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“The Pythagoreans... were fascinated by certain specific ratios, ...The Greeks knew these as the 'golden' proportion and the 'perfect' proportion respectively. They may well have been learned from the Babylonians by Pythagoras himself after having been taken prisoner in Egypt. Ratios lay at the heart of the Pythagorean theory of music.”
Graham Flegg“In the pentagram, the Pythagoreans found all proportions well-known in antiquity: arithmetic, geometric, harmonic, and also the well-known golden proportion, or the golden ratio. ... Probably owing to the perfect form and the wealth of mathematical forms, the pentagram was chosen by the Pythagoreans as their secret symbol and a symbol of health. - Alexander Voloshinov [As quoted in Stakhov]”
Alexey Stakhov, Mathematics of Harmony“We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle”
Samuel Colman, Harmonic Proportion and Form in Nature, Art and Architecture“Vegetarians have been around for a very long time - Pythagoreans forbade eating animals more than 2,500 years ago - but even as the environmental evidence mounted, they didn't appear to be winning the argument.”
Tristram Stuart“In the Pythagorean system, thinking about numbers, or doing mathematics, was an inherently masculine task. Mathematics was associated with the gods, and with transcendence from the material world; women, by their nature, were supposedly rooted in this latter, baser realm.”
Margaret Wertheim“Three passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind. These passions, like great winds, have blown me hither and thither, in a wayward course, over a great ocean of anguish, reaching to the very verge of despair. I have sought love, first, because it brings ecstasy - ecstasy so great that I would often have sacrificed all the rest of life for a few hours of this joy. I have sought it, next, because it relieves loneliness--that terrible loneliness in which one shivering consciousness looks over the rim of the world into the cold unfathomable lifeless abyss. I have sought it finally, because in the union of love I have seen, in a mystic miniature, the prefiguring vision of the heaven that saints and poets have imagined. This is what I sought, and though it might seem too good for human life, this is what--at last--I have found.With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway above the flux. A little of this, but not much, I have achieved. Love and knowledge, so far as they were possible, led upward toward the heavens. But always pity brought me back to earth. Echoes of cries of pain reverberate in my heart. Children in famine, victims tortured by oppressors, helpless old people a burden to their sons, and the whole world of loneliness, poverty, and pain make a mockery of what human life should be. I long to alleviate this evil, but I cannot, and I too suffer. This has been my life. I have found it worth living, and would gladly live it again if the chance were offered me.”
Bertrand Russell“What I Have Lived ForThree passions, simple but overwhelmingly strong, have governed my life: the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind. These passions, like great winds, have blown me hither and thither, in a wayward course, over a great ocean of anguish, reaching to the very verge of despair. I have sought love, first, because it brings ecstasy - ecstasy so great that I would often have sacrificed all the rest of life for a few hours of this joy. I have sought it, next, because it relieves loneliness--that terrible loneliness in which one shivering consciousness looks over the rim of the world into the cold unfathomable lifeless abyss. I have sought it finally, because in the union of love I have seen, in a mystic miniature, the prefiguring vision of the heaven that saints and poets have imagined. This is what I sought, and though it might seem too good for human life, this is what--at last--I have found.With equal passion I have sought knowledge. I have wished to understand the hearts of men. I have wished to know why the stars shine. And I have tried to apprehend the Pythagorean power by which number holds sway above the flux. A little of this, but not much, I have achieved. Love and knowledge, so far as they were possible, led upward toward the heavens. But always pity brought me back to earth. Echoes of cries of pain reverberate in my heart. Children in famine, victims tortured by oppressors, helpless old people a burden to their sons, and the whole world of loneliness, poverty, and pain make a mockery of what human life should be. I long to alleviate this evil, but I cannot, and I too suffer. This has been my life. I have found it worth living, and would gladly live it again if the chance were offered me.”
Bertrand Russell“The world is in A major...the earth revolves in A major, a low A.”
Thomas Ades, Thomas Adès: Full of Noises: Conversations with Tom Service