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Title: The Golden Ratio : The Story of PHI, the World's Most Astonishing Number by MARIO LIVIO ISBN: 0-7679-0816-3 Publisher: Broadway Pub. Date: 23 September, 2003 Format: Paperback Volumes: 1 List Price(USD): $14.95 |
Average Customer Rating: 3.87 (38 reviews)
Rating: 1
Summary: Predictably Prejudiced
Comment: The big problem with this book is it seems to exist only to debunk. It tends to debunk in a Matrin Gardner-ish manner, by stating only some of the facts about a subject, then simply saying that they aren't true, or stating that no one takes this subject seriously any more, or some such statement implying that any form of serious study of the subject is beneath the author's serious consideration, and, therefore, also beneath yours.
His discussion of Joseph Schillinger's monumental System Of Musical Composition is flawed by this same wet pointing approach. There's much more to Schillinger's work than the use of the Fibonacci series or the Golden Mean in musical composition or arranging, but Livio seems to think he's covered the System by a paragraph or two on its use of the Golden Mean.
I suppose I should be thankful that Schillinger is even mentioned any more these days, despite the fact that he pioneered and predicted the extensive use of electronics in music today, among other things. His work is still in extensive use by many composers, but Livio would have us believe he's a totally forgettable crackpot.
Rating: 3
Summary: Uninspired philosophy of mathematics
Comment: The book seems to have two purposes. First, it seeks to debunk the notion that the 'golden mean' is intuitively pleasing to all humans. Secondly, the book argues that we can best understand the cosmic meaning of life via numbers. From these two theses, the author establishes the 'genius' mathematician as mediator and priest between mankind and the cosmos.
Ok, enough mumbo-jumbo. If the above interests you, read the last chapter first. It should have been used as the introduction and will clarify the purpose of arguments presented throughout the book.
Getting back to the book's narrative, the early sections seek to debunk various claims that Egyptian and Mesopotamian civilization use the Fibonacci ratio. Reports of its use in China are ignored. Later, there is a section debunking the notion that great art 'uses' the Golden Mean. Scattered throughout are developments in number theory, starting with Pythagoras and continuing with the standard European mathematical genius roll call. The last chapters reveal the relationship between the Golden Mean and complexity/chaos theory/fuzzy logic/quantum theory/etc.
Livio's Fibonacci sequence, Penrose tilings, and quasi-crystals stories will probably engage the recreational mathematicians among us, and provide a handy 'all in one place' summary of such matters. Others will find the philosophic overtones tangential and/or distracting. Any successful philosophy of math needs to address the issues of cardinality and ordinality at the level of intuition. The two topics are dismissed by page 15, but they underlie the whole issue of 'intuitive acceptance of number theory'. This topic is discussed throughout the book as Livio seeks to explain why so many people see the Golden Mean in ancient works of architecture, modern art and stock market charts. Curiously, Livio argues they all got it wrong and only genius mathematicians have the gift of 'intiutive acceptance of number theory'. Not an argument which many will find satisfying, but for the passionately recreational mathematician, it may be seductive.
Rating: 5
Summary: Mathematically Profound
Comment: Broad streams of literary, historical, aethsetic and religious thought are pooled together in a concise and well-illustrated review of this powerful proportion, which recurs in the natural world in surprising places both large and small. Clearly presented mathematical proofs give the book a solid backbone. Mathematical ideas are expressed in the book through a combination of prose, appendix proofs, and plentiful illustrations & diagrams. This allows readers of varying mathematical ability and learning styles to appreciate the beautiful ideas that Livio gracefully presents. A must for serious lovers of proportion & geometry, architects, mystics, painters, graphic designers and mathematicians.
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Title: The Divine Proportion by H. E. Huntley ISBN: 0486222543 Publisher: Dover Pubns Pub. Date: 01 June, 1970 List Price(USD): $9.95 |
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Title: The Constants of Nature : From Alpha to Omega--the Numbers That Encode the Deepest Secrets of the Universe by JOHN BARROW ISBN: 0375422218 Publisher: Pantheon Books Pub. Date: 14 January, 2003 List Price(USD): $26.00 |
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Title: The Geometry of Art and Life by Matila Ghyka ISBN: 0486235424 Publisher: Dover Pubns Pub. Date: 01 June, 1977 List Price(USD): $8.95 |
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Title: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire ISBN: 0309085497 Publisher: Joseph Henry Press Pub. Date: 23 April, 2003 List Price(USD): $27.95 |
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Title: e: The Story of a Number by Eli Maor ISBN: 0691058547 Publisher: Princeton Univ Pr Pub. Date: 04 May, 1998 List Price(USD): $18.95 |
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