"It is by abstraction that one can separate movements, knowledge, and affectivity. And the analysis is, here, so far from being a real dismemberment that it is given only as probable. One can never effectively reduce an [mental] image to its elements, for the reason that an image, like all other psychic syntheses, is something more and different from the sum of its elements. […] We will always go from image to image. Comprehension is a movement which is never-ending, it is the reaction of the mind to an image by another image, to this one by another image and so on, in principle to infinity. "(Jean-Paul Sartre, "The Imaginary: A phenomenological psychology of the imagination", 1940)
Quotes and Resources Related to Mathematics, (Mathematical) Sciences and Mathematicians
17 June 2021
On Knowledge (1940-1949)
"In perception, a knowledge forms itself slowly; in the [mental] image the knowledge is immediate. We see now that the image is a synthetic act which unites a concrete, nonimagined, knowledge to elements which are more actually representative. The image teaches nothing: it is organized exactly like the objects which do produce knowledge, but it is complete at the very moment of its appearance." (Jean-Paul Sartre, "The Psychology of Imagination", 1940)
"Science, in the broadest sense, is the entire body of the most accurately tested, critically established, systematized knowledge available about that part of the universe which has come under human observation. For the most part this knowledge concerns the forces impinging upon human beings in the serious business of living and thus affecting man’s adjustment to and of the physical and the social world. […] Pure science is more interested in understanding, and applied science is more interested in control […]" (Austin L Porterfield, "Creative Factors in Scientific Research", 1941)
“A metaphor holds a truth and an untruth, felt as inextricably bound up with each other. If one takes it as it is and gives it some sensual form, in the shape of reality, one gets dreams and art; but between these two and real, full-scale life there is a glass partition. If one analyzes it for its rational content and separates the unverifiable from the verifiable, one gets truth and knowledge but kills the feeling.” (Robert Musil, “Man Without Qualities”, 1943)
"It is hard to have a good idea if we have little knowledge of the subject, and impossible to have it if we have no knowledge. Good ideas are based on past experience and formerly acquired knowledge." (George Pólya, "How to solve it", 1945)
"The first rule of teaching is to know what you are supposed to teach. The second rule of teaching is to know a little more than what you are supposed to teach." (George Pólya, "How to solve it", 1945)
"Our theory has some bleaker consequences. [...] What is knowledge, if we are but a part of the mechanical system of the world we seek to know? What becomes of our ceaseless effort to explain the universe we live in, if explanation is but a part of the mechanical process?" (Kenneth Craik, "The Nature of Explanation", 1943)
"Whenever a man increases the content of his mind he gains new knowledge, and this occurs each time a new relation is established between the worlds on the two sides of the sense-organs - the world of ideas in an individual mind, and the world of objects existing outside individual minds which is common to us all." (James H Jeans, "Physics and Philosophy" 3rd Ed., 1943)
"Science usually advances by a succession of small steps, through a fog in which even the most keen-sighted explorer can seldom see more than a few paces ahead. Occasionally the fog lifts, an eminence is gained, and a wider stretch of territory can be surveyed - sometimes with startling results. A whole science may then seem to undergo a kaleidoscopic ‘rearrangement’, fragments of knowledge being found to fit together in a hitherto unsuspected manner. Sometimes the shock of readjustment may spread to other sciences; sometimes it may divert the whole current of human thought." (James H Jeans, "Physics and Philosophy" 3rd Ed., 1943)
"The former distrust of specialization has been supplanted by its opposite, a distrust of generalization. Not only has man become a specialist in practice, he is being taught that special facts represent the highest form of knowledge." (Richard Weaver, "Ideas have Consequences", 1948)
"We all inherit a great deal of useless knowledge, and a great deal of misinformation and error (maps that were formerly thought to be accurate), so that there is always a portion of what we have been told that must be discarded. But the cultural heritage of our civilization that is transmitted to us - our socially pooled knowledge, both scientific and humane - has been valued principally because we have believed that it gives us accurate maps of experience. The analogy of verbal words to maps is an important one [...]. It should be noticed at this point, however, that there are two ways of getting false maps of the world into our heads: first, by having them given to us; second, by creating them ourselves when we misread the true maps given to us." (Samuel I Hayakawa, "Language in Thought and Action", 1949)
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A Picture's Worth
"The drawing shows me at a glance what would be spread over ten pages in a book." (Ivan Turgenev, 1862) [2] "Sometimes, half ...
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