On Patterns (-1899)

"For, among the world's incertitudes, this thing called arithmetic is established by a sure reasoning that we comprehend as we do the heavenly bodies. It is an intelligible pattern, a beautiful system, that both binds the heavens and preserves the earth. For is there anything that lacks measure, or transcends weight? It includes all, it rules all, and all things have their beauty because they are perceived under its standard." (Cassiodorus,"Variae epistolae", cca. 538–540s)

"God forbid that we should give out a dream of our own imagination for a pattern of the world." (Francis Bacon, "The Great Instauration", 1620)

"The nature, mother of the eternal diversities, or the divine spirit, are zaelous of her variety by accepting one and only one pattern for all things, By these reasons she has invented this elegant and admirable proceeding. This wonder of Analysis, prodigy of the universe of ideas, a kind of hermaphrodite between existence and non-existence, which we have named imaginary root?" (Gottfried W Leibniz, "De Bisectione Latereum", 1675)

"Some there are who make a distinction betwixt primary and secondary qualities: by the former, they mean extension, figure motion, rest, solidity or impenetrability and number: by the latter they denote all other sensible qualities, as colours, sounds, tastes, and so forth. The ideas we have of these they acknowledge not to be the resemblances of anything existing without the mind or unperceived; but they will have our ideas of the primary qualities to be patterns or images of things which exist without the mind, in an unthinking substance which they call matter. By matter therefore we are to under-stand an inert, senseless substance, in which extension, figure, and motion, do actually subsist." (George Berkeley, "Principles of Human Knowledge", 1710)

"The function of theory is to put all this in systematic order, clearly and comprehensively, and to trace each action to an adequate, compelling cause. […] Theory should cast a steady light on all phenomena so that we can more easily recognize and eliminate the weeds that always spring from ignorance; it should show how one thing is related to another, and keep the important and the unimportant separate. If concepts combine of their own accord to form that nucleus of truth we call a principle, if they spontaneously compose a pattern that becomes a rule, it is the task of the theorist to make this clear." (Carl von Clausewitz, "On War", 1832)

"Most surprising and far-reaching analogies revealed themselves between apparently quite disparate natural processes. It seemed that nature had built the most various things on exactly the same pattern; or, in the dry words of the analyst, the same differential equations hold for the most various phenomena." (Ludwig Boltzmann, "On the methods of theoretical physics", 1892)