting requirements of Mr. Dale. It is an interesting metric coincidence that 9000 meters of a single silk thread is almost exactly 1 gram. This is precisely what Dale would argue could never happen, as metric is not a natural system for textiles—ever.

I had now solved Pierre’s mystery as to why 9000 meters is the length used for a denier, and how it is actually a byproduct of non-metric “standard.” I could end this essay here, but, I just couldn’t. I continued reading The Metric Failure and found that Samuel S. Dale has a section in his millitome where he “compares”  English measures with the Metric ones. Before he gets to his comparison, he cleverly trots out an interesting argument against metric by citing the prefix cluster around unity:

Such is the present condition of our textile weights and measures. The metric proposition means that our fundamental standards, the yard, inch, pound, ounce, grain and dram shall be abolished and their places taken by the metre, decimetre, centimetre, millimetre, gramme, decigramme, centigramme and milligramme.

Throughout my copy of The Metric Failure someone with an India ink pen has corrected the text. That person found many typos or errors between mass and length and diligently corrected them. Here are a couple of examples:

I must admit I laughed out loud when some person (probably in the 1930s) seems to have called out Mr. Dale for using the prefix cluster around unity as an argument against metric (pg 197):

I think he probably should have argued for three: gram, meter and millimeter, but that is in hindsight and before Naughtin’s Laws.

Dale has a metric Goldilocks moment, where, just like in that fairy tale, all the metric measurements he finds on the table are of an appalling magnitude, and only the English measures, with which he is familiar, are “just right.”  Dale points out that John Quincy Adams was also a metric Goldilocks, but on a scale much grander than Dale’s:

None of the successive decimal divisions of the metre are suited for either the commercial or manufacturing widths of textile fabrics. For the finished widths of the wide goods the decimetre is too long, the centimetre too short. For narrow fabrics the millimetre in turn is too long and its decimal divisions too short. For all of these widths the inch, divided to suit the particular case, answers every purpose perfectly. Could there be any stronger confirmation of the following extract from John Quincy Adams’ report?
`Thus, then, it has been proved, by the test of experience, that the principle of decimal divisions can be applied only with many qualifications to any general system of metrology; that its natural application is only to numbers; and that time, space gravity and extension inflexibly reject its sway.’

I have to congratulate Mr. Dale, he used an absurd quotation from the report by John Quincy Adams that did not make it into my tome of an essay about it.

Dale tries to cram centimeters into textile usage and shows they just don’t fit, and then quickly dismisses a logical option as impractical: “The objection to the use of the millimetre is that it necessitates the use of four figures to express the width of wide cloths.” Dale earlier argued that loom widths of 1/10 of an inch are all the finer divisions one would need, so apparently 2.5 mm is just too much accuracy. I sure hope his porridge isn’t getting cold with all this long winded puffery blowing over it. He further indicates that:

The centimetre is too short for the finished widths of wide fabrics. Inches express such widths as closely as is necessary.

By the metric system the finished goods are expressed in centimetres. This necessitates the use of three figures for all goods 40 inches or more in width.

Dale asserts over and over that he is a practical man and not some lofty wooly brained academic:

The contrast between the two systems in this respect illustrates the difference between English practice and metric theory.

Believe me, I’m not going to confuse Samuel S. Dale with a professor of mathematics.

Then, I find one of the earliest examples of the “technical Darwinism” argument against metric when Dale states (pg 220):

The choice lies between these two systems, English and metric. One has been adapted to mill work by a process of natural selection. The other is the result of the artificial scheme of French geometers and is unsuited for textile processes. It is inconceivable that America should abandon the first and accept the last.

Dale then launches into a history of metric, argues that metric is only suited for effete scientists, and then begins attacking a pronoun:

The eminent scientists who designed that system were able to solve the most difficult problems in higher mathematics, but they failed to comprehend what system of weights and measures was best suited for the carder, spinner, weaver and finisher of wool, cotton, linen and silk. The glamor of their fame failed to make the centimetre suitable for counting picks. Their system had to stand or fall on its merits, and falling has proved that the highest of mathematical abilities is not inconsistent with a dense ignorance of the practical affairs of every-day life. The most eminent of the mathematicians who designed the metric system exhibited an utter disregard of principle in both private and public life and the most complete incompetency when placed in an administrative office.The son of a farm laborer he owed his education to wealthy neighbors, and as soon as he became distinguished ignored both his relatives and benefactors. Although his discoveries in mathematics were sufficient to make his name immortal, he appropriated the work of others as his own.

So who is this pronoun? It is Pierre Simon Laplace (1749-1827), one of the greatest mathematicians of all time. Wow, Dale could not even bring himself to use his name?—even when attacking Laplace for plagiarism? This is just a sad ad hominem attack on a person involved with the creation of the metric system and not actually a criticism of said system. Dale just seems to get more and more deranged and finally launches into a Goldilocks on steroids assertion of the metric system’s unsuitability as he writes:

This man could demonstrate that the “lunar acceleration was independent of the secular changes in the eccentricity of the earth’s orbit” but did not know that a weaver requires a unit of length approximating the inch. He could formulate the theory of probabilities with mathematical precision, but was ignorant of the certainty that exclusively decimal divisions of weights and measures are unsuited for manufacturing cloth. He was the first to introduce potential and spherical harmonics into analysis, but failed to recognize the advantage of the English cotton system for numbering yarn. He could prove the stability of the solar system, but failed to recognize the stability of a people’s established weights and measures. He was familiar with theories of infinity, but ignorant of the wants, necessities and limitations of textile manufacturing. The co-workers of this man in constructing the metric system differed from him only in degree. They were a party of mathematical prodigies, ignorant of the essentials of textile weights and measures.

The artificial system they evolved has failed to meet the requirements of the textile trade. Nearly every one of its standards of length, area and weight is either too large or too small, and it has no units corresponding to the inch, foot, ounce and pound, approximations of which are found in every system of natural origin and for which the human mind appears to have some innate need. It is not to be wondered at, therefore, that the system thus conceived has failed, even in France where’ it was so greatly favored.

At the end of his work Dale warns the US:

It would be a plunge into chaos to emerge no one knows when, how or where. The generation introducing the metric system into the United States would not see the beginning of that chaos. In all probability no other generation would ever see the end.

Well, there is no need to fear the metric system causing the demise of the US textile industry, just metric countries. It is my understanding that at the end of World War II the US had the largest domestic textile industry on the planet. Now we import about 97% of our garments. Imagine how much worse it might have been if Samuel S. Dale did not protect the industry by halting metric in 1904.

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.