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John Barrow is increasingly recognized as one of our most elegant and accomplished science writers, a brilliant commentator on cosmology, mathematics, and modern physics. Barrow now tackles the heady topic of impossibility, in perhaps his strongest book yet. Writing with grace and insight, Barrow argues convincingly that there are limits to human discovery, that there are things that are ultimately unknowable, undoable, or unreachable. He first examines the limits on scientific inquiry imposed by the deficiencies of the human mind: our brain evolved to meet the demands of our immediate environment, Barrow notes, and much that lies outside this small circle may also lie outside our understanding. Barrow investigates practical impossibilities, such as those imposed by complexity, uncomputability, or the finiteness of time, space, and resources. Is the universe finite or infinite? Can information be transmitted faster than the speed of light? The book also examines the deeper theoretical restrictions on our ability to know, including Godel's theorem--which proved that there were things that could not be proved--and Arrow's Impossibility theorem about democratic voting systems. Finally, having explored the limits imposed on us from without, Barrow considers whether there are limits we should impose upon ourselves. For instance, if the secrets of the atom are to be found only by recreating extreme environments at great financial cost, just how much should we devote to that quest? Weaving together this intriguing tapestry, he illuminates some of the most profound questions of science, from the possibility of time travel to the very structure of the universe.
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The meaning of the world is the separation of wish and fact. KURT GÖDEL
In memory of Roger Tayler
Impossibility The Limits of Science and the Science of Limits
JOHN D. BARROW Astronomy Centre University of Sussex
OXFORD UNIVERSITY PRESS • OXFORD 1998
Preface The Preface is the most important part of the book. Even reviewers read a preface.
PHILIP GUEDALLA Both scientists and philosophers are much concerned with impossibilities. Scientists like to show that things widely held to be impossible are in fact entirely possible; philosophers, by contrast, are more inclined to demonstrate that things widely regarded as perfectly feasible are in fact impossible. Yet, paradoxically, science is only possible because some things are impossible. The incontrovertible evidence that Nature is governed by reliable 'laws' allows us to separate the possible from the impossible. Only those cultures for whom there existed a belief that there was a distinction between the possible and the impossible provided natural breeding grounds for scientific progress. But 'impossibility' is not only about science. In the pages that follow we shall look at some of the ways in which the impossible in art, literature, politics, theology, and logic has stimulated the human mind to take unexpected steps: revealing how the concept of the impossible sheds new light on the nature and content of the actual. The idea of the impossible rings alarm bells in the minds of many. To some, any suggestion that there might be limits to the scope of human understanding of the Universe or to scientific progress is a dangerous meme that undermines confidence in the scientific enterprise. Equally uncritical, are those who enthusiastically embrace any suggestion that science might be limited because they suspect the motives and fear the dangers of unbridled investigation of the unknown. At the end of each century there seems to arise a stock-taking in science. We shall see that at the end of the last century the issue of the limits of science became a live one and attempts were made to pick out problems that could never be solved. These problems still make interesting re