Shadows of reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought.

This book explores models of fourth-dimensional space and how they are applied in physics and art. The most routine four-dimensional view of space is called the Flatland model. Robbin contrasts this model with the projection, or shadow, model. In it, parallel lines meet at infinity and create the perspective found in real life. Pablo Picasso employed the projection model when he invented cubism, writes Robbin, an artist and computer scientist. Mathematician Hermann Minkowski and physicist Roger Penrose developed the model. Physicists now use it to explain the quantum world, Robbin writes. He reviews the history of four-dimensional geometry, explains how four-dimensional models can envision a person walking through a wall, and explores the fourth dimension in art. The author summarizes how the development of computerized models can aid in the visualization of four-dimensional geometry. Yale, 2006, 137 p., b&w illus., hardcover, $40.00.