Basvan Fraassen The behaviour of pendulums and bouncing springs was well-known by Newton’s time, but he represented both as systems subject to a force varying directly with the distance from a mid-point. Today we would say that Newton’s theory provides models satisfying F = −kx, and these models can be used to represent such phenomena. To understand what is involved in such a view of science we must first of all focus on representation. To represent is certainly not simply to produce scale copies, whether physical or abstract, though scientific representations do typically trade on selective resemblances in certain respects for their success. Just as artistic representations do, they trade also on selective distortion and systematic non-resemblance in other respects, and often embed the represented phenomena in much larger structures involving non-phenomenal elements. The pertinent selectivity needs to be conveyed, somehow, if the artefact, the vehicle of representation, is to represent its target. Think of a specific use of a graph of an exponential function. Does it represent the growth of a bacteria colony, of a bank account with compound interest or of the result of radio-active decay? Nothing that is in the graph or its structural relations to those three possible targets answers that question. If the selection is indicated by signs placed in the artefact itself, that task of identification is only pushed back a step. Thus, what determines the representation relationship must be a relation of what is in the artefact to factors neither in the artefact itself nor in what is being represented. The conclusion advanced is that there is no representation except in the sense that some things are used, made or taken, to represent some things as thus or so. This conclusion places use and user, and the role of indexical judgement, centre-stage in the analysis of scientific representation.
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Bas C. van Fraassen (2010) studied this question.