Xiang Tuo

Why does the Sun or Moon look bigger near horizon?

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Xiang Tuo, a much younger contemporary of Confucius (c. 551-479 BCE), was able to instruct the Master at age 7.

Xiang Tuo (also written as Hsiang t’o, 項橐) was a much younger contemporary of Confucius (c. 551-479 BCE), who at age 7 was able to instruct the Master.
We don’t know exactly how Confucius first met this Child prodigy, and even don’t know if it’s a fact or fiction. According to the folklore, Confucius travelled to the east in a chariot with his disciples. Xiang Tuo and his friends were building a sand castle in the middle of the road. Confucius asked them to move aside and let the chariot pass. Xiang Tuo didn’t budge, and retorted: When does a castle give way to a chariot? All the while, chariots have to go round a castle to get to the other side.
 

One day, Xiang Tuo was arguing with another child. Confucius asked them what’s about. One child thought that the sun is nearer to us at daybreak and far away from us at noon, because in the morning it is as big as the canopy of a carriage, but at noon only the size of a plate or a bowl. The other contended that the sun was far away at dawn and nearby at midday, because when the sun comes out, it is very cool, but at midday it is as hot as putting your hand in boiling water. Confucius was unable to settle the matter for them.
This question has been recorded by Lieh Tse (列子 400 BC), the Taoist philosopher about one hundred years after Confucius. 
Four hundred years later, the great philosopher Wang Ch’ung (王充 27-97 AD) in Han dynasty tried again to answer this  question in his book Lun Hêng (literally “discourse balance”).
He said, “when the Sun is in the zenith, he is nearer to us than in the morning or the evening, because the perpendicular line from the zenith to the earth is shorter than the oblique lines, which must be drawn at sunrise or sunset. It is for this reason also that the sun is hottest, when he is culminating. That the Sun in the zenith appears smaller than, when he rises or sets, whereas, being nearer then, he ought to be bigger, is because in bright daylight every fire appears smaller than in the darkness or at dawn”
 
We can now very easily answer this question.
 
This phenomenon also happens to moon, the Moon look bigger near the horizon too. It’s true that the Sun and Moon is closer to us at certain times, but the size of the Sun or  Moon has nothing to do with the distance, because the difference is so small that we may totally ingore it. It’s actually caused by an optical illusion[1] which was explained by mario pnzo in 1913.
 
 
Which of the two yellow line is longer?
They are actually the same lenth, — when you move your mouse on the image, their will be two red line showing up, — but the upper line appears longer because it seems to span a greater width of track.
 
If you look at the big Moon (but don’t look at the Sun with naked eyes) through a toilet roll tube it will appear small again because your brain can no longer compare it to the size of the trees and houses on the horizon. 
Confucius took Xiang Tuo as his teacher has been told matter-of-factly in the book San Tzu Ching (三字經), otherwise called the Three-Character-Classic or Trimetrical Classic. This book is an elementary guide to knowledge for Chinese children, arranged in 356 alternately rhyming lines of three characters to each, and containing about 500 different characters in all. It is the foundation-stone of a Chinese education. Every child throughout the empire begins his or her studies with this book, learning to repeat a certain amount daily, until the whole is known by heart.  Among the others, there is one verse:
昔仲尼,  師項橐, 古聖賢, 尚勤學
Formerly Chung ni, took Xiang Tuo for his teacher. The inspired men and sages of old, studied diligently nevertheless. 
Partly by this book, Xiang Tuo has been inspirations for Chinese pupils for generations.

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