Knocking on Heaven's Door - Lisa Randall [12]
When appropriate, it makes sense to ignore minutiae in order to focus on the topic of interest and not to obscure it with inessential details. A recent lecture by the Harvard psychology professor Stephen Kosslyn reminded me how scientists—and everyone else—prefer to keep track of information. In a cognitive science experiment that he performed on the audience, he asked us all to keep track of line segments he presented on a screen one after the other. Each of the segments could go “north” or “southeast,” and so on, and together they formed a zigzagging line. (See Figure 2.) We were asked to close our eyes and say what we had seen. We noticed that even though our brains allow us to keep track of only a few individual segments at a time, we could remember longer sequences by grouping them into repeatable shapes. By thinking on the scale of the shape rather than the individual line segment, we could keep the figure in our heads.
[ FIGURE 2 ] You might choose as your component the individual line segment or a larger unit, such as the group of six segments that appears twice.
For almost anything you see, hear, taste, smell, or touch, you have a choice between examining details by looking very closely or examining the “big picture” with its other priorities. Whether staring at a painting, tasting wine, reading philosophy, or planning your next trip, you automatically parcel your thoughts into the categories of interest—be they sizes or flavor categories, ideas, or distances—and the categories that you don’t find relevant at the time.
The utility of focusing on the pertinent questions and ignoring structures too small to be relevant applies in many contexts. Think about what you do when you use MapQuest or Google maps or look at the small screen on your iPhone. If you were traveling from far away, you would first get some rough idea where your destination is. Subsequently, when you have the big picture, you would zoom into a map with more resolution. You don’t need the additional detailed information in your first pass. You just want to have some sense of location. But as you begin to map out the details of your journey—as your resolution becomes finer in seeking out the exact street you will need—you will care about the details on the finer scale that were inessential to your first exploration.
Of course, the degree of precision you want or need determines the scale you choose. I have friends who don’t pay much attention to hotel location when visiting New York City. For them, the gradations in character of the city’s blocks is irrelevant. But for anyone who knows New York, those details matter. It’s not enough to know you are staying downtown. New Yorkers care if they are above or below Houston Street, or east or west of Washington Square Park, or even whether they are two or five blocks away.
Although the precise choice of scale might differ among individuals, no one would display a map of the United States in order to find a restaurant. The necessary details won’t be resolvable on a computer screen displaying such an overly large scale. On the other hand, you don’t need the details of a floor plan just to know that the restaurant is there in the first place. For any question you ask, you choose the relevant scale. (See Figure 3 for another example.)
The Eiffel Tower
[ FIGURE 3 ] Different information becomes more obvious when viewed at different scales.
In a similar manner, we categorize by size in physics so we can focus on the questions of interest. Our tabletop looks solid—and for many purposes we can treat it as such—but in reality it is made up of atoms and molecules that collectively act like the hard impenetrable