Recurrence Quotes - page 2

We can not... escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contradiction. ...Neither can this rule come to us from experience... This rule, inaccessible to analytic demonstration and to experience, is the veritable type of the synthetic a priori judgment. On the other hand, we can not think of seeing in it a convention, as in some of the postulates of geometry. ...it is only the affirmation of the power of the mind which knows itself capable of conceiving the indefinite repetition of the same act when once this act is possible. The mind has a direct intuition of this power, and experience can only give occasion for using it and thereby becoming conscious of it. (Henri Poincaré)
While I have not lost faith in its potentialities, my views have changed since. War can not be avoided until the physical cause for its recurrence is removed and this, in the last analysis, is the vast extent of the planet on which we live. Only though annihilation of distance in every respect, as the conveyance of intelligence, transport of passengers and supplies and transmission of energy will conditions be brought about some day, insuring permanency of friendly relations. What we now want most is closer contact and better understanding between individuals and communities all over the earth and the elimination of that fanatic devotion to exalted ideals of national egoism and pride, which is always prone to plunge the world into primeval barbarism and strife. No league or parliamentary act of any kind will ever prevent such a calamity. These are only new devices for putting the weak at the mercy of the strong.
Nikola Tesla
We were thus led to organize ourselves, as men who had fought the war together, in order to support those statesmen who had truly understood the lessons of that World War, thus attempting to prevent its recurrence.
Rene Cassin
As an ardent supporter of the Nietzschean conception of the eternal recurrence, I firmly believe that one cannot validate the totality of a life unless one accepts and embraces all the experiences that comprise it. That said, I sometimes wish I'd gone to film school.
Dave Itzkoff
The standard formulation on remedy is that it ought to cure past violations and prevent their recurrence. That's what antitrust is all about.
Charles James
The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time... As the planets move around the sun, they repeat their orbits periodically; thus there is already a primitive kind of rhythm in their motion. ...Harmony ...can be considered a special kind of rhythm. ...pure musical tones are produced when the vibrations are... periodic or... repeat themselves regularly in time. Two tones harmonize if their intervals of repetition are in rhythm-or, in mathematical language, if their periods are in proportion.
Frank Wilczek
The favourite volume whose reading we commend, is inevitably connected with ourselves - it must bring to our image those lonely hours when the recurrence of an image has such influence - it invests that image with the associations of poetry and fiction, and thus redeems it from the common-place of ordinary life. There is also the sympathy of taste - and how much may be inferred from a passage pencilled originally for no other eyes but our own. Then, too, a book is the prettiest stepping stone to a correspondence ; it seems such a simple thing to write a note of thanks, and so natural to add some slight remark on the author ; and how often is the criticism of an author's sentiments but the expression of our own !
Letitia Elizabeth Landon
Bad men cannot make good citizens. It is when a people forget God that tyrants forge their chains. A vitiated state of morals, a corrupted public conscience, is incompatible with freedom. No free government, or the blessings of liberty, can be preserved to any people but by a firm adherence to justice, moderation, temperance, frugality, and virtue and by a frequent recurrence to fundamental principles.
Patrick Henry
Lack of outlets, excess capacity, complete deadlock, in the end regular recurrence of national bankruptcies and other disasters-perhaps world wars from sheer capitalist despair-may confidently be anticipated. History is as simple a that.
Joseph Schumpeter
The essential characteristic of reasoning by recurrence is that it contains, condensed, so to speak, in a single formula, an infinity of syllogisms.
Henri Poincaré
To recall this is to remind people of what the Establishment would like them to forget-the enormous capacity of apparently helpless people to resist, of apparently contented people to demand change. To uncover such history is to find a powerful human impulse to assert one's humanity. It is to hold out, even in times of deep pessimism, the possibility of surprise. True, to overestimate class consciousness, to exaggerate rebellion and its successes, would be misleading. It would not account for the fact that the world-not just the United States, but everywhere else-is still in the hands of the elites, that people's movements, although they show an infinite capacity for recurrence, have so far been either defeated or absorbed or perverted... (Howard Zinn)
It is significant that we owe the first explicit formulation of the principle of recurrence to the genius of Blaise Pascal... Pascal stated the principle in a tract called The Arithmetic Triangle which appeared in 1654. Yet... the gist of the tract was contained in the correspondence between Pascal and Fermat regarding a problem in gambling, the same correspondence which is now regarded as the nucleus from which developed the theory of probabilities. It surely is a fitting subject for mystic contemplation that the principle of reasoning by recurrence, which is so basic in pure mathematics, and the theory of probabilities, which is the basis of all deductive sciences, were both conceived while devising a scheme for the division of stakes in an unfinished match of two gamblers.
Blaise Pascal