Curiosity Makes the Kat


By The Metric Maven

Bullcat Edition

My friend Kat generously provides interesting examples that illustrate innumeracy and the foibles of our Ye Olde English irrational grouping of measurements. Long time readers may recall the response offered by the former head of NIST to a We The People Petition requesting we convert to the metric system in the U.S.. In it he said: “if the metric system and U.S. customary system are languages of measurement, then the United States is truly a bilingual nation.” I found this statement abhorrent, misleading and its metaphor designed to substitute politics for measurement. Kat provided a cute quotation I found humorous:

If math is the universal language, then the imperial system must be a speech impediment.

She also told me a tale about her husband and a potato dish he was making. As he was following the recipe, Kat’s husband checked the taste of the potatoes and suddenly realized they were very, very salty. Kat and her spouse investigated the situation and realized that he had confused Tbl with Tsp, and  accidentally introduced three times the amount of salt into the potatoes as was called for by the recipe. I myself, long before I took to a keyboard to write about the metric system, made the teaspoon/tablespoon mistake when cooking—more than once. Rather than questioning our non-system, I blamed myself for not being sharp enough to catch it. My background in magic, informs me that this situation is much like magical illusion, it has nothing to do with your intelligence, it has everything to do with your perception. Tsp versus tbl is a perceptual trap that almost everyone experiences at one time or another.

Kat brought up something that I had personally witnessed, but did not realize had also been documented. The New York Times wrote an article about American innumeracy which contains this nugget:

One of the most vivid arithmetic failings displayed by Americans occurred in the early 1980s, when the A&W restaurant chain released a new hamburger to rival the McDonald’s Quarter Pounder. With a third-pound of beef, the A&W burger had more meat than the Quarter Pounder; in taste tests, customers preferred A&W’s burger. And it was less expensive. A lavish A&W television and radio marketing campaign cited these benefits. Yet instead of leaping at the great value, customers snubbed it.

Only when the company held customer focus groups did it become clear why. The Third Pounder presented the American public with a test in fractions. And we failed. Misunderstanding the value of one-third, customers believed they were being overcharged. Why, they asked the researchers, should they pay the same amount for a third of a pound of meat as they did for a quarter-pound of meat at McDonald’s. The “4” in “¼,” larger than the “3” in “⅓,” led them astray.

Upon reading this, I can imagine some denizens of the US might begin sporting a furtive grin and retain an unshakable confidence that “they would never be that dumb.” This American hubris is why we can never reform anything in the US. I had to stop and think about the difference in fractions when I was in a hamburger chain years ago. My significant other was astonished that I had to stop and think about the magnitudes. The truth, which may not be acknowledged in the US, is that “fractions are a notation that does not allow for immediate magnitude comparison.” If you say this in the US, great joy is taken in pronouncing the person stating it to simply be a dumb-ass. When I hear this arrogant attitude that everyone else is an idiot in the US but me, I often think of the movie Idiocracy, where the people in the movie are convinced that a product called Brawndo should be used to irrigate plants, and the reason why is a tagline: “Because Brawndo’s got electrolytes.” and “it’s what plants crave.” When water is suggested as the proper substance for hydrating plants, the idea is met with derision. No controlled experiments or trials. Clearly water is a fluid only suitable for use in a toilet. Never mind the plants are dying, the idea is considered sound without investigation, because “it’s obviously true.”

I stood in line at a burger chain years ago, and heard person after person in line asking one another about the relative sizes of the fractional burgers on the menu board. Is 1/3 bigger than 1/4? I even saw a few people make it to the ordering station and directly ask the cashier which burger is larger. Can you quickly arrange these fractions in ascending order?: 5/8, 1/2, 15/16, 3/4. How about 63, 50, 94, 75? The continued use of fractions in everyday work only demonstrates how tenaciously people will cling to received ideas without ever thinking about them or challenging them. Familiarity bests simplicity. Below is a readout for an automatic feed on a vertical milling machine:


Does the use of fractions provide an intuitive feeling for the relative magnitudes of each of the fractions?–no–I would argue they don’t. Hindu-Arabic numerals do. Let’s list 1/4, 1/3, and 1/2 pound hamburgers in grams: 114 grams, 151 grams, 227 grams. Seems straightforward to me. How about 100 grams, 150 grams and 225 grams? Integers are nice.

This graphic from a recipe appeared on metric sites sometime back and illustrates the point yet again:


Years ago, my father received a really neat device to measure paper and cardboard thicknesses. Here is what it looks like:


The outer scale is in fractions, and the inner is in millimeters. It is not immediately clear to me that 31/64 is between 1/2 and 15/32 of an inch. The preference and inculcated comfort for fractions is illustrated by how they are converted to millimeters. The numbers in millimeters are all out to three places, or 1 micrometer. The fractions are in increments of 1/64 of an inch as one can see from the very first metric increment 0.397 mm. Essentially the digitized graininess of the measurement is about 0.4 mm at best. One could easily round the millimeters to a single place after the decimal point. Here is an abbreviated list of how the paper measuring device could have been labeled:

1/64    0.4 mm
1/32    0.8 mm
3/64    1.2 mm
1/16    1.6 mm
5/64    2.0 mm
3/32    2.4 mm
7/64    2.8 mm
1/8      3.2 mm
9/64    3.6 mm
5/32    4.0 mm
…and so on….

Which set of numbers looks straightforward now? The millimeters are in increments of 0.4 mm or (400 um).

When the metric system was first formalized, Mathematician and early metric system founder Pierre-Simon Laplace (1749-1827) realized how much imposed perceptual prejudice would impede it. Ruth Inez Champagne has this to say in her PhD thesis:

Laplace foresees many difficulties involved in changing the old habits of adults. He tells his students that they will encounter great resistance among those who are familiar with the customary system of measurement. He indicates that the metric system “appears very complicated to them,” because man is naturally inclined to view new things as difficult and complicated because of his habits and prejudices.

Laplace goes on to quote Jean-Jacques Rousseau (1712-1778), who stated: “something known and bad is preferable to a better way that has to be learned.” Perhaps that should be the official motto of the United States when it comes to the metric system.

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9 thoughts on “Curiosity Makes the Kat

  1. The recipe modification to make it “less” sweet is very funny and sad, at the same time.

  2. Maven:
    Is your book an “updating” of the 1982 book by Philip and Phylis Morrison titled “Powers Of Ten: About the Relative Size of Things in the Universe”?

  3. Perhaps the “point” of American kitchen measures is to avoid the use of large numbers.

  4. The Maven might remember (at age 6) when you are trying to make cookies, a hugh mistake is to read a dash of salt as a dish of salt, it was pretty bad !!!

  5. Maven:
    Regarding that 1/4 > 1/3, there is such nonsense with decimals too.
    I recently gave an exam where a student with a good grade (85) wrote the following: “P-Value = 0.0062 > alpha [symbol] = 0.05”! (This of course led her to write her conclusion incorrectly.) Thus, it looks like a similar explanation to the 4 > 3, namely that 62 > 5.

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