Physicist Davies, who has exercised his special gifts in popularizations of cosmology (The Runaway Universe) and quantum mechanics (Other Worlds), here confronts the reader with the conundrums and crises that affect astrophysics when theorems are carried to their logical conclusions. The names Hawking, Penrose, and Wheeler are significant in this context, and Davies brings them on stage as principal actors to explain how logic can lead to chaos, an end to causality, an ""anything goes"" condition where even God can be invoked without offending reductionists. The crux of Davies' book: where other physicists see black holes--as the conjectured ends of massive stars suffering gravitational collapse--Davies sees a ""naked singularity."" And while black holes involve the force of gravity becoming so great as to trap light within an ""event horizon,"" Davies' ""naked singularity"" has no such event horizon at all. His dramatization goes something like this: Suppose an exactly spherical star collapses. Then gravity's force becomes infinite as does the curvature of spacetime. Matter gets squeezed into an ever-diminishing volume of spacetime which, in the limit, is nothing. No structure. No dense lump. No ""beyond."" Just the end of spacetime; the edge of infinity. But since there is no event horizon, light was not trapped, hence a ""naked singularity."" In less able hands, Davies' account might be considered a bit melodramatic. ""The evaporating black holes and the absence of a definite proof of cosmic censorship suggest that a naked singularity is a serious proposition. If that is so. . . then nature is threatened with anarchy. When a singularity bursts upon the universe, the rational organization of the cosmos is faced with disintegration."" Or maybe integration--for Davies then adroitly proposes that the Big Bang was a singularity that began spacetime. The reader may well feel Alice-like in Davies' wonderland, but it is an exhilarating experience. For one thing, he takes pains to explain the mathematical notions of limits and orders of infinity--of ""countably"" infinite sets, and the higher order of infinity represented by points on a line. He also makes interesting analogies to earlier crises in physics when logic suggested that an electron should fall into a nucleus with a burst of infinite radiation. (Wave radiation took care of that crisis.) So there is much here to reward the reader in ingenious ideas and mathematical principles. Other recent books have dealt commendably with the beginning and end of the universe; Davies touches on those matters, but hooks all to the naked singularity--and makes it a remarkable foil.