divine proportion

“Pythagoras is in fact credited with having coined the words ‘philosophy’ (‘love of wisdom’) and ‘mathematics’ (‘that which is learned’). To him, a ‘philosopher’ was someone who ‘gives himself up to discussing the meaning and purpose of life itselt… to uncover the secrets of nature.’ Pythagoras emphasized the importance of learning above all other activities, because, in his words, ‘most men and women, by birth or nature, lack the means to advance in wealth and power, but all have the ability to advance in knowledge.’ He was also famous for introducing the doctrine of metempsychosis – that the soul is immortal and is reborn or tranmigrated in human and animal incarnation.” p. 26

“In Fechner’s experiment, 76 percent of all choices centered on the three rectangles having the ratios 1.75, 1.62, and 1.50, with the peak at the Golden Rectangle (1.62). All other rectangles received less than 10 percent of the choices each.” p.180

“Life imitates Art far more than Art imitates Life. This results… from the fact that… Art offers [Life] certain beautiful forms through which it may realize that energy [to find expression]… It is a theory that… is extremely fruitful, and throws an entirely new light upon the history of Art.”

“It follows… that external Nature also imitates Art. The only effects that she can show us are effects that we have already seen through poetry, or in paintings. This is the secret of Nature’s charm, as well as the explanation of Nature’s weakness.” (quoted from Oscar Wilde) pp.237-238

“Provability is a weaker notion than truth.” (quoted from Douglas Hofstadter) p.240

“I’m beginning to think simply that mathematics can be invented to describe anything, and matter is no exception.” (quoted from Marilyn vos Savant) p.245

The Golden Ratio, Mario Livio, 2002


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