This book is called bottom logic: looking at the cards of the world. Author Liu Run, founder of Runmi Consulting, founder of China Private Business School "Liu Run 5-minute Business School" and former director of strategic cooperation of Microsoft. Aside from so many shiny titles, I think the most important thing is that he is an expert in Internet transformation, has published many books, and is a cross-border big coffee.
The author studied mathematics in college, and never worked in this major in the later period. But to manage, start a company and study various company development and workplace strategies. But he stressed that the process of learning mathematics laid a good thinking foundation for his personal growth.
Therefore, for most people, learning mathematics is not to understand mathematical problems, nor to become mathematicians, but to cultivate mathematical thinking. With mathematical thinking, we can better understand logical thinking and master this ability.
Of course, there are many ways and modes of thinking mentioned in the book. Here, I just sort out my mathematical thinking, and the most important purpose is to deepen my understanding.
Let's look at five very important mathematical ideas.
This mathematical thinking comes from the probability theory mentioned earlier in this book, which is called finding certainty from uncertainty.
If the success rate of doing something is 20%, does it mean that you will succeed if you repeat it five times? This book classifies probabilities, but this is not the case. If the 95% probability is defined as success, then this thing with a 20% probability of success needs to be repeated 14 times to succeed!
The calculation process is as follows: the probability of a failure is 1-20% = 80% = 0.8.
The success probability of repeating 14 times can reach 95%. If you want to achieve 99% success probability, you need to repeat 2 1 time. This led me to the source of the theory of "2 1". Many people tell us that repeating 2 1 time can form an unconscious habit. Or it takes at least 2 1 day to develop a conscious behavior.
In real life, we often say that "the right thing should be done repeatedly", which is also a popular expression of probability theory.
The so-called right thing refers to something that can be successful with high probability, and what is the so-called repetition? In fact, it refers to the quantitative repetition behavior of at least 14 to 2 1 time (or even more).
In business, the success rate of 20% is not small. After all, if you repeat 14 times, the probability of success will reach 95%. Knowing this, we can understand that the probability of a successful venture is almost impossible. Knowing this, while trying to avoid more risks, we can also face entrepreneurship with a better attitude.
Someone asked, between generalists and professionals, which is the most likely to succeed? This also involves the question of probability. Focus on starting a business. If you are distracted to do too many things, the original 20% success rate may be only 1%, and the possibility of success is even smaller.
This theory originated from calculus. It is too difficult for me to understand calculus. Here is a relatively simple example to understand this difficult concept.
For example, if a car is stationary and we add a handful of oil, it will move and produce acceleration, but it has not yet produced speed. When the acceleration accumulates for a period of time (that is, we step on the gas pedal many times to refuel), it will produce a relatively balanced speed. When the velocity accumulates for a period of time, the displacement will not happen instantly. Only when the velocity is accumulated for a period of time will the displacement occur.
So in short, what we see may be a car moving from point A to point B on the macro level, but on the micro level, the whole process starts to accumulate from acceleration-acceleration accumulation becomes speed, and speed accumulation becomes displacement, which is integral.
Note: the displacement of an object is due to the accumulation of velocity over a period of time; The reason why an object has speed is because the acceleration is accumulated over a period of time. So there is a very important concept, which is time.
What is the use of understanding calculus in our daily life? The most important thing is to look at the problem from static to dynamic. That is, the principle that quantitative change produces qualitative change.
Applying this kind of thinking to any region will make people shine at the moment and produce such a feeling. For example, learning and growth can never be achieved overnight. With this kind of thinking as the basis, we can truly understand that Rome was not built in a day (of course, so is the Great Wall of our country). Then you can see such a spiral channel: I studied hard tonight, but an evening's hard work will not directly turn into my ability. In other words, efforts must be accumulated over a period of time before they can become real abilities. With the ability, you won't make achievements immediately, but you have to accumulate for a period of time to stand out in an exam and have your own achievements. With the achievements, the next step will be appreciated by teachers and classmates, or by leaders. This process is accumulated bit by bit, which is the effect of integration. Of course, this is only a simple explanation from the perspective of probability, but it is also very clear.
This mathematical thinking comes from geometry. In geometry, once different axioms are formulated, they will get completely different knowledge systems, which is axiomatic systematic thinking.
There is an example in the book. There is a branch of geometry called Euclidean geometry, also called Euclidean geometry. There are five basic axioms:
(1) Any two points can be connected by a straight line;
(2) Any line segment can be infinitely extended into a straight line;
(3) A given arbitrary line segment can take one of its endpoints as the center, and the line segment can make a circle as the radius;
(4) All right angles are equal to each other;
(5) If two straight lines intersect with the third straight line, and the sum of internal angles on the same side is less than the sum of two right angles, then the two straight lines must intersect at that side.
This example looks tall and difficult to understand, but it turns out to be just an introduction. The key points are here: first, axioms are self-evident and recognized propositions; Second, if the axiomatic system is a big tree, then axiom is the root of this big tree.
By changing this thinking with the development scale of a company, we can get a more intuitive model: the company's vision, mission and values are equivalent to the company's axioms, which will determine the development direction of various behaviors of the company, such as rules and regulations, workflow and decision-making behavior. , which is a theorem developed from these axioms, constitutes the axiom system of the company.
Note: there is no right or wrong axiom and there is no need to prove it. It is a choice, a knowledge and a benchmark principle.
This kind of thinking comes from algebra, from counting points one by one to understanding the complexity of life. From this point of view, the author's cognition connects boring numbers with artistic complex life phenomena, which deserves our deep thinking.
First, let's recall the process of learning algebra. At first, we learned natural numbers, including zero-sum integers, and then fractions. Fractions make each integer no longer split in isolation, but continuous. Just like what you see at the beginning of life. Probably only right or wrong. It is only slowly discovered that everything is more complicated than imagined, with cause and effect and gray areas.
After rational number, I learned irrational number, which is an infinite acyclic decimal and can't find any laws. This makes us realize that some things in this world are complex and irregular, and we can't try to define them in a simple and rude way. We should admit its objective existence and the complexity of the world.
Therefore, the author says that in the process of in-depth study of various numbers, he is actually understanding the complexity of the world step by step. I didn't expect boring numbers to look so good.
Looking forward, in addition to size, numbers also have a very important attribute, that is, direction. In mathematics, a directed number is called a vector. What does this inspire our life?
This refers to centripetal force. Three people work in the company, and their abilities are all good. When they cooperate, if their abilities can be combined in one direction, then this is the best result. If everyone has their own views, working in different directions according to their own abilities will only lead to mutual containment. For the development of the company, it is better to leave this matter to one of them.
Remember "Chinese Partner"? A typical story of three people starting a business together. They stumbled all the way, had * * * knowledge and differences, but again and again they formed a joint force because of a common vision.
This mathematical thinking stems from the game theory mentioned earlier in this book.
We have to make big and small decisions every day, such as what to eat for breakfast and what to do for dinner. If this decision is only related to yourself and does not involve others, it will naturally have little impact.
Once it involves other people's decision-making logic, it has a certain game nature, which is game theory.
For example, which friend do you invite to have afternoon tea with? It can be used to discuss an important decision.
Also, playing Go with friends, what I get is what you lose. This is a typical zero-sum game in game theory. In this game, we should always stay awake and see that what we want is the global optimal solution, not the local optimal solution.
In real life, we are likely to face such problems when running a company. In order to achieve the best result, we have to sacrifice some local interests or compromise on some key steps.
In addition to zero-sum game, there is also a non-zero-sum game, which pays attention to the winning technology. However, it should be noted that the premise of winning is to build trust, which is particularly difficult.
A company represents a system, and the inside of the system is complex. It is difficult to form a joint force, and it is even more difficult to build trust between two companies with different visions and values.
Far away, let's talk about the plot of office games involved in many TV dramas. Everyone has his own little black account and abacus. They always want to maximize their own interests, and sometimes even step on the low to get the high. Although the first half of my life is mainly emotional, it involves all aspects of fighting in the office, which makes people feel that the word "trust" is too difficult to write.
In this regard, the author's suggestions are: first, find a partner who can build trust; Second, take the initiative to release trustworthy signals.
With regard to the understanding and application of mathematical thinking, learning here is a small stage. Here, I also take this opportunity to convey an idea to myself and people who don't like mathematics: learning mathematics focuses on training mathematical thinking, in order to have a regular way of thinking.
Conform to the law, just stick to the viewpoint put forward in this book: understand the underlying logic and see the cards of this world clearly.
Therefore, we can get real freedom.