According to the Zhou Qiu Sutra, Zhou Gong asked Shang Gao the question that "the heavens cannot rise by steps, and the earth cannot be measured by size", that is, there is no way to measure the heavens, nor can they measure the earth with a ruler, so how did the ancients measure celestial bodies?
The book also records, "Waiting for the hook is six feet, from the hip to the sun is sixty thousand li, and the hip is not a shadow." From above to the day, it is 80,000 li. That is, when "six feet away", the observation point is 60,000 li away from the shadowless place (the direct point of the sun), and the height of the sun is 80,000 li.
The question is, since "the heavens cannot rise and the earth cannot be measured in size", where did "60,000 li" and "80,000 li" come from? What is less known is that because the ancients had a "measuring ruler", this is not a "measuring heavenly artifact" in mythical stories, but the crystallization of thousands of years of wisdom of the Chinese ancestors, and the combination of the "measuring ruler" and the "Pythagorean theorem", the ancients can measure celestial bodies.
The ancient Chinese "measuring ruler" - the inch shadow is thousands of miles
The so-called "measuring ruler" is naturally not a ruler that directly measures celestial bodies, but a celestial law discovered by the ancients, and then calculated on this basis.
In order to grasp the "agricultural time", the ancients began to visualize the timing, one of the methods is called "gui table measurement", that is, the "table" is perpendicular to the ground, and the "gui" is placed horizontally on the ground, and the season is judged by the length of the "surface shadow" (see the figure below). And in the long Gui watch measurement, the ancients mastered the "measuring ruler".
Zhou Li recorded: "The view of the sun, five inches in ruler, is said to be in the land. The so-called "earth" is the center of the earth, and the origin of the name "China" is related to it, and the ancients believed that the shadow of the sun on the summer solstice was one foot and five inches as "in the earth".
However, the Zhou Qisuan Sutra recorded, "The Japanese neutral pole measurement, this one, the number of heavenly ways." The circumference is eight feet long, and the sundial on the summer solstice is one foot six inches. Then he said, "Thousands of miles due south, hook one foot five inches, thousands of miles due north, hook one foot seven inches, more and more south, longer and longer." ”
The problem is that Zhou Li said "the ruler has five inches", and Zhou Li said "one foot six inches", why is the emphasis of the two different, and "Inch Shadow Thousand Miles" has a verification code? The reason is simple, the results of different location measurements reflect the changes in the political "middle of the earth", and modern archaeology has uncovered the mystery of the difference between the two recorded shadows of the sun and the thousands of miles of shadows, and rewritten our traditional understanding.
Tsinghua Jianbaoxun recorded that Yao Shun did not know what the reason was and "feared and saved the middle", so Shun "is Yi Li Chengyi, measuring the things of yin and yang", and finally Shun got the middle, but in the middle of the Xia Dynasty, Shangjiawei of the Shang clan (the son of Wang Hai in the historical record) thought that Shun's measurement was wrong, so Shangjiawei "chased and measured", and finally thought that Songshan was the middle of the earth.
In the last century, at the site of Xiangfen Tao Temple in Linfen, Shanxi, archaeology found a wooden tire lacquer painted ruler, and modern scholars measured at noon on the summer solstice in the place, confirming the record of "the shadow of the sun is one foot six inches" in the Zhou Qiu Sutra. In the area of Songshan, countless regimes in ancient and modern times have used this as a place to establish stargazing platforms and photodetectors in Dengfeng Jicheng Town, which can confirm Zhou Li's statement that "the ruler is five inches".
It can be seen that "one foot six inches" is the result of Shun's measurement at the site of Tao Temple, and "five inches of ruler" is the result of Shangjiawei's measurement in Songshan. The Song Mountain and the Tao Temple site are basically at the same longitude, and the distance between the two is more than 300 kilometers, and from the perspective of the cognitive level of Shang and Zhou (one mile in the Zhou Dynasty is about 415 meters), it is not surprising that the two places are separated by thousands of miles, so there is a conclusion that "the shadow is one inch apart, and the ground is thousands of miles apart".
For astrometry, "one inch of shadow difference, thousands of miles of ground difference" is a "measuring ruler".
The method of measuring the sky - the Pythagorean theorem
After mastering the measuring ruler, the ancients could measure celestial bodies, and the most central method was the Pythagorean theorem.
In the long Gui table measurement, the ancients gradually discovered the law of "hook three strands, four strings and five", and then used the Pythagorean theorem to measure everything. Modern archaeology shows that at least 6,500 years ago, at the site of the western water slope of Puyang, Henan, the Chinese ancestors already knew how to measure the surface, so the law of "hook three strands, four strings and five" did not appear suddenly, but had a long period of exploration.
The question is, after mastering the Pythagorean theorem and measuring ruler, how did the ancients measure celestial bodies and measure the height of the sun from the ground? It is almost impossible from the perspective of modern people's cognition, but from the perspective of the ancient people's understanding of the Tianyuan Place, this matter becomes simple. Interested friends, you may wish to look for a solution without looking below, and see how to measure the height of the sun from the earth.
Because of the "thousands of miles of shadow", as long as the length of the shadow of the observation point is known, the distance between the observation point and the direct point of the sun (that is, the hip without shadow) can be deduced, so that the "hip shadow" place, the sun, and the observation point constitute a right triangle. (See the picture above, where 8 feet refers to the circumference of 8 feet)
For example, if the shadow of the sun is measured at the site of the Tao Temple on the summer solstice, the distance between Song Mountain and the place where there is no shadow is 16,000 li. However, "Pythagorean four-string five" is a special ratio, and 16,000 kilometers does not form a Pythagorean ratio value, so there is no way to apply the Pythagorean theorem to calculate the other two sides, and it is impossible to calculate the height of the sun from the place where the "shadowless" is located.
In that case, what should the ancients do? One word, wait! Wait until the Pythagorean ratio value is formed.
The Zhou Qisuan recorded: "Waiting for the hook is six feet, from the hip to the sun is 60,000 li, and the hip is without a shadow." From above to the day, it is 80,000 li. "When the shadow is six feet long, the observation point is 60,000 li away from the shadowless place, to paraphrase "hook three strands and four strings five", hook six strands is eight, so "80,000 li high in the day" when "waiting for six feet".
In addition to measuring the height of the sun, the ancients also measured the height of the North Star, the distance from the North Star to the sun, the longest distance from the sun ("so it is known: 167,000 li on each side of the sun"), the diameter and circumference of the universe ("810,000 li in the diameter of the four poles, 1.43 million li on Tuesday"), etc., all calculated on the basis of the measuring ruler and using the Pythagorean theorem.
From a modern point of view, although the thousands of miles of shadows (some people have questioned during the Southern and Northern Dynasties, and the Tang monks and his party measured more accurate conclusions), 80,000 li in daily height, etc., are basically wrong conclusions, but this is only the limitation of the cognition of the times, and the normal process of human exploration of the unknown. On the contrary, it can use the measuring ruler and the Pythagorean theorem to measure various celestial bodies, reflecting the superhuman wisdom of the Chinese ancestors.