Death by Black Hole: And Other Cosmic Quandaries by Neil deGrasse Tyson Read Free Book Online

be able to read the chapter. If you put your nose right up against the page, though, your understanding of the chapter’s contents does not improve. You may see more detail, but 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 hard, pointed projections, or the long rubbery hose, or the thick, wrinkled posts, or 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 points to true complexity and sometimes just clutters 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. As we will see in Section 3, 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.
    So, 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 expect. But the answer is deeper than anyone had imagined.
    Explorers and cartographers have been mapping coastlines for centuries. The earliest drawings depict the continents as having crude, funny-looking boundaries; today’s high-resolution maps, enabled by satellites, are worlds away in precision. To begin to answer Mandelbrot’s question, however, all you need is a handy world atlas and a spool of string. Unwind the string along the perimeter of Britain, from Dunnet Head down to Lizard Point, making sure you go into all the bays and headlands. Then unfurl the string, compare its length to the scale on the map, and voilà! you’ve measured the island’s coastline.
    Wanting to spot-check your work, you get hold of a more detailed ordnance survey map, scaled at, say, 2.5 inches to the mile, as opposed to the kind of map that shows all of Britain on a single panel. Now there are inlets and spits and promontories that you’ll have to trace with your string; the variations are small, but there are lots of them. You find that the survey map shows the coastline to be longer than the atlas did.
    So which measurement is correct? Surely it’s the one based on the more detailed map. Yet you could have chosen a map that has even more detail—one that shows every boulder that sits at the base of every cliff. But cartographers usually ignore rocks on a map, unless they’re the size of Gibraltar. So, I guess you’ll just have to walk the coastline of Britain yourself if you really want to measure it accurately—and you’d better carry a very long string so that you can run it around every nook and cranny. But you’ll still be leaving out some pebbles, not to mention the rivulets of water trickling among the grains of sand.
    Where does all this end? Each time you measure it, the coastline gets longer and longer. If you take into account the boundaries of molecules, atoms, subatomic particles, will the coastline prove to be infinitely long? Not exactly. Mandelbrot would say “indefinable.” Maybe we need the help of another dimension to rethink the problem. Perhaps the