THE ROAD TO REALITY

There is a perpetual problem with popularising modern physics: what do you do with the maths? Received wisdom is that you should miss it all out, recognising that every equation cuts the readership by a few thousand. And so you have to make do with carefully chosen metaphors to try to convey the flavour of what is missing. But there is one mind-boggling alternative: you expound the maths completely from scratch, from zero knowledge up to full PhD level. This book does this in 1094 pages, mostly of detailed argument. Penrose is happy to offer some soft options - there is no need to attempt all the exercises, or you can skip all the equations. His faith in his fellow humans' abilities and perseverance is delightful, but I will have boundless admiration for anyone who manages to get all the way through. I have to admit that I have not succeeded in the task, and I will give here only a rough route map, obtained from a quick helicopter trip over the terrain of the epic safari that is on offer: namely, a superbly clear and insightful presentation of the vast sweep of argument that constitutes the author's life work, and which he proclaims as "the road to reality". I do actually recommend buying it: it's good value even if you only read 1/10 of it! The key to the book is his conception of a threefold reality, which he illustrates in the accompanying diagram - later elaborated to allow for additional unknowable areas. (His many hand-drawn diagrams, incidentally, add to the attraction of the book.) With Plato, he is convinced in the reality of a mathematical world underlying the entire physical world. At the same time he recognises that this mathematical world is in some way a product of our mental world, which is in turn a product of the brains that are lodged in the physical world. The acknowledged deep mystery of each of these links is further deepened by their cyclic relationship. Penrose's first love is the mathematical world, which takes centre stage in this book For him, the development of mathematics is not a process of construction but of discovery. He presents the unending layers of this world, of which the Mandelbrot set provides an icon that will be familiar to many readers: layers unfolding greater and greater surface complexity, which are at the same time gathered into the simplicity of the equations that generate them. The amazing beauty of mathematics, which constitutes the ground for his believing in its reality, stems from this integration of complexity and simplicity, variety and symmetry. His view of the dependence of our personal mental world on this mathematical ground comes close to determinism: if he is right, then "even our own physical actions would be entirely subject to ... mathematical control, where 'control' might still allow for some random behaviour governed by strict probabilistic principles."19 While he might have some unease about this, he would "prefer to have these actions controlled by something residing in [an] aspect of Plato's fabulous mathematical world than to have them be subject to the kind of simplistic base motives, such as pleasure-seeking, personal greed, or aggressive violence, than many would argue to be the implications of a strictly scientific standpoint." On his view, consciousness has no independent role in the world, but it is a physical process arising from the physical processes that he describes in the book.1032 He points out that all the approaches to quantum theory, except for that of David Bohm, implicitly assume as given the equivalent of a conscious observer, but that we have at present virtually no physical theory as to what this might mean. Quantum theory is thus incomplete. Following from this, his approach to the world of physics combines wonder and amazement at its mathematical riches with a distinct scepticism as to how near we are to understanding what is going on. In particular he expounds the "negative reaction" which he and his colleagues have to many of the claims of the proponents of string theory 893, a theory whose arguments "barely scratch the surface of the profound conflicts" between certain aspects of general relativity and quantum theory. These conflicts are conceptual in nature, but most workers in string theory have approached them with computational tools. The core of the book is thus the consideration of the interplay of quantum theory and relativity, where he presents his clearest argument yet for the idea that the incompleteness of quantum theory has to be resolved at the point where it engages with the geometry of space-time. Unlike most contemporary quantum theorists, he returns to the traditional idea of the collapse of the quantum state and the argument of Schrödinger's cat, but notes that "use of an actual cat would, of course, be not only inhumane, but taking an unnecessarily complicated physical system". Since he is explicitly trying not to invoke consciousness as a way out of the problems, it is sufficient for him to replace the cat by a massive "lump" which can be in one of two positions depending on the outcome of a quantum event847. Drawing on the preceding part of the book, he then argues that as a result of the lump's own gravitational field, these two positions have to be associated not just with two different geometrical structures on space-time, but on two different space-times. This is the point where his version of the collapse of the state comes in, resolving the conflict between the two possible space-times. The place of this book in the development of human understanding is fascinating. We have passed through a period in which we have recovered the lost strands of spirituality characterised by the feminine, the embodied, the participatory or the shamanic, which point to the engagement of soul within the material cosmos and to a view of the world as a dynamic interplay between matter and consciousness. Penrose is presenting a carefully argued alternative which is detached, Apollonian and Platonic. Yet I think it would be wrong to see these as exclusive alternatives. Apollo and Artemis are siblings, and in the light of Penrose's book the arena where their dance takes place may be that most overlooked mystery, physical space.