There is a figure in the Southern and Northern Dynasties that every contemporary Chinese knows. There are figures named after six lunar craters in China, and his name is one of them.
His impact on history and the people was greater than that of an emperor or general, although at that time, he was only an assistant teacher, county magistrate, and court official.
He was Zu Chongzhi who lived at the transition between Song and Qi. A beacon of light in his troubled corner.
Zu Chongzhi is best known to us for his accurate calculation of pi to six decimal places.
Pi is the ratio of a circle’s circumference to its diameter. A fixed point is the center, and a fixed radius can be used to draw a circle around it. Therefore, the circumference of the circle is always connected with the radius, but how many meters can a circle of 1 meter be drawn with a radius of 1 meter? There is no exact answer for a long circle.
Let’s think about it for a moment. Although the eyeball is spherical, we can roughly visually measure the position and length of points and lines, but the visual measurement of the circumference of a circle is far different. Therefore, if you want to find the circumference of a circle, you must have algorithm.
There are so many mathematical concepts, why did our ancestors have to calculate pi? Derived from architecture. Why did Zu Chongzhi calculate pi? It was because his grandfather was the great craftsman of the Liu Song Dynasty, the minister of housing and construction.
When drawing architectural drawings, it is impossible to use a rope to measure the circumference of the circle in every drawing, so a simple formula conversion is necessary. Liu Hui, a mathematician not long before Zu Chong, calculated the pi ratio of 3.1428 using the circle secant method, but this number is still a bit too large. In the actual application of construction, there will still be a waste of consumables. When building large buildings, follow this pi ratio. Designing a circular building often ends up being an unfinished project.
So the genius Zu Chongzhi shared his father's worries and strived to make pi accurate. Finally, he got the data between 3.1415926 and 3.1415927. This data was already quite luxurious, and it was better than the Westerners who later repeated this work. Man is 800 years older.
Now, I finally know why many ancient buildings in China are reliable because of their good science foundation.
In terms of application, this value can be used on all measuring instruments related to circles, such as funnels and cauldrons.
It is easy for us to calculate pi now, but it was a very arduous process for Zu Chongzhi to calculate pi. Why?
Because ancient Chinese arithmetic did not have a strong foundation and were all self-contained systematic algorithms.
Especially during the Southern and Northern Dynasties, there were no basic modern mathematical concepts such as Arabic numerals, negative numbers, and infinity. In other words, there was no giant on the shoulders like Newton, and many values ????were based on existing simple symbols. If this calculation were carried out by ordinary people, it would be boring.
The common people at that time may not be able to calculate the basic celestial stems and earthly branches. That is to say, what day is it today? How many days have passed? Today is my day in the world. , they may not know that even checking and recording birth dates requires the help of specialized people or institutions.
In developed places, there can be almanacs in government offices and large households, and you can go and check the time. However, the world is ever-changing and the government is in chaos. "This happened. When ordinary people wanted to tell their birthdays and determine auspicious times, they could only turn to old men who could tell fortunes accurately on the street (fortune telling is divided into bone touching, acupoint exploration, arithmetic and other schools, here is the arithmetic school). .
A large part of the quacks in ancient times made a living by selling their time. Many times, they deliberately made their statements vague and evolved mathematical calculations into a mysterious doctrine.
Enough said, let’s take a look at Zu Chongzhi’s calculation of pi.
Material: One is a unit of measurement issued by the imperial court (in the past, the unit of measurement was based on the will of the emperor. Take length as an example, ask several people to walk ten steps, take their average, and then assign a data. About how many steps equal one meter, it was promulgated in the name of the emperor, and a ruler was placed in the government office, and everyone was asked to use a rope to measure it for their own home use). The second is a small square or flat stick with an inch length (these sticks are primitive abacus. At that time, there was no abacus, nor could you use a pen to calculate formulas, let alone express the concept of decimal system with numbers. You could only use Different calculations express different numerical concepts). Three have a pen. Four are a pile of paper recording the calculation process. Five are the symbols for addition, subtraction, multiplication and division for reference, and the multiplication table is the main aid. This is all the material Zu Chongzhi can prepare.
Based on the above, if you want to calculate pi to seven decimal places, you really need to calculate it carefully and repeatedly, and record it repeatedly. As long as the thought is fragmented, the previous work will be like Wei Delay's attempt to break into Zhuge Liang's army. , the candle went out instantly.
Therefore, I say that this calculation is an arduous process, and Zu Chongzhi is a calm person, a steady and wise thinker, and a model figure in civil science.
The above is Zu Chongzhi’s greatest contribution, but he is an all-rounder because he does not only have this contribution.
Zu Chongzhi also corrected the calendar. This contribution was even more important than pi at the time.
The Southern and Northern Dynasties were a period of major breakthroughs in Chinese astronomy. I don’t know much about how to read astronomy in ancient times, so I can only explain it based on my own understanding.
In the Middle Ages, when knowledge was not as explosive as it is now, people were full of imagination about the unknown world. Qu Yuan's "Heavenly Questions" represents a series of fantasies that the ancients had about the world that could not find answers. Such as the Queen Mother of the West, the Goddess, the Xiang Concubine and other characters, as well as scenes such as the Luan driving the car, the tiger playing the harp, and the phoenix coming to the ceremony.
The earth and the sky are right in front of you. In ancient times, there were not always people like Qu Yuan who imagined the sky. There were also people who worked hard to seek true knowledge. As for the answer, that is up to the wise. However, there must be such people in every era in order to promote social progress.
The following is my own personal opinion, which briefly outlines the key and context of Chinese people’s understanding of the natural world before the Qing Dynasty and the Middle Ages.
1. Sun and moon.
The origin and role of the sun and moon are not very controversial in China. That is, they are the incarnations of gods. They represent the will of the supreme god to take care of the world. The sun and moon themselves are clumsy and are often affected by dark clouds, The oppression of thunder and lightning may be a low-level god, or it may be an animal driven by a great god, or even a large fire wheel dragged away by a mythical beast. At the same time, they are regular, bring light to the world, and are the embodiment of goodness. But generally speaking, their status among humans and gods is not high. From the incident of two children arguing about the sun, we know that the people in China do not take the sun and the moon seriously compared with other things. This is different from foreign countries.
2. Stars.
The stars are more important than the sun and the moon. This is a difference in Chinese astronomy, because the Chinese believe that the stars are more difficult to understand and more mysterious than the sun and the moon. Sometimes there are meteors, comets, nebulae, etc. The ancients were interested in them. More than the sun and the moon.
In the midst of conjecture, sometimes it is inevitable to endow the stars with human glory, such as the Cowherd and the Weaver Girl, the Milky Way Magpie Bridge, the Seven Fairy Stars, etc.
Of course, the seven planets attract the most attention.
I remember when I was a child, there was a text called "Children Counting Stars". When ancient people counted stars, they discovered that several planets moved with the greatest amplitude and very regularity, so they learned about this Several planets paid great attention to it and gave him various meanings: Venus = Taibai, Qiming, Changgeng; Jupiter = Sui Xing, Tai Sui; Mercury = Chen Xing; Mars = Yinghuo; Saturn = Zhenxing, etc.
These planets generally appear according to rules. If the rules are not accurate one day, or are covered up by something, then some predictions will appear, especially predictions about abnormal events of Venus and Mars. , much surprising. Friends who are interested in astrology know more about this aspect, so I will just give a rough summary.
3. Cosmic outlook.
A big change in astronomy during the Northern and Southern Dynasties was that the Department of Astronomy's view of the entire universe shifted from the Gaitian theory to the Huntian theory.
Some people have researched that the historical origin of the legend of Pangu opening the world should be as early as the Eastern Jin Dynasty. The god Pangu does not exist in the mainstream myth interpretations. He is a god grafted in midway, which is related to Buddhism and The introduction of the concept of the Creator such as Zoroastrianism is very related. This Pangu god is really good and has become evidence of the spread of the Huntian theory.
In the past, China thought that the sky was round and the earth was round. In the Northern and Southern Dynasties, although the sky was still round and the earth was round, there were things under the ground, and gases, liquids and other elements were injected into it. Therefore, this kind of To explain, people live in a colorful world full of vitality, energy, etc. The whole world is like the human body, composed of various elements.
Then why did China at that time slowly accept the view of the armillary sky? In addition to the armillary sphere designed by Tianguan to accurately test solar and lunar eclipses, there was also this Doctrine can divide and interpret calendar time with some accuracy.
Chinese people measure time, which is closely connected with the sun and moon, and is closely related to the Book of Changes.
The Bagua Diagram was originally a time projection diagram. The ancient Chinese people living in the Yellow River Basin first used bamboo poles to calculate the changes in the shadow of the sun. Then, people in this area measured the length of the shadow at fixed points in proportion. Row after row, they are carved on the wall.
Day after day. Decades later, someone reviewed and analyzed these shadow length records and found that the length of the shadow caused by the sun was very regular, sometimes long and sometimes short.
Further analysis is that when the shadow is long, the weather will be cold, the river will freeze, and the leaves will turn yellow; when the shadow is short, the sunshine will be fierce, the Yellow River will surge, and birds and beasts will live in the shade.
So, people with brains simply knocked down the wall, made a Bagua disk according to the cycle of shadow length, abbreviated the long and short records, and finally divided it into eight major blocks and eight main lines. .
Later, they discovered that they could also use the shadow of the sun to guide farming production. Thus, there is a relationship between the four seasons and people's life and production.
According to the rules, these four seasons can be roughly divided into about 360 days (4×9).
During the four seasons, knowledgeable people continue to carefully integrate the relationship between the 24 moon changes into 360 days around the moon's waxing and waning. In the month, the most powerful person announced which period of the moon was the new moon, and started farming for a year accurately to each month.
By analogy, in order to calculate 360 ??days in the form of written records, the heavenly stems and earthly branches were created in the past dynasties. The Heavenly Stems and Earthly Branches reincarnate repeatedly for 60 days, and the Heavenly Stems and Earthly Branches reincarnate six times a year.
Based on the reincarnation of heavenly stems and earthly branches, many data-based things are clear at a glance, and many relationships between time are also clarified. Early on, the person who was mainly responsible for managing, recording and clarifying the relationship between these numbers and time was , is the local priest, who can also be called Wu Jin in the village.
However, the above algorithm is an algorithm under an ideal state. Due to the influence of gravity, it is impossible for the real earth and the sun to reincarnate on time in 360 days. Therefore, the 360-day time needs to be fine-tuned according to the actual situation.
And this work is explained by the Huntian theory model: the movement of celestial bodies is also affected by factors such as water and air, so it will not be on time. Similarly, according to the demonstration and explanation of the armillary sphere, many astronomical phenomena have been verified, and the problem of sooner or later in a year has also been explained.
As a result, in the Middle Ages, a rigorous armillary sphere calculation system was formed that took into account the movement of the planets in the solar system. Although it was not very scientific, there were actually no major flaws in the calculations. The algorithm of the armillary sphere dominated China's later calculations. Thousands of years.
Zu Chongzhi proposed the "Da Ming Calendar" based on the theory of Hun Tian. He carefully counted and calculated the time difference between the sun shining directly on the same point every year, and then combined big data to propose the 391-year calendar. 144 The new leap month method.
Through the algorithm of 360 days plus a few leap months, the direct sunlight returned to its original position. Then, he defined a tropical year as 365.24281481 days.
This discovery was an accurate correction to the Chinese calendar at that time. Although it was not very accurate, it was already a major calendar reform.
Unfortunately, this calendar was not adopted at that time, and it was only after his son Zu Xun fought for it that it was adopted.
Zu Xun was also quite outstanding. He inherited his father's career and made great contributions to Chinese and even world history in astronomy and arithmetic. He was the first to propose the equal-area principle of spheres - "power". If the potentials are the same, the accumulations are not different." This principle was discovered more than 1,100 years earlier than Western mathematicians. Nowadays, in the field of calculus, the application of this principle is often seen.
But it is a pity that since Zongmingguan was abolished in Southern Qi, Taixue has only specialized in the other three schools of thought. Talents dedicated to arithmetic and yin and yang in the south have withered away, and talented people have also changed careers. , Yan Zhitui once said, "There are very few arithmetic schools in the south of the Yangtze River, and only Fan Yangzu is the master of it."
The development process of Chinese scientific history has once again entered a super slow tunnel lane.
Zu Chongzhi’s versatility is also reflected in machinery manufacturing.
Zu Chongzhi modified the compass. The compass is a unique invention of China. It is said that it existed during the Huangdi period. However, during the historical changes, the master-disciple inheritance was forgotten and the original technology was not retained. However, Zu Chongzhi relied on ancient fragmentary records to redesign, install and disassemble the compass, and roughly restored the original function of the compass. face.
Zu Chongzhi combined the water hammer and the water mill and invented the water mill. After this thing was invented by Zu Chongzhi, farmers could use natural water conservancy to repeatedly grind flour and pound rice in a small area. This was very beneficial to agricultural development. Du Yu, who had previously invented and improved this, has It was hundreds of years ago.
Zu Chongzhi designed the Thousand Mile Ship, the Wooden Ox and the Flowing Horse. These two cannot be seen in real form now. The Thousand Mile Ship should be a ship driven by a water wheel. This invention was helpful for water warfare in the Southern Dynasties and could also realize the rapid dispatch and transportation of food; the wooden ox and flowing horse are ancient wooden rail cars. This invention is also now No more drawings.
Zu Chongzhi made the Qi Qi. There is a similar physical object now. It is probably a timer, and it is also a tool to remind people of their conduct. I will not explore it further.
Zu Chongzhi also had achievements in literature, just like seismologist Zhang Heng. The biography of Zu Chongzhi is arranged in the biography "Literature".
In fact, as long as Zu Chongzhi has learned Chinese characters and understands rhythm, and he can randomly arrange some words based on his experience in practice, he will have more knowledge than everyone who has empty literature. When he works on architecture, he needs to get in touch with construction workers and the history of rivers and lakes; when he works on calendars, he needs to get in touch with farmers, the heaven, earth, and rivers; when he works on tools, he needs to get in touch with farmland water conservancy and on-the-ground warfare; when he does weird research, he needs to get in touch with legendary ghost stories, etc. , these life experiences are enough for him to write endless stories. His literary attainments were estimated to be able to kill the self-admiring people in blockbusters at the time.
Now let’s summarize the reason why Zu Chong is so versatile.
First, the promotion of the political and economic environment.
In feudal society, farming peoples were more creative than nomadic peoples in promoting historical development. Often nomadic peoples destroyed a farming feudal dynasty. Historians believe that this is a historical regression, not only killing the An advanced feudal system is more likely to stifle talents like Zu Chongzhi, causing the continuation of farming civilization to fail.
For example, in our history, the discovery of tools for plowing, water diversion devices, seismic measuring devices, wind and rain forecasts, pens, inks, paper and inkstones, textile machines, cloth and clothing, and even ironware and coal are presumed to have only appeared in agricultural societies. masterpiece. The most powerful nomadic nation, the Mongols, only played a role in cultural transmission between China and the West. Their achievements in promoting people's scientific and technological progress and people's livelihood development were almost zero. In addition to their massacres, their role in promoting history can be said to be It's a negative number.
In the Southern Dynasties where Zu Chongzhi lived, the land was a new land that needed to promote agriculture. The previous barbaric slash-and-burn farming methods had to be changed, and the planting advantages of the mountains and rivers in the south needed to be taken advantage of. However, this required a theoretical system. Sexual guidance also requires some practical inventions, so Zu Chongzhi and others devoted themselves to studying these things.
The second is leadership. The Southern Dynasties valued education.
This is a cliché. It has been said repeatedly in the article that in the early days of the Song and Qi Dynasties, the top leaders focused on developing agriculture and expanding their territory to the north. Therefore, they needed new weapons and grain transportation, so they attached great importance to education and cultivated special talents. Talent.
Zu Chongzhi is a special talent. Since Zu Chongzhi's father was a court architect, his youthful intelligence had long been known to outsiders. Emperor Xiaowu of the Liu Song Dynasty sent Zu Chongzhi to serve at Zongmingguan when he was in his 20s. This is Xiao Daocheng's school, but Xiao Daocheng is the student and he is the teacher.
Zu Chongzhi was a master of literature, history, and yin and yang here. At the same time, he also studied astronomy, calendar, arithmetic, architecture, etc. in the vast sea of ??books. At that time, Liu Yu of the Song Dynasty was keen on carpentry, and Zu Chongzhi also contributed his efforts, Xiao Daocheng. He was very interested in his war equipment such as wooden oxen and stray horses, thousand-mile ships, and compass chariots, and he also used these things on the battlefield.
Therefore, after Xiao Daocheng became the emperor, he paid more attention to education and allocated special project funds for the expansion of these educational institutions. As a result, Zu Chongzhi had an identity, money, and The all-round talent is ready to receive praise from people all over the world.
With the emphasis and freedom of academics in the Southern Dynasties, talents like Zu Chongzhi emerged. This can be regarded as historical luck.