The Road to Reality A Complete Guide to the Laws of the Universe;
Roger Penrose. Vintage, 2004
Hardback, 1140 pages.

There is inherent irony in the subtitle of this book. Roger Penrose is an unrelenting critic of String Theory and its proponents who believe they are on the verge of finishing the physics textbook.

Penrose has punted this book at a fairly wide readership. He implies that a reader with with a fear of mathematics might take to the gentle pace of the his elucidation. I rather think that Penrose’s whirlwind narrative from Pythagoras to complex manifolds, tensors and gauge theory in the first four hundred pages is more like a Ludovico treatment to ingrain fear and nausea of mathematics. Having one’s eyelids fastened open to the strains of Beethoven’s Ninth is perhaps the appropriate way to read this book. Survivors of Penrose’s crash course in abstract mathematics are treated to an even denser exposition on the development of modern physics that forms the bulk of the text.

It is perhaps more revealing to describe what I got out of this book than to describe its contents in any piecemeal way. I have a degree in mathematics, but I’m more disposed to logic and number theory than the mystery of manifolds or theoretical physics. Before a final exam on Relativity Theory I made sure I could spell ‘Schwarzschild’ because I knew I needed all the marks that I could get.

The section on Complex Numbers is among the most lucid parts of the book. It includes a few gems such as Lambert’s sphere of imaginary radius, that predates the Hyperbolic geometry of Bolyai and Lobachevsky. Perhaps complex mathematics is given such an elegant elucidation because of its centrality to the Twistor Theory that Penrose advocates in preference String Theory. The treatment of Pythagoras and Platonism was interesting, as were Penrose’s vivid depictions of the physics of Aristotle, Galileo and Newton that laid the foundation to the more challenging ideas of Minkowskian geometry. However, important topics such as manifolds and tensors were introduced with frightening brevity when they played such a crucial part in the physical theories. I got the impression that Penrose began the book with the intent of introducing ideas at a gentle rate, but his pace changed as he started to wonder if he would live to finish this book. (He says in the preface that he spent eight years writing it).

I have read many popular books on mathematics that surpass The Road to Reality in comprehensibility, though few authors have had the audacity to attempt such a vast and comprehensive tract as this. While I don’t feel that I have the complete understanding of the Laws of the Universe that I had hoped for, I am inclined to learn more about Spinors and Twistor Theory, thanks to the tantalising glimpse that this book has given me.

Roger Penrose is exceptionally modest and it might easily escape the casual reader’s attention that he was responsible for many of the theoretical discoveries that feature in the book such as the foundations of Twistor Theory, work on singularies in General Relatitivity and Aperiodic Tiling. The schematic representations of Minkowskian spacetime used throughout the book are actually called “Penrose diagrams”. The ‘birdtrack’ tensorial notations also appear to be a Penrose innovation. As a personal touch Penrose has eschewed tools like Mathematica, in favour of his own hand drawn diagrams, including a fanciful ‘Phase Space representation of the Creation’.

Many skeptics will be aware of Roger Penrose as the author of notorious theories of dualism espoused in popular science books such as The Emperor’s New Mind and Shadows of the Mind that speculate about the interplay of quantum gravitational effects and our neurophysiological makeup in order to explain consciousness. Quantum Gravity makes an appearance in this work too — Penrose holds strong hopes for a future theory of quantised gravitation to provide a deterministic explanation of quantum state space reduction, which he calls ‘Objective Reduction Theory’. Fortunately the reader is given clear warnings when Penrose is deviating from the orthodoxy and he proposes a falsifiability criterion for Objective Reduction Theory to counter accusations that he is embarking on a metaphysical speculation.

This multiplicity of views is one of this books many strengths. By outlining many of the strands of thought that constitute the ‘state of play’ in theoretical physics, the reader gains a more nuanced and contextualised understanding of the emerging physical theories that they might encounter in the popular science press.

Originally published in the Skeptic Vol 26, No 4 Summer 2006
(https://www.skeptics.com.au/wp-content/uploads/magazine/The Skeptic Volume 26 (2006) No 4.pdf)