Sharply Quotes (4 quotes)
Curves that have no tangents are the rule. … Those who hear of curves without tangents, or of functions without derivatives, often think at first that Nature presents no such complications. … The contrary however is true. … Consider, for instance, one of the white flakes that are obtained by salting a solution of soap. At a distance its contour may appear sharply defined, but as we draw nearer its sharpness disappears. The eye can no longer draw a tangent at any point. … The use of a magnifying glass or microscope leaves us just as uncertain, for fresh irregularities appear every time we increase the magnification. … An essential characteristic of our flake … is that we suspect … that any scale involves details that absolutely prohibit the fixing of a tangent.
Indeed, this epistemological theory of the relation between theory and experiment differs sharply from the epistemological theory of naive falsificationism.
[A plant] does not change itself gradually, but remains unaffected during all succeeding generations. It only throws off new forms, which are sharply contrasted with the parent, and which are from the very beginning as perfect and as constant, as narrowly defined, and as pure of type as might be expected of any species.
[My uncle said to me…] When I read, forty years ago, that shells from Syria were found in the Alps, I say, I admit, with a slightly mocking tone, that these shells were apparently brought by pilgrims who were returning from Jerusalem. M. de Buffon reprimanded me very sharply in his Theory of the Earth, page 281. I did not want to quarrel with him over shells, but I remain of the same opinion, because the impossibility that the sea formed the mountains is evident to me. Some may tell me that porphyry is made of sea urchin spikes, I’ll believe it when I see white marble is made of ostrich feathers.