This book tells the origin of mathematics and its role in historical and social development from a historical perspective. This paper focuses on the role of mathematics in three aspects: the influence on people's thinking logic, the influence on the development of capital society and the role in economics. The examples in the book are not very close to life, but they are quite suitable for people like me who work in government departments? And people who care more about the economy. Nevertheless, compared with the previous introduction to statistics, it is still a bit abstruse.
This book is divided into five chapters.
The first chapter is entitled "The Source of Mathematical Logic-Mathematical Logic Originated from Ancient Religion". Although modern mathematics originated in Greece, it was ancient Judaism that gave birth to formal logic earlier. Because the only god worshipped by ancient Judaism was not very amiable, Moses, a missionary, took on the role of a bridge between gods and people, and at the same time tried to help mankind persuade God to be better for mankind. Although this god has a bad temper, he is very reasonable. Thus, in the process of negotiating with God, Moses gradually mastered strict logical rules and clear Jewish teachings written in every detail. Formal logic promoted the prosperity of ancient Israel.
With mathematical thinking, the first question you will encounter is existence and non-existence. This is a philosophical concept for ordinary people, but it is actually very important. ? For example, natural numbers are the most directly used numbers in life, while decimals are more abstract. Then the concepts of rational number, irrational number, real number and imaginary number are developed. Modern people can easily understand real numbers, but it is difficult for ancient people to understand irrational numbers; Similarly, there are not many modern people who understand imaginary numbers. The more abstract things are, the more complex and advanced applications are.
? Some problems have definite solutions, some problems have no definite solutions, or there is no always correct answer. For example, economic problems, such complex problems and countless influencing factors are unlikely to be explained by an always correct model. And even if there are solutions to some problems, they may not be solved. For example, the N-degree equation has only been proved to have a solution for more than 5 times, but the current mathematical theory can't solve it. The latter phenomenon is too abstract, but the former phenomenon is very common and deserves our attention.
This book gives examples of great sailing. Zheng He sailed to the West earlier than Europe, but in the end, Europeans traveled around the world and discovered America. This is because the purpose of Zheng He's voyage to the West is not to solve problems, and he has no possibility of a new continent in his mind? This concept. The second example is being in power. The book says that many officials are good at solving problems, but politics is actually an art, not a rigorous science. Governing with a unique purpose is likely to ignore the ever-changing environmental variables. As a result, there is a saying in the book that "a good official is not necessarily a good politician".
Chapter 2: Why do you want to study math? As mentioned above, western society has developed formal logic from religion, which is a comprehensive way of thinking. This way of thinking is the basis of the evolution of scientific system. The argumentation technique developed by China is not like Greek formal logic, but the logic of consolidating friendship through pondering and speculation. China's thinking habit originated from ancient China. Kings generally made good use of scholar-officials and attached importance to literati governing the country? . Up to now, there is no such hierarchy of nobility in western society in China. In fact, the ancient emperors were only people who ruled the country, not gods, but more like a profession. It is a good thing that the class is not solidified, but it makes sophistry useful, and there is an oriental logician like Mozi. The characteristic of China's debating technique is that "although he won the debate, he didn't want to use logic to push the other side into a corner, but wanted to let the other side (especially the monarch) know that he had the idea of' That's the way it is, Mr. Wang is indeed a saint, just do as you say'". Therefore, sinology advocates that everything is tied to the square inch of political rights holders, and how to grasp the hearts of rights holders has become the key to debate technology.
Everyone likes to listen to good words, but he doesn't like to listen to opposition. Therefore, "emphasizing the place where the monarch is proud and avoiding his shame" has become the iron law of dealing. ? The purpose of dealing with kings is to develop deep friendship with kings. This can greatly reduce the cost of communicating with the king. Economic activities revolve around friendship, which is the characteristic of China culture. Not only is the price of a commodity different for people with different friendship levels, but even the truth or falsehood of a thing is not single and absolute in China society. There is no so-called objective angle to judge and decide, everything is decided by people. This is human nature. In some specific periods, such as wars, disasters and other critical moments and when materials are scarce, the efficiency of rule by man is often higher than that of rule by law. But in modern society, longing for peace and material prosperity are two major characteristics, and the rule of law and democracy will inevitably become the main theme.
In this chapter, the author analyzes the cultural and institutional differences between eastern and western societies from the influence of mathematical logic on social development, which is very reasonable. As for the theme of this chapter, why do you want to study mathematics? Everyone has a different understanding after reading the book. For me, it is more of an incentive for my work. China has been a society ruled by literati since ancient times, and the civil servants naturally take writing as their first ability. As a science student, I am also trying to change from the strict but rigid logical habit in the past to a smooth, clever and accommodating habit. In this process, you will inevitably encounter a lot of confusion. Of course, it is right not to be rigid, but if you are too smooth, you will become cunning, and if you are too smart, you will become cunning. Where is the middle boundary? At work, the style of superiors and leaders has never been related to the legal system. It seems that in their thinking, the subjective initiative of subordinates should only appear according to the wishes of leaders. Don't think when you don't need to think, you can think when you need to think. I can understand that this style of doing things, this simple and rude ruling idea, can be invincible in the past era, but it may not conform to the trend of the future era. Democracy and the rule of law are really not just slogans, but the general trend of history. As the backbone of the future society, is it necessary for us to cater to those old ideas and is it meaningful to learn social principles based on human feelings?
In fact, the answer is already there. An old friend started his business very early because of his personal interest. When she first started her business, she had a very strange feature, and she would never be a friend's business. Her reason is that the business has just started, the service is not perfect, and she is afraid of destroying the friendship between friends. But in fact, this principle has helped her to eliminate the interference of human feelings and let her hear the most real market reaction. In the continuous product iteration, the business will naturally rise. On the other hand, those who still rely on relatives, friends and related households to start their business, not to mention the cost of making enough money in the future, because without real market feedback, their business will always stop and be defeated by competitors sooner or later.
? Chapter III, Mathematics and Modern Capitalism. The logic of mathematics gave birth to capitalism. The core of the legal system of capitalist countries lies in recognizing and maintaining the private nature of property. Only by abstracting the ownership and use right of property as an attribute of private property can mathematical logic be fully applied to economic activities; Actually, the other way around is more reasonable. It is precisely because of the application of mathematical logic in economic activities that a larger and more complex commodity exchange system can be realized, thus giving birth to the abstraction of ownership and use rights and complete privatization. This chapter analyzes the differences of economic development among Europe, America, China and Japan along this main line.
The understanding of ownership is not only reflected in the differences of social systems, but also has great influence on the micro level. There are many contradictions and puzzles in real life, all of which are caused by unknown ownership or unclear ownership consciousness. In the genes of oriental culture, there is a lack of complete and absolute attribution. For example, some people borrow books, they will take notes inadvertently, and will not take the initiative to return them without urging them; Officials always regard the market as private property involuntarily, and carry out policies at will regardless of the consequences and effects. This kind of behavior is not very clear, but in fact, there is no strict definition of the ownership of things, and there is a lack of rigor in doing things. Privatization of property is an important foundation for the development of western capitalism and an inevitable result of formal logic. Because we didn't advocate formal logic, didn't develop a scientific system, and didn't naturally derive a capital society (although China's Song Dynasty was close to the capital society for the first time in world history), let alone a credit system based on the concept of property ownership.
In addition, the comprehensiveness and absoluteness of ownership is the premise of enterprise innovation, which is also commonly known as the "master" spirit. From this point of view, the innovation of an enterprise does not necessarily require the merger of the ownership and management rights of the upper level, but can also be in the field that the lower level is responsible for or with the people around it after the lower level has enough authority and interests? Collaborative innovation. Because this book was written in the late 1990s, the ideas about enterprise innovation are a bit out of date.
However, with the development and evolution of two different logics, will formal logic be unified and China logic be useless? I just read a speech by Sogou CEO and Wang Xiaochuan these days, saying that eastern philosophy focuses on the top-down holistic view, while western philosophy focuses on the bottom-up micro-construction, so mathematics has become an important foundation of western philosophy, and its role in it is the meaning of formal logic, I think. However, since the development of science, only bottom-up constructive thinking is no longer enough. Using big data and artificial intelligence, there may be a breakthrough in studying the overall thinking of the East.
Chapter four, the application of mathematical logic-proof technology: a thorough analysis of reduction to absurdity, induction, necessary and sufficient conditions and duality. ? As the name implies, this chapter is about the reasoning method of formal logic. According to my understanding, the most important feature of formal logic is rigidity. One is one, one is two. This is the so-called law of contradiction. According to this feature, several methods can be developed. Reduction to absurdity is to eliminate the wrong situation and get the correct solution; A can deduce B, but B is not necessarily caused by A, so A is a sufficient condition for B, and B is a necessary condition for A; Induction is the main method of modern scientific experiments, that is, seeing is believing, trying to deduce the full name proposition from the proper name proposition. Induction reminds me of Bayesian theorem, which is an important theorem in probability theory and related to human cognition.
The development process of formal logic is from the law of contradiction to absurdity, to deduction, and finally to various sciences and scientific methods? . In science except mathematics, the methods used are actually incomplete induction. Because in theory, all environmental variables must be consistent in order to completely replace the full name proposition. Mathematics is purely abstract and can be modeled in an ideal state. However, other scientific disciplines can't be completely abstracted, and experiments can't exclude all interference variables. Therefore, the experiments in natural science all use incomplete induction. Only by understanding this "incompleteness" can we have critical thinking and innovative consciousness. ?
Chapter 5, Mathematics and Economics-runs through economic theory and mathematical logic. This chapter explains some basic economic theories in the form of questions and answers between teachers and students, and reviews the development history of economics. The background is this: Adam Smith initiated modern economic theory, then Say invented Say's law, and Ricardo perfected Say's law. Its model is close to perfection, but it is only the last step of labor transformation, so Marx made persistent efforts to write Das Kapital and put forward four principles to measure labor value. These four principles are different from Ricardo's classical school, and the other line is Keynesian school. Keynes's achievement benefited from Walras's general equilibrium theory and Keynes's foundation in Walras.
At this point, the book is over. Looking back at the whole book, the author tries to illustrate the importance of mathematics through its fundamental great role in society, economy, humanities and other fields. But in any case, this book doesn't seem to convince ordinary people who hate mathematics to like it! I wonder what the author thinks. Maybe the target audience of this book is not the general public. Perhaps Japan's general education has reached a very high level. Speaking of general education, this is another term that has solved my puzzle for many years. European and American countries advocate general education very much. They basically don't teach professional knowledge, but only teach history, literature, art and some basic mathematics and physics, and then graduate ... This knowledge is not valued in China's education system because it can't be used to find a job. But it is precisely this humanistic knowledge that can make people understand the world, themselves and how the whole society works, so as to think about their role in this social system. With these basic cognitive thinking, we can clearly know what to do, what to learn and how to live. Learning professional skills has become secondary, because with a purpose and a practical environment, skills learning is very fast. What's more, according to my experience after graduation, college professional knowledge and diplomas are basically useless except as stepping stones when looking for a job. The most useful thing is actually the basic knowledge learned before high school, including mathematics, science, humanities and English. ?
So, a question is before me. Whether to follow the crowd and continue to mix in the existing workplace, or try to strengthen general knowledge and find a field that suits you. This is an unsolved problem, and there is no absolutely correct answer. Only by constantly trying and making progress is the best choice that can be made.