There are two major ways to approach any situation: "top-down" and "bottom-up". An understanding of how these two tactics complement each other can help reveal when each is most appropriate.
A top-down style moves from general to specific. It begins with the big picture, overarching principles, wide-angle views, and then zooms in to reveal increasing levels of fine detail. When something is clearly feasible but demands a coordinated approach, with harmonizing contributions from multiple sources, top-down methods make a lot of sense.
A bottom-up style, on the other hand, goes from atomic scales toward the macroscopic world. It begins with fundamentals, first principles, infinitesimal slivers, and then puts those building blocks together to create the whole. When something depends utterly on getting every detail right, as in proving a mathematical theorem, and when the pieces are relatively independent modules which can be clicked together in a straightforward fashion, then bottom-up methods make a lot of sense.
Flexibility in applying both top-down and bottom-up approaches can offer extraordinary power. Consider the problem of optimizing a computer program. (It's analogous to doing just about anything in life more efficiently!) A bottom-up attack focuses on the key subroutines --- chokepoints on which the processor is spending most of its time. Those are high-leverage areas where software tweaks can pay off directly in big performance gains. A top-down view, in turn, explores the gestalt structure of the program. From that kind of perspective, often it's possible to spot opportunities for radical reorganizations that can save orders of magnitude of effort. Going back and forth, moving smoothly between general and specific, gives both bottom-up and top-down methods the chance to work together, each contributing what it does best.
The short movie Powers of Ten (by Charles and Ray Eames) offers a wonderful visualization of the universe, from sub-nuclear to galactic-supercluster scales. It's an example of moving among levels in a nonalgorithmic domain. Another example is captured in a proverb of John Archibald Wheeler, describing gravitation: "Matter tells space how to curve. Space tells matter how to move." The levels work back and forth, in mutual feedback loops, each guiding the other.
Sunday, May 16, 1999 at 18:27:24 (EDT) = Datetag19990516