“The Road to Reality” is exceptionally complete, with great chapter endnotes and a few hundred drawings. Book 121 “Shadows of the Mind” has some details on Roger Penrose, who has co-authored books with other physics greats like Richard Feynman and Stephen Hawking. (For his books I've read, click on his name.)

For the serious science lay reader, this book is “the most comprehensive and sophisticated account yet written of the physical universe and its underlying mathematical theories.” It has a detailed 9-page Contents that shows the amazing scope of its coverage. Penrose prepares you for the physics by first presenting 16 chapters (382 pp) of mathematics. The thoroughness of the math, and his excitement over its beauty, especially the way he resonates to the “magic” of complex numbers and topology, is astounding. With my geometric intuition I especially liked his introduction to many ideas of topology that I hadn’t encountered before. Then the physics is systematically developed over the remaining 18 chapters (667 pp). The physics emphasizes relativity, quantum mechanics and quantum field theory, but it also covers very well “classical” physics as the necessary background from which “modern” physics grew. Penrose gives you a thorough history of the development of both mathematical and physical ideas, so you can enjoy the sense of discovery as progress was made, often in unusual and unexpected ways, in both fields. Their growth was often in parallel – a point which you would expect a great mathematical physicist like Penrose to highlight. His 36-pp Bibliography is very comprehensive.

What he accomplishes so well in this book is threefold. First, he gives an overall description of our present understanding of the universe and its physical behaviors, ranging from subatomic particles to the movements of planets, stars and black holes in the vastness of space-time. Second, he evokes the extraordinary beauty that lies in the mysterious and profound relationships between these physical behaviors and the subtle mathematical ideas that explain and interpret them. Third, as he explores the compatibility of the two grand theories of modern physics, he comes to the firm conclusion that Einstein’s general theory of relativity stands firm while quantum theory, as presently constituted, still needs to be refashioned. Along the way he confronts issues, controversies, and phenomena that arise in various ways in the two main areas: in math, with the roles of various kinds of numbers (especially complex numbers), infinities and modern geometry; in physics, with the profound challenge of the second law of thermodynamics to the big bang (w or w/o inflation), black holes, string theory, M theory, loop-quantum gravity, “twistors,” and, finally, educated guesses about science in the near future.

The “problem of measurement” in quantum physics looms large to Penrose, who has an “unpopular” idea of it. Since the solutions to Schroedinger equation are fixed by the boundary conditions, these unitary (U-space) solutions in complex variables are completely deterministic. However, the process of measurement forces us to “project” from U-space into R-space (the real-number space-time found in measurements). In so doing, we lose information and now have to deal with the probabilistic world of R-space. He sees this as a more basic and thus a more serious problem than the current inability to formulate a quantum theory of gravity – the long-sought grand unified theory (GUT) of today’s string or M theorists. He doesn’t seek a way out by invoking “hidden variables” but feels a more revolutionary approach will be needed. Roger Penrose doesn’t mention this, but I find an analogy in the ideas of “Flatland” (book 49) where the 2D “shapes” creatures of Flatland can’t even imagine a 3D world – only when a Sphere took a Circle out of Flatland into the real 3D world could the Circle imagine a third dimension. My analogy is that we (stuck in the R-space of measurement) can’t imagine the non-probabilistic solutions in the complex-number world of U-space. Penrose confronts this (and all) problems of present-day physics and suggests that solutions may have to await the unification of gravity with quantum theory. He feels strongly that gravity holds the key. If I were allowed to have only one science book with me on a long confinement, it would be this book. It is a hard read, even for a “serious science lay reader,” but I loved it!