Tobias Dantzig Quotes (25 quotes) | Quotes of famous people

...the children had to live, so while waiting for logic to sanctify their existence, they throve and multiplied.
Number: The Language of Science (1930)

Tobias Dantzig Quotes

“One part of the dreams of the eighteenth century intellectuals was realized: the resources of nature did yield a magnificent harvest. But the thinkers who helped to tap these resources… failed to attend, detained in their studies and laboratories, lost in their dreams and calculations, seeking new fields, co-ordinating old and new, spinning abstract theories… the thinkers were unequal to the task of developing these vast resources, most of which they had themselves uncovered. The shrewd declassés, who had… the world to gain, pioneered this development and took possession of the earth.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 2. The Age of Innocence

World , Dreams , Nature , Study

“d'Alembert, who wrote the introduction to the Encyclopédie, resigned his editorship with the scathing remark that the work was like a harlequin's coat: some good stuff, but mostly rags.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 2. The Age of Innocence

“The preface to the French edition of that work contains the following passage: "To me the French edition of my work is not a mere translation, but a transcription of ideas into a language in which it should have been written in the first place… I proudly acknowledge… my master. His words are among the most brilliant recollections of my youth; his piercing wisdom and potent prose have inspired my efforts of a riper age. To the memory of Henri Poincaré, the intellectual giant who was the first to recognize the role which the idiosyncrasies of the race play in the evolution of scientific ideas, I dedicate this book.”

Tobias Dantzig

Preface
Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954)

Wisdom , Books , Youth , Age

“Poincaré's mind was not subject to hysteresis or hibernation. He had the unique faculty of dismissing an idea from his mind, the instant the stimulus was gone, and to supplant it immediately with another creative idea.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 1. The Iconoclast

Idea

“The evolution of scientific thought is inseparable from the history of man's efforts to resolve the perplexities of his own existence.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 2. The Age of Innocence

History , Effort

“Barely a hundred and fifty years had passed since Galileo's experiment at Pisa had ushered in the new order of things; a mere instant as compared with the previous life of the race. Yet, this brief span had witnessed a complete shift in the outlook of the intellectual leaders of humanity: from blind adherence to authority and dogma towards a healthy habit of facing facts and an enlightened faith in the efficacy of reason. Few doubted that this buoyancy and self-reliance of the leaders would eventually reach the masses, thus causing a profound metamorphosis in the attitude of the common man towards his own life and the destinies of his race.
…Led by thinkers, and under the banners of liberty, happiness, and truth, humanity was to emerge into a Golden Age, free from oppression and strife. Alas! The French Revolution… resembled more a convention of inquisitors and hangmen than it did an assembly of enlightened emancipators. …After twenty years of adventure, the humanitarian aspirations bequeathed by the Encyclopedists, tattered and trampled first by a bloody republic, then by a still bloodier empire, were finally declared dead by the Holy Alliance.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 2. The Age of Innocence

Life , Truth , Age , Faith

“Greek thought was essentially non-algebraic, because it was so concrete. The abstract operations of algebra, which deal with objects that have been purposely stripped of their physical content, could not occur to minds which were so intently interested in the objects themselves. The symbol is not a mere formality; it is the very essence of algebra. Without the symbol the object is a human perception and reflects all the phases under which the human senses grasp it; replaced by a symbol the object becomes a complete abstraction, a mere operand subject to certain indicated operations.”

Tobias Dantzig

p, 125
Number: The Language of Science (1930)

Sense

“To describe means to classify, and the man Poincaré defies classification, as does indeed his philosophy.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 1. The Iconoclast

“Science… may be viewed as man's supreme effort to find himself in that perplexing pattern which he calls Nature. …Has he succeeded in achieving some measure of harmony with Nature? Or has he merely managed to transfer to Nature the irreconcilable duality within himself?”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 2. The Age of Innocence

Nature , Effort , Science

“There exists among the most primitive tribes of Australia and Africa a system of numeration which has neither 5, 10, nor 20 for base. It is a binary system, i. e., of base two. These savages have not yet reached finger counting. They have independent numbers for one and two, and composite numbers up to six. Beyond six everything is denoted by “heap.””

Tobias Dantzig

Number: The Language of Science (1930)

“Between the philosopher's attitude towards the issue of reality and that of the mathematician there is this essential difference: for the philosopher the issue is paramount; the mathematician's love for reality is purely platonic.”

Tobias Dantzig

p, 125
Number: The Language of Science (1930)

Love , Reality

“The great Cartesian invention had its roots in those famous problems of antiquity which originated in the days of Plato. In endeavoring to solve the problems of the trisection of an angle, of the duplication of the cube and of the squaring of the circle, the ruler and compass having failed them, the Greek geometers sought new curves. They stumbled on the conic sections…There we find the nucleus of the method which Descartes later erected into a principle. Thus Apollonius referred the parabola to its axis and principal tangent, and showed that the semichord was the mean propotional between the latus rectum and the height of the segment. Today we express this relation by x2 = Ly, calling the height the ordinate (y) and the semichord the abscissa (x); the latus rectum being… L. …the Greeks named these curves and many others… loci… Thus the ellipse was the locus of a point the sum of the distances of which from two fixed points was constant. Such a description was a rhetorical equation of the curve…”

Tobias Dantzig

Number: The Language of Science (1930)

Lying , Problem

“His essays on the foundations of science are cases in point. They strike one as extemporaneous speeches rather than edited articles. …those who knew him best insisted that he rarely, if ever, would revise a manuscript, even if he was fully aware of its stylistic shortcomings.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 1. The Iconoclast

Science

“The Industrial Revolution, too, failed to introduce a reign of freedom and happiness: it converted the medieval serf into an industrial slave; replaced the feudal baron by the industrial mogul, created in its wake an ever-growing, ever-shifting class of declassés, who had neither pride of ancestry nor love of tradition… The age of machine and competition, of capital, class-struggle, and demagogy was upon man.”

Tobias Dantzig

Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954), Ch. 2. The Age of Innocence

Love , Age , Freedom , Happiness

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