Carl Sagan (1990 Update) Cosmos: A Personal Voyage.
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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".
— Carl Sagan on World view
What It Means
This is a placeholder explanation generated by the low-overhead model. It interprets "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"." in the context of "Carl Sagan (1990 Update) Cosmos: A Personal Voyage." to mean that wisdom is timeless.
Source: Wikiquote: "World view" (Quotes, S)
The 'What it means' explanation text was generated by Google Gemini Flash (accessed January 18, 2026). https://gemini.google.com/app
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About Carl Sagan
Carl Edward Sagan (9 November 1934 – 20 December 1996) was an American astronomer, planetary scientist, cosmologist, astrophysicist, astrobiologist, author, and science communicator. His best known scientific contribution is research on extraterrestrial life, including experimental demonstration of the production of amino acids from basic chemicals by radiation. Sagan assembled the first physical messages sent into space, the Pioneer plaque and the Voyager Golden Record, universal messages that could potentially be understood by any extraterrestrial intelligence that might find them. Sagan argued the hypothesis, accepted since, that the high surface temperatures of Venus can be attributed to, and calculated using, the greenhouse effect. He testified to the US Congress in 1985 that the greenhouse effect will change the earth's climate system.
About Carl Sagan
Carl Edward Sagan (9 November 1934 – 20 December 1996) was an American astronomer, planetary scientist, cosmologist, astrophysicist, astrobiologist, author, and science communicator. His best known scientific contribution is research on extraterrestrial life, including experimental demonstration of the production of amino acids from basic chemicals by radiation. Sagan assembled the first physical messages sent into space, the Pioneer plaque and the Voyager Golden Record, universal messages that could potentially be understood by any extraterrestrial intelligence that might find them. Sagan argued the hypothesis, accepted since, that the high surface temperatures of Venus can be attributed to, and calculated using, the greenhouse effect. He testified to the US Congress in 1985 that the greenhouse effect will change the earth's climate system.
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