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I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.
R. Langlands, "Harish-Chandra," Biographical Memoirs of Fellows of the Royal Society 31 (1985) 197 - 225.
Loci: Convergence
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Mathematical Treasures
Galileo's Geometrical Compass
This is the title page of the 1640 printing of Galileo's Operation of the Geometrical and Military Compass, originally published privately in 1606. Galileo had invented a version of this geometrical compass a few years earlier and evidently gave copies of this manual to those who bought the compass. The compass had many uses, from performing square root calculations to determining ranges of cannons to solving surveying problems. Click here for more information on the compass.
On this page, Galileo demonstrates how to find the height of a distant object by using the compass twice to sight the object at different distances.