A Nobel Prizewinning chemist bridges science and philosophy in explaining how chaos theory shows that time is real and determinism untenable. To some, the title may misleadingly suggest a book about the hopelessness of knowing whether anything is real. In fact, Prigogine (coauthor, Order Out of Chaos, 1984, etc.) argues that one object of everyday belief--the irreversibility of events, or the arrow of time--is much more real than classical and quantum physics have allowed. According to Prigogine, most physicists, from Newton to Einstein to Stephen Hawking, have described the universe as deterministic and ``time-symmetrical''--with the corollary that time, probability, and free will can only be illusions resulting from human ignorance. Because that view conflicts with much of philosophy and common sense, it has contributed to the alienation of science from the rest of human culture. Prigogine moves toward ending that alienation by affirming the reality of time, arguing that advances in the physics of nonequilibrium processes and unstable systems now make it possible to revise the basic laws of physics ``in accordance with the open, evolving universe in which mankind lives.'' In passages dense with mathematics, Prigogine shows how probability and irreversibility affect particle interaction, thermodynamics, classical and quantum mechanics, and cosmology. The validity of these claims can only be judged by specialists; the general reader is given little aid in understanding them, much less in gauging how well they support the author's belief that ``we are actually at the beginning of a new scientific era.'' But the nonmathematical sections of the book concisely outline Prigogine's brand of realism: one in which actions have meaning and creativity is prized because consequences are real and the future cannot be predicted. A blend of philosophy and physics that will stir both specialists and nonspecialists to think freshly about what is real.