- Current Issue
SIGN IN to access Harper’s Magazine
1. Sign in to Customer Care using your account number or postal address.
2. Select Email/Password Information.
3. Enter your new information and click on Save My Changes.
Subscribers can find additional help here. Not a subscriber? Subscribe today!
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:
<object width=”480″ height=”385″><param name=”movie” value=”http://www.youtube.com/v/5h3FYJsIY6k&hl=en_US&fs=1&”> <embed src=”http://www.youtube.com/v/5h3FYJsIY6k&hl=en_US&fs=1&” type=”application/x-shockwave-flash” allowscriptaccess=”always” allowfullscreen=”true” width=”480″ height=”385″></embed></object></p>
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:
<object width=”480″ height=”385″><param name=”movie” value=”http://www.youtube.com/v/6Q2TEZvv9Jc&hl=en_US&fs=1&”> <embed src=”http://www.youtube.com/v/6Q2TEZvv9Jc&hl=en_US&fs=1&” type=”application/x-shockwave-flash” allowscriptaccess=”always” allowfullscreen=”true” width=”480″ height=”385″></embed></object></p>
More from Scott Horton:
No Comment — November 4, 2013, 5:17 pm
An expert panel concludes that the Pentagon and the CIA ordered physicians to violate the Hippocratic Oath
No Comment — August 12, 2013, 7:55 am
How will the Obama Administration handle Edward Snowden’s case in the long term?
No Comment — July 29, 2013, 11:36 am
Is it possible to simply disband the partisan FISA court?
Price charged by a Ukrainian company for a half-day tour of the Chernobyl nuclear-plant site:
Male Abdopus aculeatus octopuses may strangle to death rivals in defending the females whom they have seduced by swimming in a feminine manner.
A study led by a physician at Imperial College London posited that Gollum would have defeated Bilbo Baggins in J. R. R. Tolkien’s The Hobbit had he sunned himself more often or eaten quiche instead of blind fish.
Subscribe to the Weekly Review newsletter. Don’t worry, we won’t sell your email address!
Notes on South Africa’s failed revolution
“I will never know what goes on in your mind, or what that shield of a smile behind which we try to advance should tell us.”