Cornell applied mathematics professor Steven Strogatz takes readers on a pleasant trip to the square root of -1. Elementary stuff, but enjoyable nonetheless. Numbers may be carefully fixed concepts, but their relationship to one another is metaphorical, even when one doesn’t realize that a metaphor is governing thought. The real numbers are part of a metaphorical number line or ruler, and certain kinds of problems cannot be solve within that metaphorical paradigm — no square roots for negatives, for example. But that doesn’t mean the problems are actually insoluble, only that a different metaphor has to govern the solution; in this case, as Professor Strogatz shows, a two-dimensional metaphor provides a new concept, 90-degree rotation, that makes a solution possible. To a degree that is not immediately obvious, the naive assumption that a ruler or line is the best way to think about numbers limits the conclusions you can reach. It’s an illustration of the power of metaphor, both to blind us to elegant and rather simple solutions and to help us think out way out of a conceptual blind alleys.