How should ordinary people think in complex situations?

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Author: Brother Mao This article is reproduced under the authorization of Brother Mao’s Vision (ID: maogeshijue) on the official account.

The current economic situation is not good, and many people are anxious. How can we alleviate the anxiety?

I have mentioned many times in the past articles that we should not only walk with our heads down, but also look up at the sky. Walking with your head down is pragmatic, and looking up at the sky is retreat.

No matter how we behave or do things, we should combine pragmatism with modesty. Only modesty is easy to be flashy and unrealistic and not grounded. Only pragmatism is easy to get caught in complicated affairs without insight into the essence.

Today, let’s talk about a very realistic retreat topic – how should we think about complex problems?

When it comes to thinking, it is easy to think of a famous saying. When human beings think, God will laugh. This sentence describes the insignificance and ignorance of human beings.

But is there a mode of thinking that makes God laugh?


If we think like mathematicians, I believe that God’s attitude must be solemn and serious.

Mention of mathematics is a headache for many people, because in our impression, mathematics means complex numbers and difficult symbol combinations, and thinking like mathematicians is even more profound.


But this is not the case. As the basis of natural science, mathematics is for us to solve problems, not create problems


Today I try to tell a wonderful logic without complicated numbers or even a mathematical formula——

How can we think like mathematicians?

Actually, there are two principles.


Describe the problem with numbers

Many people describe the problem is often vague and difficult to understand. This way of describing the problem is often to assume that other people have the same knowledge structure (or information content) as themselves.

In fact, it is very difficult for us to meet two individuals whose knowledge structure and information content completely coincide in our life. This ambiguous way can not only solve the problem, but also cause great communication problems.

for instance.

If you are a volunteer teacher in a primary school in a mountain area, one day a child suddenly asks you: What is a person?

You may casually answer that man is a high-level mammal.

To be honest, this description is very problematic. Because for children with insufficient education, not only is mammal a strange term, but the word “advanced” is also difficult to understand.

So you are likely to encounter a series of questions raised by children.

What is a mammal?

Why are humans mammals and not other species?

Why are humans more “advanced” than other mammals?

Even if your knowledge structure can cover these questions, the process of answering them must be boring. Under normal circumstances, you may face an endless stream of problems and children’s confused vision and mood will become worse and more impatient.

So what’s the problem?

The problem is that you lack the ability to accurately describe things.

Perhaps, we can try to introduce numbers in a different way, and use numbers instead of vague nouns to define problems accurately.

What is a person?

Man is the only biped without feathers on the earth.


This answer may be a little strange to ordinary people, but it has no ambiguous nouns. More importantly, it has no ambiguous numbers for the definition and constraints of things.

Next, children’s problems will focus on numbers rather than words that are difficult to describe——

Why are people bipeds?

The answer is also obvious. Human beings evolved from apes and landed on all fours at first. But in the process of evolution, apes liberated their upper limbs, walked on two feet, and used their upper limbs to make tools, which became human beings.

Why is man the only one without feathers?

The original ape-man had thick fur, but humans migrated from Africa to all parts of the world. In the process of migration, humans encountered drastic changes in temperature difference in different regions.

In order to adapt to this environment, the ape man’s fur gradually fell off, and then made primitive clothes from animal skin leaves, and used more flexible clothes to adapt to the drastic temperature change of the outside world, while the animals covered with fur could not adapt to the drastic temperature change.

Therefore, the radius of activities of other animals on the earth is limited. Only human beings who use clothes instead of fur can reach every corner of the earth without hesitation.


Please pay attention to the same explanation of what people are. Compared with the former, the latter’s solution is not only clear and logical, but also vivid and interesting.

The answer of a few numbers briefly describes the history of human evolution and migration. Not only can the person who answers the question explain it, but also it is easy for children to arouse their interest in knowledge.

This is the charm of thinking like a mathematician.

When you learn to use numbers to accurately describe the problem, in fact, the answer to the problem will have a clear context. At some level, it can even be said that we can find the answer faster.

Note: The introduction of digital precise description of problems not only helps solve problems, but also is a sharp attack weapon in some cases.

for instance.


Recently, the Foreign Ministry launched the “Report on the United States’ Hegemony, Hegemony and Its Harm”, which won a hearty victory in the western public opinion field.

So, why can a Chinese report that exposes the hegemonic harm of the US imperialist cause a storm in the western public opinion?

First of all, the major western mainstream media basically blocked the report, but in the Internet era, it is still difficult to cover the sky with one hand. The mainstream media do not report, but there are numerous online red bloggers on Twitter, TikTok and other social media platforms who spontaneously and actively publicize the report.


Because in this report, we skillfully quoted detailed data and accurately portrayed the United States, hitting the sensitive points of the western people many times.

For example, on Twitter, the key words in the excerpt of the report that often causes millions of popular tweets are:

– Of the more than 190 countries recognized by the United Nations, only 3 countries have not fought with the United States, and these 3 countries survived because the United States did not find them on the map;

– The United States has not fought a war for only 16 years in its 240 year history;

– After the end of World War II, the United States tried to violently overthrow more than 50 foreign governments, interfere in the elections of at least 30 countries and try to kill more than 50 foreign leaders;

It is no exaggeration to say that in the era when the mainstream social media in the West is still based on images and texts, this model of using data to portray the United States burst out with powerful power to destroy the information iron curtain built by the West for China.



The answer to beauty

Back to the previous topic, when we use numbers to accurately describe the problem and find the answer, how can we measure whether the answer is correct or optimal?

Look at the method of mathematicians.

When I solve a problem, I don’t think of beauty, but when I finish it and the solution is not beautiful, I know it is wrong – Richard Buckminster Fuller

There is a very interesting phenomenon. When almost all scientists, whether mathematicians or physicists, derive a formula through experiments or calculations, the important criterion for them to judge whether the formula is correct is whether it is aesthetic!

Even numbers and simple formulas are beautiful and correct. On the contrary, it is ugly and wrong.

For example, the famous Goldbach conjecture is a typical example – any even number greater than 2 can be written as the sum of two prime numbers!

This conclusion is really beautiful, so all mathematicians think it must be a truth, but no one can prove it with strict mathematical logic.


Therefore, if we want to think like mathematicians, we must follow the second principle.

Here are two cases.

Case 1, top-level design.

If a group of human beings on an island chose eight representatives to form a committee to be responsible for the governance of the island, the question now is how to design rules for the committee system? The more specific problem is this——

How many independent committees should the committee include?

How many representatives should each independent committee have?

How many independent committees should each delegate participate in?

Such a rule design 100 people may have 100 solutions, but if such a question is given to a mathematician to design, there can only be one answer:

The committee should include six independent committees.

Each independent committee should have four representatives.

Each representative should participate in three independent committees.

Why must the corresponding numbers above be 6, 4 and 3? Why can’t we change it to other numbers?

Because in an independent system, the combination of 6, 4 and 3 has a special mathematical beauty, and their combination can perfectly build a symmetrical cube model.


The vertices in the figure represent 8 representatives, and the cube represents the committee. The six faces of the cube are exactly 6 independent committees. Each face is composed of 4 vertices, and each vertex is adjacent to three faces.

These three design conditions are just compatible. They restrict and rely on each other to build a perfect cube model.

If we make a change to any one or several numbers of 6, 4, and 3 in the top-level design, it will either be unable to build a closed model, or the model built must be ugly and distorted.

A complete cube model is aesthetic, while an ugly and distorted model is not.

Therefore, the top-level design of mathematicians is more in line with the laws of nature, and the specific operation in the future will also be smoother and more efficient.

Many years ago, when I was still working on FMCG, there was a time when the enterprise was preparing to launch a new product. At that time, the design and planning department came up with several plans to discuss, and everyone had their own opinions.

From the efficacy positioning to the design size, the public said that the public and the public said that the women were reasonable and could not agree. The boss also hesitated and did not know how to choose.

At last, the boss invited a magnate in the marketing industry to come to the consultant. The magnate was a bit absent-minded when all colleagues in the company expressed their views, but he just stared at several samples taken out by the design department for a long time without saying a word.

Then the boss asked the boss for his opinion.

In fact, I don’t care much about the efficacy positioning and product attributes you said. I think the first step to choose is to display this product!


yes! When it is placed on the shelves of the shopping mall, whether consumers like it and have the desire to own it after seeing it at the first sight.

When a product has a selling appearance, we can discuss its efficacy positioning and product attributes.

Products that do not even sell well are unlikely to achieve good results in terms of efficacy positioning and product attributes.

This story impressed me deeply. Looking back, in fact, this kind of thinking is similar to the beauty of mathematicians’ pursuit of answers.

Here, some people may have questions – I, I also know that it is important to introduce digital quantitative description, but there are many things in life that cannot be described quantitatively. So how can we think like a mathematician about this situation?

Let’s not talk about methodology here, let’s take an example.

In November last year, before opening up, I urgently stocked up an oxygen generator, which is a fish diving medical product with a price of more than 3000. It is also a large electrical appliance.

As a result, after the epidemic was released, the oxygen generator was not used. After a period of time, the father-in-law wanted us to give it to him, so his wife drove the oxygen generator to the father-in-law’s house.

The next day, the father-in-law called and said that the oxygen generator could neither be installed nor know how to use it. The manual was a thick one. It was a bit difficult for an elderly person with a low education level to read the manual.

So my wife contacted the manufacturer.

As a result, the after-sales service of this enterprise is amazing.

First, can you send someone to teach the elderly to use it?


Second, can we add WeChat guidance?


For thousands of yuan of medical devices, the after-sales service is basically zero. Well, listed companies are so arrogant.

So my wife, who was full of anger, began to look for the car keys in anger and prepare to go out. I asked what happened? The wife told the story. I asked her what to do? She said helplessly, what else can I do? You can only read the instructions yourself and then teach the elderly how to use them.

I stopped her.

Your method is wrong.


Now you go to your parents’ home and go back and forth for more than an hour. It’s very troublesome not to say. The key is that you may not be able to understand when you read the instructions. So your solution is complex and full of uncertainty. According to the logic of mathematicians’ thinking, such a solution must be wrong.

What is the right way? The wife asked.

At this time, I suddenly had a flash of inspiration and thought of a math problem that I gave my son yesterday:

How can I prove that the sum of internal angles of any triangle is 180 degrees?

This problem is a dead end if the thinking is confined to the inside of the triangle, but if it jumps out of the inside of the triangle, it proves very simple.

Draw a straight line parallel to the opposite side through any point of any triangle, so that there will also be three angles at the intersection of the triangle. These three angles must be equal to the corresponding triangle, and the sum of these three angles is exactly 180 degrees.


The key way to solve this problem is to draw an auxiliary line outside the triangle.

guide? I have a plan in mind.

Then I said what I thought.

Open the mobile phone, find 58 people in the same city, search for oxygen generator repair, and casually find a shop phone to contact. The result is that 80 yuan has secured a professional to visit, which perfectly solves the problem that once made my wife headache.

After that, my wife was curious about how I could come up with such a plan?

I said that Einstein said that the solution to complex problems cannot be solved in the dimension of the problem itself.

It is obvious that we encounter an irresponsible manufacturer. It is not the right way to fight with the manufacturer or to fight with the manufacturer. The right way is to try to draw an auxiliary line.

This is the auxiliary line to seek other similar professionals.

After listening to the process of my thinking, my wife raised her thumb and sincerely praised: beautiful!

Now I can judge that this method is probably the right one.


Because the original plan that the wife prepared to knock the instructions on her own is not only painstaking, but also not good. Such a plan must not be a good solution.

But the solution I put forward is simple and easy to solve, which naturally makes my wife convinced by comparison.

A scheme that can make people feel convincing will naturally produce a sense of beauty.

So, how to judge whether a scheme that cannot be quantified but can only be qualitative is correct?

Try to let others see their own design to see if it can make them feel beautiful.

If yes, it is the correct optimal solution;

If not, the high probability is the wrong plan.

It’s that simple.

Think like a mathematician

Now let’s sum up, how can ordinary people think like mathematicians?

Two principles.

First, learn to accurately describe problems with numbers.

Second, the correct answer must be aesthetic.

If Principle 1 is the starting point of thinking like a mathematician, then Principle 2 is the end point of thinking like a mathematician.

As for how to get from the starting point to the end point, I will be lazy and recommend a book – Think Like a Mathematician. This book is a collection of courses offered by the University of Stuttgart in Germany for non-mathematics students (formerly called “Meeting with Mathematics”).


In this book, the author introduces 22 thinking tools based on mathematical principles to the public. These tools can help you reduce complexity and learn to solve various problems with mathematical thinking.

The case of the committee in this article is quoted from this book, and the rest of the text is the distillation of my reading and thinking. I think both adults and children in middle school should read this book.

This article is reproduced with the authorization of official account Maoge’s Vision (ID: maogeshijue).

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