June 21 is the summer solstice. Traditionally, the school kids of 嘉義 would line up in the field just before the noon time. They watch their shadows disappear from there feet. And hooray, this is the way to celebrate the summer solstice. Historically, one significant event occurred more than two thousand years ago. It was Eratosthenes of Greece who used summer solstice to measure the circumference of the earth.
Eratosthenes knew that on the summer solstice at local noon in the Ancient Egyptian city Syene (located on the Tropic of Cancer), the sun would appear at the zenith, directly overhead. The sun’s ray would shine to the bottom of a well. He also knew, from measurement, that in his hometown of Alexandria, the angle of elevation (using a stick to see the shadow & measure the angle) of the Sun was 1/50 of a full circle (7°12') south of the zenith at the same time. Assuming that Alexandria was due north of Syene he concluded that the distance from Alexandria to Syene must be 1/50 of the total circumference of the Earth. The unit he used was different from km. Anyway, after some unit conversion, it turned out to be around 39,690 km. an error of less than 1% (compared with modern data).
Now came the expedition of Columbus in 1492. He started from Cadiz, Spain. He sailed about 7,500 km to reach some place in current Cuba. Since he thought it was India, the distance from Cadiz (lies about 40 degree latitude) to India (go east direction) had to be around 40,000 cos40° – 7,500. This figure turns out to be 27,900 km. Marco Polo’s book should have given him some idea how far from Spain to India (about 9,000 km). The figure of 27,900 km is just too long to accommodate his logic or calculation. Perhaps Columbus & those experts in Spain didn’t believe the data from the measurement of Eratosthenes. Otherwise, Queen Isabella would not have the courage to finance the expedition. Why? 40,000 cos40° – 9,000 = 18,930 km, really too far to sail for Santa Maria (Columbus’ flag ship). To Spain, it was a fortune in disguise. Instead of India, Spain discovered a new continent & history turned a new page. History is interesting & fascinating. Bertrand Russell (罗素) once said “那些有信心的人們都愚昧無知,而那些有理解力的人們都猶疑不决”.
2 comments:
Very good observation, "Most simple minded people are of solid faith and most knowledgeable people lack the ability of making actions." However, if we look for scientific evidence, most discoveries were made by knowledgeable people. But there are far more simple minded people, so with a little bit of luck, they sometimes made unexpected discoveries. This is similar to, 愚者千慮必有一得. i.e., 千愚亂竄,亦有遇正途者.
MarkYang said: 千愚亂竄,亦有遇正途者
Proof:
Rolle’s Theorem
Let f be continuous on [a,b] and differentiable on (a,b). If f(a) = f(b), then there is at least one number c in (a,b) such that f’(c)=0.
Application
Go from f(a) to f(b), use direction slope = 0 for all points, you get shortest distance. However, if you don’t do it this way, you are guaranteed to have at least one point c that you use the correct slope = 0.
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