Binary is a digital system widely used in computing technology. Binary data are numbers represented by 0 and 1. Its radix is 2, what is the carry rule? Every two become one? What are the rules for borrowing books? Borrow one and get two free? It was discovered by/kloc-Leibniz, a German master of mathematical philosophy in the 0/8th century. At present, the computer system basically adopts binary, and the data is mainly stored in the computer in the form of complement. The binary in the computer is a very small switch. Open? To represent 1, close? To represent 0.
The 20th century is called the invention and application of computers, which is one of the important signs of the third scientific and technological revolution, because digital computers can only identify and deal with the problems caused by? 0? . ? 1? A code consisting of a string of symbols. Its operating mode is binary. /kloc-in the 9th century, Irish logician george boole's thinking process of logical propositions was transformed into correct symbols? 0? . ? 1? In some algebraic calculus, binary is binary. 0, 1 is the basic operator. Because it only uses two digital symbols, 0 and 1, it is very simple and convenient, and easy to realize electronically.
Binary and Leibniz
1, Leibniz is? Binary? The main discoverer of
Gottfried? William? Gottfried Wilhelm Leibniz (1646 July1-1716 June114) is a leading philosopher and mathematician in German history. Together with Newton, he independently invented calculus and topology. Binary? As the main discoverer of Aristotle, he is a rare generalist in history. His research fields involve mathematics, philosophy, logic, mechanics, geology, law, history, language, law and theology, and he is known as Aristotle in the17th century. He learned about China's traditional culture through extensive reading since childhood. He is one of the earliest and most widely known Europeans in China, and he has great enthusiasm and high praise for China culture.
First of all, it is particularly important to note that Leibniz, who has been rumored for a long time in the rivers and lakes, was inspired by the Book of Changes to invent the binary system, which is actually false. First of all, the binary system was not invented by Leibniz, but was mentioned by harriot and cavalieri before him. Leibniz just rediscovered it, explained it systematically, and finally carried it forward. Then Leibniz began to think about binary before he saw the Book of Changes brought back by missionaries.
The history of binary notation is often associated with Leibniz. But in fact, Leibniz was not the earliest discoverer of this notation. This symbol has been put forward before him. For example, at the beginning of the17th century, harriot, a British algebra scientist, mentioned it in his unpublished manuscript. Cavalieri repeated this discovery in 1670. Leibniz probably didn't read the previous discussion, so when he rediscovered the binary, he always thought it was his own original. However, because the binary system is strongly advocated and expounded by Leibniz, it has attracted people's attention, so it is not wrong to associate the binary system with Leibniz as an established habit.
Leibniz rediscovered binary in about 1672- 1676. 1679 On March 5th, he wrote a paper entitled Binary Arithmetic, which fully discussed the binary system and established its representation and operation. 1696, he introduced the binary system to Duke Auguste, who was deeply interested in it. 1697 65438+ 10, Leibniz also specially made a commemorative medal for the duke. It is engraved with Latin:? Creating everything from nothingness, one is enough? . It can be seen that Leibniz's great preference for binary has theological reasons. In his view, all numbers can be created by 0 and 1, which can be regarded as the Christian Bible saying that God comes from? Nothing? Create? what's up A symbol of. In other words, from the binary, Leibniz found evidence that God created the world.
170 1 year, Leibniz submitted his paper on binary to the French Academy of Sciences, but asked not to publish it for the time being. 1703, he sent the revised paper to the French Academy of Sciences again for publication. Since then, binary has been made public.
2. Leibniz's admiration for The Book of Changes: Language of the Universe
Leibniz is convinced of the importance of the Book of Changes in mathematics. He thinks that China people in ancient times mastered the binary system, which far surpassed China people in science. Leibniz thinks the Book of Changes? Yin and Yang? Thought coincides with his own dualism. Is this his dualism? China edition? Leibniz was very surprised by this similarity. Leibniz, who always thought that the core idea of Yijing was binary, was also greatly encouraged.
In this case, if we only look at Leibniz's evaluation of the binary system, it is equivalent to the evaluation of the Book of Changes. Look at the words about binary in his manuscript:? 1 and 0, the magical origin of all numbers. This is an excellent example of creating secrets, because everything comes from God. ? He also asserted:? Binary is a universal and perfect logic language. ? On the commemorative medallion dedicated to Duke August in 1697, the inscription is Latin? Is it enough to create everything from nothingness with 1? It can be seen that he has a great preference for binary.
In this regard, Laplace commented in his masterpiece "Philosophical Exploration of Probability": In his binary arithmetic, Leibniz saw the image of creating everything. He imagined that 1 stands for God and 0 stands for chaos. God created everything in the world from chaos, just as he used 1 and 0 to represent all the numbers in his notation. This concept is very popular in Leibniz. ?
These characters are full of the shadow of Yijing and its mysterious connotation. In the memorandum of the Royal French Academy of Sciences in 1703, Leibniz published an explanation of binary operation. In the example used, Fuxi's innate eight diagrams correspond to the binary representation 07. This caused a sensation in the European intelligentsia at the beginning of18th century. In 1705, someone even wrote:? China people have lost the true meaning of six hexagrams, and a European genius rediscovered this knowledge for them. ?
Leibniz regards binary as? Cosmic language? However, his binary system can't be related to the acquired gossip, so we have to draw a conclusion that the connotation of gossip is far from being completely simulated by binary system. The rapid development of modern computer science and Internet proves the great significance of Leibniz binary system. Their information processing and transmission use binary representations and algorithms.
Binary and taiji diagrams
Taiji Bagua is extensive and profound, and occupies an important position in the traditional science and culture of the Chinese nation. Scientific analysis and research should be made on its connotation and spirit. For thousands of years, China's traditional science and western science have developed in opposite and parallel directions. After the establishment of the theory of relativity at the beginning of the 20th century, China's traditional science and western modern science have the prospect of achieving unity in the general principle of natural structure symmetry. So Einstein said:? Surprisingly, all these discoveries (in China) were made in. ?
Taiji diagram is also a binary progressive relationship. From this point of view, the inventor of the ancient Taiji diagram must have understood the binary relationship in Fuxi's eight diagrams, and then did the opposite, made the ancient Taiji diagram, and drew the symbol of the eight diagrams fish in the middle, which is very meaningful. From the Taiji diagram, we can realize that everything will develop rapidly in the early stage of development, but in the later stage, due to various reasons, it will slow down and will not develop in a straight line all the time, and finally it will only rotate along the outer edge. It is said that Einstein said a word after seeing our ancient Tai Chi map. Modern science and technology seem to express oriental ideas? . As soon as this statement came out, it attracted the world's attention to oriental culture. Einstein once proposed one? Endless? A model of the universe. So-called? Bounded? It is a circle. Endless? The circle slowly expands outward along the periphery. Now the pictures of galaxy explosions are all spiral. Why? In the later stage of galaxy explosion, because gravity can't move in a straight line, it can only move in this spiral direction. Therefore, the Taiji diagram shows the general law of the development of things. To a certain extent, you can worry about nothing, but haste makes waste. After writing Phenomenology of Spirit, Hegel thought that he had mastered the general laws of the development of the universe, nature and human society. He believes that orientals have no philosophical thoughts, but only a little hazy dialectical color in their minds. After he saw this picture, he found that it was very learned and the expression was much simpler than his idea. All divinatory symbols are opposite to each other, and we can see that the changes in them contain positive and negative thoughts, from quantitative change to qualitative change, so it is a dialectical symbol system, isn't it? a & gtb & gtc？ The symbolic relationship between them.
Binary system is just a phenomenon to express the Book of Changes. Wang Fuzhi, a Hunan philosopher in the late Ming Dynasty, once said? It is a simple fact that the binary position of congenital yi is easy. If you argue too much, you forget Yi's original intention. What you teach your children is the law of multiplication, which has nothing to do with the principle of heaven and man. Can not be regarded as a scholar, iron, taste, ineffective technique, in order to confuse the position of heaven and earth. ? In his view, the mathematical relationship in innate Yi is only? Iron accumulation, effective no gain? It's just a trick, not an avenue. If we excessively investigate its binary mathematical characteristics, we will lose the direction of explanation. Nowadays, many people are addicted to binary permutation and combination all day, forgetting the original intention and great meaning of Yi.
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