What do you think?

The following are some thoughts of Mr. Zhang Wuchang on thinking, which are very practical and I hope to be beneficial to you.

First, who is who is not unimportant.

If you analyze or argue with another person, he often emphasizes a certain point or finds that it is his, or puts "himself" above the problem, then you can be sure that he is low-handed. Thinking should never be influenced by prejudice. It is human nature to "show off" or "take credit", but in the process of thinking, the concept of "self" cannot have a special position. "Honor" is after you have the answer. In reasoning, you should objectively weigh different viewpoints.

Some people think it is wrong for people to defend their views in a competitive and unreasonable way. Friedman's thoughts are as fast as lightning, but he admits mistakes faster! Because he admits his mistake too quickly, he often gives people the impression that he does not admit his mistake. Among the masters I know, no one gives "self" the slightest weight when reasoning. It is another matter to "take credit" afterwards.

Similarly, there is no such thing as authority or guru in academic circles-these are just the names of admirers; Let's not be intimidated by fame. Any expert may be wrong, so their views or theories can only be considered and measured by us, and we can't believe them all. Of course, the expert's inference is deeper and deserves our special attention. It is necessary to know the opinions of experts in detail and weigh them carefully. But we can't be right because we are experts. The difference between a master and a low hand is mainly that the former is deep and wide, while the latter is shallow and narrow.

I have always admired Smith, Mill and Marshall. But when I study the theory of tenant farmers, I treat their theory equally and don't take their names to heart. Otherwise, I can't overturn their theory.

Second, the question should be deep, shallow and important, and there should be the possibility of different answers.

If you ask a good question, you will often get half the answer.

First, the problem should hit the nail on the head.

This is Friedman's specialty. You ask him a question, and he likes to answer it like this: "I'll correct your question." Let me rephrase your question. ) He changed his mind and went straight to the center of your problem, which was very clear. The imitation method of ordinary people is to try to ask a question in several forms in order to get to the point.

For example. When Friedman explained a French scholar's monetary theory, I asked, "If things stay the same for a long time, will his theme be boring?" Friedman replied, "Are you asking that the more time, the less the marginal value of time?" This change directly leads to the law of "diminishing marginal substitution rate" in economics. He doesn't need to answer me, the answer has already appeared!

Second, ask shallow questions.

This is A.A. Archian's specialty. When talking about monetary theory, he asked, "What is money? Why doesn't the market use potatoes as currency? " When utility is difficult to measure and becomes a hot topic in economics, Ai Zhiren asked, "What is utility? What is measurement? What criteria do we use to decide whether something is measured? " This is the way children ask questions. Later, Ai Zhiren found the world-famous answer.

Measurement is nothing more than adding numbers in any way as the standard of measurement, and function is nothing more than naming these numbers arbitrarily. Assuming that everyone wants to increase this number, it becomes a functional principle. This arbitrary method is useful if it can successfully explain human behavior, and the function itself has nothing to do with social welfare!

My own theory of tenant farmers was asked a few shallow questions. Traditionally, it is believed that since part of the harvest of land planting should be distributed to landlords, landlords will collect rents through separate accounts, just like the government levies taxes, thus reducing farmers' labor and thus reducing production. I asked, "Since the output is declining, the rental value should be reduced. Why doesn't the landlord choose other non-sub-account rent collection methods? " I asked again, "If I were the landlord, what would I do? If I were a farmer, what would I do? "

Third, we must determine the importance of the problem.

Among the experts I know, it is customary to measure the importance of a problem, and Chourafa prefers to put this measure before all considerations. When a student asks him a question, he may answer, "This question is not important." So I don't want to think about it anymore. If he thinks this is an important question, he will get up from his seat!

It is not too difficult to judge the importance of this problem. You have to ask, "What will we know if this question is answered?" If what we know has nothing to do with other knowledge, or what we know can't change what we all know, then this question is irrelevant.

There are many questions that are not only unimportant, but also stupid. What is a stupid question? If there is only one answer to a question and there is no other possibility, it is a stupid question. For example. Economics is based on the assumption that "individuals strive for interests"; This implies that individual production will reduce production costs as much as possible. A scholar made a big fuss and asked if the personal production cost would be too high. But based on the author's own hypothesis, "too high" is impossible. Friedman commented: "Stupid questions and stupid answers deserve it!"

Third, don't erase the premonition.

Logic is the norm of reasoning; But if logic comes first and non-logic doesn't work step by step, thinking will be suppressed. Illogical reasoning is full of contradictions, of course, and I don't know the so-called; However, thinking without logic often obliterates the premonition, so that nothing can be thought of. Logic-especially mathematical logic-is a profound knowledge, but if logic is preconceived, it will be counterproductive.

When I was a student, I read the letters that Einstein argued with K Popper, a master of logic. They are arguing about scientific methodology. In this debate, I think Pope has the upper hand. But his contribution to science is little known.

Logic can help the correctness of reasoning, but it is not the source of ideas or opinions. Scientific methodology is used to prove the existence of theory, but it is useless to explain phenomena. Those who insist that ideas that have not been inferred in the right way are against the law and cannot be accepted by science, and are just self-consolation for those who can hardly make great contributions. I have met many such people. They all have practical knowledge and quick thinking-what they lack is imagination.

It is the most effective way of thinking to start with a hunch, add imagination to scrutinize in many aspects, have a general idea, and then prove it repeatedly with logic. As long as the obtained theory or viewpoint conforms to the logical and methodological norms, it is not important how it is conceived. Don't listen to those disputes that advocate "deduction" or "induction" When an apple falls on Newton's head (or Newton dreams in the middle of the night), the theory of gravity is realized. Who cares if his way of thinking is correct?

There are some unique scholars whose logical reasoning ability is really unremarkable; Their important scientific contributions were revised by later generations. T.Malthus, an early British economist, is not as good at reasoning as ordinary college students! Heyek and T Schultz, who won the Nobel Prize in modern times, have no advantage in reasoning. This shows that thinking is the first, followed by logic.

When you have a little original premonition, don't give up because there is no logical support. Among the scholars I know, Coase is the first one who makes good use of hunches. No matter what I asked him, he immediately replied: "It seems right" or "It seems wrong". Have a hypothetical answer first, and then slowly analyze the hunch from the beginning.

Once, at a meeting, it was suggested that the selling price of agricultural products of big landlords would be the market price of patent rights. Without market competition, it is a waste for society. I blurted out, "How? If all the land in the world that can grow wheat is mine, I must rent it to different farmers to cultivate it separately; After the wheat harvest, farmers will compete for sales in the market, so the wheat price is the market price under competition. "

Goss immediately said to me, "You seem to be right." Three days later, when I met Gauss again, he said, "You seem to be right." I asked him what I said right. He said, "The market price of wheat." A few months later, in a chat, Gauss brought up the old story: "I think you are right about the price of wheat." Judging from a hunch that is not our own, it is indeed a famous style and worth imitating.

Another late expert friend, named R kessel, is a famous premonition wizard in the industry. 1974 (one year before his death), I was lucky enough to be with him for several months, and I could feel his premonition that I didn't know where it came from. Su Jia has a motto: "No matter how unreasonable the intuition is, it is better than no opinion at all." He also stressed: "If you don't have any opinions, then you can't win any refutation."

Every important discovery is inseparable from a hunch-there is no certain norm from there, and sometimes it is not clear what it is. In thinking, a hunch is the beginning of a road-it is difficult to know in advance how far you can go and where you are going-but you must try. When taking this road, logic drew a line on the road to separate the feasible from the infeasible. After taking the first step, the second step may be clearer. The characteristic of a good hunch is that the road can go farther and farther, clearer and clearer, and then suddenly connect. The premonition of "futility" is characterized by the opposite.

Don't think that by emphasizing the importance of premonition, I belittle logic and scientific methodology. I used to be a student of R.Carnap. How can I despise this knowledge? What I want to point out is that logic is used to assist the development of hunches. If you use it wrong, you can erase your premonition.

Fourth, the conversion angle can get twice the result with half the effort

Any thinking problem can be inferred from many different angles, in other words, the same problem can be analyzed with different premonitions. In this respect, all the masters I know are exactly the same-they will not give up a possible path easily, nor will they stick to the rules. They tried to speculate from as many different angles as possible. The conversion angle has the following effects-

First, you can open the cork.

Mental block is an unexplained mental disorder that everyone has. Shallow and important discoveries, often smart people may rack their brains and think of it! However, if you think from a different angle, it may be very different Most unexpected answers are not because they are too deep, but because it is difficult to see the shallow side from the angle. Important examples are too numerous to mention.

In order to produce, a factory pollutes the neighboring property and damages it. For a long time, economists have suggested that the government use several methods to curb the production of factories, thus reducing the loss of neighboring property. The old problem came to Gauss, who reversed the angle: "Suppressing the production of the factory means that the neighboring owners have caused some damage to the factory. Which side should be suppressed? " Gauss's law comes from this.

Another example is about "corporate finance", which has been popular internationally for more than ten years. W.Sharpe, one of the founders of this discipline, became famous for determining the market price of assets in principle for the first time in a risk situation. Although this principle has obvious shortcomings, a slightly reasonable answer to an important problem that could not be solved at that time is enough to make it famous. The starting point of Shaerbo's "solving the case" was to reverse a well-known curve at that time.

Second, the angle can measure the answer.

An answer that is correct from one angle may be wrong from another. Any tentative answer obtained by reasoning can of course be measured from several different angles. If the tentative answer is not rejected from different angles, it can increase our confidence in the answer. Of course, reliable answers still have to be tested by logic and facts.

Third, the angle is far and near.

In the process of thinking, details and details complement each other and are short-lived. No matter how thoughtful the details are and how difficult the points are, the thinker may give up all his efforts. But it is only a matter of time before the point of view with the correct theme is supplemented by details-even if the details are wrong, they are often harmless. The difficulty of thinking in this respect is that if we completely ignore the details, it is difficult for us to know the main points. If you have a reliable point and then analyze the details, the accuracy will be much higher.

As soon as you concentrate, put on a magnifying glass and pay attention to details-this is the general habit. People who are good at thinking will push the problem as far as possible and consider it as a whole.

Examples are far better than symbols.

Examples and symbols can be used in reasoning; Some people don't use either, just talk about things and add some assumptions at will, which is considered reasoning. The latter is a casual debate after dinner, not serious thinking. Scientific thinking, using examples is far better than using symbols.

Mathematics is a language composed of symbols; Strictly speaking, any language is a symbol. The picture has no signature, but it is also an expression. Using a lot of words to express the picture has become an example. Thought is abstract. To prove the correctness of abstract ideas, mathematics is of great use, because it is the most rigorous language. But the effective way of thinking is to make abstract reality. Pictures are closer to reality than symbols, so they are easier to remember; So in thinking, using examples is far better than using symbols.

Economists who are famous for their good use of mathematics, such as P. Samuelson, K. Arrow, H.Uzawa and J.Stiglitz, all use examples to help them think. After getting the gist of mathematical proof. Others who use mathematics less but are good at thinking are better at giving examples. Some scholars only use symbols or fewer examples, but rarely find important findings.

The talents of China people are world-famous, but their ability to use examples is relatively weak. I really don't understand this point (maybe the example of Buddhism is too abstract and has a bad influence; Please ask Shum Yat Fei to answer this question). In my opinion, Han Feizi is ok, but the examples used by Mencius and Sun Yat-sen are often specious and difficult to understand; It is not difficult to understand that they cannot become experts in reasoning.

People who make good use of examples can't be stupid any more. There are several basic ways to use examples. Whether you can use them well depends on your imagination. Now try to classify these methods as follows.

First of all, examples should be simple and appropriate.

Using examples to assist reasoning, the important feature of theory is that it contains all examples. The usual practice is to delete the details in the examples, make the key points stand out, and make the examples and theories have a parallel comparison in the key points. Simplifying examples requires courage and imagination. In the history of economics, D. Ricardo is best at simplifying examples-so the breadth of Ricardo's economic model is unparalleled so far. In other words, the simpler the example, the easier it is to deal with complex theories.

Second, examples should be divided into true and false.

All available examples have been simplified. According to strict standards, no example is true. But some examples are castles in the air, and unreality has nothing to do with simplification; The other example is not true because of the simplification of the facts-we call the latter "example". Examples obtained purely from fantasy are easy to change, easy to change properly, and can help reasoning. But in order to have a practical theory, there must be examples to support it. People who know little about the world can start with fake examples and then find examples to help; People who do more empirical work can often omit this step. Experience is very helpful for thinking, because we know many examples.

Third, the examples should be novel.

Well-known examples are not only unattractive; In thinking, novel examples will lead to novel ideas more easily. The first person to compare flowers to beauty is a genius, and then he uses less originality. The example of factory polluting neighbors is very novel when Pigou uses it; The more you use it, the less inspiring it is. Gauss analyzed the same problem, using the noise of dental tools and the shadows of neighbors and buildings to reduce the sunlight in the swimming pool next door. These novel examples inspired some new insights.

Fourth, we should draw inferences from other countries.

At this point, China people are particularly weak, and facts cannot tell the truth; Too many theories mean no theory. If each example is treated separately, the theory and viewpoint will become complex and logical. Inadvertently turned into explaining the facts. It is an important way to find a general theory to classify many different examples into the same category.

Marx took Ricardo's road and conceptually separated capital from land and labor. Therefore, Marx's capital theory lacks generality, making surplus value homeless. Ricardo himself never thought that value only came from labor; He doesn't know how to summarize different resources, and he knows that his theory is difficult. It was not until i. fisher clearly solved the problem.

On the issue of social consumption, Pigou used so many examples to classify it that his theory was vague and inconsistent. This problem comes to gauss, who thinks that no matter what everyone does in society, it will affect others; Then he summed up all the behaviors that affect people as property rights issues.

At the other extreme, an overly generalized theory has no explanatory function because there are no exceptional examples. To have a practical theory, it is necessary to have the possibility of being overthrown by facts. So we should summarize and classify the examples. The method of classification is to put aside the details and focus on the places that are difficult to save between different examples. In order to deal with an example alone, we should also look for other examples that are common to this example. There is not an example in the world that cannot be generalized. If there is any work, logically this example can't be explained by theory-it becomes something other than science.

Fifth, try to find an opposite example (counterexample).

Think of examples to find support; But textual research is part of thinking-textual research is trying to find the opposite example. Masters such as stigler and Becker like to use reduction to absurdity in debates. A reliable theory must have imaginable examples to disprove it-but if disproof is an example, the theory will be overthrown.

If you are confused, you should put it on hold for the time being.

The human brain has an elusive function-a brain that even a computer can think of, of course, much more complicated than a computer. Very often, when you think hard, you can't think of it, but when you don't want to, the answer comes out. What we can be sure of is that the answer that pops up inadvertently must be an old question that we have thought about before. The deeper you think before, the greater the chance of getting something for nothing. You can believe that you think about it every day and dream at night.

Mysterious question, time is not wasted. Putting problems aside and thinking about them later can work miracles. Even if you stop thinking about the answer, you may get it inadvertently. My article on price control has been written for 3 years, the company principle 12 years, and the jade market has not been written for 9 years ... these and other articles add up to at least 100 years! Not exaggerating, but putting it on hold until the time is right. Bega's articles, good, are the results of years of hard work. Gauss has been waiting for several articles for more than 30 years: he is 74 years old this year, and it is a great loss in economics to wait any longer. But everyone has his own rules, and waiting is an important step in thinking.

Scientific thinking is a major. Like other majors, practice makes perfect. Thankfully, no matter how profound the question seems, the good answer is often shallower than expected.