„It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way… Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.“

As quoted in "The Mathematician" in The World of Mathematics (1956), by James Roy Newman

Última atualização 22 de Maio de 2020. História
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John von Neumann
1903 - 1957
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„I believe that no one who is familiar, either with mathematical advances in other fields, or with the range of special biological conditions to be considered, would ever conceive that everything could be summed up in a single mathematical formula, however complex.“

—  Ronald Fisher English statistician, evolutionary biologist, geneticist, and eugenicist 1890 - 1962

The evolutionary modification of genetic phenomena. Proceedings of the 6th International Congress of Genetics 1, 165-72, 1932.
1930s

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Edward de Bono photo
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Confucius photo

„Such being its nature, without any display, it becomes manifested; without any movement, it produces changes; and without any effort, it accomplishes its ends.“

—  Confucius Chinese teacher, editor, politician, and philosopher -551 - -479 a.C.

The Analects, The Doctrine of the Mean
Contexto: To entire sincerity there belongs ceaselessness. Not ceasing, it continues long. Continuing long, it evidences itself. Evidencing itself, it reaches far. Reaching far, it becomes large and substantial. Large and substantial, it becomes high and brilliant. Large and substantial; this is how it contains all things. High and brilliant; this is how it overspreads all things. Reaching far and continuing long; this is how it perfects all things. So large and substantial, the individual possessing it is the co-equal of Earth. So high and brilliant, it makes him the co-equal of Heaven. So far-reaching and long-continuing, it makes him infinite. Such being its nature, without any display, it becomes manifested; without any movement, it produces changes; and without any effort, it accomplishes its ends.

Norbert Wiener photo

„Since Leibniz there has perhaps been no man who has had a full command of all the intellectual activity of his day. Since that time, science has been increasingly the task of specialists, in fields which show a tendency to grow progressively narrower… Today there are few scholars who can call themselves mathematicians or physicists or biologists without restriction. A man may be a topologist or a coleopterist. He will be filled with the jargon of his field, and will know all its literature and all its ramifications, but, more frequently than not, he will regard the next subject as something belonging to his colleague three doors down the corridor, and will consider any interest in it on his own part as an unwarrantable breach of privacy… There are fields of scientific work, as we shall see in the body of this book, which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology; in which every single notion receives a separate name from each group, and in which important work has been triplicated or quadruplicated, while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.
It is these boundary regions which offer the richest opportunities to the qualified investigator. They are at the same time the most refractory to the accepted techniques of mass attack and the division of labor. If the difficulty of a physiological problem is mathematical in essence, then physiologists ignorant of mathematics will get precisely as far as one physiologists ignorant of mathematics, and no further. If a physiologist who knows no mathematics works together with a mathematician who knows no physiology, the one will be unable to state his problem in terms that the other can manipulate, and the second will be unable to put the answers in any form that the first can understand… A proper exploration of these blank spaces on the map of science could only be made by a team of scientists, each a specialist in his own field but each possessing a thoroughly sound and trained acquaintance with the fields of his neighbors; all in the habit of working together, of knowing one another's intellectual customs, and of recognizing the significance of a colleague's new suggestion before it has taken on a full formal expression. The mathematician need not have the skill to conduct a physiological experiment, but he must have the skill to understand one, to criticize one, and to suggest one. The physiologist need not be able to prove a certain mathematical theorem, but he must be able to grasp its physiological significance and to tell the mathematician for what he should look. We had dreamed for years of an institution of independent scientists, working together in one of these backwoods of science, not as subordinates of some great executive officer, but joined by the desire, indeed by the spiritual necessity, to understand the region as a whole, and to lend one another the strength of that understanding.“

—  Norbert Wiener, livro Cybernetics: Or Control and Communication in the Animal and the Machine

Fonte: Cybernetics: Or Control and Communication in the Animal and the Machine (1948), p. 2-4; As cited in: George Klir (2001) Facets of Systems Science, p. 47-48

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Vannevar Bush photo

„If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.“

—  Vannevar Bush, livro As We May Think

As We May Think (1945)
Contexto: If scientific reasoning were limited to the logical processes of arithmetic, we should not get far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability. The abacus, with its beads strung on parallel wires, led the Arabs to positional numeration and the concept of zero many centuries before the rest of the world; and it was a useful tool — so useful that it still exists.

„There is no concept in the whole field of physics which is more difficult to understand than is the concept of entropy, nor is there one which is more fundamental.“

—  Francis Sears American physicist 1898 - 1975

[Francis Weston Sears, Mechanics, heat and sound, Addison-Wesley principles of physics series Volume 1, 2nd Edition, Addison-Wesley Press, 1950, 447]

Haruki Murakami photo

„I just run. I run in void. Or maybe I should put it the other way: I run in order to acquire a void.“

—  Haruki Murakami, livro Auto-Retrato do Escritor enquanto Corredor de Fundo

Fonte: What I Talk About When I Talk About Running

John Von Neumann photo

„It is just as foolish to complain that people are selfish and treacherous as it is to complain that the magnetic field does not increase unless the electric field has a curl. Both are laws of nature.“

—  John Von Neumann Hungarian-American mathematician and polymath 1903 - 1957

As quoted "John von Neumann (1903 - 1957)" by Eugene Wigner, in Year book of the American Philosophical Society (1958); later in Symmetries and Reflections : Scientific Essays of Eugene P. Wigner (1967), p. 261

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