Some Opinions on Mathematics

I don't like the psychology principle of easy mathematics

I used to have no special feelings about mathematics when I was reading books. most of the time I want to take the exam. I have not found any fun in mathematics. after work, I felt that mathematics had played an important role in many applications before I became a little interested. In fact, I used to know that mathematics has important applications in many fields. however, you can only experience it yourself. because mathematics is too abstract, it is difficult for many people to have a liking for mathematics. in fact, this can be explained by the schema of the Cognitive Psychology School. The so-called schema simply refers to the overall architecture formed by all the knowledge we learned from the outside world from birth, it is a network of existing knowledge and experience in the human brain. in fact, we can understand that through a long evolution, humans have formed some learning function in the physiological structure, which can be inherited. as a result, a child has just been given birth to such a powerful learning ability. this learning function should be based on the long years of human life experience. therefore, we are more intuitive and can directly feel through the five senses, and the knowledge closely related to life is easy to accept, and learning is fast. those empirical knowledge constitute the core of the schema.

When we learn new knowledge, if they have a lot to do with the existing knowledge in the schema, we can easily accept it, grasp it, and integrate it into the existing schema. however, if the newly learned knowledge is abstract and away from experience, it is difficult to establish a certain relationship with the existing schema. it's hard for us to accept it. We can only memorize it at most, and it's hard to make it a part of your thinking. at this time, the only way to integrate it into the schema is also the most stupid way, which is to constantly repeat and strengthen. it will be gradually integrated. for example, if we remember English words, it would be easy to remember new words by associating them with words that have already been remembered. Otherwise, we would have to repeat them.

Mathematics is a language

When we were in junior and senior high school, the number of extra words was undoubtedly the most important three courses. chinese and English are two languages that everyone agrees with, but mathematics is actually the same as they are. however, I thought back and found that no teacher ever said that mathematics is a language. english is the language of everyday life, while mathematics is a descriptive language that can be used in many disciplines. Some people even think that mathematics is the language of the world, the language of the universe, and the language of God. we know that common terms are often ambiguous, and a lot of words can express very little meaning. the biggest advantage of mathematics is non-ambiguity, and the second is conciseness. mathematical Expressions mean that all people can have only one view and understanding, and there are no multiple interpretations. in addition, mathematics can only express a large amount of information with a few simple characters. For example, many major physical principles are expressed with a simple mathematical formula. we can also completely replace Chinese with mathematics, a natural language like English. We know that every mathematics in Unicode can represent one character. then we will replace all the language characters with those mathematics, and then apply the syntax to them. it's just that numbers are not close to our experience and intuition, so it's not easy to integrate into our schema, so no one is trying to use math as a daily term.

Many people think that mathematics is complicated and mysterious. in fact, it is not mysterious at all. It is just a tool and a language, but it is concise and unambiguous. For example, it is suitable for us to describe some complicated principles, describe our ideas. it is not complicated. What is really complicated is the principles and ideas it describes. what is really complicated is the world and the universe. in the face of the complex principles in nature, apart from the knowledge of various disciplines and the description of mathematics, we can no longer explain them in the final sense. einstein said that what really impressed him was that the world was understandable. but who knows what they understand? The Skeptical School thinks that nothing is definite. we just assume that it is correct for the moment. our so-called understanding is simply to explain some rules. we cannot answer the question further. for example, if there is a universal gravitation, some people say that there is such a natural
Force, which is equivalent to not saying. Some people say that God has created this force and created various rules.

Language boundaries are world boundaries

Vitegenstan said that the boundaries of our language mean the boundaries of our world. the general meaning is that we need to use the language tool to describe the problem. Therefore, if some problems cannot be clearly described by the language, we cannot think clearly and discuss them clearly. he also came to an important conclusion that many philosophical questions are actually linguistic statements, or beyond the boundaries of the language itself. we cannot make it clear. so we don't have to worry about such philosophical issues. his original saying is that everything that can be said can be clearly stated. We will remain silent for what can't be said. he tries to clarify all philosophical questions from the perspective of linguistics and logic. however, some people disagree with him. first of all, we must use language to think about the problem. This argument is not necessarily true. we cannot prove this argument. it cannot be proved to be true or wrong. in addition, the logic is not necessarily correct. You cannot use the Logic Theory to prove that the logic system itself is correct. in addition, some ideological issues cannot be discussed by logic. for example, in Buddhism, it is often mentioned that we do not think that something is right or wrong. just use a normal heart to perceive it. this is anti-logic. in the logic, there is only right and wrong.

Although language restrictions may not be the world restrictions. but we can clearly see that the language of mathematics expands our world, expands our spiritual world, and presents some hidden things in the physical world to us. natural Language is closely tied to experience and intuitive experience. Further abstraction is difficult. it is difficult to clearly describe the theory of relativity like Einstein in natural language. Based on our experience, we really cannot understand things of time and space. only mathematical reasoning can be used. through abstraction, mathematics can describe many problems that are far away from daily experience. It can be used to derive some conclusions that we can never understand.

Mathematics and computer

We all know that many theoretical foundations of computers are mathematics. however, mathematics is only a good language, and it cannot be used as a computer by studying mathematics alone. many computer theories come from physics and biology. but there is no doubt that you are not good at mathematics, nor are you good at physics or biology. what kind of transistor is used, and what kind of computer components are naturally an object learning task. the overall architecture is based on some biological principles. the von noiman System in the computer refers to the human brain structure. feng nuoman also wrote a book called computer and human brain. like Fuzzy search and regular expressions, they are also obtained based on some neurology principles.

In addition, we have to use natural languages to write novels and poems. however, we need to develop software using a certain programming language. In fact, I think a programming language can be a combination of a broad mathematical language and a natural language. The more advanced the language is, the closer it is to a natural language, the lower the language, the closer it is to the mathematical language. the computing language is just a mathematical language. 0101 isn't that a number in mathematics?

What we like best to do is to classify things into different classes, which is easier to learn and discuss, such as calculus, ordinary differential, linear algebra, and topology. however, discrete mathematics is the most closely related to computers. for example, graph theory, state machine, and compiler cannot be separated. it's even more time to turn over the textbooks of previous universities. I am ashamed to say that I have studied software engineering in college, but I have hardly read computer books, I have not written a few lines of code, and I have never studied mathematics well. I have read a lot of books in other aspects.