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.

Furlongs per Fortnight

By The Metric Maven

At the first university I attended, it was assigned as a “joke exercise” to compute speeds in Furlongs/Fortnight. I’m not sure what the lesson was supposed to be in this case. It was clear Furlongs per Fornight was an absurd use of units, but was it because they were not metric?—-or because they are an “inappropriate” use of medieval units. My favorite reference book, Measure for Measure has a single conversion factor entry: Furlong/Fortnight -> miles/hour [Campbell Factor] 0.00 372, and thus far I have not discovered who Campbell might be, or have been. So assuming I’ve converted correctly 1 Furlong/Fortnight is 166.31 micrometers/second or about 10 mm per minute and 600 mm per hour. For those who want to add more absurdity, and for those who are just fine with US Customary, there is the FFF system, which uses the Furlong, Firkin and Fortnight as its base units.

Of course, this is just a contrived use of units that is clearly absurd right? Clearly, one would never encounter an everyday computation this absurd. Well, then you underestimate the absurdity of our “customary units.” I often look to see what search terms are used by visitors to The Metric Maven website, and the current list looked rather prosaic, until I hit the sixth entry. It reads: “How many tablespoons are in a quarter cup?” My mind lurched to a halt taking this in. In one question we find so many adverse aspects of the current non-system of measurement it requires elaboration.

First we address the tablespoon issue. Now I hope the person asking is sure it is a tablespoon and not a teaspoon. As I’ve addressed in the past, the confusion of teaspoons and tablespoons is a perennial problem in US kitchens. It also has the downside that it has the potential to kill people. Assuming the inquisitor wants tablespoons, we might just quickly convert it to metric in milliliters. A tablespoon is 14.8 mL which I will round to 15 mL for our purposes.

We next encounter a fraction to dilute the volume of the cup for reasons which are not particularly apparent. It’s quite possible, that the person involved needs 1/4 cup of water for say a taco mix recipe or something, but has only teaspoons and tablespoons in their post-high school flat, and no US measuring cups. Well, we want a quarter cup of liquid, but only have a tablespoon. So a cup converted to metric is 236.6 mL, and we will divide this by four to obtain 59.1 mL which we will round to 60 mL. I might hear some objecting to this, but if the recipe was born of precision, it would have been in metric in the first place.

So now we have a teaspoon is 15 mL and 1/4 cup is 60 mL, we use these integer values to see that wow!–it’s 4 tablespoons in a 1/4 cup! What an interesting coincidence, but also, yeah, a complete coincidence. There is no way that these medieval units would have allowed one to readily realize this fact using them exclusively.

Now let’s look at the same problem from a metric perspective. We need 60 mL of water, milk, olive oil, whatever. Well, we can find a 15 mL measuring spoon and use four of them, or we can find a measuring cup and fill to the 50 mL graduation, then estimate another 10 mL. In the case of water, you could use a scale to measure 60 grams of water which is 60 mL using any vessel after zeroing the scale. It seems like one has a lot of options with a rational measurement system. But why bother when you can just use a search engine to find out the answer? The same type of solution was offered in the early 20th century by Fredrick Halsey, author of The Metric Fallacy. The technical device he offered up that would make the metric system unnecessary was the slide rule.

Technical innovations will not eliminate poor and non-intuitive methods of measurement expression. For instance, another question in the list of search key phrases is “how to use 1/8 inch measurement on yardstick.” Well, I have written about the absurdities of yardsticks in my essay Stickin’ it to Yardsticks. US residents might find it absurd that a person doesn’t recall common denominators, and such. What is absurd is making US residents use fractions on measuring rules at all. If they had a millimeter-only meter-stick there would be no need for fractions, or decimals. The person involved would not need to look on the internet, only understand integer addition and subtraction, and there are plenty of calculators available for that.

Thank heavens we still don’t use Roman numerals when the rest of the world uses Hindu-Arabic ones with decimals, we might rationalize using them in the age of the internet.

Tim Hunkin, a designer and maker from the UK has released his first video about The Secret Life of Components. He discusses chains, and as you will see, uses nothing but millimetres, including a mm-only ruler. He threw out all his quarter-inch US chains as he found the use of “imperial” too confusing. Note that he uses the word mil for millimetre, as is common with British engineers. In the US, the mil is a feral unit. Of course, we also use a pre-metric measurement unit called the chain to build roads in the US. I’ve written about it here.

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