What is fuzzy logic? The original concept, developed in the mid- '60s by Lotfi Zadeh, a Russian-born professor of computer science at the University of California, Berkeley, is that things in the real world do not fall into the neat, crisp categories defined by traditional set theory, like the set of even numbers or the set of left-handed baseball players. In standard Aristotelian logic, as in computer science, membership in a class or set is not a matter of degree. Either a number is even, or it is not. But this on-or-off, black-or-white, 0-or-1 approach falls apart when applied to many everyday classifications, like the set of beautiful women, the set of tall men or the set of very cold days.

To deal with such cases, Zadeh proposed that membership in a set be measured not as a 0 or a 1, but as a value between 0 and 1. Thus, in the set of tall men, George Bush might have a membership value of 0.7, while Kareem Abdul-Jabbar might have a 0.99. Zadeh and his students went on to elaborate a full fuzzy mathematics, devising precise rules for combining vague expressions like "somewhat fast," "very hot" and "usually wrong".

This mathematics turns out to be surprisingly useful for controlling robots, machine tools and various electronic systems. A conventional air conditioner, for example, recognizes only two basic states: too hot or too cold. When geared for thermostat control, the cooling system either operates at full blast or shuts off completely. A fuzzy air conditioner, by contrast, would recognize that some room temperatures are closer to the human comfort zone than others. Its cooling system would begin to slow down gradually as the room temperature approached the desired setting. Result: a more comfortable room and a smaller electric bill.