However, how many families have mixed feelings when the college entrance examination is released every year? Students with good grades must have worked hard at ordinary times, but students who failed in the college entrance examination do not mean that they don't work hard at ordinary times. It is more a matter of probability.
This question of probability coincides with the probabilistic world view put forward by Professor Liu Xuefeng in his book Familiarity: Mathematical Thinking in Life. He said: "We can't guarantee the final result of many things, but the probability of this result is something we can change through our efforts."
Author Liu Xuefeng, associate professor and doctoral supervisor of Beihang University. In the book "Know the Root and Know the Bottom", he uses mathematical thinking to help you solve the puzzles in life. Encourage you to dare to predict your future, but also be good at capturing every little luck in life; On the premise of accepting imperfections, gradually improve yourself, iterate over yourself, and finally find the optimal solution of life.
First, accept temporary imperfections, and completion is far more important than perfection.
Regarding the results of the college entrance examination, it is undeniable that the probability that serious students will get good grades in the exam will definitely be much higher than those who are not serious.
The failure of the college entrance examination can be explained by the probabilistic world outlook put forward by Professor Liu Xuefeng, which is actually similar to the well-known truth that "Man proposes, God disposes".
Liu Jiaoshou said: "For a student who takes the college entrance examination, even if he usually works hard and gets good results in the mock exam, no one can guarantee that he will be admitted to a good university before the results of the college entrance examination are announced. Because some important factors, such as the difficulty of the examination questions and his improvisation, are beyond his control. "
Although failing in the college entrance examination has become an imperfection in your life, we must admit the fact that nothing in the world is perfect.
Many people think that the college entrance examination is a turning point in life. That's right! But it is not the end of life. On the contrary, the college entrance examination is only a new starting point of life.
Faced with the imperfection of the failure in the college entrance examination, we can choose to accept it completely, because it is only temporary. Life is long, and there are always many stops for you to stop and think.
If you fail the list because of abnormal performance, I suggest you analyze the reasons for this failure, and at the same time, please thank yourself for your efforts all the time, because you have completed the first important thing in your life. It's a pity, but completion is far more important than perfection.
At this time, you can choose to repeat, sum up the reasons for failure and continue to work hard to prepare for the next year. Life is different from study and further education. We can also choose employment or even start a business.
Ma Yun, the founder of Alibaba Group, was also a student who failed the college entrance examination for three consecutive times before he founded the business empire. Even the worst math score is only 1. He said, "I don't believe in first-class talents, I only believe in first-class efforts." Because of his continuous efforts, his repeated failures have not affected him to become a world-famous entrepreneur at all.
As Professor Liu Xuefeng said, we should "accept the reality calmly and try to change the probability." If you wait until the result is not satisfactory, then we will accept the temporary imperfection, complete what you should do and change what you should change. After all, the perfect result can only be achieved after completion.
When you are really working hard, let's not worry too much, just wait for the result, what should come will always be on the way.
Second, I dare to predict the future, and I am also good at capturing the little fortunate things in life.
Gold is not enough, no one is perfect. Everyone is imperfect and has advantages and disadvantages. Those successful people don't mean that they have three heads and six arms or how perfect they are, but that they tend to make bold predictions.
In the story of Ceres' discovery, why did Gauss, who was only 24 years old, become famous in the field of European astronomy? That's because he dared to predict the position of ceres. In addition to using the least square estimation method he invented to eliminate the observation error when calculating the trajectory of celestial bodies, he also invented many methods to estimate the accuracy of planetary orbits.
Finally, a year after Ceres disappeared from people's sight, Ceres was found again in the position predicted by astronomer von Zack according to Gauss. Prior to this, several famous mathematicians failed to find a method to determine the orbit of the planet from a series of short-term observation data.
The main reason why Gauss can conquer European astronomy at once is that he successfully predicted the position of Ceres before it was observed again. If Gauss explains why Ceres appeared in this position after being observed again, his explanation will be meaningless.
In this story, Professor Liu Xuefeng thinks that "prediction" is much more important and difficult than "explanation". In other words, daring to "predict" means daring to act, while "explaining" is an afterthought. Obviously, it is easier for you to succeed by action than by hindsight.
In fact, "prophecy" is particularly important not only in the story of Ceres, but also in our lives. If you dare to paint your own blueprint for the future, you may have a bright future.
Maybe you will say that having a bright future is a kind of happiness, and this kind of happiness always belongs to people with high academic qualifications and a high starting point, or to lucky people.
If you have this idea, you are wrong. Why? Professor Liu Xuefeng believes that the so-called happiness can actually be that when I miss my mother, her phone calls; You can be lucky to walk on the roadside only to find that the trees on the roadside have sprouted.
In the book Know Well, Professor Liu Xuefeng used the mathematical concept of convolution to analyze whether occasional great happiness or frequent small happiness can make us happier.
The purpose of convolution is to describe the response of the system to external input. System is one of the concepts in control theory. Simply put, the system receives an input signal and then generates an output signal.
The system outputs external inputs, and life is everywhere, including what we call happiness.
The concept of convolution can help us make correct choices in our daily life. If we feel, experience, capture and even create every little happiness in life with our heart, then the happiness brought by frequent little happiness will definitely bring more happiness than the occasional big happiness.
For example, if you work in the center of a big city, you will feel happier if you buy a small house in the city than a big house in the suburbs. Because I work in the city, I don't have to worry about the long commute time every day, not to mention the inconvenience of life.
Third, grow up and iterate in imperfection to find the optimal solution of life.
Why do you suggest going out more when you are young? In his book Know Well, Liu Xuefeng used the well-known simulated annealing algorithm in the computer field to explain it.
Simulated annealing algorithm is a numerical method to solve the function optimization problem, and it is necessary to find the extreme value of the function. Taking the extreme value of function y=-x2+2x as an example, Professor Liu Xuefeng listed several algorithms, including analytical solution, gradient method, mountain climbing method and so on.
Among them, the analytical solution is undoubtedly the best, but it is not so easy to find it. So there are two numerical solutions: gradient method and mountain climbing method.
For young people with ideals who have just entered the society, Professor Liu Xuefeng suggested that we can first use the core idea of gradient method to "find the right direction and strive for perfection" in our work. With the direction, as long as we strive for perfection, we can get closer to the optimal solution.
Besides the gradient method, Professor Liu Xuefeng also suggested that we can use the mountain climbing method. As the name implies, climbing a mountain is just like climbing a mountain at ordinary times. Every time we set out, we will stand higher than before, which means that you need to iterate in your work and get better every time.
However, Professor Liu Xuefeng also pointed out the shortcomings of the mountain climbing method, that is, when you climb to the highest point of a mountain, you may think that you have climbed to the highest point because of the great influence of the fog in the mountain, but there is actually another highest peak. At this time, you may start from a nearby low point, and you may reach a higher peak.
In fact, there are many such examples in life. For example, when you change jobs, you must expect the salary of the new job to be higher than before. Because you are a newcomer and because of the company's assessment system, it is impossible to give you the highest salary in the previous company from the beginning. If you think the company has a good prospect and is more suitable for you, then you can accept the result that the salary is temporarily lower than before, and then make continuous efforts to achieve your expected salary.
These algorithms of mountain climbing method will fall into the disadvantage that local maximum can't jump out. Just like our life, when you constantly seek the highest point of interests, you will inevitably be blinded by temporary interests and even unable to accept short-term setbacks. But in fact, it is possible to get a better future by accepting temporary imperfections.
When we realized this, the problem came again. How should we accept imperfection? Professor Liu Xuefeng also gives an algorithm that introduces randomness, that is, accepting temporary imperfections with a certain probability.
Finally, the professor uses simulated annealing algorithm to get the optimal solution. Simulated annealing algorithm tells us that there is a great probability of imperfection at first, but with the increase of time, this probability will gradually decrease and reach a balance.
All algorithms are closely related to our lives. Professor Liu Xuefeng said, "Life is actually a process of finding the optimal solution. No one is perfect at first, but we can constantly strive to improve ourselves, and the ultimate goal is to achieve the best position we can achieve. "
These algorithms tell us that when you are young, you can randomly start more businesses, constantly try various occupations, and constantly grow and iterate in imperfections, so as to find a job that you really like and can stimulate your potential, so that your potential can be infinitely enlarged. However, as you get older, you need to control randomness, dig deep into your best field, and don't change careers easily.
Write it at the end
Professor Liu Xuefeng's Know the Root and Know the Bottom won the list of good books in China in May 2022. It is not only a popular science book focusing on the field of computer algorithms, but also a book that teaches you how to use algorithms to see the world clearly and let you know fairly well. It is also a book that allows you to gain wisdom in the algorithm, constantly iterate yourself and find the optimal solution in life.
Once upon a time, I thought that mathematics was mathematics and life was life. They are completely different. After reading this book, I was shocked that "life is full of mathematics".
Although the probabilistic world outlook tells us that we can't guarantee the final result of many things, the probability of this result can be changed through our efforts. Therefore, I strongly suggest that you calm down and chew slowly. I wish you wisdom and the best solution in life.