On Models (1800-1899)

“There are no rules or models; that is, there are no rules except general laws of nature which hover over art and special laws which apply to specific subjects.” (Victor M Hugo, “Cromwell”, 1827)

"Given the nature of the subject, we must remind ourselves that it is simply not possible to construct a model for the art of war that can serve as a scaffolding on which the commander can rely for support at any time. Whenever he has to fall back on his innate talent, he will find himself outside the model and in conflict with it; no matter how versatile the code, the situation will always lead to the consequences we have already alluded to: talent and genius operate outside the rules, and theory conflicts with practice." (Carl von Clausewitz, "On War", 1832)

"[…] the conduct of war branches out in almost all directions and has no definite limits; while any system, any model, has the finite nature of a synthesis. An irreconcilable conflict exists between this type of theory and actual practice." (Carl von Clausewitz, "On War", 1832)

"The first process therefore in the effectual study of science must be one of simplification and reduction of 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." (James C Maxwell, "On Faraday’s lines of force", 1855)

"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)

"In order to depict nature in its exalted sublimity, we must not dwell exclusively on its external manifestations, but we must trace its image, reflected in the mind of man, at one time filling the dreamy land of physical myths with forms of grace and beauty, and at another developing the noble germ of artistic creations." (Alexander von Humboldt, "Cosmos: A Sketch of a Physical Description of the Universe" Vol. 2, 1869)

"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)

"It seems to me that the test of 'Do we or do we not understand a particular subject in physics?' is, 'Can we make a mechanical model of it?'" (William Thomson, "Notes of lectures on molecular dynamics and the wave theory of light", 1884)

" […] as a general rule, that in selecting a particular case for constructing a model the first prerequisite is regularity. By selecting a symmetrical form for the model, not only is the execution simplified, but what is of more importance, the model will be of such a character as to impress itself readily on the mind." (Felix Klein, 1893)

"Harmonious order governing eternally continuous progress - the web and woof of matter and force interweaving by slow degrees, without a broken thread, that veil which lies between us and the Infinite - that universe which alone we know or can know; such is the picture which science draws of the world, and in proportion as any part of that picture is in unison with the rest, so may we feel sure that it is rightly painted." (Thomas H Huxley, "Darwiniana", 1893–94)

"Experience teaches that one will be led to new discoveries almost exclusively by means of special mechanical models." (Ludwig Boltzmann, "Lectures on Gas Theory", 1896)

"To use an old analogy - and here we can hardly go except upon analogy - while the building of Nature is growing spontaneously from within, the model of it, which we seek to construct in our descriptive science, can only be constructed by means of scaffolding from without, a scaffolding of hypotheses. While in the real building all is continuous, in our model there are detached parts which must be connected with the rest by temporary ladders and passages, or which must be supported till we can see how to fill in the understructure. To give the hypotheses equal validity with facts is to confuse the temporary scaffolding with the building itself.” (John H Poynting, 1899)