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24 of 25 people found the following review helpful:
5.0 out of 5 stars
Thoughtful Numerology, March 11, 2007
One of the most famous and mysterious of numbers is pi, the ratio of a circle's circumference to its diameter. If you know some mathematics and work with logarithms, you know another important constant, e. Less well known is the number phi (the Greek symbol looks like a capital I superimposed on an o); it is in many ways simpler than the other two and is just as interesting. All you have to do is take a line segment of any length, and put a point on the line so that the point divides the line into a big segment and a little one, and so that the little segment is to the big segment as the big segment is to the line you started with. The section you made, and the connected mathematics and art, are described and illustrated in _The Golden Section: Nature's Greatest Secret_ (Walker Books) by Scott Olsen, which ought to get an award for the book with the greatest density of information in the smallest package. It has but 58 small pages, and half of those are taken up with illustrations (which are wonderfully selected ). But if you follow the pages, and have pencil, paper, and a calculator beside you, there are depths here that bigger books never touch.
It's not too interesting to put a point directly in the middle of a line. You get equal segments that way, or a ratio of one to one, or 1:1; and if a segment is 1, the whole line you bisected is 2, a ratio of 2:1. Plato knew, though, that that was one point that would divide the whole line into shorter and longer portions so that "the whole to the longer equals the longer to the shorter"; or if shorter is a, longer is b, and the whole is a + b, then a + b is to b as b is to a; in symbols, a + b : b as b : a, or a + b : b : a. The ratio is phi (pronounced "fye"). It's numerical equivalent is 1.6180339... (the ellipsis indicating its never-ending nature). There are plenty of surprising properties of this number, some of which you can find on your calculator. For instance, divide phi into one, and you get 0.6180339..., which is exactly one less than phi itself. If you square phi, you get 2.6180339..., which is exactly one more than phi itself. Phi shows up closely related to the Fibonacci Sequence, a series of numbers that shows up all over nature. Rectangles based on phi show up in architecture and art and even music.
"Because of its aesthetic qualities, embodied in its unique ability to relate the parts to the whole," writes Olsen, "golden ratios are used in the design of many modern household items." Credit cards, for instance, are very close to the 8 by 5 Fibonacci approximation of phi. Surely no one ever designed the first credit cards to reflect phi, but the ratio does seem to be inherently attractive. Olsen demonstrates that phi shows up in spirals of DNA, in human proportions, in icosahedrons, and so many other places. His handsome and accessible book is an exercise in an appealing numerology.
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13 of 14 people found the following review helpful:
5.0 out of 5 stars
The Platonists super-model for the cosmos. The Pythagorean secret, October 7, 2006
Scott's book on the golden section, unlike all the other books I have on the subject delves into the early Platonic fascination and significance of the Golden section as the Cosmic and metaphysical model for the Emanationist explanation for empirical and metaphysical ratios both of empirical life and of the Absolute itself.
Specifically, the extreme importance of Phi, or the Golden section in every facet of phenomena, and therefore as the archetype for unraveling the nature of the Absolute (not God, but the Platonic One which is not a sentient Being!) is gone into great details in a pithy and concise manner, other books 10 times the size are verbose exercises in petty logomachy; much talk, little or no substance.
Scotts capacity to synthesize the overall importance of the Golden section and the original and ancient paradigm of the Pythagorean (and to some extent the Gnostic) model for the metaphysical universe is certainly evident.
As someone (myself) that gives 1 star reviews to 95% of books, I don't lightly recommend this small and pithy book. Phi is the religious and metaphysical paradigm which is both contrary and inclusive and the antinomy to Creationism and Nihilism (nothing-morism); and the hidden religious doctrine of Plato and his Pythagorean ancestors as well and Neoplatonic `sons'; of this Scott unveils the significance of same.
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10 of 11 people found the following review helpful:
5.0 out of 5 stars
A really wonderful book, October 18, 2006
The Golden Section is a subject many have tried and failed to cover comprehensively. Generally these books either over-romanticize the subject and fail scientifically, or they tend instead to be over mathematical and run scared from the genuine (and still unexplained) mystery of why the Golden Section appears so widely in nature.
Scott Olsen's little book admirably steers a middle course through these choppy waters, covering everything from Lucas numbers and phyllotaxis to the common use of the 8:5 Fibonacci approximation to the Golden Section in nature and the visual arts.
I heartily recommend this book to anyone - from those with just a passing interest in the Golden Section like painters and musicians to more experienced mathematicians (check out for instance Bryson's extraordinary equations for the Solar Year on the back page!). It is an excellent book, beautifully produced and wonderfully illustrated. I'm giving it 5 stars.
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