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Singer's book stands class of its own in these respects. All the basics of the geometrical "machinery" are there, in a book that is only 224 pages in length. Chapter one starts with a standard derivation of the equations of the "two-body planetary motion" problem; subsequent chapters proceed to introduce the necessary modern geometrical and mathematical concepts (differential geometry). The final chapter then revisits the "planetary motion" problem using the modern concepts previously introduced. Excellent!
There are some misprints, but the author has a Web page of errata. The book has numerous exercises, with many solutions included. I find myself rereading parts of this book over and over.
Reader be warned; the concepts are new, and it does take work to internalize them. However, this is the most accessible book on the subject available, and also one of the most affordable. The author references many other books, for the reader who wants to go further in the mastery of this subject (one excellent book which is not mentioned, however, is "Differential Forms: A Complement to Vector Calculus", by Weintraub). Enjoy!
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In this fascinating book it is a reevaluation of older principles (the ancient Greek belief about lower and higher destiny for one) connected with modern psychology (C.Jung primarily) that leads to a mesmerising study of the phenomenon of synchronicities: events that we today tend to describe as "incredible coincidences" or dejavues without actually realising that there could be a meaning, a "code", which can reveal to us either things about to happen or can function as warnings about the future, or even, "messages" about ourselves and what we can do to alter the "higher destiny" which is the part of fate we actually can manipulate.
In the hi-tech, fast paced and materialistic modern world all this may sound like another book for "weirdos", but it can't be dismissed as others in its genre exactly because synchronicities are something mostly everyone notices at one point of life or another, and the more aware you are about them the more apparent they become.
Being a natural sceptic the first time i picked up this book i abandoned it after only being 1/3 into it becuase i felt it wasn't compatible with my own personal system of beliefs and understanding. It was only after i started noticing some startling synchronicities myself that i read it (through this time) again , only to realise that there's way more to synchronicities than, well, meets not only the eye but any of our senses.
I tend to think that the "truth" (whatever that may be) is not only something one can "learn" but it's also something one can feel and i consider both processes equally important.
The author divides synchronicities into 17 categories and studies them providing in the process numerous truly incredible examples about them. At certain parts of the book it's the examples themselves that steal the show and you may find yourself recognising situations that are in one way or the other familiar to you but you hadn't paid attention when they happened. Attention is of primary importance as you will find out if you go ahead and read it. Frank Joseph attempts to find what most of us would call a "rational explanation" about synchronicities. He's never dogmatic (to his credit) about his own thoughts and his book reads like a conversation with the reader making it one definite "cantputdowner".
In the end what he proposes is essentialy that the reader examines this his/herself and explain it in his/her terms. It doesnt actually matter how one decides to explain synchronicities he muses, what matters is that there is a different dimension of reality present for everyone waiting to be explored, discovered and deciphered.
Put this book in your bag of valuable tools.
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This is really funny to me because I caught no such traits whatsoever in these two characters! This book can easily be read in one sitting, it is so enjoyable!