Life of a Rooster

Memoirs of a psychiatrist, journalist and educator

How long was a king’s foot?

on March 17, 2014

Actually, I recently looked up what I have called for years the French method of regrouping in subtraction, and found on the internet that it is called the Austrian method. Well, I suppose we might as well say it is the continental European method, and I would assume several European countries probably share this method.

At the risk of boring my readers, I will mention just one more arithmetic trick that might make learning math so much easier for our American elementary students. It is the subject of learning about metric units. The metric system is also called SI or International System of Units, so few people know that it originated in France, and was proposed by the French back in 1799. Note the date: it indicates that it happened ten years after the great French Revolution, and when you overthrow one thing you want to overthrow other things you are unhappy about, such as measure units named pied (foot), pouce (thumb), toise, lieue, arpent, roquille, perche, vergee, demiard, chopine, feuillette, litron, boisseau, quart, minot, etc. You are giving up? Me too. Apparently, these units were set by the great Emperor Charlemagne, (the one who was crowned in the year 800, according to my forever-etched-in-mind history lesson) (by the way, I loved Emperor Charlemagne, because he had the good sense to get crowned in a year that was easy to memorize!) who wanted to unify the way people measured stuff within his large dominion. So he used his own foot length and called it the official “king’s foot”, shortened later to just “foot”. And I assume he also used his own thumb to set in stone the “inch”. I don’t think it’s the length of his thumb as much as the width, otherwise it might have been a thumb badly mutilated during battle.

Charlemagne, whose foot is used as the standard for a foot.

Charlemagne, whose foot is used as the standard for a foot.

This was a wonderful innovation, except that as humans love to always do their own thing unless forced to do otherwise, soon variations of these measurements sprouted like mushrooms all over Europe. For example, that famous King’s Foot (pied du roi) is actually 1.066 of the English foot, while the French pinte actually equals 1.68 of an imperial pint. Just imagine travelers to other countries or trans-continental merchants trying to buy and sell goods, why they would be fighting and calling each other cheaters and liars.

And that’s only Europe. I was surprised to see that in Taiwan, oh, about 20 or 30 years ago, when I went home to visit my parents, they still used traditional units of measurement in small stalls in the markets. I wanted to buy eggs, and Mama said, go here and there and turn here and there, and there is a shop selling nails and hammers, and you will ask there for eggs. Really? hardware with eggs? Whatever. So I got there, and asked for eggs. The shop owner stared at me stone-faced. I thought it was because he was thinking, Can’t you see I sell nails and hammers? Do you actually see eggs anywhere in this tiny dark black place? But then he asked, “How much?” That got me. Don’t you all buy eggs in cartons like I do? So I wanted to say, maybe a couple dozens, when he asked again, “how many liang?” Wow! A liang? What’s a liang? I knew vaguely that it was a unit of weight/mass, but how much should I say? What about a nice round figure like 10?  I didn’t want to sound stupid. What if I said 10 liang and ended up with a hundred eggs? Then ping! Lightbulb time! I suddenly remembered a phrase that we often used, “ban jin ba liang!” which meant “it’s all the same!” So then, “ban jin” is half a jin or half a pound, and it’s equal to ba liang, or eight liang. So far so good. Thankfully, I did know that a Tai jin (Taiwanese pound) was a little less than half a kilogram, but how much did an egg weigh? At this point, the egg seller interrupted my musings by repeating in a very exasperated and impatient tone, “So how many liang do you want?” I took a deep breath, and said, pretending to be very sure of myself, “Ba liang!” Eight liang.  He got up, went to the side of the shop, squatted down, and pulled open a metal drawer, which was padded with straw and had brown eggs in it. He picked up a few eggs, placed them carefully in a tiny plastic bag, tied the bag with a long string of straw, and hooked it to a metal scale, the type that looks like a long metal arm hanging from a chain. I actually wanted at least a dozen eggs, but decided I was going to leave that to someone else to purchase.

Traditional Chinese scales. For eggs, remove the plate and hang the bag of eggs directly on the horizontal bar.

Traditional Chinese scales. For eggs, remove the plate and hang the bag of eggs directly on the horizontal bar.

To come back then to the SI, since the metre des Archives (prototype of a meter) and the kilogramme des Archives (prototype of a kilogram) are kept and displayed in Paris, it takes simple logic to deduce that the French are very good at teaching the metric system. It is such a logical system that I did not know anyone was learning it differently until I tutored American school children. We encountered somewhere in a word problem, the case of converting cm to m. The child said, “Wait, is it times? or divide? Is it 100 or 1000?”  Then only did I discover that in US Math textbooks, both imperial and metric systems are taught, and the latter is taught only partially. You get to learn about the kilogram and the gram, then about the kilometer, the meter and the centimeter. Children do not understand the logical relationship between all units, and come up with strange questions, such as the one I got recently from a little girl. “Teacher, I can’t measure centimeters on my ruler!”

International prototype of the kilogram, made of platinum iridium alloy

International prototype of the kilogram, made of platinum iridium alloy

“Why not?” I was puzzled. “Your ruler has inches on one edge and centimeters on the other edge!”  The little girl looked at me like I was stupid. “No, Teacher, it has millimeters! not centimeters!” Indeed, it did have a “mm” printed under the zero line. I couldn’t believe my ears. Did she not know that ten millimeters were a centimeter?

So here is how little French children are taught. You get a table that looks like the one below, with all units heading the columns, from left to right: kilometer, hectometer, decameter, meter, decimeter, centimeter, millimeter. Say the question is: how many meters are in a kilometer? You write 1 in the column for km, and add zeros, one per column, until you reach the target unit: m. Now read the answer: 1,000.  Really simple. You can try for example, 53 meters equal how many centimeters? Write the 53 as follows: the 3 in the meter column, the 5 in the decameter column. Then add zeros until you reach the cm column. Answer: 5,300. It works equally easily the other way around. How many km is 270 meters? Write the 0 in the meter column, the 7 in the decameter column, the 2 in the hectometer column, and add zeros (only one in this case) until you reach the km column. Now put a point (comma, in Europe) after the first zero. Answer: 0.270.  You can easily substitute -gram or -liter to -meter and master all unit conversions like a dream.

How to convert numbers from one unit to another in the metric system.

How to convert numbers from one unit to another in the metric system.

This table system is excellent also for moving into areas and volumes. Say you want to teach conversions of squared meters to squared centimeters. Your table should now show two columns per unit. The rest is exactly the same. As for volumes, just add one more column, three per unit.

 


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