"It is more important to have a clear understanding of general principles, without, however, thinking of them as fixed laws, than to load the mind with a mass of detailed technical information which can readily be found in reference books or card indexes." (William I B Beveridge, "The Art of Scientific Investigation", 1950)
"In a sense, of course, probability theory in the form of the simple laws of chance is the key to the analysis of warfare; […] My own experience of actual operational research work, has however, shown that its is generally possible to avoid using anything more sophisticated. […] In fact the wise operational research worker attempts to concentrate his efforts in finding results which are so obvious as not to need elaborate statistical methods to demonstrate their truth. In this sense advanced probability theory is something one has to know about in order to avoid having to use it." (Patrick M S Blackett, "Operations Research", Physics Today, 1951)
"Instead of asking for a cause of the universe, the scientist can ask only for the cause of the present state of the universe; and his task will consist in pushing farther and farther back the date from which he is able to account for the universe in terms of laws of nature." (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)
"[…] observation is not enough, and it seems to me that in science, as in the arts, there is very little worth having that does not require the exercise of intuition as well as of intelligence, the use of imagination as well as of information." (Kathleen Lonsdale,"Facts About Crystals", American Scientist Vol. 39 (4), 1951)
"On the basis of what has been proved so far, it remains possible that there may exist" (and even be empirically discoverable) a theorem-proving machine which in fact is equivalent to mathematical intuition, but cannot be proved to be so, nor even be proved to yield only correct theorems of finitary number theory." (Kurt Gödel, 1951)
"The concept of an average, the equation to a curve, the description of a froth or cellular tissue, all come within the scope of mathematics for no other reason than that they are summations of more elementary principles or phenomena. Growth and Form are throughout of this composite nature; therefore the laws of mathematics are bound to underlie them, and her methods to be peculiarly fitted to interpret them." (D'Arcy W Thompson, "On Growth and Form", 1951)
"The picture of scientific method drafted by modern philosophy is very different from traditional conceptions. Gone is the ideal of a universe whose course follows strict rules, a predetermined cosmos that unwinds itself like an unwinding clock. Gone is the ideal of the scientist who knows the absolute truth. The happenings of nature are like rolling dice rather than like revolving stars; they are controlled by probability laws, not by causality, and the scientist resembles a gambler more than a prophet. He can tell you only his best posits - he never knows beforehand whether they will come true. He is a better gambler, though, than the man at the green table, because his statistical methods are superior. And his goal is staked higher - the goal of foretelling the rolling dice of the cosmos. If he is asked why he follows his methods, with what title he makes his predictions, he cannot answer that he has an irrefutable knowledge of the future; he can only lay his best bets. But he can prove that they are best bets, that making them is the best he can do - and if a man does his best, what else can you ask of him?" (Hans Reichenbach, "The Rise of Scientific Philosophy", 1951)
"To seek not for end but for antecedents is the way of the physicist, who finds causes" in what he has learned to recognise as fundamental properties, or inseparable concomitants, or unchanging laws, of matter and of energy." (Sir D’Arcy W Thompson, "On Growth and Form", 1951)
"Being built on concepts, hypotheses, and experiments, laws are no more accurate or trustworthy than the wording of the definitions and the accuracy and extent of the supporting experiments." (Gerald Holton, "Introduction to Concepts and Theories in Physical Science", 1952)
"In mathematics […] we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials [….] being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations." (David Hilbert,"Geometry and the imagination", 1952)
"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschieldsw & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)
"The primary fact is that all isolated state-determined dynamic systems are selective: from whatever state they have initially, they go towards states of equilibrium. These states of equilibrium are always characterised, in their relation to the change-inducing laws of the system, by being exceptionally resistant." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)
"All great discoveries in experimental physics have been due to the intuition of men who made free use of models, which were for them not products of the imagination, but representatives of real things." (Max Born,"Physical Reality", Philosophical Quarterly Vol. 3 (11), 1953)
"Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practice to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuitions of man." (Morris Kline,"Mathematics in Western Culture", 1953)
"The construction of hypotheses is a creative act of inspiration, intuition, invention; its essence is the vision of something new in familiar material." (Milton Friedman,"Essays in Positive Economics", 1953)
"The world is not made up of empirical facts with the addition of the laws of nature: what we call the laws of nature are conceptual devices by which we organize our empirical knowledge and predict the future." (Richard B Braithwaite, "Scientific Explanation", 1953)
"We cannot define truth in science until we move from fact to law. And within the body of laws in turn, what impresses us as truth is the orderly coherence of the pieces. They fit together like the characters of a great novel, or like the words of a poem. Indeed, we should keep that last analogy by us always, for science is a language, and like a language it defines its parts by the way they make up a meaning. Every word in a sentence has some uncertainty of definition, and yet the sentence defines its own meaning and that of its words conclusively. It is the internal unity and coherence of science which gives it truth, and which makes it a better system of prediction than any less orderly language." (Jacob Bronowski, "The Common Sense of Science", 1953)
"[…] if the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics." (Pierre-Maurice-Marie Duhem, "The Aim and Structure of Physical Theory", 1954)
"Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined. Its validity is of the same order as that of ordinary perception; memory, and understanding. Its test is found, like theirs, in actual intuition, which sometimes consists in perception and sometimes in intent." (George Santayana,"The Life of Reason, or the Phases of Human Progress", 1954)
"The important point for us to observe is that all these constructions and the laws connecting them can be arrived at by the principle of looking for the mathematically simplest concepts and the link between them. In the limited number of mathematically existent simple field types, and the simple equations possible between them, lies the theorist’s hope of grasping the real in all its depth." (Albert Einstein, "Ideas and Opinions", 1954)
"The laws of science are the permanent contribution to knowledge - the individual pieces which are fitted together attempt to form a picture of the physical universe in action." (Edwin P Hubble, "The Nature of Science and Other Lectures", 1954)
"The methods of science may be described as the discovery of laws, the explanation of laws by theories, and the testing of theories by new observations. A good analogy is that of the jigsaw puzzle, for which the laws are the individual pieces, the theories local patterns suggested by a few pieces, and the tests the completion of these patterns with pieces previously unconsidered." (Edwin P Hubble, "The Nature of Science and Other Lectures", 1954)
"The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them." (Albert Einstein,"Ideas and Opinions", 1954)
"It is not only the smallest features of the Universe that are controlled by the laws of physics. The behavior of matter on the very large scale that concerns us in astronomy is also determined by physics. The heavenly bodies dance like puppets on strings. If we are to understand why they dance as they do, it is necessary to find out how the strings are manipulated." (Fred Hoyle, "Frontiers of Astronomy", 1955)
"[…] as every law of nature implies the existence of an invariant, it follows that every law of nature is a constraint. […] Science looks for laws; it is therefore much concerned with looking for constraints. […] the world around us is extremely rich in constraints. We are so familiar with them that we take most of them for granted, and are often not even aware that they exist. […] A world without constraints would be totally chaotic." (W Ross Ashby, "An Introduction to Cybernetics", 1956)
"General systems theory is a series of related definitions, assumptions, and postulates about all levels of systems from atomic particles through atoms, molecules, crystals, viruses, cells, organs, individuals, small groups, societies, planets, solar systems, and galaxies. General behavior systems theory is a subcategory of such theory, dealing with living systems, extending roughly from viruses through societies. A significant fact about living things is that they are open systems, with important inputs and outputs. Laws which apply to them differ from those applying to relatively closed systems." (James G Miller, "General behavior systems theory and summary", Journal of Counseling Psychology (2), 1956)
"The forms of a person’s thoughts are controlled by inexorable laws of pattern of which he is unconscious. These patterns are the unperceived intricate systematizations of his own language - shown readily enough by a candid comparison and contrast with other languages, especially those of a different linguistic family." (Benjamin L Whorf, 1956)
"By some definitions 'systems engineering' is suggested to be a new discovery. Actually it is a common engineering approach which has taken on a new and important meaning because of the greater complexity and scope of problems to be solved in industry, business, and the military. Newly discovered scientific phenomena, new machines and equipment, greater speed of communications, increased production capacity, the demand for control over ever-extending areas under constantly changing conditions, and the resultant complex interactions, all have created a tremendously accelerating need for improved systems engineering. Systems engineering can be complex, but is simply defined as 'logical engineering within physical, economic and technical limits' - bridging the gap from fundamental laws to a practical operating system." (Instrumentation Technology, 1957)
"By the laws of statistics we could probably approximate just how unlikely it is that it would happen. But people forget - especially those who ought to know better, such as yourself - that while the laws of statistics tell you how unlikely a particular coincidence is, they state just as firmly that coincidences do happen." (Robert A Heinlein, "The Door Into Summer", 1957)
"Indeed, the laws of chance are just as necessary as the causal laws themselves." (David Bohm, "Causality and Chance in Modern Physics", 1957)
"[...] the whole course of events is determined by the laws of probability; to a state in space there corresponds a definite probability, which is given by the de Brogile wave associated with the state." (Max Born, "Atomic Physics", 1957)
"If simple perfect laws uniquely rule the universe, should not pure thought be capable of uncovering this perfect set of laws without having to lean on the crutches of tenuously assembled observations? True, the laws to be discovered may be perfect, but the human brain is not. Left on its own, it is prone to stray, as many past examples sadly prove. In fact, we have missed few chances to err until new data freshly gleaned from nature set us right again for the next steps. Thus pillars rather than crutches are the observations on which we base our theories; and for the theory of stellar evolution these pillars must be there before we can get far on the right track." (Erwin Schrödinger & Martin Schwarzschild, "Structure and Evolution of the Stars", 1958)
"Our craving for generality has [as one] source […] our preoccupation with the method of science. I mean the method the method of reducing the explanation of natural phenomena to the smallest possible number of primitive natural laws; and, in mathematics, of unifying the treatment of different topics by using a generalization. Philosophers constantly see the method of science before their eyes, and are irresistibly tempted to ask and answer in the way science does. This tendency is the real source of metaphysics, and leads the philosopher into complete darkness. I want to say here that it can never be our job to reduce anything to anything, or to explain anything. Philosophy really is ‘purely descriptive’." (Ludwig Wittgenstein, "The Blue and Brown Books", 1958)
"The new always happens against the overwhelming odds of statistical laws and their probability, which for all practical, everyday purposes amounts to certainty; the new therefore always appears in the guise of a miracle." (Hannah Arendt, "The Human Condition", 1958)
"Statistical laws are indisputably noncausal, even though some of them may be shown to be partly derivable from laws having a causal component." (Mario Bunge, Causality: The place of the casual principles in modern science, 1959)
"The simplicities of natural laws arise through the complexities of the languages we use for their expression." (Eugene P Wigner, 1959)
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