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The Golden Ratio by Mario Livio

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It’s one of the books I got for joining the Scientific American bookclub. The others are on infinity, 0, i, e, and pi. The last 4 books surely bring up the Euler equation e^{i pi} + 1 = 0, considered by many the most beautiful equation in the universe.

The Da Vinci Code mentioned phi in a few places, mostly for pentagram and Da Vinci’s Vitruvian Man. 方舟子 wrote a nice article about phyllotaxis (叶序).

The book is quite a nice read, compared to the other books I read recently, the dull and dry Brunelleschi’s Dome by Ross King and the incredibly verbose Mont Saint Michel and Chartres by Henry Adams (I’ll never be able to finish it). The subtitle of the book is “the world’s most astonishing number”, but it actually dispels quite a few myths that everything is related to phi, such as the design of pyramids and Parthenon, paintings of Da Vinci and Seurat, and music of Bach and Debussy (the author may not know that Da Vinci and Debussy are both grandmasters of Priory of Sion, so they’re deeply related to the pentagram, and thus Pythagras, and thus phi :))

The title of the last chapter of the book is “Is God a Mathematician”. It started with the extraordinary Benford’s Law about the probability of the first digit in a collection of random numbers. Then it goes on to ask why math is so powerful and what’s its nature. One view is “Platonic view” that math is objective and doesn’t depend on human. Human can only discover the truth. Another “modified Platonic view” is that math just happens to be the universe’ language, so it’s not something totally abstract. There’s also “formalism” view that math is purely a human invention that only exists in our head. The author’s take is somewhere in between, that math comes from subjective perception of the universe, and math theories evolve and are subject to “natural” selection in the same way as biological evolution. Math is just a symbolic representation of the universe we perceive, and it has been continuously enhanced when our perception gets deeper and wider, in many cases with the help of math.

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January 13, 2006 at 4:24 am

Also finished the book on e and 0. The book of e by Eli Maor is ok, focusing mostly on calculus. The book of 0 by Charles Seife is well written, stringing many topics and events together, such as Arabic numerals (invented in India), perspective, projective geometry, Cantor’s set theory , and quantum mechanics. Cantor’s theory is quite interesting: rational number and natural number has the size set size, but real number set is much bigger, i.e. there’re many more irrational numbers than rational numbers (the book of e also mentions this). Actually rational numbers take NO space at all on the number line.