On Laws (1890-1899)

"The history of thought should warn us against concluding that because the scientific theory of the world is the best that has yet to be formulated, it is necessarily complete and final. We must remember that at bottom the generalizations of science, or, in common parlance, the laws of nature are merely hypotheses devised to explain that ever-shifting phantasmagoria of thought which we dignify with the high-sounding names of the world and the universe. In the last analysis, magic, religion, and science are nothing but theories of thought." (Sir James G Frazer, "The Golden Bough", 1890)

"The laws of science are products of the human mind rather than' factors of the external world. Science endeavors to provide a mental resume of the universe, and its last great claim to our support is the capacity it has for satisfying our cravings for a brief description of the history of the world." (Karl Pearson, "The Grammar of Science", 1892)

"With our notion of the essence of intuition, an intuitive treatment of figurative representations will tend to yield a certain general guide on which mathematical laws apply and how their general proof may be structured. However, true proof will only be obtained if the given figures are replaced with figures generated by laws based on the axioms and these are then taken to carry through the general train of thought in an explicit case. Dealing with sensate objects gives the mathematician an impetus and an idea of the problems to be tackled, but it does not pre-empt the mathematical process itself." (Felix Klein, Nicht-Euklidische Geometrie I: Vorlesung gehalten während des Wintersemesters 1889–90", 1892)

"The natural world has its laws, and no man must interfere with them in the way of presentment any more than in the way of use; but they themselves may suggest laws of other kinds, and man may, if he pleases, invent a little world of his own, with its own laws; for there is that in him which delights in calling up new forms - which is the nearest, perhaps, he can come to creation. When such forms are new embodiments of old truths, we call them products of the Imagination; when they are mere inventions, however lovely, I should call them the work of the Fancy: in either case, Law has been diligently at work." (George MacDonald, "The Fantastic Imagination", 1893)

"All physicists agree that the problem of physics consists in tracing the phenomena of nature back to the simple laws of mechanics." (Heinrich Hertz, "The Principles of Mechanics Presented in a New Form", 1894)

"The images which we may form of things are not determined without ambiguity by the requirement that the consequents of the images must be the images of the consequents. Various images of the same objects are possible, and these images may differ in various respects. We should at once denote as inadmissible all images which implicitly contradict the laws of our thought. Hence we postulate in the first place that all our images shall be logically permissible or, briefly, that they shall be permissible. We shall denote as incorrect any permissible images, if their essential relations contradict the relations of external things, i.e. if they do not satisfy our first fundamental requirement. Hence we postulate in the second place that our images shall be correct. But two permissible and correct images of the same external objects may yet differ in respect of appropriateness. Of two images of the same object that is the more appropriate which pictures more of the essential relations of the object, the one which we may call the more distinct. Of two images of equal distinctness the more appropriate is the one which contains, in addition to the essential characteristics, the smaller number of superfluous or empty relations, the simpler of the two. Empty relations cannot be altogether avoided: they enter into the images because they are simply images, images produced by our mind and necessarily affected by the characteristics of its mode of portrayal." (Heinrich Hertz, "The Principles of Mechanics Presented in a New Form", 1894)

"There is no subject more captivating, more worthy of study, than nature. To understand this great mechanism, to discover the forces which are active, and the laws which govern them, is the highest aim of the intellect of man." (Nikola Tesla, "The Inventions, Researches and Writings of Nikola Tesla|, 1894)

"We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry. There will come with the greater love of science greater love to one another. Living more nearly to Nature is living farther from the world and from its follies, but nearer to the world's people; it is to be of them, with them, and for them, and especially for their improvement. We cannot see how impartially Nature gives of her riches to all, without loving all, and helping all; and if we cannot learn through Nature's laws the certainty of spiritual truths, we can at least learn to promote spiritual growth while we are together, and live in a trusting hope of a greater growth in the future." (Maria Mitchell, "Maria Mitchell: Life, Letters and Journals", 1896)

"The history of civilization proves beyond doubt just how sterile the repeated attempts of metaphysics to guess at nature’s laws have been. Instead, there is every reason to believe that when the human intellect ignores reality and concentrates within, it can no longer explain the simplest inner workings of life’s machinery or of the world around us." (Santiago Ramón y Cajal, "Reglas y Consejos sobre Investigacíon Cientifica: Los tónicos de la voluntad", 1897)

"The whole task of psychology can therefore be summed up in these two problems :" (1) What are the elements of consciousness ?" (2) What combinations do these elements undergo and what laws govern these combinations?" (Wilhelm M Wundt,"Outlines of Psychology", 1897)

"Every deep thinker and observer of the Natural Laws is convinced that Nature is an orderly arrangement of matter and forces; that, in a word, Nature is not chaos, but cosmos." (Frederick Hovenden, What is Life?", 1899)

"Logic sometimes makes monsters. For half a century we have seen a mass of bizarre functions which appear to be forced to resemble as little as possible honest functions which serve some purpose. More of continuity, or less of continuity, more derivatives, and so forth. Indeed, from the point of view of logic, these strange functions are the most general; on the other hand those which one meets without searching for them, and which follow simple laws appear as a particular case which does not amount to more than a small corner. In former times when one invented a new function it was for a practical purpose; today one invents them purposely to show up defects in the reasoning of our fathers and one will deduce from them only that. If logic were the sole guide of the teacher, it would be necessary to begin with the most general functions, that is to say with the most bizarre. It is the beginner that would have to be set grappling with this teratologic museum." (Henri Poincaré, 1899)