"We want to have certainties and no doubts - results and no experiments - without even seeing that certainties can arise only through doubt and results only thorough experiment." (Carl G Jung, "The Structure And Dynamics Of The Psyche", 1960)
"When evaluating the reliability and generality of data, it is often important to know the aims of the experimenter. When evaluating the importance of experimental results, however, science has a trick of disregarding the experimenter's rationale and finding a more appropriate context for the data than the one he proposed." (Murray Sidman, "Tactics of Scientific Research", 1960)
"Model-making, the imaginative and logical steps which precede the experiment, may be judged the most valuable part of scientific method because skill and insight in these matters are rare. Without them we do not know what experiment to do. But it is the experiment which provides the raw material for scientific theory. Scientific theory cannot be built directly from the conclusions of conceptual models." (Herbert G Andrewartha,"Introduction to the Study of Animal Population", 1961)
"The first [principle], is that a mathematical theory can only he developed axiomatically in a fruitful way when the student has already acquired some familiarity with the corresponding material - a familiarity gained by working long enough with it on a kind of experimental, or semiexperimental basis, i.e. with constant appeal to intuition. The other principle [...] is that when logical inference is introduced in some mathematical question, it should always he presented with absolute honesty - that is, without trying to hide gaps or flaws in the argument; any other way, in my opinion, is worse than giving no proof at all." (Jean Dieudonné, "Thinking in School Mathematics", 1961)
"The functional validity of a working hypothesis is not a priori certain, because often it is initially based on intuition. However, logical deductions from such a hypothesis provide expectations (so called prognoses) as to the circumstances under which certain phenomena will appear in nature. Such a postulate or working hypothesis can then be substantiated by additional observations or by experiments especially arranged to test details. The value of the hypothesis is strengthened if the observed facts fit the expectation within the limits of permissible error." (R Willem van Bemmelen, "The Scientific Character of Geology", The Journal of Geology Vol 69 (4), 1961)
"Both the uncertainty principle and the negentropy principle of information make Laplace's scheme [of exact determinism] completely unrealistic. The problem is an artificial one; it belongs to imaginative poetry, not to experimental science." (Léon Brillouin, "Science and Information Theory" 2nd Ed., 1962)
"The physical sciences are used to 'praying over' their data, examining the same data from a variety of points of view. This process has been very rewarding, and has led to many extremely valuable insights. Without this sort of flexibility, progress in physical science would have been much slower. Flexibility in analysis is often to be had honestly at the price of a willingness not to demand that what has already been observed shall establish, or prove, what analysis suggests. In physical science generally, the results of praying over the data are thought of as something to be put to further test in another experiment, as indications rather than conclusions." (John W Tukey, "The Future of Data Analysis", The Annals of Mathematical Statistics, Vol. 33 (1), 1962)
"Observation, reason, and experiment make up what we call the scientific method." (Richard Feynman, "Mainly mechanics, radiation, and heat", 1963)
"[…] it is more important to have beauty in one's equations that to have them fit experiment. […] It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress." (Paul Dirac, Scientific American, 1963)
"A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe." (Paul Dirac, Scientific American, 1963)
"[…] it is more important to have beauty in one's equations that to have them fit experiment. […] It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress." (Paul A M Dirac, "The Evolution of the Physicist’s Picture of Nature ", Scientific American, 1963)
"Mathematical statistics provides an exceptionally clear example of the relationship between mathematics and the external world. The external world provides the experimentally measured distribution curve; mathematics provides the equation (the mathematical model) that corresponds to the empirical curve. The statistician may be guided by a thought experiment in finding the corresponding equation." (Marshall J Walker, "The Nature of Scientific Thought", 1963)
"Observation, reason, and experiment make up what we call the scientific method." (Richard Feynman, Mainly mechanics, radiation, and heat", 1963)
"Thus science must begin with myths, and with the criticism of myths; neither with the collection of observations, nor with the invention of experiments, but with the critical discussion of myths, and of magical techniques and practices." (Karl Popper, "Conjectures and Refutations: The Growth of Scientific Knowledge", 1963)
"Perfect logic and faultless deduction make a pleasant theoretical structure, but it may be right or wrong; the experimenter is the only one to decide, and he is always right." (Léon Brillouin, "Scientific Uncertainty and Information", 1964)
"The trouble with group theory is that it leaves so much unexplained that one would like to explain. It isolates in a beautiful way those aspects of nature that can be understood in terms of abstract symmetry alone. It does not offer much hope of explaining the messier facts of life, the numerical values of particle lifetimes and interaction strengths - the great bulk of quantitative experimental data that is now waiting for explanation. The process of abstraction seems to have been too drastic, so that many essential and concrete features of the real world have been left out of consideration. Altogether group theory succeeds just because its aims are modest. It does not try to explain everything, and it does not seem likely that it will grow into a complete or comprehensive theory of the physical world." (Freeman J Dyson, "Mathematics in the Physical Sciences", Scientific American Vol. 211 (3), 1964)
"No experimental result can ever kill a theory: any theory can be saved from counterinstances either by some auxiliary hypothesis or by a suitable reinterpretation of its terms." (Imre Lakatos, "Falsification and the Methodology of Scientific Research Programmes", 1965)
"After all, without the experiment - either a real one or a mathematical model - there would be no reason for a theory of probability." (Thornton C Fry, "Probability and Its Engineering Uses", 1965)
"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)
"If science is to progress, what we need is the ability to experiment, honestly in reporting the results - the results must be reported without somebody saying what they would like the results to have been - and finally - an important thing - the intelligence to interpret the results. An important point about this intelligence is that it should not be sure ahead of time what must be. It cannot be prejudiced, and say 'That is very unlikely; I don’t like that.'" (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)
"No experimental result can ever kill a theory: any theory can be saved from counterinstances either by some auxiliary hypothesis or by a suitable reinterpretation of its terms." (Imre Lakatos, "Falsification and the Methodology of Scientific Research Programmes", 1965)
"Nature does not seem full of circles and triangles to the ungeometrical; rather, mastery of the theory of triangles and circles, and later of conic sections, has taught the theorist, the experimenter, the carpenter, and even the artist to find them everywhere, from the heavenly motions to the pose of a Venus. (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)
"The method of least squares is used in the analysis of data from planned experiments and also in the analysis of data from unplanned happenings. The word 'regression' is most often used to describe analysis of unplanned data. It is the tacit assumption that the requirements for the validity of least squares analysis are satisfied for unplanned data that produces a great deal of trouble." (George E P Box, "Use and Abuse of Regression", 1966)
"Applying this approach, systems belonging to different scientific disciplines are investigated in their natural forms. On the basis of experimental results, isomorphic relations between different systems are studied and, finally, some general principles applicable for all systems of a certain class are formulated." (George Klir, "An approach to general systems theory", 1969)
"Any theory starts off with an observer or experimenter. He has in mind a collection of abstract models with predictive capabilities. Using various criteria of relevance, he selects one of them. In order to actually make predictions, this model must be interpreted and identified with a real assembly to form a theory. The interpretation may be prescriptive or predictive, as when the model is used like a blueprint for designing a machine and predicting its states. On the other hand, it may be descriptive and predictive as it is when the model is used to explain and predict the behaviour of a given organism." (Gordon Pask, "The meaning of cybernetics in the behavioural sciences", 1969)
"It is not enough to observe, experiment, theorize, calculate and communicate; we must also argue, criticize, debate, expound, summarize, and otherwise transform the information that we have obtained individually into reliable, well established, public knowledge." (John M Ziman, "Information, Communication, Knowledge", Nature Vol. 224 (5217), 1969)
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