Monday, May 22, 2006
I keep hearing on the news that the U.S. border with Mexico is a certain length, say, 3000 miles. This makes no sense, since part of that border is formed by the Rio Grande, a natural feature. You can't measure the length of a river's banks. The same with the coastline of a country. Think about it: at what level are you measuring? A river can have basically an infinite number of twists and turns. Depending on how close you look, you'll see twists and turns of different sizez. In other words, from space, or on a map with a scale of an inch is a hundred miles, you'll only see the turns that measure several miles or more. Flying over in a helicopter, you might see the ones that measure a few meters. Kneeling on the shore, you'll see those that measure a few inches. Depending on what size indentation you measure, you'll get a different measurement. The smaller features you measure, the longer the river will be. It's like a drunk guy staggering down the street: the more he lurches from one side to another, the farther he travels. Are you starting to get it?
Or call it by its real name: fractal geometry, which models the way natural features, such as clouds, are formed. As Benoit Mandelbrot, one of the founders of the field, put it in his 1977 book "The Fractal Geometry of Nature": "Clouds are not spheres, mountains are not cones, coastlines are not circles..." Natural features basically look the same no matter what the scale is; you can't tell from a picture of a mountain whether it's a hundred feet high or ten thousand. (They call it "self-similarity".) The best example - or at least the first - of fractal geometry is the Koch snowflake. You can't say how long its perimeter is, though you can say what its area is.
I have no idea how they come up with the measurements given for the length of rivers. Maybe there is some international standard of measurement - "use a map scale of x", or "don't measure anything smaller than y".
Then, too, rivers are constantly changing their courses, overflowing their banks, changing their lengths in another way.
Of course, large parts of the U.S. - Mexican border are straight lines, which can be measured. You can say how long California's border with Mexico is, or Montana's with Canada along the 49th parallel. So I hope the media will stick with what can actually be accurately described, and stop feeding us numbers that don't make any sense....
Was that too mean for my first post?
Or call it by its real name: fractal geometry, which models the way natural features, such as clouds, are formed. As Benoit Mandelbrot, one of the founders of the field, put it in his 1977 book "The Fractal Geometry of Nature": "Clouds are not spheres, mountains are not cones, coastlines are not circles..." Natural features basically look the same no matter what the scale is; you can't tell from a picture of a mountain whether it's a hundred feet high or ten thousand. (They call it "self-similarity".) The best example - or at least the first - of fractal geometry is the Koch snowflake. You can't say how long its perimeter is, though you can say what its area is.
I have no idea how they come up with the measurements given for the length of rivers. Maybe there is some international standard of measurement - "use a map scale of x", or "don't measure anything smaller than y".
Then, too, rivers are constantly changing their courses, overflowing their banks, changing their lengths in another way.
Of course, large parts of the U.S. - Mexican border are straight lines, which can be measured. You can say how long California's border with Mexico is, or Montana's with Canada along the 49th parallel. So I hope the media will stick with what can actually be accurately described, and stop feeding us numbers that don't make any sense....
Was that too mean for my first post?
# posted by the Commando Etymologist @ 5/22/2006 07:02:00 PM 
