Blogtrek

Simplicity is not simple

The theme for SUUSI 2003 is "Simple Gifts", i.e., the idea of simplifying your life as much as possible. Yesterday the lead article title of a magazine "Math Horizons" startled me. It's title: "Simplicity is not Simple: Tessellations and Modular Architecture". The article was about dividing up two-dimensional space (e.g., office space) into identical regions or cubicles. The square grid is one way of doing it, but hexagons save on partitions (but I have yet to see a workplace that resembled a beehive). Their point was that the problem of making things simple is not simple. In this case the obvious answer was not the optimal one. A quote from a mathematician in the article named Gregg Fleishman: "Making a good system from only a few pieces which are not too hard to machine or build is quite difficult".

Another example I can think of is, say, a UU District Executive who wants to visit all the congregations in his District. To make the job as simple as possible, she would want to minimize the total mileage she has to drive or fly. The very problem of determining the order of congregations she should visit (which one first, which one second, and so forth) is itself one of the most difficult problems in mathematics. You could check all the possible routes but with 15 congregations that would take millions of years. However, no one has come up with a solution that is that much better, and many think there isn't one. However, even that problem, that of proving for certain there isn't one, is itself an even harder mathematical problem (the P = NP conjecture).

Seeking simplicity leads to contradictions. We get contradictions when we look at the Ultimate. An omnipotent God that can lift a stone that is so big that even God can't lift it; an omnipotent, omniscient, good God in a world with evil, the smallest number that cannot be expressed in less than twenty words (that phrase has less than twenty words), the SET of EVERYTHING (just add that very idea of such a SET to that SET), and the set of all sets that are not members of themselves (is the set in itself?) are all examples of such contradictions. And simplicity joins this list.

So simplicity is not all that simple. Seeking simplicity is a complex journey, and one of the things I hope we learn next year is how to pursue simplicity in a world of antinomous complexity.