"Science is the attempt to make the chaotic diversity of our sense-experience correspond to a logically uniform system of thought. " (Albert Einstein, "Out of My Later Years", 1950)
"The technical analysis of any large collection of data is a task for a highly trained and expensive man who knows the mathematical theory of statistics inside and out. Otherwise the outcome is likely to be a collection of drawings - quartered pies, cute little battleships, and tapering rows of sturdy soldiers in diversified uniforms - interesting enough in the colored Sunday supplement, but hardly the sort of thing from which to draw reliable inferences." (Eric T Bell, "Mathematics: Queen and Servant of Science", 1951)
"When, for instance, I see a symmetrical object, I feel its pleasurable quality, but do not need to assert explicitly to myself, ‘How symmetrical!’. This characteristic feature may be explained as follows. In the course of individual experience it is found generally that symmetrical objects possess exceptional and desirable qualities. Thus our own bodies are not regarded as perfectly formed unless they are symmetrical. Furthermore, the visual and tactual technique by which we perceive the symmetry of various objects is uniform, highly developed, and almost instantaneously applied. It is this technique which forms the associative 'pointer.' In consequence of it, the perception of any symmetrical object is accompanied by an intuitive aesthetic feeling of positive tone." (George D Birkhoff, "Mathematics of Aesthetics", 1956)
"Exact truth of a null hypothesis is very unlikely except in a genuine uniformity trial." (David R Cox, "Some problems connected with statistical inference", Annals of Mathematical Statistics 29, 1958)
"[A] sequence is random if it has every property that is shared by all infinite sequences of independent samples of random variables from the uniform distribution." (Joel N Franklin, 1962)
"Science is the reduction of the bewildering diversity of unique events to manageable uniformity within one of a number of symbol systems, and technology is the art of using these symbol systems so as to control and organize unique events. Scientific observation is always a viewing of things through the refracting medium of a symbol system, and technological praxis is always handling of things in ways that some symbol system has dictated. Education in science and technology is essentially education on the symbol level." (Aldous L Huxley, "Essay", Daedalus, 1962)
"Statistics is the description in numerical terms of experiences concerning phenomena not subject to regular uniformity. […] Statistic is therefore a specific method of history." (Ludwig von Mises, "The Ultimate Foundation of Economic Science: An Essay on Method", 1962)
"Theories are usually introduced when previous study of a class of phenomena has revealed a system of uniformities. […] Theories then seek to explain those regularities and, generally, to afford a deeper and more accurate understanding of the phenomena in question. To this end, a theory construes those phenomena as manifestations of entities and processes that lie behind or beneath them, as it were." (Carl G Hempel, "Philosophy of Natural Science", 1966)
"[A] sequence is random if it has every property that is shared by all infinite sequences of independent samples of random variables from the uniform distribution." (J. N. Franklin" (1962)"[…] random numbers should not be generated with a method chosen at random. Some theory should be used." (Donald E. Knuth, "The Art of Computer Programming" Vol. II, 1968)
"In the definition of a coordinate system we have required that the coordinate neighborhood and the range in Rd be open sets. This is contrary to popular usage, or at least more specific than the usage of curvilinear coordinates in advanced calculus. For example, spherical coordinates are used even along points of the z axis where they are not even 1-1. The reasons for the restriction to open sets are that it forces a uniformity in the local structure which simplifies analysis on a manifold" (there are no 'edge points') and, even if local uniformity were forced in some other way, it avoids the problem of. spelling out what we mean by differentiability at boundary points of the coordinate neighborhood; that is, one-sided derivatives need not be mentioned. On the other hand, in applications, boundary value problems frequently arise, the setting for which is a manifold with boundary. These spaces are more general than manifolds and the extra generality arises from allowing a boundary manifold of one dimension less. The points of the boundary manifold have a coordinate neighborhood in the boundary manifold which is attached to a coordinate neighborhood of the interior in much the same way as a face of a cube is attached to the interior. Just as the study of boundary value problems is more difficult than the study of spatial problems, the study of manifolds with boundary is more difficult than that of mere manifolds, so we shall limit ourselves to the latter." (Richard L Bishop & Samuel I Goldberg, "Tensor Analysis on Manifolds", 1968)
"Scientific knowledge is not created solely by the piecemeal mining of discrete facts by uniformly accurate and reliable individual scientific investigations. The process of criticism and evaluation, of analysis and synthesis, are essential to the whole system. It is impossible for each one of us to be continually aware of all that is going on around us, so that we can immediately decide the significance of every new paper that is published. The job of making such judgments must therefore be delegated to the best and wisest among us, who speak, not with their own personal voices, but on behalf of the whole community of Science. […] It is impossible for the consensus - public knowledge - to be voiced at all, unless it is channeled through the minds of selected persons, and restated in their words for all to hear." (John M Ziman, "Public Knowledge: An Essay Concerning the Social Dimension of Science", 1968)
"Scientific knowledge is not created solely by the piecemeal mining of discrete facts by uniformly accurate and reliable individual scientific investigations." (John M Ziman, "Public Knowledge: An Essay Concerning the Social Dimension of Science", 1968)
"The machine rules. Human life is rigorously controlled by it, dominated by the terribly precise will of mechanisms. These creatures of man are exacting. They are now reacting on their creators, making them like themselves. They want well-trained humans; they are gradually wiping out the differences between men, fitting them into their own orderly functioning, into the uniformity of their own regimes. They are thus shaping humanity for their own use, almost in their own image." (Paul A Valéry, "Fairy Tales for Computers", 1969)
"The figures which excite in us the ideas of beauty seem to be those in which there is uniformity amidst variety. […] What we call beautiful in objects, to speak in the mathematical style, seems to be in compound ratio of uniformity and variety: so that where the uniformity of bodies is equal, the beauty is as the variety; and where the variety is equal, the beauty is as the uniformity." (Francis Hutcheson,"An Inquiry Concerning Beauty, Order, Harmony, Design", 1973)
"In order to describe meanders, then, we can invoke a model involving scour and centrifugal force, a model that describes the uniform expenditure of energy, or a model based on probability theory. All three models describe the same phenomenon. As far as meanders are concerned, all three models happen to be interrelated - but not out of any fundamental necessity. That is to say, the cross circulation induced by centrifugal force need not necessarily result in a uniform distribution of effort or produce a path that is especially probable. In a world of limited patterns, however, the meander answers several entirely different sets of specifications, so that scour, uniform effort, and probability produce the same design." (Peter B Stevens, "Patterns in Nature", 1974
"The spiral is beautifully uniform; it curves around on itself in a perfectly regular manner. It can fill all of two-dimensional space, being capable of infinite expansion, and it is also quite short. But [...], as measured by the mean of distances to its center, the spiral is extremely indirect." (Peter B Stevens, "Patterns in Nature", 1974)
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