Mixed Megaphors

By The Metric Maven

It struck me recently that a number of science writers that I’ve read don’t use measurement units to truly convey any actual numerical information, but instead have at best decanted them into metaphors, and at worst use mixed units, which then become mixed metaphors. The science writers offer numbers that appear to convey quantities, but actually offer literary impact rather than numerical impact.

For instance, the book Rust The Longest War, by Johnathan Waldman, has a very interesting chapter on the restoration of The Statue of Liberty. He states on page 26:

But still, the coal tar remained. The coal tar was more stubborn, reacting as it had with various corrosion products. Sandblasting would have removed it, but also would have  damaged the copper which was only  3/32 of an inch thick.

later he then states:

Wisely, he compared the thickness of the exposed copper to a spot where some of the black coal tar had oozed out and covered it, thus protecting it from both sides, and determined the rate at which the copper was corroding. It was vanishing at a rate of .0013 millimeters per year. At that pace, he figured, it’d last a thousand years.

The mixing of Olde English and metric does not produce a numerical continuum but causes one to think in terms of metaphor. A person, if they are American, can get a vague idea of how large 3/32″ is, and realize that 0.0013 millimeters is a very small number compared with it, but much like good writing style, a good science writer should have good numerical style. If the author appears to believe that he can use millimeters as a unit, then why doesn’t he adopt metric exclusively? A thickness of 3/32″ is 2.38 mm. I doubt this value is more than an average so we could round it to 2.4 mm. Then when discussing the corrosion rate of 0.0013 millimeters it would be much easier to compare the actual numbers. When you change units, you force your comparison to become entirely visceral, and eschew any direct numerical comparison. Mixing measurement units does not aid numerical communication, it hinders it. There is no literary excuse for this—if one is a science writer.

On page 97 the author mentions how thin the metal on a pull-tab must be to function is discussed:

The score line is only  1/1000 of an inch thick, and technically it’s not coated ….

…Give or take two or three millionths of an inch,” Elmer, the plant’s assistant manager, once told me while pointing to a can, “and this won’t open.

One can see the fraction has been changed to emphasize how small the tolerance is, or perhaps over emphasize? The score line is about 25 micrometers thick, and this thickness must be within about 5-7 micrometers to work. One could then point out that a human hair has a diameter of about 100 micrometers for a tangible reference. Both information, and a reference are provided, and the forced metaphor is vanquished. Fractions in a lot of ways are equivalent to an uncountable number of Olde English prefixes. For example, the author talks about the diminishing mass of aluminum saved from ongoing design changes:

In the last twenty-five years, cans have only gotten one-hundredth of a pound lighter

One-hundredth of a pound? This one hundredth modifier leaves one translating from a large value of pounds to the minute value which could be expressed more straightforwardly. One hundredth of an avoirdupois pound is 16/100 of an avoirdupois ounce, 70 grains, or about 4.5 grams. The value in grams is about the mass of four to five chocolate m&ms. What is the mass of a current empty can of 12 oz soda? Well, as far as I recall this value is not given. It would seem important to know. The author is emphasizing in this chapter the importance of interior coatings in cans (page 79):

Consider a can of Coke. It’s a corrosion nightmare. Phosphoric acid gives it a pH of 2.75, salts and dyes render it still more aggressive, and the concoction exists under ninety pound per square inch of pressure, trying to force its way out of a layer of aluminum a few thousands of an inch thick.

Later on the same page:

Without this epoxy lining, only microns thick, a can of Coke would corrode in three days.

Once again, we see inches, and then microns, and then we are given a mass value for the inside coating:

Beer, for example, isn’t very corrosive, so coatings on beer cans are extremely thin, and weigh in the neighborhood of 90 milligrams.

on the next page:

The most anyone revealed is that the average is 120 milligrams per can.

We have no idea what the mass of an empty aluminum can is. Without context, milligrams becomes a Metaphor with a number attached. A quick look on the web gives a value of about 15 grams for an empty Coke can. We now realize that the can has a mass of about 15 000 milligrams, the coating is about 120 milligrams, and in the last 25 years, the amount of aluminum reduction is about 4500 milligrams. If you prefer decimals: 15 grams for the mass of the can, 0.120 grams for the coating, and 4.5 grams in aluminum per can in the last 25 years. Either way of expressing the values in metric is better than the Mixed Megaphors offered.

I want to emphasize that I’m not singling out the author of Rust. The book is an interesting read, when the author does not get bogged down in the personal details of people about which he is writing. I had planned on using examples from other contemporary science writing, but kept adding examples from this particular book. This is not just the fault of science writers. Editors take grammar and syntax seriously, but don’t seem to have anything but a dismissive sniff to offer when numerical expression in a literary context is criticized. Until science writers and “science communicators” take the numerical basis of science seriously, we will end up with prose metaphors in place of numeracy.



The citizens of the State of Iowa have seen fit to return Senator Charles Grassley to the US Senate. He is 89 years old. Back in the 1970s:

Representative Charles Grassley (1933- )  waged political war against metric road signs and single-handedly killed them on June 8, 1977. The Thursday June 9th Des Moines Register reported that:

“The Iowa Republican told his House colleagues that Federal Highway Administrator William Cox will withdraw proposed regulations that would have forced the conversion of highway signs to the metric system”

The Des Moines paper further related Grassley as:

“Denouncing kilometers as a “foreign system of measurement,” Grassley said that “forcing the American people to convert to the metric system goes against our democratic principles.”

The metric system was conceived and articulated by an Englishman, Bishop John Wilkins in 1668. Apparently because the French initiated its international stewardship and adoption, it is forever foreign. I suspect that—Now Senator Grassley—never bothered to research his forgone conclusion. He just didn’t like metric and had a Senatorial sized tantrum to stop it.

See my essay A Tale of Two Iowans for more.

Measurement : A very short introduction

by The Metric Maven

My friend Dr. Sunshine brought the book Measurement A Very Short Introduction by David J. Hand to my attention. I enthusiastically purchased it, as it is 1) short, and 2) about measurement. I was a bit dubious when I read a blurb on the cover where Marcus Du Sautoy praised the book. My review of his series is here. What I discovered immediately is that despite its 2016 publication, by a person from Oxford no less, there was no mention of John Wilkins as the creator of the system part of the metric system. What is stated is:

One of the earliest proposals for a unified system of physical measurements was made around 1670, when Gabriel Mouton suggested that France’s many different units should be replaced by a decimal system, with increasing units being defined in multiples of ten. (page 6)

I realize it’s a very short introduction, and he leaves cracks in his prose for others, but perhaps just a mention of Wilkins might be good?

The book hits all proverbial the metric system stories, the crash of the Mars Climate Orbiter (but no mention of the DART failure), the redefinition of the meter over many years, the current problem with the Kilogram standards are all discussed.

The book moves at a nice pace and is succinct.

The author carves out a type of measurement with which I’m unfamiliar, he calls it pragmatic measurement. He states:

In contrast, for the social science and economic examples, we construct a measure (e.e. from the prices of goods people purchase) which has the right sort of properties for our intended use. This sort of measurement is called  pragmatic measurement. (page 13)

He argues that this must be done in socioeconomic areas. I have a different name for this, I call it inaccurate, or the stuff that dreams are made of measurement.  When measurements are based on perception, they are hardly measurements.

He starts Chapter 2 affirming his assertion:

In Chapter 1 we saw that measurement procedures could be placed on a continuum which stretched from representational at one end to pragmatic at the other.

This is an expression of the continuum fallacy, that if assumed, could philosophically preclude the very notion that measurement exists.

Then in what appears to be a strange semantic shift, the author then argues:

Note that even measurements of physical attributes involve a pragmatic aspect: such measurements and their application in science, engineering, and life in general, require a choice of unit. There is nothing in nature which allows us to choose between units, so the choice must be based on pragmatic considerations. To take an exaggerated example, if I wanted to study the impact of childhood diet on adult height, pragmatic considerations would lead me away from measuring in light years, where a difference of 0.0000000000000000027 light years would matter. (this is one inch, expressed in light years)

First, I think my long-time readers know what I think about light-years. Second, in modern expression why would it not be “0.000 000 000 000 000 002 7 light years would matter.” It bothers me when an academic is not all that academic it appears. Third, an inch?—seriously? I assume it’s the Anglo-Saxon compromise inch which is clearly not part of SI.

Well, we gave Professor Hand an inch, and so when he offers up Cuisenaire rods he takes a centimeter, as pragmatic measure of academic ossification. (page 19 illustration) and on Page 20:

Again, we might give the new shortest stick a name–a centimetre, say.” Using the sticks as a guide:

Suppose for example, that we have assigned numbers using the inch as our basic unit of length. To get to the numbers we would have assigned if we had used the centimeter as our basic unit, all we have to do is multiply all the numbers by 2.54, which is the number of 1-centimetre sticks which stretch 1 inch. So, if one of our sticks is 10 inches long, all we have to do is multiply by 2.54, and we have 25.4 as the length of this stick in centimetres.

I’ve had visceral denials when I have asserted that a centimeter is simply a pseudo-inch, that allows people to use metric measure in a pre-metric manner, rather than in an efficient modern way. I’ve addressed this many times, and in my view, a university professor in a metric country like the UK, is committing academic malpractice by using these examples. Why not use barleycorns? He has already introduced a conversion factor of 2.54. What is the conversion unit for metric?—in his metric country?—how about 1000?

Much time is then spent converting from Fahrenheit to Celsius and back. Perhaps I will now argue that a sentence about John Wilkins should have been given space in this short introduction. After all of this he never mentions Celsius is directly convertible to Kelvin, with a simple addition of 273.15 and the problem of zero that he spends considerable time explaining goes away!

Perhaps time explaining absolute zero might be worth the effort?–which he does not—rather than enabling Fahrenheit? (on page 54 he finally introduces Kelvin as a temperature scale.)

Professor Hand goes on to discuss how quantities that are non-linear are added together, and uses relativity theory as an example. Then he returns to pragmatic measurement:

Since pragmatic measurement simultaneously defines the attribute being measured, and specifies how to measure it, pragmatic measurement is closely related to the philosophical position of operationalism.

Ok, I’ve dabbled in a lot of philosophy over the years and “closely related” is not what one analyzes when discussing a philosophical attribute. The examples he uses, such as measuring people’s happiness, does not really encompass scientific legitimacy in a hard sense, as there is no standard of measure to measure against, and no obvious way to set up a repeatable experimental protocol. A scientific measurement should be connected to a hypothesis or theory that predicts and has explanatory power. Dr Hand’s discussion all sounds very new-age, and then a quick assertion about IQ:

A classic example of the psychometric approach to combining items arises in the measurement of general intelligence, base on measurements of such things as scores on arithmetic tests, verbal tests, viso-spacial reasoning tests, and so on. We explore this in more detail in Chapter 5.

The notion of a single number to express intelligence, or other complex “models” of humans, assaults my understanding of information theory. I cannot look at a complex photograph and reduce it to a binary 1 or 0, or 00 to 11. That is clearly not enough information to describe a photo of a section of the Grand Canyon in black and white or color. One can call the reduction of complex and ill-defined attributes pragmatic, but a different term enters my mind, and if I’m limited to a single binary attribute to describe it, it’s a zero. What is intelligence?—why it’s what intelligence tests measure—of course! QED

To be fair, Dr. Hand does mention some of the difficulties and problems involved, but appears to then double down with his continuum argument of measurement by questioning the reality of gravity, and magnetism as quantities. (page 34) As electromagnetism is my specialty, I see that a certain reality has to exist for electricity and magnetism. They are both very measurable in a repeatable and definable way. They were also once viewed as separate phenomenon. James Clerk Maxwell extended the theoretical equations and combined them in a way that described and predicted electromagnetic waves. His equations predicted these waves would travel at the speed of light. Light was suspected to be an electromagnetic wave, and so it is. Heinrich Hertz first measured these waves after Maxwell’s death. I’ve never see a situation where a theory had been attached to the sort of pragmatic measurements described, that provide larger explanatory power, that is, have made a testable prediction.

Measurement is what connects a our world to a theory. Quantifying ignorance and hiding it behind a notion of pragmatism does not further scientific explanation. The scores at a cat show have no solid measurement relevance when the notion of what makes a “more perfect cat” is completely and arbitrarily defined by those making the judgement. A perfect cat one year, can become a zero cat the next as the “measurement criterion” change in a capricious manner.

Professor Hand’s retrograde unit usage continues, in a section within his Chapter on the physical sciences:

A windmill may have worked very well with tolerances of 1/16th of an inch, but a modern jet engine requires something better. (page 40)

Yeah, like the metric system. Would using 1.5 millimetres have killed him? Forty pages into the book and their is not a millimeter to be found. After a while, one begins to suspect that Dr. Hand is not very hip on the metric system:

A caliper is appropriate for very small lengths (typically these would be called widths), a foot ruler is appropriate for lengths on a human scale, laser rangefinders, hodometers, or tellurometers for longer scales on the Earth,….

Let me stop there, his other examples have no metric length units either. He goes on:

Measuring the distance to a nearby star using end-to-end concatenation of a foot ruler is impracticable to say the least, and measuring a human height using a caliper would be difficult at best.

A foot ruler?

These are long discussions, for a very short book, of how the distances to stars are measured, but never does a Petameter or Exameter find ink on his pages. He continues to discuss measurement methods and when pressed for a volume uses—cups! (page 47)

Finally when discussing the invariability of mass on the Earth and the Moon, he mentions a Kilogram. Mass can be measured with acceleration, and so he finally defines a newton. The joule follows. Watts (and equivalent horsepower) are quickly mentioned along with the curious inclusion of the decibel as shorthand.

The aim of the book in many places appears to be to provide an overview of how measurements are done, without much involvement with units.

The Author presents medical descriptions such as the severity of heart disease as an example of “pragmatic measurement” in Chapter 4: “Measurement in the life sciences, medicine and health.” Hand states: “different measurement cultures have different answers to these questions.” (Page 67). A measurement that depends on culture, is not a measurement in my view. Measurements generally require calibration to a standard and numerical expression of the defined quantity. The metric system has been adopted by many cultures around the globe, and requires no cultural exegesis to be used, it is universal.

For instance, when I was a boy I was in an F5 tornado. Especially In those days, the physical damage seen, was used as a proxy to estimate the wind speed that caused the damage. At the time, it was estimated that the wind speed of the tornado I experienced, was about 576 Kilometers per hour (360 miles per hour). Wind speed is a quantity that in principle can be measured. It has a number as a function of time and position. One can integrate the energy at a given time, and in principle, estimate the strength of a tornado. The proxies for this estimation are constantly refined, but there may be a way to use satellite data at some point to get more exact numbers.

Professor Hand when discussing “pain measurement” essentially asserts self-reported perception is a measurement. In my view it is not, it is a metaphor. I can envision a future where a device could be created that measures the pain impulses in a human being, much like an MRI or CT scan. It could compute a value for the magnitude of these impulses, and their phase, perhaps correlated with other proxies. We would have a repeatable measurement, but one could not be certain at that point if each person perceives the same pain “amount.”

After all this discussion of “practical measures,” the author has a sort of drive by paragraph concerning actual measures near the end of the chapter:

Measurement issues in medicine are not restricted to the health of patients. They also arise in other contexts. For example, it is critical that doses of medicines are properly measured. The consequences of failing to do so can be catastrophic: newborn Alyssa Shinn died in November 2006 when, instead of receiving a dose of 330 micrograms of zinc to boost her metabolism, she received a dose of 330 milligrams. The standard “unit-dose” drug dispensing system uses pre-packaging of unit doses so that they are ready to administer to the patient, meaning that a nurse or other clinician need not measure up the dose on the fly.

This error took place in Las Vegas Nevada. A news story reported:

I put in the 330 and when I went to pick the units … [I] grabbed 330 milligrams per decaliter instead of micrograms per decaliter,” said Goff.

This meant that 1,000 times more zinc than had been prescribed was transfused into baby Alyssa.


The investigation revealed that a series of safeguards simply failed. Two other pharmacists neglected to check Goff’s calculation. A safety stop on the mixing machine had not been set, and a technician reading the order had replenished the machine 11 times with zinc; using 48 vials of zinc total to fill the baby’s TPN bag. Nurses didn’t notice that the nutrition bag was much larger than normal.

The details do not appear to exactly comport with what has been reported in the US press. There are a lot of questions I have about this error. First of all, who knows what a decaliter is? I’ll leave that question for now, as it could create a separate essay. Was there a confusion between MG and MCG abbreviations that are used in the US? How many mistakes might be attributable to not using mg and ug which are more symbolically distinct? It sounds like the computation was done by hand? We in the US never bother with such detailed concerns or thoughts. We just say “the system broke down” as if we had created a thoughtful one to begin with.

Dedicating but a single paragraph to this important problem, compared with the other “practical measurements” that gained a majority of prose, is not how I would have approached the chapter

His chapter on measuring in the Behavioral Sciences points out:

The scope and range of measurement in the social and behavioral sciences is illustrated by a 1992 American Psychological Association advertisement in Monitor, which estimated that 20,000 psychological measures are created each year. I doubt the rate of creation of tests has declined since then. In part this diversity reflects the range of different psychological attributes which people want to measure, and in part it represents the challenges of measurement in this domain.

The phrase “practical measures” appears to have disappeared from his monograph at this point, replaced with the single word measures.

The author then moves on to IQ:

Although some people ridicule the very notion of measuring intelligence, it is clear we all thinking of intelligence as quantitative in some sense: we say X is very intelligent, or more intelligent than Y. The question is, how can we give more concrete numerical values to this apparently quantitative attribute?

I’m apparently one of those people, the reduction of the attributes of a human mind to a single number has always seemed absurd. But the author is on board with IQ as a measurement. It seems much like accepting astrology because people talk about a person being a Gemini, because they have a certain trait.

The author states:

Another way of looking at this is that IQ is a pragmatic reduction of a multidimensional space of different aspects of intelligence to a single dimension.

Wow, with all those words, it sure sounds scientific.

The final chapter is on Measurement and Understanding. The conversion of grams of diamonds to carats is introduced to show that inferences remain constant despite the changing of measurement unit.

There is no effort to discuss the presentation of measures and data for best understanding. Perhaps he thought this was beyond the scope of his book?

Any reader who has made it this far, clearly sees that using a single binary digit to pragmatically measure if I recommend this book is legitimate, where 1 is recommended, and 0 is not recommended. I pragmatically measure zero.

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