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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's inspiration for creating the binary system comes from Fuxi Gua Tu. These conclusions are controversial.

The first is the spread of ""in Europe

Zhouyi is an ancient divination book in China, which consists of Zhouyi and Yi Zhuan. It was written in the Western Zhou Dynasty and used unknown words and phrases. Zhouyi consists of divinatory symbols and divinatory symbols. Later, Confucian scholars expounded the divinatory symbols from the perspective of justice, and wrote the Book of Changes. After repeated research by scholars of past dynasties, the Book of Changes was formed.

French father Niels Triboy came to China twice in 16 10 and 1620. He translated this work in Latin in Hangzhou, but this translation has no influence in Europe.

Italian priest Martino Martini is 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 the Ancient History of China in Munich, which contained the contents of the book and a picture of 64 hexagrams, which was 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" formed by them 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 of this 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 power of 2 principle. Bisell is an academic friend of Leibniz, and there are many letters between them to discuss philosophical issues. After 1660, there is no doubt that Leibniz read China Literature and History Review, and he probably learned about this book and Fuxi's hexagrams at this time.

Belgian father Bai Yingli/KLOC-0 came to China in 659. He devoted himself to spreading China culture. Together with his fathers, 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, and 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 to a gentleman named von Hesse Rheinfelters, describing his delight in reading Confucius, a philosopher in China. 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, a philosopher in the Northern Song Dynasty, is a master of Imagism. He found another way, bypassed the fetters of hexagrams, repackaged hexagrams with esoteric terms and mysterious schema, and creatively drew the sequence diagram of Fuxi's sixty-four hexagrams and the orientation diagram of Fuxi's congenital sixty-four hexagrams, which were called sequence diagram and the first hexagrams. The biggest 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 before 1687, all kinds of Fuxi hexagrams that Leibniz saw were arranged according to the philosophical meaning, without highlighting the ordinal characteristics of binary.

Secondly, Leibniz really understood the process of Fuxi's divination.

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 this book as a book, saying that it contained the philosophical thoughts of Fuxi, the founder of China monarchy, and was as reasonable and perfect as Plato and Aristotle. Soon, Bai Jin read Leibniz's book "Recent Events in China", and they began to write to each other. They kept as many as fifteen letters, starting with 1697, 10 and 18, many of which discussed the contents of binary and Fuxi hexagrams.

1698 On February 28th, Bai Jin wrote a letter to Leibniz and introduced Fuxi's divination: "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 English. Father Bai Yingli listed these Chinese characters in the preface of China philosopher Confucius. " The list of Chinese characters mentioned by Bai Jin is Fuxi hexagrams in Bai Yingli's book, which Shao Yong has never drawn before and does 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. 17001October 8th, 165438+ Bai Jin wrote a letter to Leibniz, saying that Fuxi was the earliest code-maker of human beings, and Fuxi's hexagrams were the most primitive figures in China culture, with a complete metaphysical system. These numbers have both arithmetic and linguistic functions, and the language expressing ideas can be analyzed through the accuracy of mathematics. Bai Jin specifically 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 numbers in the book and the numbers 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 didn't think about binary numbers.

Leibniz has been trying to create the idea of "universal words", using special numbers to represent general concepts, so that the thinking process is like geometric reasoning, using logical calculus to discover and invent truth. Leibniz considered the relationship between Fuxi hexagrams and "universal characters". Therefore, he didn't find that the numbers converted by Bai Jin were binary numbers, and lost an opportunity to find that Fuxi hexagrams contained binary numbers, which delayed a major scientific discovery for some time.

Leibniz wrote back to Bai Jin on1701February 15, 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 the decimal system uses ten numbers from 0 to 9, it is enough to use only two numbers: 0 and 1." 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.

Letter from Leibniz1701February 15 to Bai Jin Leibniz introduced the binary system to Bai Jin 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, but it didn't come true. He also tried to introduce binary into theology and prove the existence of God through binary arithmetic. A manuscript by Leibniz entitled "1 and 0, the magical origin of all numbers" is kept in the library of the 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 thinks that explaining the meaning of binary from a theological point of view can provide a scientific explanation for God's theory of creation. 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 the letter, Leibniz designed a "Creation Map" commemorative medallion, with a binary number table from 0 to 16, examples of addition and multiplication, and the words "nothingness produces one" and "one creates everything". On February 20th, Leibniz wrote a letter to Zheng Mingfu, the supervisor of Qin Dynasty, introducing binary arithmetic in detail, listing the binary number table from 0 to 3 1, and illustrating the addition and multiplication operations with examples. Min Ming I taught Kangxi mathematics, and Leibniz hoped that Min Ming 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 creation process of God. 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 still 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.

Bai Jin, the manuscript of Leibniz's binary paper, learned the knowledge of binary from Leibniz's letter and immediately discovered the relationship between binary and priority. He wrote to Leibniz on 170 1 year 1 1 month 4, and sent a preface with the letter, clearly pointing out that only 65438 can be used instead of the solid line. It was Bai Jin's unique insights that unveiled the mystery of 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 binary paper, and at the same time included the first paper entitled "On the Simple Use of Binary Arithmetic of 0 and 1-Also 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 on "/kloc"

Letter to Bai Jin from Leibniz1May, 70318th. After Leibniz finished his paper, he replied to Bai Jin and mailed it on May 18. Leibniz wrote: "This photo 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 binary arithmetic to you, which was an amazing 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 systems 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. Therefore, Leibniz questioned why the traditional hexagrams were not arranged according to the binary ordinal number 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 Since then, 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 section "On Characters and Numbers in Fuxi's Binary Arithmetic", which is a summary of his correspondence with Bai Jin and represents their common 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, with a total of 64 numbers. They are considered as the oldest and simplest characters in China. In the centuries after Fuxi, five centuries later, Zhou Wenwang, his son, Duke Zhou, and Confucius all explored philosophy in divinatory images, 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 gave false praise to Fuxi. He didn't explain that it was first drawn by Shao Yong, which led Leibniz to 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 made him believe that Fuxi founded the binary system and praised it. However, this reflects that Leibniz does not have the idea of predatory beauty, and is very indifferent to his own discovery of 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, and its arithmetic knowledge is extremely simple, with 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 a sequence, 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, we can know that the female hexagram evolved from even number, while the male hexagram evolved from odd number. After the formation of these numbers, although the philosophical significance is prominent, there are still fuzzy digital images. Therefore, mathematicians associate this book with mathematics. The initiator was Liu Hui in Wei and Jin Dynasties. He wrote in the "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, and made the number of ninety-nine to change together." Bao Xi family is an alias of Fuxi. Liu Hui's views influenced later mathematicians. Qin Jiushao in the Northern Song Dynasty said in the Nine Chapters of Numerology: Mathematics "originated from the Book of Hutuluo, developed in a mysterious way, and was extremely useful to the great emperor." Cheng Dawei of the Ming Dynasty contained illustrations of Fuxi hexagrams in his Algorithmic Family, which wrote, "What is number?" ? It originated from books! Fuxi got it by painting hexagrams, Dayu got it by order, and enlightened it. There are countless celestial officials, local officials, legal calendars, military fu and exquisite notes, 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 advocated: "Intention must have words, words must have images, and images must be counted. A few numbers are like life, like life, and the words are obvious, and the words are obvious. The number of elephants also has hooves. "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, images and numbers are tools to express ideas. This is quite consistent with Leibniz's thought of "universal characters". 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 unintentional substitution, so we can't think that Shao Yong founded the binary system, and 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 not made any achievements in mathematics, has not written any mathematical works, and has never seen any academic connection with any mathematicians. Shao Yong never talked about binary system, and he didn't understand binary theory at all. He did not clearly define and name the mathematical concept of binary, nor did he scientifically express the important nature and significance of binary, nor did he 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 existed in Zhouyi for a long time. Before the Song Dynasty, there was no binary system in Zhouyi and Fuxi hexagrams. Shao Yong reordered these numbers from the beginning, not on his own initiative according to the binary principle, but just happened to remember the order of binary numbers. Therefore, we can only say cautiously that there is a bud of binary at first. 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 "multiplication" means 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 the yin into the yang, and use soft and hard. "This is a complete decimal statement, which has nothing to do with the binary" every binary one ". From the original meaning of the concept, the number of hexagrams 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 they could be represented by binary numbers. First of all, in the process of drawing, Shao Yong uses decimal system to solve the counting problem. For example, in the classification of gossip, he said: Ganyi, Duier, Li San, Zhensi, Xunwu, Liu Kan, Genqi and Kunba. If Shao Yong knew the binary principle, the order of the divinatory symbols would be very clear, and it would be 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 (), (), Gen Fu Wan () and Kao Zhongman (). This reflects from one side that neither Shao Yong nor Zhu realized the close relationship between the two. During the reign of Qianlong and Jiaqing in the Qing Dynasty, there was a famous mathematician, Wang Lai. His book "Two Calculations" was a work devoted to the theory of the carry system. He did not first point out that it was binary. So, how did it happen to be the same as the binary ordinal in the first place? This problem has puzzled many people, and some scholars even think that there are 64 elements in total with the explanation of probability theory! In this arrangement, it is almost impossible to find the one that is exactly the same as the binary number in this astronomical number arrangement! Then it is concluded that if Shao Yong is not familiar with the binary principle, how can he find this arrangement? In fact, both the first and binary numbers are represented by two basic numbers, which is actually a combination problem of elements that can be arranged repeatedly. Take three numbers from two kinds of numbers at a time and arrange them in a row, with a total of 23=8 arrangements, and get the eight diagrams and the first eight binary numbers in Zhouyi. Take six numbers from two kinds of numbers at a time and arrange them in a row, with a total of 26=64 arrangements, and get the sixty-four hexagrams in Zhouyi and the first sixty-four binary numbers. In fact, it is inevitable that the 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 the first necessary condition for drawing. 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 a sequence diagram of sixty-four hexagrams 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 is more obvious. Just arrange each hexagram in the sequence diagram into eight rows from left to right. It should be noted that this method still maintains symmetry, but the axial symmetry in the sequence diagram becomes central symmetry. It is easy to prove by mathematics that two hexagrams with symmetrical centers are also symmetrical in a circle 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 does not mean 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 letter to Bai Jin mentioned that he invented binary more than 20 years ago, when he founded calculus in Paris. Leibniz wrote in his letter to Bourgaie Ye on170765438+February 15: "When I founded binary arithmetic, I didn't know much about the divinatory symbols of …" "Leibniz has a manuscript" Interpretation of Binary Arithmetic ",which was written on 1679. 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 the history of China through 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. Shao Yong didn't draw Fuxi hexagrams that Leibniz saw first, and the hexagrams were arranged according to philosophical thoughts, not in binary order. Leibniz's academic interest is to develop the idea of "universal characters". He cares about the language and logical meaning of hexagrams, and 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's divination, his binary paper would have been published more than twenty years in advance. In addition, some people say that the phrase "binarium multiplicatis" mentioned in Bisell's works when introducing Fuxi hexagrams means binary, which inspired Leibniz. This is a guess 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 idea what binary is. This phrase does not refer to binary, but refers to the power of 2, which means the way Fuxi hexagrams are produced. In fact, Leibniz's chance to discover binary is very simple, which is a natural result. Considering the law of mathematical cognition, it is a common inference to put forward any carry system as long as people with basic mathematical literacy are familiar with the theory of 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 is Professor Erhard weigel. Wegelius has a lot of experience in the study of ancient Greek mathematical thought, advocating Pythagoras and Plato's mathematical views, and holding 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 Jena University, and systematically put forward the concept of quaternary. All numbers are represented by 0, 1, 2 and 3, and "full three into one" symbolizes that "three" is perfect. Soon, Leibniz wrote the manuscript of Binary Arithmetic Interpretation. 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 Wegelius. "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 his teacher and had nothing to do with Fuxi's divination. Some people criticized Leibniz and questioned his intention to cover up the binary discovery inspired by Fuxi hexagrams, which is groundless. Leibniz never took the binary invention for himself. On the contrary, he boasted that Fuxi invented the binary system as early as 4000 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, one of Babylonians invented the value system, using sexagesimal, others used decimal system, while China invented the value system alone, which was the first system to use decimal system. 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, with null representing 0, 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 deal with the counting in human secular life mathematically. 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 many achievements in mathematics and physics 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 the addition, subtraction and multiplication algorithms are proposed. The related problems of using continued fraction to represent binary system are also discussed. Note 1, and more textual research on Leibniz binary and Fuxi gossip, Shanghai Shanghai Publishing House, 2006, 2, see R. Widmaier: Leibniz Korean MIT China: der brief we csel MIT den jesuiten mission Aren (1689-17/kloc-). Frankfurt am Main: klostermann. 19903, edited by Chen Le, Jiangsu Education Press, 2005,1.4, Shao Yong's Yellow Poetry, Zhengzhou Zhongzhou Ancient Books Publishing House, 2007, 1.5, see translation by Bash Makova, etc. Higher Education Press 65438+June 6th 0959. 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 Chinese zodiac in 2022, and it is about binary sharing. After reading the chronology of the Chinese zodiac in 2022, I hope it will help everyone!