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Manifold theory. An introduction for mathematical physicists
Book reviews A Critique for Ecology. By Robert Henry Peters. Pp. 366. Cambridge University Press. 1997. Hardback f45.00, US $79.50 ISBN 0 521 140017 1; paperback f 17.95, US $29.95 ISBN 0 521 39588 7.
This stimulating book offers a critical examination of current ecological theory (competition, niche, stability, etc.) which is central to mainstream textbooks on ecology. The author argues that, at best, ecology is a soft science for, unlike hard sciences, it does not provide information about nature through predictions. Rather, ecology uses logical rationalization, historical explanation, and mechanistic understanding. Because of this weakness, ecology is becoming increasingly irrelevant in the search for solutions to pressing environmental problems, an area where it should be pre-eminent. Political will, as well as ecological skill, is of course essential in solving environmental problems. Natural selection is central to much of ecological theory. The author argues that it is a logical truth, a tautology, not a scientific theory, and ecologists’ fascination for it has led to the loose thinking which pervades much of ecological theory. For example, concepts such as ‘the niche’ and ‘stability’ have so many definitions that they become non-concepts. Ecologists consistently pose apparently important questions which are impossible to answer. The author’s way forward is predictive ecology, developing simple predictive models based on pal data. Ecologists in resource management have always worked thus, with little recourse to the ecological theory of textbooks. C. F. Mason Science and Technology in Japan, 2nd Edn. By Jon Sigurdson and Alun M. Anderson. Pp. 382. Longman, Harlow. 1991. f85.00 ISBN 0 582 03684 4.
The Longman Guides to World Science and Technology are now widely recognized as useful and authoritative international works of reference. At the present time Japan is very much at the centre of interest and the publication of a second edition of the original Guide, which appeared in 1984, is timely and welcome. In its preparation the original author, Alun Anderson, has been joined by Jon Sigurdson, Professor of Research Policy in the University of Lund, who has long specialized in scientific and industrial technology development in East Asia, and has spent seven years there. This is a powerful combination, well reflected in the book. In this up-dated revision the main characteristics of the original work have been maintained, especially in the area of education, Endowour New Series, Volume 18, No. 1,1992. 0160-9237/w so.00 + 0.00. Pergamon Press pk. Printed in Great Britain.
where there has been relatively little structural change. Other sections have been rewritten, and somewhat shortened by excluding detailed reference on specific research institutes. A short general introduction and a lo-page review of Japan’s islands and peoples help to put the subject in perspective. The weak part of the work is R & D activity in Japanese industry, a substantial part of the total research scene. This is not through lack of diligence on the part of the authors but arises from the practical difficulties of acquiring the necessary information. Trevor I. Williams Manifold Theory. An Introduction for Mathematical Physicists. By Daniel Martin. Pp. 423. Ellis Horwood, Chichester. 1991. f55.00 ISBN 0 13 543877 2.
This is a good, well-prepared book and a welcome addition to the libraries of geometers and mathematical physicists and, especially, their research students. After the necessary algebraic preliminaries (and the topological ones which are contained in a useful appendix) the author proceeds to develop the idea of a differentiable manifold and the standard structures associated with manifolds (vector fields, tensor fields, forms, linear connections and their associated curvature, and metrics of general signature). His approach is thorough and precise and, as theoretical physicists will be pleased to hear, he is not afraid to use indices. There is a particularly thorough treatment of the Lie derivative and discussions of Minkowski space, Maxwell’s equations, and Hamiltonian structure. The extensive chapter on Lie groups covers the basic theory and contains many examples of Lie groups and their algebras, including the Lorentz group. Local and global Lie group actions on manifolds are also considered. The penultimate chapter on fibre bundles, including principal bundles and their connections, will be useful to gauge theorists. Also treated are manifolds with boundary, de Rham cohomology, almost complex manifolds and Hermitian and Klhlerian manifolds. There are several appendices and many useful exercises at the end of each chapter, together with some hints and solutions. Inevitably, there is a (small) number of slips and omissions but the book has been carefully written in a rigorous but clear and readable style. G. S. Hall The Detection of Gravitational Waves. Edited by David G. Blair. Pp. 481. Cambridge University Press. 1991. f95.00, US $125.00 ISBN 0 521 35278 9.
This is a very good book on a topic of great interest, albeit highly specialized. The detection of gravitational waves will open up a whole new and additional method of study-
ing what goes on in the cosmos, one with the great merit that the sources of gravitational waves are likely to be amongst the most curious and least familiar objects found in that very well stocked laboratory, the universe. Their observation will require very substantial advances in instrumentation, which is now under way in several centres. The book is edited by David Blair who has succeeded not only in making the wealth of material digestible, but also in giving one the impression that this state-of-the-art survey will not lose its validity and significance for many years to come. David Blair himself is the author of the first two chapters which respectively set out the theoretical background to the relativistic prediction of the existence of gravitational waves, and the astrophysical expectation of the objects likely to act as sources, with the probable character of the radiation emanating from them. As throughout the book, reference to earlier work is clear, especially to Kip Thorne’s illuminating diagrams. The third chapter is an overview of methods of detection which are then discussed one by one by their progenitors and makers in the rest of the volume. These are all extremely competent and critical descriptions showing both the limitations and the aspirations of these various experimental arrangements. One is left very hopeful that in the not too distant future gravitational wave astronomy will have a good beginning, but I cannot help feeling that the enormous improvements in accuracy striven for may also reveal something unexpected. Anybody interested in gravitation or in a prospective new typ of astronomy will find this an excellent book. Hermann Bondi Atoms, Stars and Nebulae. 3rd Edn. By Lawrence H. Aller. Pp. 366. Cambridge University Press. 1991. Hardback f50.00, US $84.50 ISBN 0 521 32512 9; paperback f 17.95, US $34.50 ISBN 0 52131040 7.
It must be rare for an author to bring out the third edition of a book half a century after the first. Lawrence Aller, together with the late Leo Goldberg, published the original version of this book in 1943. The great excitement in those days focused on the new possibilities offered by modern quantum and atomic physics. It had at last become feasible to make an analysis of stellar atmospheres, to deduce what stars were to made of, and to establish the overwhelming importance of hydrogen in all astrophysical processes. Some reflections of those far-off days are still visible. The Bohr atom finds a place in the text, and Chandrasekhar’s work on the H- ion is presented as though it were a recent development.
43
This stimulating book offers a critical examination of current ecological theory (competition, niche, stability, etc.) which is central to mainstream textbooks on ecology. The author argues that, at best, ecology is a soft science for, unlike hard sciences, it does not provide information about nature through predictions. Rather, ecology uses logical rationalization, historical explanation, and mechanistic understanding. Because of this weakness, ecology is becoming increasingly irrelevant in the search for solutions to pressing environmental problems, an area where it should be pre-eminent. Political will, as well as ecological skill, is of course essential in solving environmental problems. Natural selection is central to much of ecological theory. The author argues that it is a logical truth, a tautology, not a scientific theory, and ecologists’ fascination for it has led to the loose thinking which pervades much of ecological theory. For example, concepts such as ‘the niche’ and ‘stability’ have so many definitions that they become non-concepts. Ecologists consistently pose apparently important questions which are impossible to answer. The author’s way forward is predictive ecology, developing simple predictive models based on pal data. Ecologists in resource management have always worked thus, with little recourse to the ecological theory of textbooks. C. F. Mason Science and Technology in Japan, 2nd Edn. By Jon Sigurdson and Alun M. Anderson. Pp. 382. Longman, Harlow. 1991. f85.00 ISBN 0 582 03684 4.
The Longman Guides to World Science and Technology are now widely recognized as useful and authoritative international works of reference. At the present time Japan is very much at the centre of interest and the publication of a second edition of the original Guide, which appeared in 1984, is timely and welcome. In its preparation the original author, Alun Anderson, has been joined by Jon Sigurdson, Professor of Research Policy in the University of Lund, who has long specialized in scientific and industrial technology development in East Asia, and has spent seven years there. This is a powerful combination, well reflected in the book. In this up-dated revision the main characteristics of the original work have been maintained, especially in the area of education, Endowour New Series, Volume 18, No. 1,1992. 0160-9237/w so.00 + 0.00. Pergamon Press pk. Printed in Great Britain.
where there has been relatively little structural change. Other sections have been rewritten, and somewhat shortened by excluding detailed reference on specific research institutes. A short general introduction and a lo-page review of Japan’s islands and peoples help to put the subject in perspective. The weak part of the work is R & D activity in Japanese industry, a substantial part of the total research scene. This is not through lack of diligence on the part of the authors but arises from the practical difficulties of acquiring the necessary information. Trevor I. Williams Manifold Theory. An Introduction for Mathematical Physicists. By Daniel Martin. Pp. 423. Ellis Horwood, Chichester. 1991. f55.00 ISBN 0 13 543877 2.
This is a good, well-prepared book and a welcome addition to the libraries of geometers and mathematical physicists and, especially, their research students. After the necessary algebraic preliminaries (and the topological ones which are contained in a useful appendix) the author proceeds to develop the idea of a differentiable manifold and the standard structures associated with manifolds (vector fields, tensor fields, forms, linear connections and their associated curvature, and metrics of general signature). His approach is thorough and precise and, as theoretical physicists will be pleased to hear, he is not afraid to use indices. There is a particularly thorough treatment of the Lie derivative and discussions of Minkowski space, Maxwell’s equations, and Hamiltonian structure. The extensive chapter on Lie groups covers the basic theory and contains many examples of Lie groups and their algebras, including the Lorentz group. Local and global Lie group actions on manifolds are also considered. The penultimate chapter on fibre bundles, including principal bundles and their connections, will be useful to gauge theorists. Also treated are manifolds with boundary, de Rham cohomology, almost complex manifolds and Hermitian and Klhlerian manifolds. There are several appendices and many useful exercises at the end of each chapter, together with some hints and solutions. Inevitably, there is a (small) number of slips and omissions but the book has been carefully written in a rigorous but clear and readable style. G. S. Hall The Detection of Gravitational Waves. Edited by David G. Blair. Pp. 481. Cambridge University Press. 1991. f95.00, US $125.00 ISBN 0 521 35278 9.
This is a very good book on a topic of great interest, albeit highly specialized. The detection of gravitational waves will open up a whole new and additional method of study-
ing what goes on in the cosmos, one with the great merit that the sources of gravitational waves are likely to be amongst the most curious and least familiar objects found in that very well stocked laboratory, the universe. Their observation will require very substantial advances in instrumentation, which is now under way in several centres. The book is edited by David Blair who has succeeded not only in making the wealth of material digestible, but also in giving one the impression that this state-of-the-art survey will not lose its validity and significance for many years to come. David Blair himself is the author of the first two chapters which respectively set out the theoretical background to the relativistic prediction of the existence of gravitational waves, and the astrophysical expectation of the objects likely to act as sources, with the probable character of the radiation emanating from them. As throughout the book, reference to earlier work is clear, especially to Kip Thorne’s illuminating diagrams. The third chapter is an overview of methods of detection which are then discussed one by one by their progenitors and makers in the rest of the volume. These are all extremely competent and critical descriptions showing both the limitations and the aspirations of these various experimental arrangements. One is left very hopeful that in the not too distant future gravitational wave astronomy will have a good beginning, but I cannot help feeling that the enormous improvements in accuracy striven for may also reveal something unexpected. Anybody interested in gravitation or in a prospective new typ of astronomy will find this an excellent book. Hermann Bondi Atoms, Stars and Nebulae. 3rd Edn. By Lawrence H. Aller. Pp. 366. Cambridge University Press. 1991. Hardback f50.00, US $84.50 ISBN 0 521 32512 9; paperback f 17.95, US $34.50 ISBN 0 52131040 7.
It must be rare for an author to bring out the third edition of a book half a century after the first. Lawrence Aller, together with the late Leo Goldberg, published the original version of this book in 1943. The great excitement in those days focused on the new possibilities offered by modern quantum and atomic physics. It had at last become feasible to make an analysis of stellar atmospheres, to deduce what stars were to made of, and to establish the overwhelming importance of hydrogen in all astrophysical processes. Some reflections of those far-off days are still visible. The Bohr atom finds a place in the text, and Chandrasekhar’s work on the H- ion is presented as though it were a recent development.
43