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Ces longues chaînes de raisons, toutes simples et faciles, dont les géomètres ont coutume de se servir pour parvenir à leurs plus difficiles démonstrations, m’avaient donné occasion de m’imaginer que toutes les choses qui peuvent tomber sous la connaissance des hommes s’entresuivent en même façon, et que, pourvu seulement qu’on s’abstienne d’en recevoir aucune pour vraie qui ne le soit, et qu’on garde toujours l’ordre qu’il faut pour les déduire les unes des autres, il n’y en peut avoir de si éloignées auxquelles enfin on ne parvienne, ni de si cachées qu’on ne découvre.
The long chains of reasonings, simple and easy, by which geometricians are wont to achieve their most complex proofs, had led me to suppose that all things, the knowledge of which man may achieve, are strung together in the same way, and that there is nothing so distant as ultimately to be beyond our mental grasp, or so hidden that we cannot uncover it, provided only we avoid accepting falsehoods as true, and always preserve in our thoughts the discipline essential for the deduction of one truth from another.
–René Descartes, Le Discours de la méthode pt 2 (1637)(S.H. transl.)
Descartes, a towering figure of the seventeenth century, made no contribution greater than his rules for the discipline of thinking. He comes to compelling conclusions, but he starts from simple premises. In fact, it would be no simplification to say that he starts with Euclidian geometry. He notes how it builds from simple thoughts–first principles and definitions–and steadily develops more and more complex notions from them. In a like manner, Descartes tells us, man can aspire to know even the most complex and distant truths–it requires the patience and resolve to approach the problem in increments. But the key to the success of this approach is the rigorous commitment to truth and willingness to reject whatever is false. Descartes is presenting a cloaked criticism of the great scientific controversy of his time: the trial of Galileo and the posture of the Church, which adhered to Aristotelian precepts about the structure of the universe long after they had been scientifically disproven. A dogmatic adherence to falsehood of the sort frequently claimed by religions which claimed a special knowledge of ultimate questions was, in Descartes’s thinking, one of the greatest challenges to the human species. But for Descartes, the illogical adherence to uttered falsehoods is a human constant which the scientific mind must struggle to overcome. “Since the pressure of things to be done does not always allow us to stop and make such a meticulous check, it must be admitted that in this human life we are often liable to make mistakes about particular things, and we must acknowledge the weakness of our nature.”
Among Descartes’s contemporaries, the Stuttgart-born composer J.J. Froberger assumes a special role as a master of the keyboard and a stylistic conciliator. He mastered the stylus fantasticus of Frescobaldi and the Roman School and merged this with the North German and French styles, and he developed the notion of the keyboard suite. But he was also an early experimenter with programmatic music. Froberger also approaches the task of composition as an essentially mathematical exercise in which each chord has a relationship to the one that proceeded and the one that followed it.
Listen to Johann Jakob Froberger’s Tombeau fait à Paris sur la mort de Monsieur Blancrocher (1652) performed by Blandine Verlet on a Ruckers II harpsichord from 1624:
And then listen to the Lamentation faite sur la mort très douloureuse de Sa Majesté Impériale, Ferdinand III (1657), a work composed in the unusual key of F (for obvious reasons), and particularly the three notes of F struck at the conclusion, which fade off into eternity, a notion that Froberger stressed in his extraordinary manuscript of the score:
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Flor Arely Sánchez had been in bed with a fever and pains throughout her body for three days when a July thunderstorm broke over the mountainside. She got nervous when bolts of light flashed in the sky. Lightning strikes the San Julián region of western El Salvador several times a year, and her neighbors fear storms more than they fear the march of diseases — first dengue, then chikungunya, now Zika. Flor worried about a lot of things, since she was pregnant.
Late in the afternoon, when the pains had somewhat eased, Flor thought she might go to a dammed-up bit of the river near her house to bathe. She is thirty-five and has lived in the same place all her life, where wrinkled hills are planted with corn, beans, and fruit trees. She took a towel and soap and walked out into the rain. Halfway to the river, the pains returned and overcame her. The next thing Flor remembers, she was in a room she didn’t recognize, unable to move. As she soon discovered, she was in a hospital, her ankle cuffed to the bed, and she was being investigated for abortion.
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An Indianapolis fertility doctor was accused of using his own sperm to artificially inseminate patients, and a Delaware man pleaded guilty to fatally stabbing his former psychiatrist.
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“Matt was happy enough to sustain himself on the detritus of a world he saw as careening toward self-destruction, and equally happy to scam a government he despised. 'I’m glad everyone’s so wasteful,' he told me. 'It supports my lifestyle.'”