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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 cu… - Carl Sagan
" "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".
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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.
Biography information from Wikiquote
Also Known As
Native Name:
Carl Edward Sagan
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Sagan
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Carl E. Sagan
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Carl E Sagan
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C. E. Sagan
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C.E. Sagan
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C E Sagan
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C. Sagan
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C Sagan
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Sagan C
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Sagan C.
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Sagan C. E.
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Sagan CE
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Shorter versions of this quote
The Pythagoreans were fascinated by the regular solids, symmetrical three-dimensional objects all of whose sides are the same regular polygon. The cube is the simplest example, having six squares as sides. There are an infinite number of regular polygons, but only five regular solids. (The proof of this statement, a famous example of mathematical reasoning, is given in Appendix 2.) For some reason, knowledge of a solid called the dodecahedron having twelve pentagons as sides seemed to them dangerous. It was mystically associated with the Cosmos. The other four regular solids were identified, somehow, with the four “elements” then imagined to constitute the world; earth, fire, air and water. The fifth regular solid must then, they thought, correspond to some fifth element that could only be the substance of the heavenly bodies. (This notion of a fifth essence is the origin of our word quintessence.) Ordinary people were to be kept ignorant of the dodecahedron.
Additional quotes by Carl Sagan
When an object impacts the Moon at high speed, it sets the Moon slightly wobbling. Eventually the vibrations die down but not in so short a period as eight hundred years. Such a quivering can be studied by laser reflection techniques. The Apollo astronauts emplaced in several locales on the Moon special mirrors called laser retroreflectors. When a laser beam from Earth strikes the mirror and bounces back, the round-trip travel time can be measured with remarkable precision. This time multiplied by the speed of light gives us the distance to the Moon at that moment to equally remarkable precision. Such measurements, performed over a period of years, reveal the Moon to be librating, or quivering with a period (about three years) and amplitude (about three meters), consistent with the idea that the crater Giordano Bruno was gouged out less than a thousand years ago.
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