Essays on Image and Time
1. Visualization and the Horizons of Scientific Realism
Galileo’s often-quoted formula, according to which the universe is written in the language of mathematics, continues with the elucidation, “its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it”.1 Above the doorway of Plato’s Academy, some two millennia earlier, there was engraved, as tradition has it, the inscription “Let no-one ignorant of geometry enter here” – rendered not infrequently, and not without justification, as “Let no one ignorant of mathematics enter here”: since for the Greeks it was precisely geometry that constituted the essence of mathematics. And for Plato in a sense all branches of mathematics, and indeed all branches of thought, had to do with shapes. He chose the words idea and eidos to designate abstract mental contents. These words, which he used alternately, mean “form” or “shape”. Both idea and eidos come from the verb idein, “to see”; from eidos there descends the word eidolon, “the visible image”.2 In the writings of Archimedes and Apollonius eidos, along with schēma, again with the meaning “figure” or “shape”, emerged as parts of the mathematical lexicon.3 History shows mathematics to be inherently bound up with visuality. In fact any dimension of abstract reasoning does essentially rely on the perceptual, in particular on the visual: mental processes invariably involve the component of imagery.
As a fairly recent, succinct summary by Kosslyn et al. puts it: “Mental imagery occurs when perceptual information is accessed from memory, giving...
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