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COPYRIGHT 2004 Natural History Magazine, Inc.
Most people assume that the more information you have about something, the better you understand it. Up to a point, that's usually true. When you look at this page from across the room, you can see it's in a magazine, but you can't make out the words. Get closer, and you'll be able to read the article. If you put your nose right up against the page, though, your understanding of the article's contents will not improve. You may get more visual detail, but by being so close you'll sacrifice crucial information--whole words, entire sentences, complete paragraphs. The old story about the blind men and the elephant makes the same point: if you stand a few inches away and fixate on the bard, pointed projections, the long rubbery hose, the thick, wrinkled posts, and the dangling rope with a tassel on the end that you quickly learn not to pull, you won't be able to tell much about the animal as a whole.
One of the challenges of scientific inquiry is knowing when to step back--and how far back to step--and when to move in close. In some contexts, approximation brings clarity; in others it leads to oversimplification. A raft of complications sometimes point to true complexity and sometimes just clutter up the picture. If you want to know the overall properties of an ensemble of molecules under various states of pressure and temperature, for instance, it's irrelevant and sometimes downright misleading to pay attention to what individual molecules are doing. A single particle cannot have a temperature, because the very concept of temperature addresses the average motion of all the molecules in the group. In biochemistry, by contrast, you understand next to nothing unless you pay attention to how one molecule interacts with another.
Let me put the issue this way: When does a measurement, an observation, or simply a map have the right amount of detail?
In 1967 Benoit B. Mandelbrot, a mathematician now at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York, and also at Yale University, posed a question in the journal Science: "How long is the coast of Britain?" A simple question with a simple answer, you might...
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