The Scale Of Proportion and Grace


Listening to my third grade granddaughter lecture me about the wonders of the metric system reminded me that there are still any number of primary school educators out there trying to teach American children that the best way of solving life’s everyday problems is by counting on your fingers.

 And of course, made me wonder what it will ever take to shut them up. 

 Or at least not breathlessly announce in class, “guess what kids?  What we’re going to find out today is that the entire rest of the world uses a much easier system of measurement  than fractions and inches and feet and yards and miles because it’s based on the number ten.  It’s called the Metric System and we’re going to learn all about it so that you can go home and show your parents how easy it is.”

But since parents are already too busy trying to solve school bus behavior issues not to mention having to deal with the littler trials of life like work and getting the dinner on the table to learn how dumb adults are about the way we measure things in this country, the gospel of the kilometer invariably gets marched over to Grandma’s house.

Metric SystemWhere its four foot tall missionary finds me looking like I have nothing to do.

“Grandpa, do you know what a centimeter is?”

I look up startled, “yes, did you see one?  I hope not because we had a lot in the cellar last year and had to hire an exterminator.”

“Nooo” she says patiently, “a centimeter not a centipede.”

I scratch my chin trying to give the best impression I can of a ponder and then snap my fingers, “right, I remember.  It’s what the French use because they can’t figure out inches and feet.”

“Grandpa, be serious.”

So I do my best to look contrite and settle down to listen as she pulls out the Xeroxed sheet of notes from class and reads a long list of Metric System  benefits like easy division and multiplication and how you never, ever, never have to use fractions.  Then she ends  by raising a finger in the air and stumbles through a delightfully mushy paragraph about how wonderful it would be if everybody in the world used the same math language and temperature scale.

“Hmmm” I scratch my chin again, take a deep breath and then, strike like a cobra.

“Honey” I ask sweetly, “do you know there is only one country in the whole world in which the people made up their own natural minds, as opposed to being told by the government that is, how little or how much of the metric system they should adopt, and what that country was?”

 “No, I didn’t know that” she replied brightly thinking no doubt that for once Grandpa was serious about something, “was it uh, Sweden?”

 “No” I shook my head slowly, “it was your country.  The United States of America.  Back in the sixties and seventies the Federal Government made a big push for the metric system, funding school materials, forcing states to post the speed limits in both miles and kilometers per hour, even bank signs to give the degrees in Celsius.  And do you know what happened after the American people chewed on it for a while.”

 “No Grandpa I don’t.”

 “Well” I winked, “they decided it made them want to throw up.”


 “And maybe you should understand why.”

 So here’s roughly, how the conversation went.

 “Take feet honey.  What Americans found when they thought about it is that feet were a pretty convenient measurement for most things in life.  A foot is based on the size of a man’s foot and even if your feet are smaller you still have a rough idea in your head about how big it is because there’s always one or two attached to most men.  Which means of course that a man can pace things off without any ruler or tape measure and come up with a pretty accurate measurement.  Like suppose he wants to go to Home Depot on Saturday morning and buy some lawn fertilizer.”

 “I hate Home Depot” she glowered.

 “I know you do honey but men like it.  Anyway if he doesn’t know how big the lawn is he can pace it off both ways, easily multiply those two numbers then go shopping because he’s confident, this being a free country, the fertilizer maker is allowed to put the square footage each bag covers right on the outside in big letters and after a little simple head division he can immediately know how many bags to buy.”

 “Fine” she put her hands on her hips “but you could figure that out using the Metric System too, even easier.”

 “I don’t think so because when you think it through the Metric System means extra steps.  First of all he’d either have to find a very long tape measure or know how many meters his foot is and believe me it never is an even number, it will always be something like point two nine meters because the meter isn’t based on  those two things he has hanging on the end of his legs.  And of course, decimal points are a bother, an extra tricky step when he multiplies things in his head so may he has to get a pencil and paper which is another extra step.  Even forgetting about pacing things off just finding a tape measure is another extra tricky step especially when the kids are in the car already and if you don’t hurry one of them is going to let the dog out again.”

 “Of course if you’re taking a really long measurement and have to be super accurate the Metric System is simpler because it’s simpler work with a number like eight hundred point four six meters than whatever the measurement is in feet and inches and then a fraction of an inch but the point is that you don’t take measurements like that in daily life, specialists like surveyors or engineers do.  So for most people feet is easier.”

 I could she her thinking about that and she finally nodded, “okay Grandpa I’ll give you the feet thing for now, but what about miles?  You don’t have anything around you that makes a mile more understandable and simpler to understand than a kilometer.”

 “Sure you do because a mile isn’t measurement of distance.”

 “What?” she shook her head.

 “I mean we try to make it a measurement of distance by calculating that there’s five thousand two hundred eighty feet in one, or at least I think that’s what the number is, but that’s not what a mile really is.”

 “Then what?” she held her arms out, “does a mile measure?”



 “Sure, it’s just a simple natural human measurement  designed to make travel and geography understandable in terms of how long it takes to get from point A to point B.”

 “You’re going to have to explain that?” she took a quick look down at her talking points.

 “It’s the distance people walk, actually I think it was originally the distance Roman armies could march in an hour divided by three.  The Romans like a lot of people had a thing about threes and even today the distance most people can walk at a reasonable pace is roughly three miles an hour.  And so a mile is the distance people can walk in twenty minutes.”

 “But so what?” those arms went up again.

 “But so what” I repeated, “is the fact that just like you roughly know how long a foot is you naturally know how fast most people walk and so when you say something is ten miles away you naturally know it’s going to take you about three and a third hours to get there on your feet.  In fact you naturally know the human scale of any distance without even thinking about it.”

 “And that’s why Americans didn’t want to give up miles because it well, just made things distances easier to understand, more natural if you take my drift.”

 “But people don’t walk anywhere anymore.”

 “Yes” I patted her on the head, “but everybody learns to walk well before they learn how to drive and it’s the lesson in time and space that sticks with them and make it seem more natural.”

 She thought about that wavering, “but it’s easier to figure out the smaller measurements from a kilometer than a mile because you don’t have to divide by five thousand two hundred eighty.”

 “Sure” I shrugged, “but who ever has to do that in normal and everyday life.  Most people just need a feel for a distance and you get that much easier in miles than you do in kilometers.  I mean long would it take you to hike ten kilometers up there on the mountain where your mother and you go hiking.”

 “I dunno.”

 “I dunno either” I shrugged again.

 “But I betcha I could figure it out” she put her hands on her hips.

 “I bet you could too honey, but my point is why bother when from the moment you first waited for your Mom to walk across the floor to pick you up you were instinctively learning what a mile was and about how long it would take you to walk that ten miles.”

 “Hmmm” she frowned “the teacher didn’t say anything about a mile being a measurement of time” then lowered her head and doggedly went on to the next point, “but you have to admit when you use the Metric System you never have to worry about adding or multiplying or dividing fractions.”

 “But who does anything like that pumpkin?”

 “I dunno” little knots of concentration ran across her brow, “somebody must, I learned how in school.”

 “I never have” I snapped my suspenders, “I just use fractions naturally, just like your Mom does when she cuts up your birthday cake.”

 “Birthday cake?”

 “Sure, in fact that’s another one of the big reasons Americans didn’t adopt the Metric System because of the way it makes birthday cakes much harder to deal with.”

 She looked around rolling her eyes and I knew what she was going to say before she said it, “maybe I should talk to Grandma for a while.”

 But I was only warming to the subject.  “Look honey, the next time someone asks you to cut their birthday cake up you’ll find that it can’t be done neatly with the Metric System because you need a protractor and calipers.  Indeed the only way to cut a birthday cake evenly by eye is the way your Mom does it by first cutting it in half, then turning it and cutting it into halves again so that you have quarters then by turning it twice more and cutting it into eighths.  Finally if there’s more than eight hopeful bodies standing around with a fork in their hand, by cutting it once again by eye into sixteenths.”

 “But what?” she whooshed, “has that got to do with anything.”

 “I dunno, you started it” I shrugged, “but a birthday cake is a good demonstration of how using natural fractions, instead of the Metric System’s insistence on decimals, enables you to perform life’s little tasks with style, in a natural way.”

 “Grandpa you keep using the word natural.”

 “That’s because I’m trying to explain why people when they’re free to do what they want to do, which usually means acting naturally, don’t decide to use the Metric System for everything, because it has severe limitations in every day life.  And coming back to fractions for my final point, maybe what your teacher doesn’t understand is that just like a mile is a measurement in time not distance, fractions aren’t a measurement of either distance or time but a measurement of proportion and grace.”

 “Grace?  Like what you say before dinner?”

 “A related word honey, like in graceful.  And the best way to describe what graceful is, is what woodworkers, architects, masons, anybody who makes anything for that matter, has been aware of for thousands of years, the golden section.  A proportion that occurs over and over again in nature like in your arm.  Your hand is to your forearm what your forearm is to the length of both.  You have the same proportion in your leg, a dolphin has about the same proportions in it’s body parts as do many, many other things in nature.  It’s one of mother nature’s recurring themes and while I don’t want to get into the geometry the point about the golden section is that when you see it in say the relationship between the width of a table and it’s length or in a Greek temple it just looks naturally pleasing.  And that’s what fractions do, approximate these relationships just like the fraction five eighths to one approximates the golden section.  And the wonderful thing about these natural fractions is that most of the time you can juggle them by eye just like you cut a birthday or maybe the way your Mom places the furniture in a room so that it’s stylish and pleasing.”

 But while I was saying I was her watching her own eye glaze over and I snatched the paper from her hand, folded it and stuck it back in her pocket.

 “So whatayousay we hold off learning why a dozen is easier to divide up then ten or why our temperature scale is more precise than Celsius or any discussion of pounds, ounces, quarts and gallons for another day.”

 “And do what?” she asked.

 “Well I was thinking and since Grandma is busy in her office drive the three miles down to the pizza place because if we walked it would take us what?”

 “A hour” she nodded smiling.

 “Then order a large, not a point one nine meter, pie with extra cheese and pepperoni and hope he doesn’t make a mess of it by trying to cut it using the Metric System so that you, me, Grandma and your brother who I know is on the way over can each have?”

 “A quarter of it” she laughed, “only…”

 “Only what?

“Grandma doesn’t like pepperoni.”