The oldest work on astronomy and mathematics in China, the Zhou Ji Sutra, records: "From this day above the solstice, it is 80,000 li." Winter solstice day, summer solstice night. The difference and the sunlight also look at it, the four poles are 810,000 li, and the 2,430,000 li. From the south of Zhou to Rizhao 302,000 miles, north of Zhou to Rizhao 508,000 miles. ”
That is to say, the ancients calculated that the height of the sun from the earth is 80,000 li, the diameter of the universe (four poles) is 810,000 li, the circumference of the universe is 2.43 million li, 302,000 li to the south of the sun, and 508,000 li to the north of the sun.
The problem is: the ancients did not have advanced knowledge of mathematics and astronomy, and "the heavens cannot rise in steps, and the earth cannot be measured by size", so how to calculate the height of the day is 80,000 li, the diameter of the universe is 810,000 li, and the circumference of the universe is 2.43 million li?
The measuring ruler of the ancients
Chinese have always advocated "living learning and application", and measuring the earth, celestial bodies, and the universe is the living study and application of the Pythagorean theorem.
In the Zhou Ji Sutra, Shang Gao pointed out that "the square moment is based on the positive rope, the Yan moment is based on the height, the covering moment is measured by the depth, the horizontal moment is known by the distance, the ring moment is thought to be round, and the closing moment is taken as the square", in which the "moment" is a right-angle ruler, and the hypotenuse becomes a right-angled triangle. Shang Gao believes that the "moment" can measure height, depth, distance, circle, square, etc.
The specific measurement method is to measure one side, and then apply the hook three strands, four strings and five, you can calculate the length of the other two sides. For example, if you want to measure the height of a mountain, you need a "moment", that is, the two points of the "string" are in the same straight line as the peak, walk from the right-angle point to the foot of the mountain, and finally roughly convert the mountain height step distance according to the Pythagorean theorem.
The problem is that you can measure the height of mountains, the depth of valleys, the width of rivers, etc., but when measuring cosmic celestial bodies, the so-called "heaven cannot rise in steps", so how would the ancients measure it? In fact, the ancients mastered a "measuring ruler" in the long standing table measurement.
The Zhou Ji Sutra recorded: "The sun is in the middle of the pole to measure the shadow, this one, the number of the way of heaven." The circumference is eight feet long, and the sundial on the summer solstice is one foot six inches. Thousands of miles to the south, hook one foot five inches, due north thousands of miles, hook one foot seven inches, increasingly southern, the sundial is getting longer and longer. Therefore, through long-term measurement of the shadow in different places, the ancients found that the shadow length of different places at the same time was different, and finally concluded that "the shadow difference is one inch, and the difference is thousands of miles".
Of course, this data is not accurate, there have been objections in the Northern and Southern Dynasties, Tang Seng "line" later presided over the measurement, came to a more accurate conclusion, this topic has nothing to do with this article, not to talk about it for the time being, interested friends can consult.
After mastering the "measuring ruler", the ancients were able to measure the celestial bodies and the universe through the "shadow length", and establish a model of the universe, and finally put forward the "Gaitian Theory" based on the data.
How to measure the universe
Before talking about measuring the universe, we must emphasize one thing, that is, the earth in the eyes of the pre-Qin ancients was flat. They don't think that the earth is round, because if the earth is round, they will inevitably have to think about "why don't people fall", and they will also lack a sense of "security", and the limitations of the times make them not imagine that the earth is round. The history of the circle of the earth in ancient Greece in the West is really not very credible.
On this basis, after mastering the measuring scale, the measurement of the height of the sun becomes very simple. Because, "on the day of the summer solstice, the sundial is one foot six inches, a thousand miles south, and a hook is one foot five inches", the further south you go, the shorter the shadow length, and finally to the place where there is no shadow on the hips, the distance between the two is 1,000 miles multiplied by 16 inches, which is 16,000 miles. The place where there is no shadow on the hips, the sun, and the place where the sundial on the day of the summer solstice is one foot six inches form a right triangle, from which the height of the sun can be calculated.
Of course, because of the reason of hooking three strands, four strings and five, it is not easy to apply directly with 16,000 kilometers, and the ancients had to wait until "Hou Gou six feet", when the shadow is six feet long, it is calculated that "from the hip to the sun 60,000 li, and the hip has no shadow", according to which the height of the sun can be seen to be 80,000 li, and the "evil solstice" is 100,000 li.
Compared with calculating the height of the sun, calculating the length of the universe is much more complicated, and because it involves too complex pre-Qin astronomical cognition, the following can only be briefly described:
First of all, the North Star is on the extension line of the Earth's axis, and the Zhou Sutra believes that all the sun, moon and stars move in a circle around the North Star. According to the calculation of "standing eight feet to see the pole, and its hook is one foot and three feet", the distance from the observation point - the circumference to the North Star is 103,000 miles.
Secondly, the following figure is the universe model range of the Zhou Ji Sutra, in which the summer solstice, spring and autumn equinox, winter solstice sun movement chart, this is the ancients believed that the Sunday movement in a year has three roads, began 5000 years ago Hongshan culture Niuheliang site, now Beijing Temple of Heaven around the three huan originated here. Divide it into three equal parts, it becomes seven concentric circles, that is, seven balances and six rooms, the solar cycle is divided into six sections, and a back and forth cycle is 12 parts, which is the origin of December in ancient China, not according to the moon.
Third, the distance from Zhoudi to Polaris is 103,000 miles, and by the summer solstice is 16,000 miles, and the distance from the summer solstice to the North Star is 119,000 miles. According to the shadow of the winter solstice, the distance from the Zhou to the winter solstice is 135,000 li, so subtract the 16,000 li from the Zhou to the summer solstice, which is still equal to 119,000 li, and the distance from the spring and autumn equinox to the summer solstice and the winter solstice is 59,500 li.
Fourth, the Zhou Sutra holds that the range of the sun is the scope of the universe. The movement of the sun around the North Star causes the polar day and night phenomenon around the North Star, that is, "Xuanji", the ancients calculated that the diameter of Xuanji is 23,000 li, and the radius is 11,500 li. At the spring and autumn equinox, the sun just shines on the polar regions, so the range that the sun can illuminate is 11.9 + 5.95 minus 1.15 = 167,000 li.
Therefore, if you want to judge the diameter of the universe, you must choose the winter solstice, when the sun is farthest from Polaris and closest to the edge of the universe. According to the data in the figure above, the radius of the universe is: the distance from the winter solstice to the North Star is 11.9 + 11.9 = 23.8, plus the distance of the sun 16.7, the total is 405,000 li. Thus, the diameter of the universe is 810,000 li, which is the sum of "302,000 li to the sunshine in the south and 508,000 li to the sunshine in the north".
There is a saying in the Zhou Sutra that the circumference is three times the diameter, so the circumference of the universe is 81 times 3 equal to 2.43 million li. Regarding pi, the Chinese are gradually exploring, from crude to more and more precise, more in line with materialist epistemology than the West, and Zu Chongzhi made great contributions to pi during the Southern and Northern Dynasties.
Finally, there are two more points worth thinking about the topic of this article:
First of all, the "Gaitian Theory" of the Chinese Shang Zhou Dynasty and even earlier days was not based on feelings, but through long astronomical observations and many calculations, especially with mathematical knowledge that is not as good as that of today's primary school students, a complete "model of the universe" was established, and even a year was calculated as 365 days and a quarter (i.e., the "Quarter Calendar"), which shows the wisdom of the ancient Chinese.
Secondly, the "cosmic model" based on long observations and calculations also points out that "Zhou is 103,000 miles south of the sky", that is, it is objectively recognized that Zhou people are not at the center of the universe. Although it seems that there are many mistakes in these things, this is not scientific exploration and the embodiment of the scientific spirit? Some scholars have opened their mouths to claim that there was no science in ancient China, and that they can only say that they are either stupid or bad.
References: "Zhou Ji Sutra", "Cao Huiqi - <周髀算经>Astronomical Views of the Pre-Qin Dynasty and Problems in the Earth from the Perspective of Mathematics", etc