
“You see, this war came to us, not the other way around.”
Remarks at the U.S. embassy in Baghdad, Iraq http://usinfo.state.gov/usinfo/Archive/2005/May/16-275013.html, May 15, 2005.
The Unreasonable Effectiveness of Mathematics (1980)
Context: The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.
“You see, this war came to us, not the other way around.”
Remarks at the U.S. embassy in Baghdad, Iraq http://usinfo.state.gov/usinfo/Archive/2005/May/16-275013.html, May 15, 2005.
“The past is the place we view the present from as much as the other way around.”
Now and Then: A Memoir of Vocation (1983)
Source: Mathematics as an Educational Task (1973), p. 476-477
As quoted by Sir Thomas Little Heath, The Thirteen Books of Euclid's Elements (1908) Vol.1 https://books.google.com/books?id=UhgPAAAAIAAJ Introduction and Books I, II p.1, citing Proclus ed. Friedlein, p. 68, 6-20.
Savitri Devi, Souvernirs et Réflexions d'une Aryenne, p 273, quoted in Koenraad Elst: The Saffron Swastika, p. 561
37 min 45 sec
Cosmos: A Personal Voyage (1990 Update), The Backbone of Night [Episode 7]
Context: There can be an infinite number of polygons, but only five regular solids. Four of the solids were associated with earth, fire, air and water. The cube for example represented earth. These four elements, they thought, make up terrestrial matter. So the fifth solid they mystically associated with the Cosmos. Perhaps it was the substance of the heavens. This fifth solid was called the dodecahedron. Its faces are pentagons, twelve of them. Knowledge of the dodecahedron was considered too dangerous for the public. Ordinary people were to be kept ignorant of the dodecahedron. In love with whole numbers, the Pythagoreans believed that all things could be derived from them. Certainly all other numbers.
So a crisis in doctrine occurred when they discovered that the square root of two was irrational. That is: the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were. "Irrational" originally meant only that. That you can't express a number as a ratio. But for the Pythagoreans it came to mean something else, something threatening, a hint that their world view might not make sense, the other meaning of "irrational".