James Franklin, "Diagrammatic reasoning and modelling in the imagination"
the secret weapons of the Scientific Revolution
Abstract:
The first successes of the Scientific Revolution were exclusively geometrical, if geometry is taken in a wide sense.
They were possible because Europe had had several centuries of training with reasoning with diagrams -- not only the Euclidean ones labelled "geometry", but anything from simple family trees to complicated perspective constructions to gridded maps.
The Scientific Revolution could exist because it inherited a medieval Mathematical (mostly Geometrical) Revolution. The evidence includes not only the surviving pictures themselves, but descriptions of what those pictures produced in the astonishingly vivid medieval visual imagination. The imagination was regarded as literally full of pictures, and so a medium for scientific visualisation. It was the medium Galileo used successfully for his thought experiments.
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In 1543 and All That: Image and Word, Change and Continuity in the Proto-Scientific Revolution, ed. G. Freeland & A. Corones (Dordrecht, 1999), pp. 53-115.
http://web.maths.unsw.edu.au/~jim/image.html