Monday, March 23, 2009

A Reasonable Measure

The French Revolution set out to replace tradition with pure reason. One of the most concrete things they bequeathed to us is the famously rational metric system. There are a hundred (rationally named) centigrams in a gram, 1,000 grams in a kilogram (cent = 100, kilo = 1,000) -- certainly more logical than 12 ounces in a pound. Centigrade temperature places freezing at 0, boiling at 100, instead of the unthinkable 32 and 212. And there are a hundred centimeters to the meter, 1,000 meters to the kilometer, as opposed to the ungainly twelve inches to the foot, three feet to the yard, and -- horrors -- 5,280 feet to the mile.

Money has been standardized, too. Most modern countries are similar to the U.S. The dollar is divided by 100; coins come in 1, 5, 10, or 25; dollars in 1, 5, 10, 20, 50, 100. Reasonable. Compare the old British system. A farthing was 1/4 of a penny; 12 pennies to a shilling; 5 shillings to the pound; 21 shillings to a guinea. Who can make sense of such things?

The one rationalization that did not survive the Revolution was the calendar: 365 days = ten months, each with three ten-day weeks ("decades"), plus five holidays at the end, and a sixth for leap year. The day was divided into ten hours, each consisting of 100 minutes of 100 seconds. Rational. Orderly.

And all the new systems are based on modern science. The meter is 1/10,000,000 of the distance from one pole of the earth to the equator (though it has subsequently been given a more obscure definition in terms of the wave length of light, since the earth itself isn't perfectly rational or consistent). A gram is 1/1,000,000 of the weight of a cubic meter of water (and mass, of course, does not vary, as weight does, depending on the force of gravitation). Only money avoids any scientific grounding -- on the perfectly rational realization that money is merely a means of exchange, with no fixed value.

The problem is, none of these things are all that reasonable. Begin with the idea of 10s in the first place. It looks very nice on paper, until you realize that if we didn't have ten fingers, ten is the last number we would choose to orient our counting around. We are used to it, to be sure, but five is an awfully clumsy number, stretching the limits of simple math; 100 is so big as to be beyond visualization.

It makes far more sense to orient things around threes and fours, both of which are far more intuitive. Consider the day. The 24-hour system actually consists of 12 hours before noon, 12 after. 12 divides easily by 3 and 4. 6 is half way, 3 and 9 a quarter of the way. 7 and 8 are decent divisions between 6 and 9 (whether morning or night): to further subdivide by 2's would either make the hours too long (only one division between 6/the evening and 9/night?) or too short (my head begins to spin when I consider half of half of half). Once you divide the day into quarters -- 12, 3, 6, 9 -- three is a manageable way to break things down further.

Why do we do it this way? Because it's manageable. Because it's easy to think about. 2's and 3's, even 4's, are easy to think about. 10 is too big: you have to subdivide to get a picture of it. But it only subdivides into 5's, which are still just too clumsy. Imagine, in the Revolutionary system, dividing all the time from midday to midnight into 5 parts. It's just clumsy; there's no midway, no easy parts. 100 minutes certainly doesn't help. 60 breaks into 4 fifteens -- and it's awfully nice to talk of quarter-hours. And that breaks down into 3 x 5. All right, so we have 5-minute intervals -- but notice that we really can't think in much smaller units than that; we all joke about how absurd it is to say 6:03; we rarely even break the hour down to less than quarters. In any case, those 5-minute intervals just divide 60 into 12 parts: 12 is a manageable amount, because we can visualize 4 groups of 3. Imagine asking the time and being told, "it's 2/5ths past the hour." "??"

I see this with my little boy, who's just getting into numbers. "So, 8 is four and four?" he asked the other day. Yes, Joseph. But how did he get there? Then he tells me, "8 is two squares?!" Yes. He gets there because he can see it, because four is a manageable number. Apart from fingers, 5 is just too much. A base-10 number system forces us into nothing but 2's and 5's. Pentagons are weird.

Imagine how convenient the old British system was. A penny breaks into two (hay penny) or four (farthing). A shilling is 12 pennies -- and the standard coins were 3 and 6 pennies (three pence and six pence). Yeah. I can think about that. A pound, I'll grant you, was 5 shillings. But how delightful that a guinea was 21 shillings: 4 pounds-and-a-bit. This is a coin system designed for people to think about and do math in their head, not to look nice (with lots of 0's) on paper.

Apart from the lovely 3's and 4's, the old system is based on our senses. There are 12 inches to a foot -- partly because that makes it easy to think of a quarter-foot. But how perfect that an inch is the size of a man's first knuckle, a foot the size of a man's foot. Now that's useful. 1/10,000,000 of the quarter-circumference of the Earth might sound "scientific," but who knows how big a centimeter is? It's not based on anything.

A yard is one big stride. A mile -- did you know this? -- is from the Latin "mille," a thousand; a 1,000 big steps would be 3,000 feet, a 1,000 with each foot is 6,000 feet -- and a 1,000 slightly shorter steps, the kind you take when you're walking a long distance, comes to roughly 5,280 feet. Precise? No. But workable. How much less precise is it to use the kilometer, a distance, the kilometer with no reference to anything in our experience? How would you even approximate a kilometer? Anyway, if you want to be precise, you use a machine, which doesn't need the numbers to be nice. When the numbers matter is when you're using a rule of thumb: a thousand right-foot steps.

(Note, by the way, that here, 1,000 is a decent number, since you'll end up using your fingers.)

Fahrenheit? When do you want to know temperatures? When you're boiling water, you just wait for the water to boil. When you're going higher than that, or need to be more precise than that, you use a thermometer. (Though every candy chef knows the real signs are hard crack, soft crack, etc.) But when you want a number you can look at is when you're going outside. And you know, 0 - 100 F. is actually a pretty good range for outside temperatures. Here, we use base-10 numbers, because yeah, it's just a number to look at. Centigrade may seem real scientific, but your entire range of outdoor temperatures is significantly cut down. How useful is that?

And the Revolutionary Calendar might look very neat, but isn't a seven-day work week a little easier to think about? And when was the last time you complained that May has more days in it than February?

Here's the point I'm trying to make. Rationalism isn't rational -- certainly not reasonable. Rationalism means trying to make everything fit into a system. On the way, it throws out the data. It throws out tradition, which includes both some smart systems that have been worked out over time (like the utility of the number 12, and measures based on body parts) and all our historical documents (do you really want to have to convert every date before 1793?) It throws out the senses, so that you're more interested in things like 1/10,000,000 of the quarter-circumference of the earth than the length of your own foot. Rationalism turns Reason into a creator, instead of a receiver, a way to overrule the world around you instead of understanding it. And in the end, that isn't rational at all.

Conversely, there's nothing rationalistic about being reasonable. We who keep company with St. Thomas often get dismissed for thinking too much about syllogisms, definitions, and logical consequences. But these are the things our minds can get ahold of. Working with reasonable measures, with things we can actually wrap our brains around, is not rationalism -- it is the ultimate way to prevent rationalism.

Just like knowing how long an inch is keeps the fabric merchant from ripping you off.