Alec Nevala-Lee

Thoughts on art, creativity, and the writing life.

Posts Tagged ‘Jacques Hadamard

The sudden awakening

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One phenomenon is certain and I can vouch for its absolute certainty: the sudden and immediate appearance of a solution at the very moment of sudden awakening. On being very abruptly awakened by an external noise, a solution long searched for appeared to me at once without the slightest instant of reflection on my part—the fact was remarkable enough to have struck me unforgettably—and in a quite different direction from any of those which I had previously tried to follow. Of course, such a phenomenon, which is fully certain in my own case, could be easily confused with a “mathematical dream,” from which it differs.

Jacques Hadamard, An Essay on the Psychology of Invention in the Mathematical Field

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December 10, 2017 at 7:30 am

The act of combination

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Twyla Tharp

In the empty room you’re trying to connect the dots, linking A to B to C to maybe come up with H. Scratching is a means to identifying A, and if you can get to A, you’ve got a grip on a slippery rock wall. You’ve got purchase. You can move on to B, which is mandatory. You cannot stop with one idea. You don’t really have a workable idea until you combine two ideas.

Twyla Tharp

I have coined the term “bisociation” in order to make a distinction between the routine skills of thinking in a single “plane,” as it were, and the creative act, which, as I shall try to show, always operates on more than one plane.

Arthur Koestler

If there is any novelty in the suggestion I am about to make—and I must confess I fear there is—it lies only in the juxtaposition of ideas.

Charles Sanders Peirce

Henri Poincaré

Every day I seated myself at my work table, stayed an hour or two, tried a great number of combinations, and reached no results. One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination.

Henri Poincaré

Scientists who have made important original contributions have often had wide interests or have taken up the study of a subject different from the one in which they were originally trained. Originality often consists in finding connections or analogies between two or more objects or ideas not previously shown to have any bearing on each other.

W.I.B. Beveridge

It is obvious that invention or discovery, be it in mathematics or anywhere else, takes place by combining ideas.

Jacques Hadamard

Jacques Derrida

The philosopher must form a new combination of ideas concerning the combination of ideas.

Jacques Derrida

The essential possibility of [metaphor] lies in the broad ontological fact that new qualities and new meanings can emerge, simply come into being, out of some hitherto ungrouped combination of elements.

Philip Wheelwright

Instead of thoughts of concrete things patiently following one another in a beaten track of habitual suggestion, we have the most abrupt cross-cuts and transitions from one idea to another, the most rarefied abstractions and discriminations, the most unheard of combination of elements, the subtlest associations of analogy; in a word, we seem suddenly introduced into a seething cauldron of ideas, where everything is fizzling and bobbling about in a state of bewildering activity, where partnerships can be joined or loosened in an instant, treadmill routine is unknown, and the unexpected seems only law.

William James

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