…I have been interested, for a long time, in the psychological process of discovery as the most concise manifestation of man’s creative faculty — and in that converse process that blinds him towards truths which, once perceived by a seer, become so heartbreakingly obvious. Now this blackout shutter operates not only in the minds of the ‘ignorant and superstitious masses’ as Galileo called them, but even more strikingly evident in Galileo’s own, and in other geniuses like Aristotle, Ptolemy, or Kepler. It looks as if, while part of their spirit was asking for more light, another part had been crying out for more darkness. (p. 10-11)
The Pythagorean discovery that the pitch of a note depends on the length of the string which produces it, and that concordant intervals in the scale are produced by simple numerical ratios (2:1 octave, 3:2 fifth, 4:3 fourth, etc.), was epoch-making: it was the first successful reduction of quality to quantity, the first step towards the mathematization of human experience — and therefore the beginning of Science. (p. 28)
The ecstatic contemplation of geometrical forms and mathematical laws is… the most effective means of purging the soul of earthly passion, and the principal link between man and divinity. (p. 28)
…the Pythagoreans regarded the body as a kind of musical instrument where each string must have the right tension and the correct balance between opposites such as ‘high’ and ‘low’… The metaphors borrowed from music which we still apply in medicine — ‘tone’, ‘tonic’, ‘well-tempered’, ‘temperance’, are also part of our Pythagorean heritage. (p. 29)
They were much more interesting within the context of his discussion. Oh well.