Celestial Encounters [Hardcover]

Florin Diacu (Author), Philip Holmes (Author)

Book Description

ISBN-10: 0691027439 | ISBN-13: 978-0691027432 | Publication Date: November 11, 1996

Starting with the story of Poincare's work on the phenomenon of chaos, this study traces the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's "Principia" in 1686. In describing how mathematical rigour was brought to bear on one of our oldest fascinations - the motions of the heavens - they introduce the people whose ideas led to the field now called nonlinear dynamics. In presenting the modern theory of dynamic systems, the models underlying much of modern science are described pictorally, using the geometrical language invented by Poincare. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

Editorial Reviews

Review

"A lively introduction to the fascinating story of celestial mechanics." -- Jacques Laskar, Nature

"A particular strength of Celestial Encounters is the impression, conveyed with a deft touch, that mathematics is an international and collective effort made by real people for real reasons in the real world. All the players in the drama, alive or dead, come over as human beings who happen to have a passion for mathematics and an ability to fulfill that passion. This feature alone justifies buying the book." -- Ian Stewart, New Scientist

"This book, which should be required reading for every nonspecialist astronomer, may well be headed toward becoming a classic." -- Choice

"Throughout the book one finds a vital quality that derives from the authors' real success in presenting mathematics as a human endeavor.... A valuable and accessible contribution to the chaos literature." -- June Barrow-Green, Isis

"[S]tories about the history of celestial mechanics are the subject of this delightful book. The authors interweave numerous anecdotes about the personalities involved in the discoveries with technical details of the mathematical ideas themselves. . . . a pleasant mix of things technical and things historical. . . . written in a lively and informative way. -- Robert L. Devaney, Science

"A pleasant mix of things technical and things historical.... Written in a lively and informative way." -- Robert Devaney, Science

An excellent book combining scientific integrity and popular appeal. -- Steve Smale, City University of Hong Kong

From the Publisher

Celestial Encounters is for anyone who has ever wondered about the foundations of chaos. In 1888, the 34 year old Henri Poincare submitted a paper that was to change the course of science, but not before it underwent significant changes itself. "The Three Body Problem and the Equations of Dynamics" won a prize sponsored by King Oscar II of Sweden and Norway and the journal Acta Mathematica, but after accepting the prize, Poincare found a serious mistake in his work. While correcting it, he discovered the phenomenon of chaos.

Starting with the story of Poincare's work, Florin Diacu and Philip Holmes trace the history of attempts to solve the problems of celestial mechanics first posed in Isaac Newton's Principia in 1686. In describing how mathematical rigor was brought to bear on one of our oldest fascinationsthe motions of the heavensthey introduce the people whose ideas led to the flourishing field now called nonlinear dynamics.

In presenting the modern theory of dynamical systems, the models underlying much of modern science are described pictorially, using the geometrical language invented by Poincare. More generally, the authors reflect on mathematical creativity and the roles that chance encounters, politics, and circumstance play in it.

See all Editorial Reviews

Product Details

• Hardcover: 233 pages
• Publisher: Princeton Univ Pr (November 11, 1996)
• Language: English
• ISBN-10: 0691027439
• ISBN-13: 978-0691027432
• Product Dimensions: 9.3 x 6.2 x 1 inches
• Shipping Weight: 15.2 ounces
• Average Customer Review: 4.4 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #2,156,114 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

5.0 out of 5 stars A VALUABLE BOOK ON NONLINEAR DYNAMICS, November 22, 2004

By 

Alwyn Scott (Tucson, Arizona USA) - See all my reviews
(REAL NAME)   

This review is from: Celestial Encounters (Paperback)

Most popular books on scientific topics are by professional writers who know how to construct interesting narratives but don't really understand the science. Thus they are overly impressed by those whom they have recently interviewed, remaining ignorant of the broad picture and history of their subject. Seldom does one come across a well-written book for the general public by scientists, but "Celestial Encounters" is an exception to this general rule.

Both of the authors (Florin Diacu and Philip Holmes) are distinguished researchers in the area of nonlinear science and also fine writers. Thus the reader is ever in good hands as the technical parts of the book are not dumbed down; the more technical sections (which can be skipped in a first reading) are correctly and carefully written in simple English. Anyone reading through this book will come away with greater understanding of the famous N-body problem of celestial mechanics - including both the history and how it fits into the fabric of modern mathematics, particularly in connection with the development of nonlinear dynamics and the modern theory of chaos.

The historical perspectives presented are particularly vivid and informative. I don't know where one would find a more interesting and better informed discussion of the curious events surrounding the award of the 1889 mathematics prize by King Oscar II of Sweden to Henri Poincaré.

5 of 6 people found the following review helpful:

4.0 out of 5 stars It was a dark and stormy seminar..., September 2, 1997

By 

[e-mail] (Portland,OR) - See all my reviews

This review is from: Celestial Encounters (Hardcover)

If you enjoy math and astronomy-related topics and are curious about the history of some fascinating 20th century discoveries concerning the n-body problem, this book should satisfy you. Warning: this book could also annoy you, if you are the least bit sensitive to empty calories such as: "Napolean gazed deeply into Laplace's eyes...", which liberally lard up the text.

2 of 2 people found the following review helpful:

5.0 out of 5 stars A nice historical and mathematical introduction to Chaos, March 21, 2000

By 

Ingmar Prada & Ma. Teresa Valdés - See all my reviews

This review is from: Celestial Encounters (Paperback)

It is a complete history of Dynamical Systems theory and at the same time an exposition of the mathematical ideas involved in this theory. An excellent introduction for beginers, and a good panoramic vision for people interested in science.