We learned the linear function shown in the figure below in middle school:
At that time, we were forced to solve problems, solve problems, and solve problems. Soon, everyone would use a function in a fancy way:
- Given a point and a slope, you can find the primary function
- Given two points, you can find the function once
- Given a primary function, you can draw a line in the coordinate system
- ……
After you are proficient, you will no longer lose points on a question such as a function in the exam! That feeling is great!
Unfortunately, however, we quickly put the characteristics of primary functions into practice. We always look at what is happening around us in a linear way , and then actively throw away a lot of possibilities.
railroad thinking
Let's look at an example first.
A friend M who graduated from Nanjing University got offers from three places in Beijing, Shanghai and Changsha.
M said: "The two offers in Shanghai and Beijing have a monthly salary of 10,000 yuan. The housing prices in these two places are so high that I feel that I can't afford a house in my lifetime."
I asked him, "Why do you say you can't afford a house in your whole life?"
M said: "You think, even if the monthly salary is 10,000, even if the annual increase is 10%, it will take 40 years for a month to buy a house of 51,000 square meters! By then, I don't know how many ten thousand square meters of the house will be!"
As soon as I heard it, oh my god, 40 years! So desperate, so desperate!
I said, "It looks really difficult. What about the offer in Changsha?"
M said: "The offer in Changsha is given by a real estate company with a monthly salary of 8,000. I am from a county next to Changsha, with a salary of 8,000. I can live very well in Changsha."
I said, "Then you prefer the offer from Changsha?"
M said: "No, Changsha, the development is definitely much slower than Shanghai and Beijing, I still want to grow faster in work, but go to Shanghai and Beijing, 10,000 yuan a month, I don't see any hope... So I'm very confused..."
……
Please pay attention to the above dialogue, the method used by M to calculate the salary increase is a function:
y = kx + b
Among them, k = 1000, b = 10000, y = 50000, and the functional formula becomes:
5000 = 1000x + 10000
In this way, x is indeed equal to 40!
However, this calculation method is obviously wrong. First of all, he ignores the compound interest effect !
Simply put, each time you raise your salary, it is adjusted proportionally based on the existing salary, rather than adding a constant each time. So, the correct calculation method should be:
50000 = 10000 * 1.1^n
n = log(5)/log(1.1) ≈ 16.89
That is to say, maintaining an annual growth rate of 10%, as long as 17 years, your monthly salary can be changed from 10,000 to 50,000!
After accounting for compounding effects, the results are huge: 40 years becomes 17 years.
But many people feel hopeless and frustrated at the thought of waiting 17 years before they can afford a home.
Don't be discouraged, because this simple compound interest calculation is still a linear way of thinking!
Some friends may disagree with my statement, because the compound interest method is obviously an exponential curve:
Don't worry, the reason why our views are inconsistent is because our understanding of the term linear thinking is inconsistent.
The so-called linear thinking is a linear, one-way, one-dimensional, lack of change way of thinking, thinking along the trajectory of a certain linear or linear type (either a straight line or a curve) to seek solutions to problems A way of thinking about a program.
Whether you think along a straight line or along a curve, it is all under a certain premise, only considering one direction, lack of change, it is all rail-like linear thinking - static that is limited to a given track and a given direction thinking .
In our real world, there is actually no fixed track to follow!
derail the mind
Let's take a look at the story of one of my former company's friends, L.
At the beginning of 2015, L was in my team (Xi'an), with one year's work experience, and the salary was close to 7000.
At the end of 2015, the team disbanded and L started looking for a job. I recommended him to an e-commerce company in Beijing, where his monthly salary has more than doubled to nearly 15,000.
In November 2017, L returned to Xi'an from Beijing. We chatted together and learned that he had entered a company to develop big data, with an annual salary of more than 300,000. At this time, he had only been working for less than 4 years!
We saw that L changed his salary by changing the city at the end of 2015, and changed his salary again at the end of 2016 by changing the direction of his work. Only these two times, his salary has nearly quadrupled!
And if calculated according to M's railroad thinking method, in 3 years, L's monthly salary should only be 9,100 yuan!
What happened to L is a typical "derailment" incident. This kind of "derailment" is the result of divergent thinking, that is, when we think about how to achieve a goal, we must jump out of the familiar thinking track, make premise assumptions from scratch, and cover multiple possibilities to achieve the goal .
Taking increasing income as an example, in addition to the general annual increase understood by M, there are the following possibilities:
- job hopping
- part-time
- financial management
- Passive income such as house rent
- Passive income from sales of products with zero marginal cost
- Information for sale
- Resource replacement
- ……
Many times we don’t see more possibilities because we habitually use railroad thinking to deduce the future from the status quo, and unconsciously filter out the possibilities that do not conform to our reasoning logic.
You know, where a railroad track will stretch, you can imagine with your eyes closed wow! And our use of railroad thinking to deduce the things around us will inevitably limit our imagination.
One day a friend told me that he would make 10 million this year!
When I thought about it, he is doing development now, and his annual salary is less than 400,000 yuan. It is absolutely impossible to earn 10 million yuan this year, so I think he is joking.
But now that I think about it, the reason why I don't believe it is not because his idea is unrealistic, but because his statement goes against my regular thinking! I don't see that possibility, so I think he's joking. This is actually how stupid I am!
Why do you say this, because this kind of sudden change, which is impossible in our minds, can indeed happen to some people!
Xue Zhaofeng, a well-known economist and professor at the National School of Development of Peking University, launched the column "Xue Zhaofeng's Economics at Peking University" on the "Get" app on February 20, 2017.
This column extracts the essence of the two courses "Principles of Economics" and "Law and Economics" taught by Xue Zhaofeng at Peking University, using more than 260 audio + graphic online courses, dedicated to letting the general public discover the fun of economics , and build an authentic economic way of thinking.
Within a week of its launch, it attracted more than 40,000 "get" users to pay for subscriptions. By the morning of November 10, 2017, the total number of subscribers to the column "Xue Zhaofeng's Economics at Peking University" exceeded 200,000.
Let's do a simple calculation. The column "Xue Zhaofeng's Economics at Peking University" is priced at 199 yuan, 200,000 people subscribe, and the sales volume is 39.8 million!
With this column, Professor Xue Zhaofeng's personal annual income has jumped from hundreds of thousands to tens of millions!
Before this happened, if Professor Xue told his colleagues that he was going to make 40 million in 2017, his colleagues would have laughed in their hearts - how is that possible, your income is less than 1 million now? !
However, that's how it happened.
Therefore, when we think that something is impossible, what we call impossible is often "this thing is impossible under certain conditions". If we can find this implicit assumption, it may overturn our reasoning, Change "impossible" to "possible" .
make the impossible possible
So, how can I change my conclusion from impossible to possible?
It's easy to say. When you encounter something you don't understand, don't rush to say it's impossible. Stop and think about it first:
- How did I come to the conclusion that it is impossible?
- What presuppositions did I make? What happens when you take them off?
- In addition to the way I think about it, is there any other way to achieve it?
- How would someone who is 5 times better than me do this?
- If it were someone who didn't understand the field at all, how would he accomplish this?
- If a McKinsey consultant were to analyze the matter, what would he do?
When you can introduce this kind of thinking into your daily life, practice it deliberately, and over time, you will be able to break your railroad thinking habit and see more possibilities.
How do you bring this kind of thinking practice into your life?
Three steps: pause, think, confirm .
For example, when you browse the website and see a news article with the headline "Mother selling pancakes earns 100,000 a month", you will definitely want to click on it.
Don't do it, stop, stop, stop yourself. ( pause )
Then, pondering in your own mind, how to sell pancakes to make a monthly income of 100,000, and sort out the methods you can think of. ( thinking )
Next, click on the news to see if there is any news about what the aunt has done to make her a monthly income of 100,000. Compare it with your thoughts, maybe you will see different possibilities. ( verified )
Not just news, but other things as well.
For example, if you see a street-facing store downstairs in the community, the one around the corner, the store changes every three months, and if no one has been in business for more than half a year, you can stop, think about why, and discuss with others, or go to this store Look inside and ask questions.
Slowly, when you get used to this way of thinking, you can formulate hypotheses from scratch, look at various problems with research ideas, and verify each other with people from various backgrounds, you can form a divergent style. The habit of thinking, you can see more possibilities when encountering a problem.
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