Tuesday, September 7, 2010

If We Only Had Twelve Fingers

Standard Kilogram Mass, one of 40 made in 1884 which were exact copies of the international prototype kilogram kept at the Bureau International des Poids et Mesures in Sèvres, France

Sitting around tonight arguing with my friend Gwyan about the Metric System, I found myself embroiled in a very interesting discussion about the nature of measurement and the extent to which people will follow rationalism.

The thing is, despite the fact that it's based on our own ten fingers, I don't like the metric system. I don't like a system that requires decimal calculations and which won't easily divide by anything other than 5 or 2. It is not ultimately logical for people who make clothes out of four basic panels (and have to size those panels up and down), and in my opinion anything that requires an infinitely repeating decimal to represent a third of the measuring unit is crazy. It just doesn't make my life better. The system was made up by a bunch of rationalists who got carried away with creating a completely new system that people in different countries would accept -- for the sole reason that they wanted something new. It figures that it caught on -- only something this untidy and bizarre would.

Well, mostly. The British didn't accept the metric system for many, many years, despite the Victorian institution of universal education -- probably because the system had originated in France. But that's a whole 'nother story. Curiously, though, the idea originated with an Englishman, John Wilkins, first secretary of the Royal Society of London, in 1668. The idea didn't catch on, and the English went right on with their intricate monetary system and their 20-ounce pints.

But then "in 1670, Gabriel Mouton, a French abbot and scientist, proposed a decimal system of measurement based on the circumference of the Earth... His ideas attracted interest at the time, and were supported by both Jean Picard and Christiaan Huygens in 1673." [wiki]

Well, that explains a lot. In the days of Reason and Enlightenment, systems which tidied up numbers and arranged them in clean lines and shapes were all the rage. Metrics are a perfect example:

"1000 litres = 1 cubic metre ≈ 1 tonne of water; 1 litre = 1 cubic decimetre ≈ 1 kilogram of water; 1 millilitre = 1 cubic centimetre ≈ 1 gram of water; and 1 microlitre = 1 cubic millimetre ≈ 1 milligram of water."

This would appeal enormously to a culture of gleeful intellectualism, the same one that came up with Napier's Bones and calculus.

It was dear, rational, idealistic France who went for the wholehearted changeover, of course:

"The inconsistency problem was not one of different units but one of differing sized units. Instead of simply standardising the size of the existing units, the leaders of the French revolutionary Assemblée Constituante decided that a completely new system should be adopted. It was felt that no country would accept standardising on the units of another country, but that there would be less resistance if a completely new system made change compulsory for all countries." [wiki]

In other words, they threw out measurements that had been working for individual people for hundreds of years or more, because of an ideal. Not a bad thing, maybe, and in talking with Gwyan, I was hard-pressed to describe my aversion to base-10 systems of measurement. I don't have a problem with base-10 monetary systems; money is, after all, pretty much about numbers, and our numeric system is base-10, so it follows. It's pretty straightforward that any being with ten digits is going to have a base-10 number system. And the beauty of the metric system is that if the units you're working with start to need dividing, you can simply slide down into the next unit level and viola! You're working with whole numbers again. It's a different way of thinking: you're not working so much with pieces and parts, but rather with a sort of layered mesh of wholes, through which you can move as needed. Which is fine for distance or weight, but not so good for discreet objects like eggs or minutes.

And that 1/3 measure, that sticks in my throat. You can go on sliding downward in unit size forever and never get to the bottom of the number; it will always be an estimate, a rounding-up or -down. And it bothers me, as someone who used to work in the garment industry, that dividing things in fourths involves such an awkward number as 2.5, or even 25. Those are not friendly numbers (*see below); they don't show up in the kind of kitchen that has a cast-iron pot at the fire and herbs hanging from the ceiling. These numbers don't believe in us and our four-cornered world; so I don't believe in them, either (so there).

The madness of post-Revolutionary France bears me out on this. They redesigned everything to be about tens: the 10-hour clock (as opposed to 12-hour); their new calendar had 12 months but with 10-day weeks; and of course, money, length, weight, volume and so on. The breadth of it was staggering: they were redesigning the universe to fit itself to our hands -- our five-fingered, flower-like hands.

(Image by Sue Ford)

True, there is something beautiful and otherworldly about the number 5. It exists in nature, but it doesn't fit into everyday symmetry the way the simple triangle can. Drawing a pentagram accurately is a tricky proposition. We don't think in fives: when we count pennies, most people make groups of twos and threes. It is beyond and above the natural grooves of our minds, and this may be why the pentagram (and pentagon) has always had such magical significance**.

But really -- should we be redesigning our whole cultural definition of space and mass into fives? They may be beautiful, but they are absolutely not practical, at least not in any world that I inhabit.

(Image thanks to The Steampunk Home)

Interestingly, Gwyan pointed out that the metric system is more useful in bureaucracies, mass-production, and science, where the numbers need to be able to go very large or very small. This is a wonderful point, because I think what I object to about the conversion is that it is designed to benefit those industries -- not individual people, moving through their individual lives. This is precisely why the calendar is still divided into twelves, and why the 10-hour clock simply failed; why dozens and grosses are still used in bakeries and eggs in many places. People like to be able to divide time and goods many different ways, not simply into two possible factors, and fractions thereof. The Romans had a unit called an uncia, which is the basis of our words for "inch" and "ounce"; it was part of a fractional system based on twelfths.

Interestingly, there are several languages who use duodecimal number systems (otherwise known as base-12). I'm not referring to Elvish here (apparently it's one example); in Nigeria, there are several, as well as a few obscure Nepalese and Indian languages.

Another place, at least in the US, that is unlikely to change very soon is in the kitchen. Cups, ounces, and teaspoons were arrived at through usage, through what worked easily with the tools at hand.

I have to say, it's not that I dont like tens; they work just fine in a mathematical context -- for counting things, it's certainly a good idea to have your counting system match your number of fingers. It's more that for everyday use you sometimes simply can't beat the number twelve. Even those of you who write in saying you're fine with the metric system still use a 12-hour clock and a 12-month year; would you prefer it differently? And for those of you, who like me, simply like the number 12, there are "dozenal" societies in the US and the UK (they forsake the word duodecimal because it means ten plus two, which they feel is beside the point). Perhaps I'll join. After all, what a fabulous number: dividable by 2, 3, 4, and 6. Definitely a keeper.

*Note: when I say friendly numbers here, I am referring to a different property than that of the friendly numbers of number theory; nor are they amicable numbers or sociable numbers, some of which have been around since Pythagorean times.

**Pentacles, on the other hand, do not originally have an association with the number five. I didn't know that until the moment of this writing.


Oldfool said...

Well said. Although I understand and can/do use the metric system I am not comfortable with it. I may speak it but I think in feet and inches as well as pounds and ounces. Having been an aviator and a mariner most of my life I prefer nautical miles.
Dividing your fingers into quarters or thirds would be painful.
I never cared for Celsius either.

Mero said...

I've always wondered how countries that have kept the Imperial system could find it practical while counting numbers with a 10-base system, so it I had a lot of fun reading your article ^^

"We don't think in fives", you say. However, living in Argentina, where we use the metric system, at least we do think in 5s, and 10s too!

As we've also kept dozens and grosses for stuff such as pastries (!) and eggs, I can also think rather comfortably in 2s, 3s, 4s and 6s. If you add that up to our decimal 5s and 10s, I think we have quite a large scope of basic divisors to perform everyday operations. And measuring distances, area, capacity, etc is a lot more comfortable when you can go up and down leves instantaneously, as you've said.

After reading your post it gave me the impression it was more a matter of taste and custom. It's natural for someone who has grown using the imperial system to find it more comfortable than the metric, and both have their strengths and weaknesses. Yet, I believe the metric system is more useful in our (post)modern world, when we have to think not as much in countable goods but in services, money, really small or big distances, etc.

(sorry for my English!)

Christophe said...

"in 1670, Gabriel Mouton, a French abbot and scientist, proposed a decimal system of measurement based on the circumference of the Earth" : this is where it begin to get interesting.

Since the decimal system was based on the circumference of the Earth (1 meter = 10^–7 Q, where Q is the quarter of the meridian), they needed to have an exact mesure of the meridian.
So from 1792 to 1799, Jean-Baptiste Joseph Delambre and Pierre Méchain where send on an scientific expedition across Europe to triangulate the distance from England to spain.

It took them 7 years, but they manage to get a mesure of the meridian. There was only one small problem ... A small anomaly in the measurements of the ark ... Pierre Méchain was so obsessed with it that he refused to publish his result and return to Spain to start again the measurement. He died there from the yellow fever.

They didn't know yet that they'd just managed to prove that the earth was not a perfect sphere ... and so the merdian was not a valid base for the metric system :)

some links :
http://fr.wikipedia.org/wiki/Figure_de_la_Terre_et_m%C3%A9ridienne_de_Delambre_et_M%C3%A9chain (in french)

a book about this events, haven't read it : http://www.amazon.com/Measure-All-Things-Seven-Year-Transformed/dp/0743216768/ref=sr_1_1?ie=UTF8&s=books&qid=1283984729&sr=8-1

spacedlaw said...

Of course, since I grew up with the decimal system, I find it the most logical system in the world. Except for eggs. It would be silly and awkward to have just 5 if you didn't want to buy 10 (I seem to recall that I have seen eggs sold by 10 in Holland but no 5 boxes, only 4 or 6).

Patricia said...

As someone who has grown up with the metric system in both measurements and currency I have no issue with it, echoing the sentiments of my fellow metric commenters.

Patricia said...

Also: I'm 35 from Australia in case you're wondering.

Mero until you mentioned it I had no idea that English was your second language :)

Simon Forster said...

I can use both, but much prefer the old Imperial system of inches and feet, yards and miles, pounds and so forth. Partly because I'm in my 30s and British, but also because I am an old school role-player brought up on D&D :)

Anonymous said...

An advantage of nondecimal systems is that fractions of the smallest unit tend to be binary. For example, if you see a nut that's about half an inch, you confidently grab the half-inch socket. 3/8 is substantially smaller, and no one would use 9/16 or 15/32 without a reason.

Contrast metric: half an inch is 12 or 13 mm, or 11 or 14 maybe. There's no good reason to prefer one to another, so you'll need all those sockets.

Odd that we're standardizing on decimal when we've come to realize that binary is a good thing.

Heather McDougal said...

My friend Ben writes to me to say this:

"I love the anthropocentric methods of measurement that spawned the inch (knuckle to knuckle) the cubit (forearm), the yard (fingers to mid-chest), the pace (footstep) the foot etc. I love how human they are. The measurements are a part of us in a way that the meter never will be. They are human-scaled and meant for phenomological observation and understanding of the world. Something, that in our mechanistic world of precision, should be nurtured so that it is not altogether driven from us.

"The ancient systems of measurement and counting (which I am to some extent conflating unfairly) are largely based on our own bodies but also rely greatly on the divisions of circles by ancient astrologers/shamans/geomancers. We divide time into sixes and twelves being based on Mesopotamian divisions of the circle by walking its radius. Their whole number system was base-6 due to those circle divisions (and also the 360 degrees in a circle is based on the divisions of walking the circle. Of course 360 was this really perfect multiple of 6 so they were quite annoyed to find a full year was 365 1/4 days -- a much more fractious number. They conveiniently swept that under the rug by declaring 5 and 1/4 days somehow stolen or created by gods or magical beings (think Horus and Khons and their game of senet in Egyptian mythology)

"I agree the metric system is somewhat inhuman and less likely to evoke hestian sympathies. But westerners from the Roman/Byzantine/Arabic traditions have been base-10 for several millenium now, and in truth I think the ancient systems make for a messy job when trying to translate them into our number system. Even our spoken words have tend to be muddled on the matter on what number system we're using (what the heck are these "elevens" and a "twelves"? They are not "teens" which come from "ten" and they are not one of the first nine ordinals. If we are base-10 shouldn't we speak as the Japanese speak -- ju-ichi, ju-ni? In their language place value is inherent in the word)

"I think it is often confusing to many children -- and most come out as adults with poor understanding of how numbers work. The US and England are two of the very few hold-outs (and perennial underacheivers in their Math scoring) and my guess it does not help us to teach kids to have a better number sense when we continue to use a base ten to count but we still use these ancient systems to go about the math that is involved in our daily lives. We spend almost a year and a half worth of time in school trying to help them manipulate fractions in weight, measure, and abstractly because our systems needed to do these things are quite awkward in base-10 when we aren't using decimals or metrics. Then we spend an additional 1/2 year trying to teach them to convert from fraction to decimal and back. Plus, because only use the decimal systems some of the time, we don't get steady reinforcement of the skill.

"It is wonderfully anthropocentric to use these ancient systems, and maybe that is best. But it could also be considered egocentric in an international age.

"Maybe this is good, though. You're right, the metric system is indeed an excessively rational system, with all irrationality of rationality built right into it for all the world to see (a la old David Hume). The perfect pentagon is near impossible to build from a circle -- it's construction a secret held closely by many occult religions. And it is a symbol of divine construction, whereas the hexagon is for humankind to use. And look what we have done with it -- our awesome architecture, our machines and our spaceships and our sciences. It's as if we have stolen yet another sacred fire, we have eaten yet another apple...

"Which, I guess, is an interesting remark on the technological wonders that have been spawned by our rationality, as represented by our decimal system...perhaps a bit unnatural -- almost monstrous..."

Anonymous said...

As a nerdy anthropologist I just want to chime in too. I recall from way back in graduate school that the base 12 (and base 16) are very old indo-european systems. We do have these makrers on our hands as well if you look beyond the blatantly obvious. Base twelve is easy to calculate as each finger has three parts so each hand is a 12 unit calculator. Base 16 is more rare (not really related to 16ths found in inches as that is half and half and half). You can count base 16 by using the creases of each finger plus the tip.

Now the Babylonian base 60 still hiding in our system...

Anonymous said...

Oh yes, I forgot to mention, great post by the way.

nofixedstars said...

ooooh...i so enjoyed his post! i've had vague, unquantifiable objections to the metric system ever since being exposed to it; i attributed this to my general lack of mathematical (though not logical or scientific) ability, to a Luddite tendency, to aesthetics, and also to a gut feeling that there was a significant element of hubris in creating and foisting this system on large numbers of people. i LIKE small. i LIKE culturally conditioned. i don't like monolithic, industrialized, globalized, whatever-ized force-fed uniformity. your post brought clear the underlying causes of my instinctive dislike of metric usage.

Anonymous said...

Very interesting post and very good comments to boot! Yet it still seems like the objection to the metric system is entirely from a romantic perspective. Certainly, the metric system (with Celsius) was made for science but as much as people were taught the new system instead of the old ones, it is wrong to view it simply as a replacement. After all, cubits, feet and inches are still with us.

My personal objections to the imperial system partly stem from the fact that they are not even the same as American measurements (what is with that?) and that not even Brits grown up with it can easily convert between scales. I once asked, out of curiosity, how much a friend weighed in pounds only. He had no idea; he couldn't remember how many pounds there are to a stone. And neither could three other Britons in the same room.

JC said...

"A pint's a pound the world around". I thought that had something to do with the price of beer for just the longest time.
As a musician of some seniority, though, I must go on record as opposing any attempt to introduce a ten tone musical scale.
OTOH, my sisters in law (all from SA or EU) all seem to operate on the metric clock (which I introduced in an article in The Journal of Irreproducible Results sometime around 1980) using the 100 minute hour. Thjey consistently will say "I'll be there in half an hour" which equals 50 minutes.

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