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This is the definitive popular exploration of what the fourth dimension means, both physically and spiritually. Mathematician and science-fiction novelist Rudy Rucker takes readers on a guided tour of a higher reality that explores what the fourth dimension is and what it has meant to generations of thinkers. The exciting and challenging journey is enhanced by more than 200 illustrations and a host of puzzles and problems (with answers).'This is an invigorating book, a short but spirited slalom for the mind.'— Timothy Ferris, The New York Times Book Review'Highly readable. One is reminded of the breadth and depth of Hofstadter's Gödel, Escher, Bach.'— Science'Anyone with even a minimal interest in mathematics and fantasy will find The Fourth Dimension informative and mind-dazzling... [Rucker] plunges into spaces above three with a zest and energy that is breathtaking.'— Martin Gardner'Those who think the fourth dimension is nothing but time should be encouraged to read The Fourth Dimension, along with anyone else who feels like opening the hinges of his mind and letting in a bit of fresh air.'— John Sladek, Washington Post Book World'A mine of mathematical insights and a thoroughly satisfying read.'— Paul Davies, Nature Magazine

To see objects that live in the fourth dimension we humans would need to add a fourth dimension to our three-dimensional vision. An example of such an object that lives in the fourth dimension is a hyper-sphere or “3-sphere.” The quest to imagine the elusive 3-sphere has deep historical roots: medieval poet Dante Alighieri used a 3-sphere to convey his allegorical vision of the Christian afterlife in his Divine Comedy. In 1917, Albert Einstein visualized the universe as a 3-sphere, describing this imagery as “the place where the reader's imagination boggles. Nobody can imagine this thing.” Over time, however, understanding of the concept of a dimension evolved. By 2003, a researcher had successfully rendered into human vision the structure of a 4-web (think of an ever increasingly-dense spider's web). In this text, Stephen Lipscomb takes his innovative dimension theory research a step further, using the 4-web to reveal a new partial image of a 3-sphere. Illustrations support the reader's understanding of the mathematics behind this process. Lipscomb describes a computer program that can produce partial images of a 3-sphere and suggests methods of discerning other fourth-dimensional objects that may serve as the basis for future artwork.