" data-original-title="" title="">John Coltrane. For Alexander, Trane's tune "Giant Steps" and his mandala musical diagram of five-pointed stars circumscribed by the circle of the chromatic scale embody his insights into modern physics. Alexander suggests that Coltrane's knowledge of relativity theory and modern physics enabled him to expand the scope of jazz to its farther reaches. That contention seems exaggerated. In light of Coltrane's wide-ranging interests in philosophy, spirituality, literature, and world music, physics was only one of many intellectual influences. "Giant Steps" and the mandala were the products of a synthesizing mind drawing from many sources, a mind that was obsessed with music, not physics. (As Alexander points out, rare were the moments when Coltrane was found without a horn in his hands.)

Despite his almost fanatical zeal about the jazz-physics connection, Alexander's arguments are thorough-going and rooted in mathematics, theoretical discussions, and decisive experiments and observations. The particulars of such research and theories are difficult for the uninitiated reader to grasp. Even with the considerable help generously given by the author, non-physicists can only begin to understand what these sophisticated equations and experiments represent. However, a lay person's approximation of what it all adds up to might be as follows.

Jazz and physics, Alexander tells us, are linked by analogies, striking similarities that make for useful comparisons. To begin with, Einstein's relativity theories state that time and space bend over into one another, sort of the way a jazz musician bends notes and rhythms. Thus, a very fast moving projectile (approaching the speed of light) shrinks in length and its time slows down (now verified by countless measurements). By analogy, in jazz, the use of the same note in a different chord makes the note itself sound different. (The notes we hear are "bent" in musical time/space by their context.) Next enters quantum theory, which says that there is a degree of unpredictability in the universe, analogous to improvised music that can't be known in advance. Finally, string theory (which despite the author's enthusiasm is still controversial) says that the most fundamental subatomic elements are comparable to vibrating strings whose frequencies in various dimensions ultimately determine the way the universe is constructed. Scientists used to think everything was built from atoms and the void; then the physicists discovered that atoms are made of wavelike fuzzy particles called quanta, an example being a photon of light. String theory says these wave/particles result in turn from the actions of infinitesimally small vibrating strings that fill the vacuum of time/space. Similarly, in jazz, a sequence of notes (vibrations) in a melody fills the vacuum of silence, resulting in extended improvisations. Overall, both the cosmos and jazz are resilient time/space vibrations that result in shapes and forms that are not entirely predictable.

Alexander's perspective is thus largely based on string theory, the theory that the universe is a vast array of vibrations analogous to musical notes. If string theory is true, then it makes sense that music and the cosmos both ultimately consist of vibrations which, in the case of music, follow the rules of melody and harmony (