THE UNIVERSE AND THE TEACUP

A short paean to mathematics in the vein of Cole's earlier volume, Sympathetic Vibrations (1984), which explored creativity, art, and beauty in relation to physics. Curiously, however, Cole, a science writer for the Los Angeles Times, does not really lead the reader into mathematical waters so much as point to the special features and charms of a mathematical perspective. No need to wrestle with equations here. Instead, Cole surveys mathematical concepts, which she groups into four parts. Part one exposes the unreality of large numbers to most of us and the human propensity to interpret risk in all the wrong ways (e.g., the risk of flying compared to that of one's everyday commute on a beltway). Part two deals with measurement and scale, noting that what we decide to measure can in itself be questionable—like intelligence—and depends on what we know. ``Astronomy is a humbling science in this regard,'' Cole says, because every time a new way to measure the universe is found, astronomers discover new types of objects. Part three covers the social world with replays here of game theory, why altruism can pay off, and how right Lani Guinier was in questioning the ``sacred ideal of majority rule.'' Lastly, she pursues the mathematics of truth as revealed in rules of probability and logic, but especially at the core of our conceptions of the universe. Here she discusses Einstein's special and general theories of relativity, singling out Emmy Noether, the brilliant German mathematician whose proof that the laws of conservation in physics are equivalent to laws of symmetry resolved questions raised about Einstein's four-dimensional space-time. Alas, Cole doesn't tell us how that was done. In sum, lots of good ideas, telling examples, and even amusing trivia that point to the importance of math, yet without revealing how mathematicians work. (line art)