Евгений Рудный (evgeniirudnyi) wrote,
Евгений Рудный

Investigations into the Applicability of Geometry

Douglas Bertrand Marshall, Investigations into the Applicability of Geometry, Ph.D. Thesis, Harvard University (2011)

Challenging the Applicability of Geometry

p. 21 “[Protagorean Challenge] For all phi in Gamma, phi is a theorem of geometry, and when it comes to physical and material things, not phi.”

p. 25 “[No-Shapes Challenge] There are no geometric objects in nature. That is, there are in nature no points, lines, or surfaces which satisfy the axioms of geometry.”

p. 37 “[No-Structure Challenge] Nothing in nature is isomorphic either to Euclidean space, or to any Euclidean curve, or to any Euclidean surface.”

p. 41 “[No-Discrepancies Challenge] Given any natural item N and any geometric item G, there is no determinate or well-defined discrepancy between N and G.”

p. 41 ‘An intended consequence of the No-Discrepancies Challenge is that geometric objects do not even approximate things in nature. This already implies the truth of the No-Structure Challenge, but it implies a good deal more. An apt motto for the No-Discrepancies Challenge would be: “Nature is blurry.”‘


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