Customer Reviews

Celestial Encounters

5 star:		(4)
4 star:		(2)
3 star:		(1)
2 star:		(0)
1 star:		(0)

 

 

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.

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.

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.

The book is a great pleasure to read. The style is light and profound at the same time. It talks to a sientifically mature reader but does not sacrifice the simplicity and the elegant clarity of the exposition. History and mathematics are well balanced. What I liked, probably, the most was that the process of scientific discovery is described is highly emotional (and as a scientist I share the same sentiment). It's also nice to see that Eastern European mathematicians received a fair credit here, which does not happen too often in histories of mathematics published in the States.

O placuta si interesanta carte de istoria matematicii,accesibila si profanilor in materie,scrisa cu verva si extrem de bine documentata

This book introduces the study of dynamical systems through the n-body problem, the study of how n bodies move when each exerts a gravitational force on the n-1 other bodies. The book is a good mix of history and real science, but the technical sections move too quickly. Nothing in the book is too hard for someone who has taken a course in differential equations or who has some physics knowledge, but the difficult material should be said in a few different ways to help the reader master it. (Two topics I think should have been explained more slowly are the "homoclinic tangle" and the intersection of stable and unstable manifolds on pp. 38-42.)

Phase space is the most important idea in the book. There is no single phase space; for every dynamical system there is some phase space that corresponds to it. It will be a high dimensional space where each point represents the configuration of the system we are analyzing; so if we have n bodies, since each has a 3-dimensional position and 3-dimensional momentum, phase space is 6n-dimensional, and knowing where a system is in phase space tells us everything we need to know about it. Dynamics is the study of how the states of systems change, so how they move around phase space. A "phase portrait" lets us see all at once the different ways a system changes. If we have a dyanmical system that models fluid flow and we have can change some parameter like viscosity, then the way the phase portrait changes as we change the parameter is the study of "structural stability" and "bifurcations". These ideas are explained in the book.

Poincaré started the field of dynamical systems, although some earlier work on the n-body problem was done by Lagrange and Laplace; they say that Laplace was the first to use the term "celestial mechanics".

Chapter 3 is my favorite chapter in the book, because it was really new to me. It's about the kinds of singularities that can happen in the n-body problem. Since the gravitational force a particle exerts on another particle is proportional to the inverse square of their distance, if they hit each other then there is infinite force between them and we call this a singularity. The Painlevé conjecture was that when there are more than 3 bodies there can be singularities other than bodies hitting each other, and this chapter talks about this and the solutions of Xia and Gerver.

I recommend this book to someone who has taken either a course in differential equations or a university physics course, preferrably both. The book will still be tough in places because it's explaining some big ideas. I recommend reading it beside a computer, and looking up things you don't understand, like homoclinic tangle. It might still not make sense, but if you spend an hour thinking about it and reading what you find online, you'll be comfortable enough with it to continue reading. If you don't pause like this you might get lost.

I have an engiineering degree and an inclination to study mathematics, yet the book demands a level of sophistication that is ver high (at least to me), and the book only has 1 equation!!!! I bought it thinking into would lead me by the hand into the complex land...I find myself working very hard to keep the pace