The author of Paradigms Lost and Alternative Realities shakes the reputation of mathematics as the irresistible force of scientific exploration in this lively series of lectures on everyday systems (like

 weather forecasting and the stock market) that refuse to yield to predictability. Casti's casual, wide-ranging command of number theory makes his working metaphors, such as a ``Chocolate Cake Machine''

analogy for algorithms, seem patronizingly simple, but this friendly touch ensures that even the casual science reader may peek over the edge of the mathematics reality that today's theorists live on. The five

frontiers of prediction covered here represent a spectrum of sciences from socio-biology to the nature of computation itself. Ironically, several of Casti's cases are so well-developed that even his concise,

simplified expositions obscure the book's real theme: we are approaching the limits of reliability in science. Readers of Martin Gardner's recreational math titles--Mathematical Carnival etc.--will recognize the spell of numbers that holds this collection together.