Wednesday, 31 August 2011

Rabbits and Pineapples

The Golden Ratio: The Story of Phi, the Extraordinary Number of Nature, Art and Beauty, Mario Livio

A good short popular guide to perhaps the most fascinating, and certainly the most irrational, of all numbers: the golden ratio or phi, which is approximately equal to 1·6180339... Prominent in mathematics since at least the ancient Greeks and Euclid, phi is found in many places in nature too, from pineapples and sunflowers to the flight of hawks, and Livio catalogs its appearances in both realms, with particular attention to rabbit-breeding and the Fibonacci sequence, before going on to debunk mistaken claims of its appearances in art, music, and poetry. Dalí certainly used it, but da Vinci, Debussy, and Virgil almost certainly didnt, and neither, almost certainly, did the builders of the Parthenon and pyramids. Finally, he examines what has famously been called (by the physicist Eugene Wiegner) the unreasonable effectiveness of mathematics: why is this human invention so good at describing the behavior of the Universe? Livio quotes one of the best short answers Ive yet seen to the question:
Human logic was forced on us by the physical world and is therefore consistent with it. Mathematics derives from logic. That is why mathematics is consistent with the physical world. (ch. 9, Is God a mathematician?, pg. 252) Any book that can quote Jef Raskin, the creator of the Macintosh computer, with Johannes Kepler, William Blake, Lewis Carroll, and Christopher Marlowe, has to be recommended, and recreational mathematicians should find lots of ideas for further investigation, from fractal strings to the fascinating number patterns governed by Benfords law. It isnt just human beings who look after number one: as a leading figure, 1 turns up much more often in data from the real world, and in mathematical constructs like the Fibonacci sequence, than intuition would lead you to expect. If youd like to learn more about that and about many other aspects of mathematics, hunt down a copy of this book.

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