[Toplanguage topic discussion] Today we are thinking

[Toplanguage topic discussion] Today we are thinking

By Liu weipeng

 

Recently, I have read many books on psychology and thinking, some books on mathematics and problem solving, and I have made some questions. The two combined and made some thoughts. It was originally written to maillist, but some thoughts and summaries that have been written since this time have come out, beyond the normal length of a mail, so I posted it.

 

Polia's "how to solve it" contains a chapter listing a lot Of Heuristics ), for example, you can generalize the question, investigate the special cases of the problem, compare the analogy, check whether the conditions can be discarded, check whether the conditions can be modified, and pay attention to unknown quantities at all times... and so on.

I have a belief that the so-called inspiration must have its rules behind it. Although the inspiration comes from an unconscious level (refer to "traces of memory pursuit" (Kandel ), as well as the "subthreshold stimulation" section in "attitude change and social impact" (jinbadu), we cannot perceive the process of inspiration at the consciousness level before inspiration, however, we can indeed sum up the most possible ideas through review and rational reasoning after inspiration. In a sense, the development of mathematics is like this, from the simplest reasoning, to the generation of mathematical methods-from the general thinking rules of the Three-field theory, formal logic, mathematical induction, analogy, and divide and conquer to the principle of the pigeon cage, the principle of extreme value, and the principle of greedy to solve specific problems, all of them summarize and organize the thinking process afterwards. For example, in my opinion, formal logic is the largest rule of thinking after the event. Humans are naturally capable of reasoning at the unconscious level (see piyajie's cognitive development principles), just like (maybe) natural numbers are the same concepts rooted in the brain. These concepts are evolved and can be skillfully used unconsciously. However, to make them develop, grow, or even form on paper, and become a methodology that can be operated by anyone, consciousness is required.

When we do questions, do questions, And do questions, we often think that the only way to be proficient is to do the questions. We think that only by doing the exercises can we improve our ability. Exercise is necessary. However, some exercises are more effective than others.

We thought hard and came up with an idea from the unconscious layer at a certain moment, so we realized that we were inspired, So we cheered; over time, this kind of inspiration may increase, so we think this is the most effective way to practice. I don't think so. I think that the thinking behind the question is basically the same. It is passive to practice by waiting for inspiration again and again. After the emergence of inspiration, I will summarize the reasons for the emergence of inspiration and what kind of thinking rules may be behind it to see if it can be generalized to a category of questions. This is the way to get twice the result with half the effort.

In fact, have you found that when you solve a problem, the thought process you are aware of is a leap, along with the ideas that come up from the unconscious layer one by one, every such idea will push your thinking to the previous step. The most important one is called inspiration. Because our consciousness layer cannot perceive the logic of reasoning on the unconscious layer, people can only think that there is no other way to exercise neurons on the unconscious layer in the case of multiple problems. However, the emergence of the heuristic method is breaking this idea. The so-called heuristic method is actually "we used it unconsciously", and "it was formally proposed later, methods that can be guided by consciousness ". Once an important and general rule of thinking is summed up, we may not have to wait for the inspiration to flash, instead, you can systematically try various feasible methods (enlightening methods.

To achieve this goal (that is, to summarize the thinking rules behind your own inspiration and then generalize them into general solutions), I think it is advisable to use one method, that is, the so-called "visible thinking"-write your thinking process in detail on paper. People's consciousness is like the light in the dark night. They can only light a small part. If they don't write down the light, the light of thinking is always limited, and they may leave it behind, it is also possible that you simply stop at the local area and cannot think further. If you write it down, you can avoid this problem. You can move your mind down, expand your mind, and tap into more and more lights. In addition, "Write down" allows you to go back and view your entire thinking process-maybe you think of something at the beginning, but if you don't remember it, you will soon forget it, however, you may have a lot of inspiration. Maybe you have accidentally introduced a hypothetical assumption in a certain part of your thinking, so as to fall into the mindset trap. By writing it down, you can avoid this trap to a certain extent.

Obtain the most from a question, which is the purpose of the question.

Have you ever had such an experience? You can't make a question. You ask a person, who thinks for a while, and then points out a key step, so everything becomes open.

But this is far from all!

If you continue to ask him what he thinks, experience tells me that almost all possibilities point to an answer "I don't know ".

Why? In my own experience, I believe that most people do not reflect on their own processes. If you cannot figure it out, pull it down. If you come up with it, everything is fine. But polia said in how to solve it that he always encountered such a problem during his teaching: "How did you think of it "? This problem prompted him to sum up the patterns of thinking. With these patterns, even less inspired people can use these patterns to make his mind more open. We may also call these enlightening Methods The "recipe" of thinking)

The answer is not important. If you tell me the key step, I will not get anything. Even if I come up with the most critical step, maybe I still don't get anything. This is because this experience can only be very limited to help me with my next problem; unless I can further think about the rules behind my thinking, I can make the most things for my future use.

Therefore, the important thing is the process of thinking, whether or not this process leads you to the answer. I believe that only by reflecting deeply on the true process of thinking can we get the most from the question.

I initiated this series "Today we think" (originally I wanted to write "Today we do the question", but I thought that the purpose of this discussion was actually to think about it and changed it ), everyone sends the most exciting questions they think (add [Today we think <No.>] to facilitate future searches ), I think it is a very beneficial thing for others.

There is no need for a new question, and it doesn't matter if many people have done it. My experience is that even if the previous questions come up, now, with the "how did I think about it" attitude, we can rethink and get useful things. Therefore, the key is that the question should be classic and reflect some ideas.

The key of this series is to discuss the idea of doing the question, instead of the question itself. The answer is not the goal at all. Even if you don't get the answer, it will be of great value. If you think of some ideas, but it seems that they are far from the answer, there is no relationship between them. It may be a great inspiration for others' ideas. This is a brainstorm in the mail list. If you think of the answer and can sum up the key rules in your own ideas (How do you think of it), I think everyone will benefit a lot.

If you have a good idea about the previous ideas, you are welcome to share with us ~

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