It's exactly a century since publication of Flatland, that romance of life in other dimensions by the Victorian schoolmaster Edwin Abbott Abbott. Fittingly, a latter-day mathematician, logician, and sf writer has used the anniversary to expand and expound upon the meaning of space. In particular, Rucker supplies images and constructions to lead the reader to a more concrete grasp of four- and higher-dimensional spaces, all the way to the infinite dimensional Hilbert space that is the mathematical model of quantum mechanics. Early on he explores the kinds of space build-up familiar to geometry classes. Thus, if one draws a line perpendicularly to a straight line, one can fill out a two-dimensional plane; add a mutually perpendicular axis, and you have the dimensions of 3-space, and so on; In this way, a well-known model of four-dimensional space--the tesseract or hypercube--is conceived and illustrated. Rucker also frequently works by analogy to Flatland, using cartoon figures and diagrams to sketch how geometric figures (the people of Flatland) can be flipped over and transported through higher dimensions. The pages of the text themselves become multidimensional--with running text, sidebars composed of quotes, puzzles, and the cartoons. But this animated, often amusing excursion into purely mathematical ideas then passes into the kind of other-universe/time-travel/blackhole-wormhole ideas popularized in many cosmological and science fiction works, and finally into the realms of mysticism of the all-is-one-one-is-all thinking of an Ouspensky. Rucker even discusses a kind of synthesis-matter, antithesis-space concept in which both are synthesized into a continuous aether. As Martin Gardner aptly says in the foreword, the all-is-one-one-is-all approach may not be to everyone's taste or liking; but there's no denying that Rucker's ingeniousness sets the reader thinking in new ways on fascinating puzzles. For special tastes: rare treats.