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— Verlyn Klinkenborg"Nearly everyone is aware of dramatic changes in the world. Yet we continue to live in the assumption that we can ride out the changes without changing ourselves, coasting, as we have always coasted, on the historic wave of human development. What it will take to wake us up is a wave of equal size traveling in the opposite direction. That wave is already on its way."
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A paradigm is a powerful theoretical and methodological framework which defines the working lives of thousands of intelligent and disciplined minds. And paradigms do not attract the loyalty of such minds unless they 'work'. One of the first things a graduate student learns is that if there is a discrepancy between the paradigm and what he or she has discovered, then the automatic assumption is that the paradigm is right and the student wrong. Just as a good workman never blames his tools, so the diligent student never blames his paradigm
— John Naughton
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An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical.
— David Berlinski
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