Mind and Nature: Selected Writings on Philosophy, Mathematics, and Physics - Hardcover

Weyl, Hermann

Hardcover

ISBN 10: 0691135452 ISBN 13: 9780691135458

Verlag: Princeton University Press, 2009

Inhaltsangabe

Hermann Weyl (1885-1955) was one of the twentieth century's most important mathematicians, as well as a seminal figure in the development of quantum physics and general relativity. He was also an eloquent writer with a lifelong interest in the philosophical implications of the startling new scientific developments with which he was so involved. Mind and Nature is a collection of Weyl's most important general writings on philosophy, mathematics, and physics, including pieces that have never before been published in any language or translated into English, or that have long been out of print. Complete with Peter Pesic's introduction, notes, and bibliography, these writings reveal an unjustly neglected dimension of a complex and fascinating thinker. In addition, the book includes more than twenty photographs of Weyl and his family and colleagues, many of which are previously unpublished.


Included here are Weyl's exposition of his important synthesis of electromagnetism and gravitation, which Einstein at first hailed as "a first-class stroke of genius"; two little-known letters by Weyl and Einstein from 1922 that give their contrasting views on the philosophical implications of modern physics; and an essay on time that contains Weyl's argument that the past is never completed and the present is not a point. Also included are two book-length series of lectures, The Open World (1932) and Mind and Nature (1934), each a masterly exposition of Weyl's views on a range of topics from modern physics and mathematics. Finally, four retrospective essays from Weyl's last decade give his final thoughts on the interrelations among mathematics, philosophy, and physics, intertwined with reflections on the course of his rich life.

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Über die Autorin bzw. den Autor

Peter Pesic is Tutor and Musician-in-Residence at St. John's College in Santa Fe, New Mexico. His books include Abel's Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability and Seeing Double: Shared Identities in Physics, Philosophy, and Literature.

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"Hermann Weyl was not only a great mathematician who made a significant impact on physics, but he was also a thinker. He pondered at length on the philosophical implications of his work and he expressed himself with clarity and style both in his native German and subsequently in his adopted English. Bringing together all his general writing is an immense service to the English-reading public."--Sir Michael Atiyah, Fields Medalist

"Hermann Weyl ranks among the greatest mathematicians, and his deep contributions to physics were decades ahead of their time. But to know him only through his science is to miss the soul of a seeker. For Weyl, the experienced world in all its aspects was an inexhaustible source of wonder and inspiration. Here you can share in the life adventure of a beautiful mind."--Frank Wilczek, Nobel Prize--winning physicist

"For the first time, this marvelous book collects Hermann Weyl's most important and intriguing writings on the philosophy of physics and mathematics. These pieces shed light on aspects of his thought that are still only partially understood and that have not gained sufficient attention, especially in the English-speaking world, including his engagement with Heidegger, his exploration of the relations between mind and nature, and his attempt to create a kind of natural philosophy."--Norman Sieroka, ETH Zurich

"This is an important complement to Weyl's Philosophy of Mathematics and Natural Science because most of the pieces in this new collection were written later and demonstrate that his contribution to the philosophical reflection on mathematics goes far beyond his earlier work. These pieces were written over a period of thirty years in which much changed: not only the shape of mathematical physics but also Weyl's own understanding of the role of mathematics in physical science and of how to approach the problem of matter, as well as his metaphysical sympathies."--Erhard W. Scholz, University of Wuppertal, Germany

"A very worthwhile volume."--Harold Kuhn, author of Lectures on the Theory of Games

"Weyl's writings are well worth reading, over and over again. This is a very nice volume."--Robert Gunning, Princeton University

"A great volume."--David Ruelle, author of The Mathematician's Brain

Aus dem Klappentext

"Hermann Weyl was not only a great mathematician who made a significant impact on physics, but he was also a thinker. He pondered at length on the philosophical implications of his work and he expressed himself with clarity and style both in his native German and subsequently in his adopted English. Bringing together all his general writing is an immense service to the English-reading public."--Sir Michael Atiyah, Fields Medalist

"Hermann Weyl ranks among the greatest mathematicians, and his deep contributions to physics were decades ahead of their time. But to know him only through his science is to miss the soul of a seeker. For Weyl, the experienced world in all its aspects was an inexhaustible source of wonder and inspiration. Here you can share in the life adventure of a beautiful mind."--Frank Wilczek, Nobel Prize--winning physicist

"For the first time, this marvelous book collects Hermann Weyl's most important and intriguing writings on the philosophy of physics and mathematics. These pieces shed light on aspects of his thought that are still only partially understood and that have not gained sufficient attention, especially in the English-speaking world, including his engagement with Heidegger, his exploration of the relations between mind and nature, and his attempt to create a kind of natural philosophy."--Norman Sieroka, ETH Zurich

"This is an important complement to Weyl's Philosophy of Mathematics and Natural Science because most of the pieces in this new collection were written later and demonstrate that his contribution to the philosophical reflection on mathematics goes far beyond his earlier work. These pieces were written over a period of thirty years in which much changed: not only the shape of mathematical physics but also Weyl's own understanding of the role of mathematics in physical science and of how to approach the problem of matter, as well as his metaphysical sympathies."--Erhard W. Scholz, University of Wuppertal, Germany

"A very worthwhile volume."--Harold Kuhn, author of Lectures on the Theory of Games

"Weyl's writings are well worth reading, over and over again. This is a very nice volume."--Robert Gunning, Princeton University

"A great volume."--David Ruelle, author of The Mathematician's Brain

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MIND AND NATURE

Selected Writings on Philosophy, Mathematics, and PhysicsBy HERMANN WEYL

PRINCETON UNIVERSITY PRESS

Copyright © 2009 Princeton University Press
All right reserved.
ISBN: 978-0-691-13545-8

Contents

Introduction............................................................................................11921 1 Electricity and Gravitation......................................................................201922 2 Two Letters by Einstein and Weyl on a Metaphysical Question......................................251927 3 Time Relations in the Cosmos, Proper Time, Lived Time, and Metaphysical Time.....................291932 4 The Open World: Three Lectures on the Metaphysical Implications of Science.......................341934 5 Mind and Nature..................................................................................831946 6 Address at the Princeton Bicentennial Conference.................................................162ca. 1949 7 Man and the Foundations of Science...........................................................1751954 8 The Unity of Knowledge...........................................................................1941955 9 Insight and Reflection...........................................................................204Notes...................................................................................................223References..............................................................................................241Acknowledgments.........................................................................................253Index...................................................................................................255

Chapter One

Electricity and Gravitation

1921

Modern physics renders it probable that the only fundamental forces in Nature are those which have their origin in gravitation and in the electromagnetic field. After the effects proceeding from the electromagnetic field had been coordinated by Faraday and Maxwell into laws of striking simplicity and clearness, it became necessary to attempt to explain gravitation also on the basis of electromagnetism, or at least to fit it into its proper place in the scheme of electromagnetic laws, in order to arrive at a unification of ideas. This was actually done by H. A. Lorentz, G. Mie, and others, although the success of their work was not wholly convincing. At the present time, however, in virtue of Einstein's general theory of relativity, we understand in principle the nature of gravitation, and the problem is reversed. It is necessary to regard electromagnetic phenomena, as well as gravitation, as an outcome of the geometry of the universe. I believe that this is possible when we liberate the world-geometry (on which Einstein based his theory) from an inherent inconsistency, which is still associated with it as a consequence of our previous Euclidean conceptions.

The great accomplishment of the theory of relativity was that it brought the obvious problem of the relativity of motion into harmony with the existence of inertial forces. The Galilean law of inertia shows that there is a kind of obligatory guidance in the universe, which constrains a body left to itself to move with a perfectly definite motion, once it has been set in motion in a particular direction in the world. The body does this in virtue of a tendency of persistence, which carries on this direction at each instant "parallel to itself." At every position P in the universe, this tendency of persistence (the "guiding field") thus determines the infinitesimal parallel displacement of vectors from P to world-points indefinitely near to P. Such a continuum, in which this idea of infinitesimal parallel displacement is determinate, I have designated as "affinely connected." According to the ideas of Galileo and Newton, the "affine connection" of the universe (the difference between straight and curved) is given by its geometrical structure. A vector at any position in the universe determines directly and without ambiguity, at every other position, and by itself (i.e., independently of the material content of the universe), a vector "equal" to itself. According to Einstein, however, the guiding field is a physical reality which is dependent on the state of matter, and manifests itself only infinitesimally (as a tendency of persistence which carries over the vectors from one point to "indefinitely neighboring" ones). The immense success of Einstein's theory is based on the fact that the effects of gravitation also belong to the guiding field, as we should expect a priori from our experience of the equality of gravitational and inertial mass. The planets follow exactly the orbit destined to them by the guiding field; there is no special "gravitational force" necessary, as in Newton's theory, to cause them to deviate from their Galilean orbit. In general, the parallel displacement is "non-integrable," i.e., if we transfer a vector at P along two different paths to a point P' at a finite distance from P, then the vectors, which were coincident at P, arrive at P' in two different end-positions after traveling these two paths.

The "affine connection" is not an original characteristic of the universe, but arises from a more deeply lying condition of things-the "metrical field." There exists an infinitesimal "light cone" at every position P in the world, which separates past and future in the immediate vicinity of the point P. In other words, this light cone separates those world-points which can receive action from P from those from which an "action" can arrive at P. This "cone of light" renders it possible to compare two line-elements at P with each other by measurement; all vectors of equal measure represent one and the same distance at P. In addition to the determination of measure at a point P (the "relation of action" of P with its surroundings), we have now the "metrical relation," which determines the congruent transference of an arbitrary distance at P to all points indefinitely near to P.

Just as the point of view of Einstein leads back to that of Galileo and Newton when we assume the transference of vectors by parallel displacement to be integrable, so we fall back on Einstein when the transference of distances by congruent transference is integrable. But this particular assumption does not appear to me to be in the least justified (apart from the progress of the historical development). It appears to me rather as a gross inconsistency. For the "distances," the old point of view of a determination of magnitudes in terms of each other is maintained, this being independent of matter and taking place directly at a distance. This is just as much in conflict with the principle of the relativity of magnitude as the point of view of Newton and Galileo is with the principle of the relativity of motion. If, in the case in point, we proceed in earnest with the idea of the continuity of action, then "magnitudes of condition" occur in the mathematical description of the world-metrics in just sufficient number and in such a combination as is necessary for the description of the electro-magnetic and of the gravitational field. We saw above that, besides inertia (the retention of the vector-direction), gravitation was also included in the guiding field, as a slight variation of this, as a whole, constant inertia. So in the present case, in addition to the force which...

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 2009
• Sprache: Englisch
• ISBN 10: 0691135452
• ISBN 13: 9780691135458
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 261
• Herausgeber: Pesic Peter
• Kontakt zum Hersteller: Princeton University Press; https://press.princeton.edu/books; ; 7th Floor, New South Building; PRINCETON; NJ; 8544; USA
• Verantwortliche Person: Buchbär; info@buchbaer.de; ; Weberstr. 67; Osnabrück; 49084; Deutschland