In principle, a computer is a very simple thing. It is a logic processor. All the work done by a computer is finally converted into logical operations. Therefore, anything that can perform basic logical operations (non, and, and) can be used to form a computer. The idea of computer was proposed as early as the 17th century, but it can only be mechanically used. The first computer in the modern sense is implemented by electronic tubes, but its application is very limited, huge, extremely expensive, slow, and consumes a huge amount of energy. There is also a fatal defect, that is, the reliability is not good. The current CPU is integrated with hundreds of millions of devices. If an electronic tube is used, it means hundreds of millions of plug-ins and billions of solder joints. Such complicated things have no way to ensure quality, and it is even less likely to produce them on a large scale. Computer development-Progress of integrated circuits. The wide application of computers has completely changed the lives of mankind. The hardware is based on the people headed by Einstein thirty years ago, with quantum physics and relativity, only then can there be condensed state physics and integrated circuits, and then computers and networks can be widely used. I remember someone on the Internet discussing Which of the following is more awesome about Einstein and Edison. This is a little too much. Two people are not at the same level and they are far away from each other. Einstein is a scientist. Wikipedia is also a thinker. I thought it was good. He laid the foundation of modern physics and had a fundamental impact on mankind, it has greatly changed our lives and our understanding of the world. Times Magazine named him the greatest character of the last century. Edison was just an inventor who invented incandescent lamps and phonograph products. The method of his invention has expired, and no one has ever used the product. For example, the United States is no longer producing incandescent lamps. In the future, the lighting will certainly use light emitting diodes, which are close to perfection and have a very long life. This is also based on Einstein's theory. In general, scientists have the greatest impact on mankind. They are permanent. What politicians and empire are just shadows. The foundation of computer software is mathematical logic. It can be seen as the most important progress of mathematics in the last century, almost changing the overall appearance of mathematics. At the same time, computer science can be regarded as a specific application of mathematical logic in this field. Of course, General "Code workers" may not need to know the mathematical logic, because some people have made some computer language for them, but for those who have made the language, it is impossible to use mathematical logic as the foundation. This problem may be easy to tell where the computer is located. It cannot be said about what a computer can do, because it can do too many things. It can only say that a computer cannot do anything, or that it is a problem of artificial intelligence. This word seems to be easy to misunderstand, because we need to strictly define artificial intelligence to define people's intelligence or thinking, while human thinking is an undefinable thing that we cannot clearly understand. This problem needs to be explored from the mathematical aspect, because the computer is a logic processor, which is determined by the computer's hardware and cannot be changed. Then the question becomes: what can the logic do? This issue was clarified by the work of three people, freger, Russell, and Godel. This is one of the most amazing aspects of mathematics. Some basic research in mathematics was not helpful at the beginning, but it was just a game-style thing or a philosophical question. However, subsequent developments have made these things extremely practical. At that time, people did not know what computers were. I'm afraid most people haven't heard of freger's name, but he is the founder of mathematical logic. He is considered to be the greatest logistician in the future. With the set theory tool, Russell wants to complete an extremely ambitious job based on freger, and wants to establish the foundation of all mathematics on the logic. Of course, Russell does not want to do anything for computers. Instead, he does not care much about such things. Instead, he comes from a philosophical thought. This is the so-called Occam Razor. Before freger, mathematics and logic were separated. If mathematics is a hypothesis and logic is another hypothesis (not everyone acknowledges that mathematics is just a hypothesis. I have discussed this question in detail when talking about vitegenstan, let's take it as an assumption that it will not affect the discussion below.) then, turning them into something will be of great value, because Occam Razor said: "If there is no need, do not add entities. "If there is only one assumption, errors may be reduced. This is a basic scientific principle. Of course, if mathematics reflects objective reality, it should be more unified. However, Russell failed because he found the so-called Russell paradox and reached the conclusion of the Law of incomplete Godel, it was impossible to succeed, as said Godel: "Some facts are recognized as true, but not necessarily verifiable." Of course, if mathematics is not necessarily verifiable, how can logic be the foundation of mathematics. Although Russell failed, the efforts of these people have greatly promoted the development of mathematics and philosophy. They can be considered as the mainstream of mathematics and Philosophy in the last century, their work later formed the foundation of computer science. Turing is widely regarded as the father of Computer Science: "Turing's important thesis on the number of computeable computers and Its Application in determining problems", he re-elaborated on the results of the limitations in proof and computation in January 1931. He replaced Godel's formal language based on general arithmetic with a simple form called a Turing machine." In Wikipedia, this section roughly illustrates the relationship between Turing and Gödel. However, Turing uses the law of Gödel on computers (Turing machines can be seen as an ideal computer ), behind this consistency is the logic of the Turing Machine and the formal language. The most important task of Turing is: "halting problem is a problem in the theory of Computability in logical mathematics. In general, the downtime problem is to determine whether any program will end up running within a limited period of time. This problem is equivalent to the following judgment question: Given a program and input, can the program be finally stopped under input. Alan Turing proved in 1936 that a general algorithm that can solve the downtime problem does not exist. The key to this proof lies in the mathematical definition of computers and programs, known as Turing machines. The problem of downtime is unknown on the Turing machine. This is one of the first decisive questions raised. In mathematical language, the essential problem is: Given a Turing Machine T and an arbitrary language set S, whether T will eventually stop at every one. The meaning is the same as that of the deterministic language. Obviously, any limited S is deterministic, and only a few (countable) s can be stopped. The nature of the downtime issue is the inconsistency and completeness of the first-order logic. Similar propositions include the barber paradox and the all-powerful paradox ." (All references in this article come from Wikipedia, Unless noted) Here, the barber paradox and the all-powerful paradox are another forms of expression of the Russell paradox. Here, I will explain it by myself. If you want a computer to do a job, you must know whether it is competent, that is, you cannot get a result in a limited time. Otherwise, the so-called guiding role of the theory is actually to understand something about the computer. I think it is not difficult to understand the importance of this. Without a doubt, language is the most important and great tool for humans, but it is still a tool for communication between people. For a tool, the most important thing is to know what it can do, and perhaps more importantly, to know what it cannot do, for example, you know that it is much more important that a car cannot be driven in the water than it can. In the perspective of the philosophers of language, the absurd part of the past philosophy lies in the widespread use of language, and they do not know the limitations of language, just as they have been driving cars in the water and are still claiming to feel great, I also learned the true meaning of the world while opening up. There is a correlation between the philosophy of language and the issue of downtime. They all attempt to find a line that cannot be done. One is for the language, and the other is for the computer, it is also accidental that mathematical logic is used as the basis. In vitegenstan's view, what we can really understand is that what can achieve consistency must be based on logic, because logic is a natural thing and everyone is the same. In addition, achieving consistency is impossible, just as you cannot tell what is beautiful. If we acknowledge that the language can only express the logical structure, it is easier to understand the language from a computer perspective. If some computer programs and databases are the same, then of course they will come to the same conclusion on the same issue. So it may be said that the difference between people lies in that their respective procedures and databases are not the same. This difference can be considered to be related to genetics and early years of experience and education. I am afraid no one of them may be the same, therefore, the difference between people cannot be avoided. In the words of vitgenstan, the difference between people lies in their different atomic propositions and different starting points. Therefore, the world in the eyes of each person cannot be the same. Godel tells us that on the basis of logic, we cannot build a perfect mathematical system. In Turing's words, a general algorithm that can solve the problem of downtime does not exist. This problem can be seen in this way, we want the computer to solve the godebach conjecture (any number larger than 2 can be expressed as the sum of the two geometries) and write a program, from small to large, we try to divide such an even number into two prime numbers. If it encounters an even number that cannot be decomposed into the sum of two prime numbers, it will stop and output these two even numbers; otherwise, it will continue to run. In this way, the problem becomes to determine whether the computer can be shut down and whether the computer will be shut down. Many math guesses can actually be converted into downtime problems. Therefore, if there is a general method, we can prove many math guesses. However, Turing tells us that there is no general algorithm and there are only ways to address different problems. Of course, if we find a way to judge the shutdown problem of the godebach conjecture, this conjecture is solved. Because the computer is a machine for logical operation, we can understand the saying of Godel, not that the godebach conjecture cannot be proved by logic (the so-called proof is logic ), we just cannot build a comprehensive mathematical system. Then, of course, on the basis of logic, we cannot establish an ideal language system to express everything, because mathematics can be considered as a language, it is much simpler than the daily language. Furthermore, for computers, the difference between a prostitute and a lady is only two different words of code, and it is impossible for them to feel bad. From this perspective, we can easily understand ethics. aesthetics is irrelevant to logic. Therefore, if we cannot reach the same level, it is not a question that philosophy should discuss. As Russell said, the so-called good or bad is the same as the ugly one. It is like radish and cabbage. The logic is a limited thing, so computers cannot do anything. Similarly, logical limitations lead to language limitations. The so-called absolute truth expressed by language must have logical faults. We cannot conclude that there is no such truth, but there is something that we can't say. Therefore, the knowledge of people is very limited. We can only rely on logic, but the logic is limited. We may also be able to say that if we can construct a perfect computer to solve all mathematical problems, then of course this computer can be an absolute reference, it must be used by other computers to determine whether the computer is right or not. But Godel tells us that this is logically impossible. Likewise, there cannot be one person who can do this. No one can know the absolute truth and allow us to follow it unconditionally. Then, of course, doubt and criticism are what we always need. Of course, if it is God, it is another story, because God is a Superman and religion has nothing to do with logic. Someone has another saying that God is actually explained by man, or artificial. Therefore, computers cannot be either Shakespeare or A Dream of Red Mansions. In addition, even some mathematical theories are not obtained by computers and depend on human intuition, the creative ability of people cannot be logical. The genius of Einstein will always be what we need. Godel is a strange man. His family members know his position in the field of mathematics only from others. Many people think of him as the greatest mathematician of the last century and known as Einstein in mathematics. Another great genius at the same time with him, noriman, once made great efforts on that issue, but failed. "At the time of Prince, geode and eminstan became good friends. Later people often compare them. Both Gode and eminstan have been very curious and straightforward in their own collections. However, Edison is an extrovert, which is quite different from geode. The death of aintan is a big hit on the situation of the coder ." Here are some of the stories from Godel (not from Wikipedia): "Godel once revealed that his friendship with Einstein was based on their different views rather than on their consistency. Godel achieved significant results in his later years of general relativity and was awarded the Einstein Award in 1951. In his later years, Einstein said, "my own job is boring. I came to work to enjoy the pleasure of walking home with Godel ." I'm always curious. What can I talk about together these two days? Can we understand this? But "when he visited Princeton, he went to Einstein's house every week to discuss with Einstein, Godel, and poili. He was disappointed: "They are all Jews in exile, and all of them are well-known, but they all have a German tendency towards metaphysics. Godel is simply a plato ." In fact, Godel is not Jewish ." Godel believes in thetheistic view, while Russell has always been a critic of Christianity. The important reason is that Plato's philosophy is a direct source of the Christian philosophy (the philosophy of the Institution of Economics, plato was criticized by Russell as his lifelong task. "Together with Einstein, the digital scientist, economist Morgan ston and Einstein were witnesses of godder's entry to the United States (at that time, witnesses were required for citizenship ). On the way to immigration, Godel claimed that it could prove that the US Constitution would logically lead to dictatorship. Both Einstein and Morgan ston suggested that Godel not be on the premise of immigration officers, but Godel still mentioned it. Einstein attracted the attention of immigration officers, and Godel was able to become a citizen ." I am afraid this is a good idea for such a great logical man. "He is ill from childhood and suffering from obsessive-compulsive disorder (suspected illness ). He is also suffering from pregnancy suppression. Later, he died when eating at the Prince's School of Medicine because he thought the food was poisonous ." "Adele Nimbursky, the wife of God, is six times bigger than God. When both of them met, Adele was married and worked for der nachtfalter at night. Their marriage was opposed by the family of Gode, but a lover married in September 20, 1938. They have no children ." Genius seems to be far from ordinary people like us. I 've been to the Princeton institute of higher learning, where the last two days of work were. It was the first spring, the sun was shining, but the shade was still visible in the snow, and the spring breeze was still chilly. Just like the beautiful American campuses, which are wide and rarely found, they can't help but sigh that their work has completely changed the world and the way they live. However, this is so lonely! However, this is in line with their nature, indifference, and even dislike of fame and fortune, quietly doing what they like best. But I have no doubt that as long as science and mathematics still exist in this world, they will never be forgotten!
[Switch] logic and Computer
