Edited By András Benedek and Kristof Nyiri
Visualization and the Horizons of Scientific Explanation: Kristóf Nyíri
Visualization and the Horizons of Scientific Explanation Kristóf Nyíri Galileo’s often-quoted formula, according to which the universe is written in the language of mathematics, continues with the elucidation, “its characters are tri- angles, circles, and other geometrical figures, without which it is humanly im- possible to understand a single word of it”.1 Above the doorway of Plato’s Academy, some two millenia earlier, there was engraved, as tradition has it, the inscription “Let no-one ignorant of geometry enter here” – rendered not in- frequently, 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 sch- ma, again with the meaning “figure” or “shape”, emerged as parts of the math- ematical 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. The Visual Mind As a fairly recent, succinct summary by...
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