"[...] if there is one important result that comes out of our inquiry into the nature of the Universe it is this: when by patient inquiry we learn the answer to any problem, we always find, both as a whole and in detail, that the answer thus revealed is fi ner in concept and design than anything we could ever have arrived at by a random guess." (Sir Fred Hoyle, "The Nature of the Universe", 1950)
"The scientist who discovers a theory is usually guided to his discovery by guesses; he cannot name a method by means of which he found the theory and can only say that it appeared plausible to him, that he had the right hunch or that he saw intuitively which assumption would fit the facts." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)
"Sometimes [the word theory] is used for a hypothesis, sometimes for a confirmed hypothesis; sometimes for a train of thought; sometimes for a wild guess at some fact, or for a reasoned claim of what some fact is - or even for a philosophical speculation." (John O Wisdom, "Foundations of Inference in Natural Sciences", 1952)
"On every scientist’s desk there is a drawer labeled UNKNOWN in which he fi les what are at the moment unsolved questions, lest through guess-work or impatient speculation he come upon incorrect answers that will do him more harm than good. Man’s worst fault is opening the drawer too soon. His task is not to discover final answers but to win the best partial answers that he can, from which others may move confidently against the unknown, to win better ones." (Homer W Smith, "From Fish to Philosopher", 1953)
"Anything new that we learn about the world involves plausible reasoning, which is the only kind of reasoning for which we care in everyday affairs.[...] Certainly, let us learn proving, but also let us learn guessing." (George Pólya, "Mathematics and Plausible Reasoning" Vol. 1, 1954)
"In an honest search for knowledge you quite often have to abide by ignorance for an indefinite period. Instead of filling a gap by guesswork, genuine science prefers to put up with it; and this, not so much from conscientious scruples above telling lies, as from the consideration that, however irksome the gap may be, its obliteration by a fake removes the urge to seek after a tenable answer." (Erwin Schrödinger, "Nature and the Greeks", 1954)
"The result of the mathematician's creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing. If the learning of mathematics reflects to any degree the invention of mathematics, it must have a place for guessing, for plausible inference." (George Pólya, "Induction and Analogy in Mathematics", 1954)
"You have to guess the mathematical theorem before you prove it: you have to guess the idea of the proof before you carry through the details. You have to combine observations and follow analogies: you have to try and try again. The result of the mathematician’s creative work is demonstrative reasoning, a proof; but the proof is discovered by plausible reasoning, by guessing" (George Polya, "Mathematics and plausible reasoning" Vol. 1, 1954)
"There never was a great scientist who did not make bold guesses, and there never was a bold man whose guesses were not sometimes wild." (Jacob Bronowski, "Science and Human Values", 1956)
"The shrewd guess, the fertile hypothesis, the courageous leap to a tentative conclusion - these are the most valuable coin of the thinker at work." (Jerome S Bruner, "The Process of Education", 1960)
"The way in which knowledge progresses, and especially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our problems, by conjectures. These conjectures are controlled by criticism; that is, by attempted refutations, which include severely critical tests. They may survive these tests; but they can never be positively justified: they can neither be established as certainly true nor as 'probable' (in the sense of probability calculus). Criticism of our conjectures is of decisive importance: by bringing out our mistakes it makes us understand the difficulties of the problem which we are trying to solve. This is how we become better acquainted with our problems, and able to propose more mature solutions: the very refutation of a theory - that is, of any serious tentative solution to our problem - is always a step forward that takes us nearer to the truth. And this is how we can learn from our mistakes." (Karl R Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)
"We know many laws of nature and we hope and expect to discover more. Nobody can foresee the next such law that will be discovered. Nevertheless, there is a structure in laws of nature which we call the laws of invariance. This structure is so far-reaching in some cases that laws of nature were guessed on the basis of the postulate that they fit into the invariance structure." (Eugene P Wigner, "The Role of Invariance Principles in Natural Philosophy", 1963)
"Another thing I must point out is that you cannot prove a vague theory wrong. If the guess that you make is poorly expressed and rather vague, and the method that you use for figuring out the consequences is a little vague - you are not sure, and you say, 'I think everything's right because it's all due to so and so, and such and such do this and that more or less, and I can sort of explain how this works' […] then you see that this theory is good, because it cannot be proved wrong! Also if the process of computing the consequences is indefinite, then with a little skill any experimental results can be made to look like the expected consequences." (Richard P Feynman, "The Character of Physical Law", 1965)
"It is only through refined measurements and careful experimentation that we can have a wider vision. And then we see unexpected things: we see things that are far from what we would guess - far from what we could have imagined. Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there." (Richard P Feynman, "The Character of Physical Law", 1965)
"Never make a calculation until you know the answer: Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every puzzle. Courage: no one else needs to know what the guess is. Therefore make it quickly, by instinct. A right guess reinforces this instinct. A wrong guess brings the refreshment of surprise. In either case, life as a spacetime expert, however long, is more fun!" (Edwin F Taylor & John A Wheeler, "Spacetime Physics", 1965)
"The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way." (Richard Feynman, "The Character of Physical Law", 1965)
"What are the facts? Again and again and again - what are the facts? Shun wishful thinking, ignore divine revelation, forget what ‘the stars foretell,’ avoid opinion, care not what the neighbors think, never mind the unguessable ‘verdict of history', - what are the facts, and to how many decimal places? You pilot always into an unknown future; facts are your only clue. Get the facts!" (Robert A Heinlein, "Time Enough for Love", 1973)
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