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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:
More from Scott Horton:
Conversation — March 30, 2016, 3:44 pm
Joseph Hickman discusses his new book, The Burn Pits, which tells the story of thousands of U.S. soldiers who, after returning from Iraq and Afghanistan, have developed rare cancers and respiratory diseases.
In Havana, the past year has been marked by a parade of bold-faced names from the north — John Kerry reopening the United States Embassy; Andrew Cuomo bringing a delegation of American business leaders; celebrities ranging from Joe Torre, traveling on behalf of Major League Baseball to oversee an exhibition game between the Tampa Bay Rays and the Cuban national team, to Jimmy Buffett, said to be considering opening one of his Margaritaville restaurants there. All this culminated with a three-day trip in March by Barack Obama, the first American president to visit Cuba since Calvin Coolidge in 1928. But to those who know the city well, perhaps nothing said as much about the transformation of political relations between the United States and Cuba that began in December 2014 as a concert in the Tribuna Antiimperialista.
Amount traders on the Philadelphia Stock Exchange can be fined for fighting, per punch:
Philadelphian teenagers who want to lose weight also tend to drink too much soda, whereas Bostonian teenagers who drink too much soda are likelier to carry guns.
Nuremberg’s Neues Museum filed a criminal complaint against a 91-year-old woman who completed a crossword puzzle that was in fact a $116,000 piece of avant-garde Danish art.
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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.'”