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John D. Barrow is Professor of Mathematical Sciences and Director of the Millennium Mathematics Project at Cambridge University, Fellow of Clare Hall, Cambridge, a Fellow of the Royal Society, and the current Gresham Professor of Geometry at Gresham College, London. His principal area of scientific research is cosmology, and he is the author of many highly acclaimed books about the nature and significance of modern developments in physics, astronomy, and mathematics, including The Origin of the Universe, The Universe that Discovered Itself; The Book of Nothing, The Constants of Nature, The Infinite Book- a Short Guide to the Boundless, Timeless and Endless, The Artful Universe Expanded, New Theories of Everything, and Cosmic Imagery.
What an elegant exposition lies here: not for everyone, to be sure, but for those familiar with astronomer Barrow's rich background in mathematics and in the history and philosophy of science, a treasure of learning and insight. Barrow (Astronomy/Univ. of Sussex; coauthor, The Anthropic Cosmological Principle, 1985, etc.) takes as his target the Theories of Everything or T.O.E's, which have become fashionable as particle physicists and astronomers come together to ponder the origin and fate of the universe. The evidence that there really was a Big Bang some 15 billion years ago (by virtue of uniform low-temperature background radiation) and the proof (through collider experiments) of the existence of massive particles predicted by theories aimed at unifying first two, then three of the four fundamental forces of nature, have spurred cosmologists to seek the ultimate TOE. There are problems, however, not the least of which concerns the present confusion about the structure of the visible universe (lumpy and bumpy; dense in some places; empty elsewhere). Then there's the problem of the missing mass. Check out Riordan and Schramm (The Shadows of Creation, reviewed below) for a survey of the current state of cosmological science (or art). Barrow deals with these problems but casts them in the context of intellectual history and contrasting metaphysical views - the idealism of Plato and Kant; the realism of Aristotle and Helmholtz. Into this heady mix he stirs a fine analysis of the evolution of mathematical thought; indeed, the implicit role that mathematics has played in cosmology is a recurrent, finely drawn theme that adds considerably to the book's scholarly luster. In the end, Barrow states there can be no ultimate TOE. The reasons lie in the limits of reductionism and the evidence for phenomena (truth, beauty, but also theorems) that are not decidable, not computable, not listable. In the end, No Theory of Everything can ever provide total insight. For to see through everything, would leave us seeing nothing at all. Marvelous. (Kirkus Reviews)
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