Leibniz, Binary System and Fuxi Guatu
: Jiang Hui Ma Hongyun's workNo.: 00 1 Date of submission: May 8, 2022.
Leibniz was a modern scientist, and his life years overlapped with the third year of Shunzhi in Qing Dynasty (1646) and the fifty-fifth year of Kangxi (17 16). He is very familiar with the history and culture of China. He mentioned Fuxi hexagrams in a binary paper, and repeatedly mentioned binary and Fuxi hexagrams in his correspondence with others. Two scholars, Hu Yang and Tudor, believe that Fuxi Gua Tu is a binary system, and Leibniz founded the binary system inspired by Fuxi Gua Tu. These conclusions are controversial.
First, the spread in Europe.
Zhouyi is an ancient divination book in China, which consists of Zhouyi and Yi Zhuan. Written in the Western Zhou Dynasty, it uses unfamiliar words and phrases. Zhouyi consists of hexagrams and hexagrams. Later, Confucian scholars expounded the hexagrams from the perspective of justice, and wrote Yi Zhuan, which was repeatedly studied by scholars and formed Yi Xue.
French father Nielas TriBauit came to China twice at 16 10 and 1620. He translated the book in Latin in Hangzhou, but this translation did not have an impact in Europe.
Martino Martini is an Italian priest, proficient in mathematics, astronomy and measurement technology. He came to China twice and made important contributions to Chinese and western science and culture. 1658, he published "Ancient History of China" in Munich, which contained the contents of the book and attached sixty-four diagrams, marked as painted by Fuxi, which was one of the hexagrams that Fuxi introduced to Europe. Martino Martini introduced that the basic figures in hexagrams are "Yin Yao" and "Yang Yao", and Yin Yao represents hidden and incomplete things. Yang Yao represents an open and complete thing. The "three-line number" they form is the Eight Diagrams, which respectively represent heaven, earth, water, fire, thunder, mountain, ze and wind in natural phenomena. On this basis, from the combination of trilinear numbers and pairwise numbers, 64 hexagrams can be formed.
1660, Bisell's Review of China Literature and History was published in Leiden, the Netherlands. Some materials are quoted from Martino Martini's Ancient History of China. The content in the book is very detailed, including 64 Fuxi diagrams, and the phrase "binary multiplication" appears, which means that the generation method of Fuxi diagrams follows the principle of power of two. Bisell is a schoolmate of Leibniz, and there are many letters between them to discuss philosophical issues. After 1660, there is no doubt that Leibniz read the book China Literature and History Review, and it was probably at this time that he learned about this book and Fuxi's hexagrams.
Belgian father Bai Yingli 1659 came to China. He devoted himself to spreading China culture. Together with his parents, he translated The Great Learning, The Doctrine of the Mean, The Doctrine of the Mean and Western languages into Latin, including Fuxi's gossip sequence diagram and Fuxi's gossip orientation diagram, as well as Zhou Wenwang's sixty-four hexagrams, in which the numbers 1, 2, 3, 4, 5, 6, 7 and 8 were used. This book was published in Paris on 1687, and its title is Confucius, the philosopher of China. Leibniz wrote a letter in 1687 12 19 to a gentleman named von Hesse Reinfeldt, describing his pleasure in reading China philosopher Confucius. Leibniz also saw Fuxi hexagrams in the book.
There is a school called Xiang Mathematics in the field of Yi studies, which mainly explores people's psychology of seeking good fortune and avoiding evil through Fuxi hexagrams and prays for controlling the changing law of nature. Its theory is full of mystery. Shao Yong was a philosopher in the Northern Song Dynasty and a master of Imagism. He found another way, bypassed the fetters of the hexagram system, repackaged the hexagram system with abstruse terms and mysterious schema, and creatively drew the sequence diagram of Fuxi sixty-four hexagrams and the orientation diagram of Fuxi congenital sixty-four hexagrams, referred to as the sequence diagram and the first hexagram. The bigger difference between sequence diagram and Fuxi hexagrams is that it is arranged according to binary ordinal number. These pictures are contained in the original meaning of Zhouyi by Zhu, a philosopher in the Southern Song Dynasty. It should be pointed out that until 1687, all kinds of Fuxi hexagrams that Leibniz saw were arranged according to the philosophical meaning, without highlighting the ordinal characteristics of binary.
Second, the process of Leibniz's real understanding of Fuxi Guatu.
It was Bai Jin who made Leibniz know more about Fuxi's divination. Bai Jin, a French priest, was a math teacher of Kangxi. He was ordered by Kangxi to go back to Europe to recruit scientific talents, and arrived in Paris in 1697, where he gave a lecture on Yi-ology, criticizing some people for treating Yi as a book, saying that it contained the philosophy of Fuxi, the founder of China's monarchy, and was as reasonable and perfect as Plato and Aristotle. Soon, Bai Jin read Leibniz's "Recent Situation in China", and the two began to write to each other. They kept as many as fifteen letters, starting with 1697, 10, 18, and many of them discussed binary and Fuxi hexagrams.
1698 On February 28th, Bai Jin wrote a letter to Leibniz, introducing Fuxi's divination sequence: "The original Chinese characters were composed of dotted lines or solid lines, and it is said that Fuxi created them. I think I have found the real secret of learning it. Father Bai Yingli listed these Chinese characters in the preface of Confucius, a philosopher in China. " The list of Chinese characters mentioned by Bai Jin is Fuxi hexagrams in Bai Yingli's book, which was not drawn by Shao Yong before and did not follow the binary system. He thinks this is just a simple and natural Chinese character.
After returning home, Bai Jin had a clearer understanding of this book. 1Oct.8th 1700, 165438+ Bai Jin wrote to Leibniz, saying that Fuxi was the earliest code-maker, and Fuxi Guatu was the most primitive figure in China culture, with a complete metaphysical system. These numbers have both arithmetic and linguistic functions, and the language of expressing ideas can be analyzed through the accuracy of mathematics. In particular, Bai Jin said that in Fuxi's hexagrams, if the dotted line is changed to 0 and the solid line is changed to 1, the sixty-four hexagrams are perfect numbers. "The secret figures in the book and the figures in Pythagoras, Plato and Egyptian Jewish philosophy are all due to the mysterious revelation of the creator." Bai Jin is well versed in the theory of image number, and is familiar with China's way of expressing numbers by several pieces, which is very similar to the image of two hexagrams overlapping. Naturally, he thought of converting hexagrams into numbers. At this time, although Bai Jin combined Fuxi's hexagrams and numbers, he just didn't understand binary arithmetic and never thought about binary numbers.
Leibniz has been trying to create the idea of "universal words", using special numbers to represent general concepts, making the thinking process like geometric reasoning and using logical calculus to discover and invent truth. Leibniz considered the relationship between Fuxi hexagrams and "universal characters". Therefore, he did not find that the number converted from platinum was a binary number, and lost an opportunity to find that Fuxi hexagrams contained binary numbers, which delayed a period of important scientific discovery.
Leibniz wrote back to Bai Jin on 170 1 February 15, 2008, still introducing the idea of "universal characters", and he also mentioned calculus and binary system he invented. Binary system, he explained to Bai Jin: "Just like decimal system uses ten numbers from 0 to 9, only 0 and 1 are enough." The letter mentioned binary arithmetic and listed a list of binary numbers from 0 to 3 1. Leibniz also suggested that Bai Jin introduce binary to Kangxi.
Leibniz1701February 15 Letter to Bai Jin The reason why Leibniz introduced the binary system to Bai Jin was because he had just become an academician of the Royal Lanxi. He planned to submit a binary paper "The Theory of Digital New Science" to Bai Jin, and told him the contents of the paper by the way. On February 26th, Leibniz submitted the paper to. On April 30th, De Fontenelle wrote to Leibniz, suggesting that this paper should not be published in journals because it does not reflect the practical value of binary system. In fact, Leibniz has been looking for the practical value of binary. He once had the idea of using a binary principle calculator, which didn't come true. He also tried to introduce binary into theology and prove the existence of God by binary arithmetic. A manuscript of Leibniz, entitled "1 and 0, the magical origin of all numbers", is kept in the library of Turing Palace in Germany. This is a mysterious and wonderful example of creation, because everything is in God. "1696 In May, Leibniz visited the Duke of Ruud Fag in Hanover. When talking about theological culture, he introduced binary arithmetic to the duke. The Duke believes that explaining the meaning of binary from a theological point of view can provide a scientific explanation for God's theory of genesis. 1697 On New Year's Day, Leibniz wrote a letter to the Duke, detailing the idea of "starting from scratch" contained in the binary system. In his letter, Leibniz designed a "Creation Map" commemorative medallion, with a binary number table from 0 to 16, examples of addition, subtraction, multiplication and division, and the words "nothing gives birth to one" and "one creates everything". 1696 1696 On February 20th, 2006, Leibniz wrote a letter to Qin Jian Zheng Mingfu, introducing binary arithmetic in detail, listing the binary number table from 0 to 3 1, and illustrating the arithmetic of addition and multiplication with examples. Minming I taught Kangxi mathematics, and Leibniz hoped Minming I could teach Kangxi binary system and let Kangxi understand the superiority of culture.
Leibniz's "Creation Map" commemorative medallion was written by Leibniz to Bai Jin, which also revealed a strong theological complex. He wrote that the greatness of binary is that it simulates the process of God's creation. There are only two states in the world, God and nothingness. God represents perfection, nothingness represents imperfection. Everything in the world was created by God from nothingness. At this time, Leibniz did not know the relationship between binary system and Fuxi hexagrams, and the so-called application of binary system in theology was not suitable for writing in scientific papers.
Leibniz's manuscript of the binary paper Bai Jin learned the knowledge of binary from Leibniz's letter and immediately discovered the relationship between binary and priority. He wrote a letter to Leibniz on 170 1 year 1 1 month 4, and sent a preface with the letter, clearly indicating that only solid lines were used instead of 65438. It was Bai Jin's unique insights that unveiled the mysterious veil on Fuxi's hexagrams. The letter reads: "You should not regard binary as a new science, because Fuxi in China has invented it."
Bai Jin's first letter to Leibniz arrived in Leibniz on April 2, 703. He immediately studied the first one, marked the corresponding number on each hexagram, and confirmed that the arrangement of the hexagram map was consistent with the binary ordinal number. He completely agrees with Bai Jin's point of view. As a practical example of binary system, he absorbed Bai Jin's discovery into a paper on binary system, and included the first one, entitled "On the Simple Use of Binary Arithmetic of 0 and 1-On the Use of Binary System and the Significance of Fuxi in Ancient China", which was sent to the French Royal on May 5, 1703, and later in "/kloc".
Letter from Leibniz1May 703 18 to Bai Jin. After writing the paper, Leibniz replied to Bai Jin and mailed it on May 18. Leibniz wrote: "This painting is the oldest scientific relic in the world. It has not been understood for thousands of years, but it is so consistent with binary arithmetic. When you explained these figures to me, I happened to introduce you to binary arithmetic, which was a strange coincidence. If I hadn't invented binary arithmetic, I couldn't understand Fuxi's divination even if I studied it deeply. I started thinking about binary 20 years ago and realized that the numbers represented by 0 and 1 are more perfect and the calculation is very simple. " Because the previous Fuxi diagrams were not arranged according to binary ordinal numbers, no one ever discovered this secret, but they were first arranged strictly according to ordinal numbers, which was discovered by Bai Jin and Leibniz. So Leibniz questioned why traditional hexagrams are not arranged according to binary ordinal numbers as before. In his letter, he asked Bai Jin why the Fuxi hexagrams of Confucius, a philosopher in China, were different from the previous ones.
Sixty-four hexagrams in Bai Yingli's book From then on, Leibniz no longer said that he invented the binary system, but only said that he rediscovered Fuxi's knowledge. In his "On China's Natural Philosophy", there is a passage about the founder Fuxi's words and the numbers used in binary arithmetic, which is a summary of his communication with Bai Jin and represents their * * * same views. The article wrote: "Father Bai Jin and I discovered the original meaning of the hexagrams created by Fuxi, the founder of this empire. They are composed of some dotted lines and solid lines, and there are 64 numbers in * *, which is considered to be the oldest and simplest characters in China. In the centuries after Fuxi, Zhou Wenwang, his son, Duke Zhou and Confucius five centuries later all used hexagrams to explore philosophy, and some people wanted to get things like geomantic omen and harmony from them. In fact, the sixty-four hexagrams are binary arithmetic founded by the great economist Fuxi. Thousands of years later, I rediscovered 3. " Although Bai Jin has a lot of experience in the study of Yi-ology, he still lacks in-depth understanding of the field of Yi-ology. He conveyed many mistakes to Leibniz, regarded myths as historical materials and praised Fuxi wrongly. He didn't say that Shao Yong painted it first, which made Leibniz mistake it for an ancient cultural relic. Bai Jin didn't even name Yin and Yang, which led Leibniz to call Yin a dotted line and Yang a solid line in his manuscript. Leibniz is not a god. Influenced by Bai Jin, he worshiped the Yi-ology culture, which led him to believe that Fuxi founded the binary system and praised it. But this reflects that Leibniz has no idea of plundering beauty, and he is indifferent to discovering binary. Three, Fuxi hexagrams and binary Yin Shang period, China has a relatively complete decimal counting method. According to the common sense of the development history of human civilization, Zhouyi, as the source of civilization, is in the embryonic stage of culture, with extremely simple arithmetic knowledge and no binary content at all. Reading through Zhouyi, we can see that the so-called arithmetic knowledge is nothing more than counting, expressed in decimal system. There are many kinds of Fuxi hexagrams in the Book of Changes, including eight diagrams and sixty-four hexagrams. The ranking of gossip is generally symmetrical, while the ranking of sixty-four hexagrams is based on divination. The popular Zhouyi and the silk book Zhouyi unearthed from Mawangdui Han Tomb in Changsha are not in the same order, but they are not arranged by binary ordinal number. There is a saying in the field of Yi studies that Yin and Yang have numerical characteristics. From some pottery, Oracle Bone Inscriptions and bamboo slips unearthed in Shang Dynasty, it can be known that the female ones evolved from even numbers, while the male ones evolved from odd numbers. After the formation of these numbers, although the philosophical significance is highlighted, there are still fuzzy images of the numbers. Therefore, mathematicians associate this book with mathematics. The initiator was Liu Hui in Wei and Jin Dynasties. He wrote in "Notes on Nine Chapters of Arithmetic": "The former Bao family began to draw eight diagrams, with the virtue of Ming and the love of all things as the number of nine and nine, so as to change together." Baojia is another name for Fuxi. Liu Hui's views influenced later mathematicians. In the Nine Chapters of Numerology, the Qin Dynasty in the Northern Song Dynasty said: Mathematics "originated from the book of Hutuluo, developed in a mysterious way, gossip and nine fields, and was extremely useful to the great emperor." Cheng Dawei of the Ming Dynasty contained diagrams of Fuxi hexagrams in his "Algorithm Unification", and wrote in the book: "What is number? It originated from books! Fuxi got it by painting hexagrams, Dayu got it by order, and enlightened it. Celestial officials, local officials, legal calendars, military fu, and subtle notes are countless, all based on the Book of Changes. " Shao Yong used image number deduction instead of philosophical thinking, giving people the feeling that he was doing mathematical operations. In the External View of Things, he argued: "Intention must have words, words must have images, and images must have numbers. A few numbers are like life, like life, and they make sense. The number of elephants is also hoofed. " This means that ideas can be expressed in language, language can be expressed in images, and images can be expressed in numbers. And vice versa, Dallas to the auditorium. Therefore, image numbers are a tool to express ideas. This is quite consistent with Leibniz's "generality" thought. In the first part of Shao Yong's drawing, as long as Yin is regarded as 0 and Yang as 1, its arrangement is exactly the same as the binary ordinal number, which is undoubtedly a binary model. However, this binary model is only the result of an unintentional substitution, so we can't think that Shao Yong founded the binary system. We can only think that mathematical thought unified the first one into the theoretical system of the binary system. Common sense in the history of mathematical development tells us that any mathematical achievement has two reasons, one is the progress of theoretical research inside mathematics, and the other is the requirement of external development and progress of mathematics. First of all, Shao Yong is not a mathematician. He has made no achievements in mathematics, has not written any mathematical works, and has not seen any academic exchanges between mathematicians. Shao Yong never talked about binary system, and he didn't understand binary theory at all. He didn't clearly define and name the mathematical concepts of binary, didn't scientifically express the important nature and significance of binary, and didn't perfect the logical relationship between binary and other mathematical concepts. From Shao Yong's works, we can't see that he has a mathematical literacy beyond ordinary people. It is absolutely impossible for Shao Yong to create a binary system, just as today's "people's mathematicians" want to solve the Gothic conjecture. Not to mention him, even his contemporary mathematicians, no one has set foot in the field of binary research. The number of hexagrams has a long history in Zhouyi. Before the Song Dynasty, Zhouyi and Fuxi hexagrams had no binary system. Shao Yong reordered these numbers from the beginning, not on his own initiative according to the binary principle, but happened to remember the order of binary numbers. Therefore, it can only be said cautiously that there was a bud of binary from the beginning. Some people suggest that Shao Yong's "double law" is the law of "every two enters one", which is totally groundless speculation. They are not just the same thing in meaning. The method of "doubling" is doubling, that is, multiplying by 2, which refers to the generation process of Fuxi hexagrams. If each hexagram in the upper layer is added in turn, the number of hexagrams will be doubled. That is, "one divides into two, two divides into four, four divides into eight, eight divides into sixteen, sixteen divides into thirty-two, and thirty-two divides into sixty-four." Therefore, it is easy to divide yin into yang and soften it. "This is a completely decimal statement, which has nothing to do with the binary" every binary one ". From the original meaning of the concept, the number composed of yang and yin represents abstract philosophical things. Even if they have numbers, they are 1-64 in decimal. Yi scholars and mathematicians in the Song, Yuan, Ming and Qing Dynasties, including Shao Yong, did not propose that it can be represented by binary numbers. Shao Yong used decimal system to solve the counting problem in the process of drawing the first picture. For example, in the classification of gossip, his opinions are: Cognac, Duier, Li San, Zhensi, Xunwu, Liu Kan, Genqi and Kumba. If Shao Yong knew the binary principle, the order of hexagrams would be clear and easy to remember without any help. However, until the Southern Song Dynasty, Zhu also wrote a memory formula according to the intuitive image of the Eight Diagrams: Gan Sanlian (), Kun Liuduan (), Yu Zhenyang (), Genfu Pill (), Li () and Kan Zhongman (). This reflects from one side that neither Shao Yong nor Zhu realized the close relationship between priority and duality. During the reign of Qianlong and Jiaqing in the Qing Dynasty, there was a famous mathematician, Wang Lai. His book "Two Calculations and Cross-Reference" was a work devoted to the theory of carry system, and he did not point out that it was binary first. So, how can it happen to be the same as the first binary ordinal? This problem has puzzled many people, and even some scholars use the explanation of probability theory to think that there are always 64 out of 64 elements! This arrangement, in this astronomical number arrangement, it is almost impossible to find the one that is exactly the same as the binary number! Then it comes to the conclusion that if Shao Yong is not familiar with the binary principle, how can he find this arrangement? In fact, both one and binary are represented by two basic numbers, which is actually the combination of elements that can be arranged repeatedly. Take three numbers from two numbers at a time and line them up. * * * There are 23=8 permutations, and the eight diagrams in Zhouyi and the first eight numbers in binary are obtained. Take six numbers from two kinds of numbers at a time and line them up. * * * There are 26=64 permutations, and the sixty-four hexagrams of Zhouyi and the first sixty-four binary numbers are obtained. In fact, it is inevitable that the hexagram order of the first hexagram is the same as the binary ordinal number. Shao Yong doesn't need to know binary knowledge, and binary is not a necessary condition for drawing first. In fact, Shao Yong creatively used another kind of mathematics, and naturally generated a binary "mathematical tree" with a "tree diagram", which is the sequence diagram of Fuxi's sixty-four hexagrams.
Shao Yong painted the yin pulp black and the yang pulp white according to the drawing method of "tree diagram". First, Tai Chi, from bottom to top, according to the "double method", draw Yin first, then Yang, and draw alternately. Starting from Taiji, two instruments, four images, eight diagrams, sixteen hexagrams, thirty-two hexagrams and sixty-four hexagrams are generated in turn, and finally become a sequence diagram of sixty-four hexagrams, which can be drawn indefinitely. Because the sequence diagram is generated in strict accordance with the "tree diagram", the sixty-four hexagrams are formed by reading from bottom to top. From the Kun divination on the left to the dry divination on the right, the order of the first 64 binary numbers is naturally satisfied. Understanding the structure of sequence diagrams makes it easy to draw the first one. Look at its outer circle first, as long as the right semicircle is straightened, it is the left half of the symmetry axis of the sequence diagram. Straighten the left semicircle, which is the right part of the symmetry axis of the sequence diagram. Look at the square diagram inside, and the law will be more obvious. Just arrange each line in the sequence diagram into eight lines from left to right. It should be noted that this method still maintains symmetry, but the axial symmetry in the sequence diagram is changed to central symmetry. It is easy to prove by mathematics that in the circle diagram, two hexagrams with symmetrical centers are also symmetrical in the sequence diagram. In a square diagram, two hexagrams with symmetrical centers are also symmetrical in a sequence diagram. Because priority and binary are algebraically isomorphic, priority order and symmetric structure are no longer secrets, which is easy to understand. Generally speaking, the mathematical properties in binary arithmetic can also be extended to priority. This is not to say that Shao Yong discovered a lot of modern mathematical knowledge at that time, but that mathematical thought unified the simple binary factors contained in the first one. Four, Leibniz and binary Leibniz 1703 May 18 wrote to Bai Jin that he invented binary more than 20 years ago, when he founded calculus in Paris. Leibniz wrote in his letter to Bourgaie in170765438+February 15: "When I founded binary arithmetic, I didn't know much about the divination of". Leibniz had a manuscript, Interpretation of Binary Arithmetic, which was written in 1679 March/kloc. It has not been published and has been shelved for more than 20 years. However, all innovations and discoveries in mathematics follow the path pioneered by predecessors, and in the process of surpassing predecessors, there is no guarantee that all enlightening ideological achievements can be taken care of. Before the invention of binary system, Leibniz only indirectly understood Martino Martini's Ancient History of China and Bisell's Analysis of China Literature and History. These documents are not mathematical works, although Martino Martini called them mathematical works, which is just a guess. The Fuxi hexagrams that Leibniz saw were not drawn by Shao Yong first, and the hexagrams were arranged in accordance with philosophical thoughts, not in binary arrangement. Leibniz's academic interest is to develop the idea of "universal characters". What he cares about is the language and logical meaning of hexagrams, and he doesn't consider the problem from the mathematical point of view at all. Therefore, it is impossible for Leibniz to know the binary in the Yi-ology literature. If Leibniz had been inspired when he saw Fuxi hexagrams, his binary paper would have been published more than twenty years in advance. In addition, some people say that the phrase "binary multiplication" mentioned in Bisell's works when introducing Fuxi hexagrams means binary, which inspired Leibniz. This is speculation regardless of historical facts. When Bisell wrote this book, the concept of binary had not been clearly put forward. The word "binary" was introduced into academic circles by Leibniz. At that time, he hadn't thought about binary. Bisell is not a mathematician. He has no way of knowing what binary is. This sentence does not refer to binary system, but refers to the power of 2, indicating the way Fuxi hexagrams were produced. In fact, Leibniz's chance to discover binary is simple and natural. Considering the law of mathematical cognition, as long as people with basic mathematical literacy are familiar with the theory of carry system, it is a common inference to put forward any carry system. In fact, any natural number greater than 1 can be used as the radix of the carry system, and in theory, an infinite number of carry systems can be constructed, which is an extremely simple mathematical common sense. Leibniz went to the University of Jena to study mathematics in the summer vacation of 1663. His teacher was Professor Erhard weigel. Wegelius has a lot of experience in the study of mathematical thought in ancient Greece, advocates Pythagoras and Plato's mathematical views, and thinks that the material world conforms to mathematical laws. Leibniz was deeply inspired by the teacher's thoughts. 1672, Vigelius published the article "Ten Structures" in the journal of the University of Jena, and systematically put forward the concept of quaternary system, in which 0, 1, 2 and 3 are used to represent all numbers, and "full three into one" symbolizes that "three" is perfect. Soon, Leibniz wrote the manuscript of Interpretation of Binary Arithmetic. There is no doubt that Leibniz is familiar with the theory of carry system, whether in the teacher's class or in the teacher's thesis. From Leibniz's On China's Philosophy of Nature, we know that Leibniz is very familiar with the history of the decimal system. He mentioned that the ancient Romans used mixed decimal and decimal arithmetic, and that there were quaternary and decimal in history. He clearly wrote: It is the quaternary system of Weigelius, "It gave me an opportunity to propose that all numbers can use binary 0 and 65438+. Therefore, Leibniz's invention of binary system was inspired by the teacher and had nothing to do with Fuxi's divination. Some people criticized Leibniz and questioned his intention to cover up the discovery of binary system inspired by Fuxi hexagrams, which is unfounded. Leibniz never took the binary invention for himself. But vigorously touted Fuxi's invention of binary system as early as 4,000 years ago, and he also attributed this great discovery to Bai Jin. In fact, various counting methods of the carry system have long existed in human activities. In the birthplace of world civilization, a Babylonian invented the value system, using sexagesimal, others used the decimal system, and only China invented the value system and used the decimal system first. In Shang Dynasty, Oracle Bone Inscriptions had the number and position notation of 1-9, and in the Warring States period, the decimal notation appeared, which was very advanced. Tribes on the Areba volcanic island in the Pacific Ocean used binary as early as 1450 years ago. Until now, some indigenous people in Polynesia and Australia still use binary 5. In fact, the so-called invention of mathematicians is to mathematically process the counting in human secular life. Therefore, the invention of binary system is not a great mathematical achievement. In fact, the mathematician Y.Lobkowitz, who was contemporary with Leibniz, also discussed binary and binary in Double-sided Mathematics published in 1670. Leibniz may not know that there was a brilliant mathematician harriot 6 in England at that time, and there were a lot of mathematical and physical achievements in his manuscript. Because there were no scientific journals at that time, these results were nowhere to be published. Harriot's 1603 manuscript "Mathematical Calculation and Annotation" has discussed the contents of binary arithmetic in detail. Its theoretical structure is almost the same as Leibniz's. Taking 0 and 1 as the basic counting units, it is named binary notation, and an algorithm of addition, subtraction, multiplication and division is proposed. The related problems of using continued fraction to represent binary system are also discussed. Note 1, and many textual researches on Leibniz binary and Fuxi gossip, Shanghai Shanghai Publishing House, February 2006, see R.Widmaier: Leibniz Korea, Massachusetts Institute of Technology, China: der brief WeChat Selmit den Jesuitenmissionaren (1689-17/kloc-0. Frankfurt am Main: klostermann. 19903, editor-in-chief, read by Jiangsu Education Publishing House in 2005,1kloc-0/.4, Shao Yong's Yellow Poetry Book, Zhengzhou Zhongzhou Ancient Books Publishing House in 2007, 1.5, see Liu Shao translated by Bash Makova and others. Higher Education Press1June 6, 959. For the story of harriot, please refer to Robin Ariane Rhodes' Thomas Harriot: Life in Science. Cambridge University Press, 2022.
The above is related to the age table of the zodiac in 2022, and it is about binary sharing. I read the chronology of the Chinese zodiac in 2022, and hope it will help everyone!