James C Maxwell - Collected Quotes

"They say that Understanding ought to work by the rules of right reason. These rules are, or ought to he, contained in Logic; but the actual science of logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true logic for this world is the calculus of Probabilities, which takes account of the magnitude of the probability which is, or ought to be, in a reasonable man's mind." (James C Maxwell, "Quetlet on Probabilities", Edinburgh Review 92, 1850)

"In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data." (James C Maxwell, [letter to Lewis Campbell] 1851)

"All the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers." (James C Maxwell, "On Faraday’s lines of force", 1855)

"In order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies. By a physical analogy I mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the other. Thus all the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers." (James C Maxwell, "On Faraday's Lines of Force", 1856)

"The first process therefore in the effectual study of the science, must be one of simplification and reduction of the results of previous investigation to a form in which the mind can grasp them. The results of this simplification may take the form of a purely mathematical formula or of a physical hypothesis. In the first case we entirely lose sight of the phenomena to be explained; and though we may trace out the consequences of given laws, we can never obtain more extended views of the connexions of the subject. If, on the other hand, we adopt a physical hypothesis, we see the phenomena only through a medium, and are liable to that blindness to facts and rashness in assumption which a partial explanation encourages. We must therefore discover some method of investigation which allows the mind at every step to lay hold of a clear physical conception, without being committed to any theory founded on the physical science from which that conception is borrowed, so that it is neither drawn aside from the subject in pursuit of analytical subtleties, nor carried beyond the truth by a favourite hypothesis." (James C Maxwell, "On Faraday’s lines of force", 1855)

"The dimmed outlines of phenomenal things all merge into one another unless we put on the focusing-glass of theory, and screw it up sometimes to one pitch of definition and sometimes to another, so as to see down into different depths through the great millstone of the world." (James C Maxwell, "Are There Real Analogies in Nature?", 1856)

"Every existence above a certain rank has its singular points; the higher the rank the more of them. At these points, influences whose physical magnitude is too small to be taken account of by a finite being may produce results of the greatest importance." (James C Maxwell, [letter] 1865) 

"Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express." (James C Maxwell, "A Dynamical Theory of the Electromagnetic Field", 1865)

"[...] Scientific truth should be presented in different forms, and should be regarded as equally scientific whether it appears in the robust form and the vivid colouring of a physical illustration, or in the tenuity and paleness of a symbolic expression." (James C Maxwell, [address] 1870)

"The figure of speech or of thought by which we  transfer the language and ideas of a familiar  science to one with which we are less acquainted  may be called Scientific Metaphor." (James C Maxwell, British Association for the Advancement of Science, 1871)

"These generalized forms of elementary ideas may be called metaphorical terms in the sense in which every abstract term is metaphorical. The characteristic of a truly scientific system of metaphors is that each term in its metaphorical use retains all the formal relations to the other terms of the system which it had in its original use. The method is then truly scientific - that is, not only a legitimate product of science but capable of generating science in its turn." (James C Maxwell, British Association for the Advancement of Science, 1871)

"Hence all these theories lead to the conception of a medium in which the propagation takes place, and if we admit this medium as an hypothesis, I think it ought to occupy a prominent place in our investigations, and that we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise."(James C Maxwell, "Treatise on Electricity and Magnetism" Vol. II, 1873)

"It is difficult, however, for the mind which has once recognised the analogy between the phenomena of self-induction and those of the motion of material bodies, to abandon altogether the help of this analogy, or to admit that it is entirely superficial and misleading. The fundamental dynamical idea of matter, as capable by its motion of becoming the recipient of momentum and of energy, is so interwoven with our forms of thought that, when ever we catch a glimpse of it in any part of nature, we feel that a path is before us leading, sooner or later, to the complete understanding of the subject." (James C Maxwell, "A Treatise on Electricity and Magnetism" Vol. II, 1873)

"The scientific value of a theory of this kind, in which we make so many assumptions, and introduce so many adjustable constants, cannot be estimated merely by its numerical agreement with certain sets of experiments. If it has any value it is because it enables us to form a mental image of what takes place in a piece of iron during magnetization." (James C Maxwell, "Treatise on Electricity and Magnetism" Vol. II, 1873)

"There is a maxim which is often quoted, that ‘The same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more that once, so that the causes and effects cannot be the same in all respects. [...] There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course." (James C Maxwell, "Matter and Motion", 1876)

"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)

"An Experiment, like every other event which takes place, is a natural phenomenon; but in a Scientific Experiment the circumstances are so arranged that the relations between a particular set of phenomena may be studied to the best advantage. In designing an Experiment the agents and the phenomena to be studied are marked off from all others and regarded as the Field of Investigation." (James C Maxwell)

"One of the severest tests of a scientific mind is to discern the limits of the legitimate application of the scientific method."  (James C Maxwell)

"Thus number may be said to rule the whole world of quantity, and the four rules of arithmetic may be regarded as the complete equipment of the mathematician." (James C Maxwell)