March 14, 2004

• Clarity and Certainty

  “At the age of 12 I experienced a second wonder of a totally different nature: in a little book*
  dealing with Euclidean plane geometry, which came into my hands at the
  beginning of a schoolyear. Here were assertions, as for example the
  intersection of the three altitudes of a triangle in one point, which
  — though by no means evident — could nevertheless be proved with
  such certainty that any doubt appeared to be out of the question. This lucidity and certainty [Klarheit und Sicherheit] made an indescribable impression upon me….  For example I remember that
  an uncle told me the Pythagorean theorem before the holy geometry
  booklet* had come into my hands. After much effort I
  succeeded in ‘proving’ this theorem on the basis of the similarity of
  triangles … for anyone who experiences [these feelings] for the first
  time, it is marvellous enough that man is capable at all to reach such
  a degree of certainty and purity [Sicherheit und Reinheit] in pure thinking as the Greeks showed
  us for the first time to be possible in geometry.”

  – from “Autobiographical Notes” in Albert Einstein: Philosopher-Scientist, edited by Paul Arthur Schilpp

  “Although our intellect always longs for clarity and certainty, our nature often finds uncertainty fascinating.”

  – Carl von Clausewitz at Quotes by Clausewitz

  For clarity and certainty, consult All About Altitudes (and be sure to click the “pop it up” button).

  For murkiness and uncertainty, consult The Fog of War.

  Happy birthday, Albert.

  * Einstein’s “holy geometry booklet” was, according to Banesh Hoffman, Lehrbuch der Geometrie zum Gebrauch an höheren Lehranstalten, by Eduard Heis (Catholic astronomer and textbook writer) and Thomas Joseph Eschweiler.

  • 3:28 pm
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