Sir Roger Penrose is one of the most distinguished theoretical physicists and mathematicians working today. He is known for his work on general relativity, including the Penrose-Hawking Singularity Theorems, which were a central part of the renaissance of general relativity and the acceptance of the physical reality of black holes in the 1960s and 1970s. Penrose has contributed to cosmology, argued that consciousness is not a computational process, speculated that quantum mechanical processes are involved in consciousness, proposed experimental tests to determine whether gravitation is involved in the apparent mysteries of quantum mechanics, explored the extraordinarily special conditions which appear to have obtained at the time of the Big Bang and suggested a model which might explain them, and, in mathematics, discovered Penrose tiling, a non-periodic tessellation of the plane which exhibits five-fold symmetry, which was used (without his permission) in the design of toilet paper.

“Fashion, Faith, and Fantasy” seems an odd title for a book about the fundamental physics of the universe by one of the most eminent researchers in the field. But, as the author describes in mathematical detail (which some readers may find forbidding), these all-too-human characteristics play a part in what researchers may present to the public as a dispassionate, entirely rational, search for truth, unsullied by such enthusiasms. While researchers in fundamental physics are rarely blinded to experimental evidence by fashion, faith, and fantasy, their choice of areas to explore, willingness to pursue intellectual topics far from any mooring in experiment, tendency to indulge in flights of theoretical fancy (for which there is no direct evidence whatsoever and which may not be possible to test, even in principle) do, the author contends, affect the direction of research, to its detriment.

To illustrate the power of fashion, Penrose discusses string theory, which has occupied the attentions of theorists for four decades and been described by some of its practitioners as “the only game in town”. (This is a piñata which has been whacked by others, including Peter Woit in Not Even Wrong [Saturday Night Science, 2014-11-15] and Lee Smolin in The Trouble with Physics [2014-09-13].) Unlike other critiques, which concentrate mostly on the failure of string theory to produce a single testable prediction, and the failure of experimentalists to find any evidence supporting its claims (for example, the existence of supersymmetric particles), Penrose concentrates on what he argues is a mathematical flaw in the foundations of string theory, which those pursuing it sweep under the rug, assuming that when a final theory is formulated (when?), its solution will be evident. Central to Penrose’s argument is that string theories are formulated in a space with more dimensions than the three we perceive ourselves to inhabit. Depending upon the version of string theory, it may invoke 10, 11, or 26 dimensions. Why don’t we observe these extra dimensions? Well, the string theorists argue that they’re all rolled up into a size so tiny that none of our experiments can detect any of their effects. To which Penrose responds, “not so fast”: these extra dimensions, however many, will vastly increase the functional freedom of the theory and lead to a mathematical instability which will cause the theory to blow up much like the ultraviolet catastrophe which was a key motivation for the creation of the original version of quantum theory. String theorists put forward arguments why quantum effects may similarly avoid the catastrophe Penrose describes, but he dismisses them as no more than arm waving. If you want to understand the functional freedom argument in detail, you’re just going to have to read the book. Explaining it here would require a ten kiloword review, so I shall not attempt it.