Maths, the universe and fried-egg theory

One can think of rather few writers of academic books one would like to have as dinner companions. But the intelligence of John Barrow, the clarity of his prose and the roundedness of his erudition, as manifest in this highly readable collection of essays, place him in that select group.

One is as likely to learn about psephology as cosmology - Barrow's particular field of research - in this volume, which includes among its subjects discussions of time, aesthetics and, of course, cosmology. In a series of early essays, Barrow argues that what we observe about the universe is necessarily atypical, because we are biased by the conditions of our own existence. Equally, our existence is the outcome of a set of physical laws, corresponding to the breaking of an underlying symmetry. Barrow argues that we cannot from here deduce the far more general state of unbroken symmetry that obtained before life as we know it evolved. His wry remark to do with humans having "a habit of perceiving in nature more laws and symmetries than actually exist there" is here doubly apposite.

Another issue Barrow addresses is the very non-random size distribution of structures in our universe. Most objects, from atoms to stars, lie in a region of approximately constant density, the reason for this curious clustering being the need for a balance between atomic forces and gravity. Particularly endearing in Barrow's exposition of this is his constant appeal to more everyday notions such as (in the context of size distributions) the textural evolution of fried eggs, why a kitten's tail is bolt upright while a cat's is not, why insects could never be arsonists, and why, while human beings

can read, we cannot walk upside down on the ceiling.

In one of his imaginative leaps, Barrow sees monotheistic traditions as being responsible for the age-old tendency to unify seemingly disparate scientific theories - "unity", he quips, "is a many-splendoured thing". However, his cautionary point that the "sudden appearance of candidates for a 'Theory of Everything' has led to much confusion about what is meant by 'everything'", is well made, as is his attempt to impose some form of discipline on self-styled theorists, by demanding that "an acid test of a Theory of Everything would be its ability to predict the values of (fundamental) constants".

Unfortunately, the chapters on complexity (where Barrow appears to be enchanted by what is often known as the Santa Fe style of physics) are a disappointment, because little attempt is made at imposing such standards of rigour in a field somewhat distant from his own.

There are particular themes that pervade this rather dense book, such as whether the universe is open or closed, the relevance of boundary conditions in the early universe, the idea of science being a search for compressions, and whether the universe is more like a "symmetric continuum" or a "discrete computation".

Among the markedly original chapters is one on the limits of science, where Barrow argues on existential, conceptual, technological and fundamental grounds that we will never know all there is to know about our world. More refreshingly, he attaches a value to our not knowing, by saying that the totality of what we cannot know "characterises the universe more precisely than the catalogue of things that we can know".

Another outstanding chapter discusses why mathematics provides a good foundation for our understanding of the universe, and homes in on another favourite Barrow theme: is the universe a pattern or a program? Yet another chapter, lighter but outstanding for its wit, concerns voting, where the author demonstrates the inevitability of an individually rational vote leading collectively to an irrational outcome.

Last but not least, the section on cosmology reveals Barrow on his own turf, as he takes us through the origins of cosmological time, the entropy of the universe and the scenario of multiple universes, with the ease born of mastery.

A disadvantage with a collection such as this is the repetition of ideas. But in Barrow's case, it is not a major drawback, as the depth and intricacy of his arguments are well able to withstand repetition - in fact, they occasionally need it. Some of the essays are themselves book reviews and in these Barrow reveals himself to be a formidable critic of others' thoughts. While the reviews are pedagogical, they do not hesitate to bite when appropriate. Not a respecter of persons or disciplines, Barrow demands greater rigour from philosophers of science: until this is achieved, it cannot be said that "the science of science is a science". Similarly, he expresses his disapproval of (some) literary deconstruction quite succinctly: "There is no more reason to expect new literary insights from the application of chaos theory to literary texts than to expect that the Meteorological Office will discover new structures in weather systems from a careful study of The Tempest ."

Throughout the book, Barrow's delightful literary style clearly demonstrates his adherence to his own diktat: "Think no jargon, speak no jargon, write no jargon." Most memorable, though, is the appeal of his view of the nature of science, the spirit behind its investigations, the "rules and inheritances" of the intellectual process. "They are not all we are, nor all we can be, but that is very different from saying that they have no part to play in revealing to us how we think, what we are and what we might become."

Anita Mehta is reader in theoretical physics, S. N. Bose National Centre for Basic sciences, Calcutta, India.