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Descartes
If you have been the proverbial fly on the wall in Descartes’s bed-room in La Flèche, in southern France, in 1636, you may have watched Descartes laying in bed observing you. His most remarkable idea came to him while observing a fly crawl along a curved path, which he thought about illustrating in terms of its distance from the walls. A revolution in thought was in the making; mathematics would certainly never be similar. The...
Gelegentlich ergreifen wir die Feder and schreiben Zeichen auf ein weisses Blatt, Die sagen dies and das, es kennt sie jeder, Es ist ein Spiel, das seine Regeln hat. —Hermann Hesse. Das Glasperlenspiel From time to time we take our pen in hand and scribble symbols on a blank white sheet. Their meaning is at everyone’s command; It is a game whose rules are nice and neat. —Hermann Hesse, The Glass Bead Game, When Hermann...
checkerboard
Paradoxes appear in all shapes and forms. Certain are uncomplicated paradoxes of reasoning with minimal potential for investigation, while others sit atop icebergs of full scale scientific disciplines. Many may be solved by mindful consideration of their hidden assumptions, one or more of them could be faulty. These, strictly stating, really should not be referred to as paradoxes at all, because as soon as a puzzle is solved it stops to be a paradox. “One...