Charlie Munger repeatedly mentioned multi-disciplinary thinking in interviews and books. Mathematics is the most frequently mentioned subject thinking. From elementary school to junior high school, high school, and finally to university, I seem to have learned a lot of math knowledge, but I always don’t know how to use it in work and life. Today, let’s take a look at how some math knowledge we have learned is used in work and life, especially some math knowledge learned in high school and college. Is it really as we think and difficult to use in our lives?
From childhood to adulthood, we have learned a lot of mathematical thinking. We started to learn the addition, subtraction, multiplication and division of numbers in elementary school, and then to the university's advanced mathematics , calculus and other knowledge. It seems that what we often use in life is addition, subtraction, multiplication and division, or more extreme points, and the highest frequency is addition, subtraction, is the truth? Is it because we have a wrong understanding of mathematics? In fact, a lot of mathematical thinking can help us solve problems in our work and life.
First, let’s talk about what the hell is thinking? Some people may say that thinking is a reaction of the brain, thinking is a high-level cognitive activity of human beings, etc. These statements are not wrong, but I prefer to compare thinking to algorithms, which is a set of thinking steps . How to understand the steps to think? For example, Lei Feng’s spirit of helping others is the first step to encounter something, and the second step is to judge whether he needs help? The third step is to make decisions or not. We see many people with strong thinking, and in essence, their algorithms are relatively powerful. Mastering thinking means mastering a specific set of thinking steps .
There are many thinking in mathematics, which we often use, but we rarely realize that these are the knowledge learned in mathematics before, such as decomposition, classification, collection, classification, sequence, variable sequence, limit and transformation. Among them, decomposition, classification, classification and transformation can help us quickly find answers, allowing us to go from not solving to being able to solve, while sets, sequences, variable sequences (paths) and limits can help us quickly make decisions and let us know how to choose.
decomposition
These names seem to have an impression, but it seems difficult to combine with specific scenes in work and life. Let’s first look at how decomposition is applied in work and life. When we were in elementary school, we were exposed to decomposition, such as the sum of which two numbers can 7 be divided into? In junior high school, we will be exposed to factorization , such as X²-9X+18=(X-3)*(X-6). And the differential in college are all decompositions, but the form has changed. To put it bluntly, it helps us simplify complex problems.
It seems that these are still irrelevant to life and work. Let’s take a look at the scene of car selling in 4S stores. If the salesperson asks: “What kind of car do you want to buy?” This is a complicated question for car buyers, because not everyone who sees cars is so clear about what kind of car they like. Often, they like Car A after seeing Car A and Car B after seeing Car B. At this time, another thoughtful salesperson would ask: "What is your budget? SUV or a sedan? What color do you like? How many seats do you want?" This is what helps users break it down.
Have you found it amazing? It is actually used in work? Let’s see how to decompose it if you write 10W+ copy? An article can usually be divided into a cycle of (reading, forwarding). A person can read an article into a title, reading the first paragraph, reading the second paragraph... Reading the last paragraph, reading the comments (I often read the comments myself), while a person forwarding an article requires thinking about what reasons the article provides to readers to forward it to their circle of friends? Did he help him create an image and show his style? Or did he make a wave of presence in his circle of friends? The above are a breakdown of how to write a 10W+ copywriting.
Category
Next, let’s take a look at some usages of the classification. Qiming Business School mentioned a case, a milk tea snack shop located near the subway entrance, which has entered a takeaway platform, and the online and offline turnover accounts for about 50% each. Due to the commissions and discount activities of takeaway platforms, the profit margin of online turnover is more than half lower than that of offline. What kind of operational goals should be set at this time? From the above description, it can be seen that online and offline constitute two different categories. The online profit margin is low and offline profit margin is high. In this case, new categories can be added, such as adding repurchase users and non-repurchase users, high-a-terminal-price users and low-a-terminal-price users, high-frequency consumption users and low-frequency consumption users.
If you don’t know which category is valid, you can check it one by one. For example, the added repurchase users and non-repurchase users. Combined with the online and offline dimensions, you can be divided into online non-repurchase users, online repurchase users, offline non-repurchase users and offline repurchase users. For online non-re-purchase users, why not repurchase? Are the products and services provided not good enough? Assuming it is this problem, operations need to solve this problem. For online repurchase users, when they place an order online for the first time, the profit they give up can be regarded as a user who bought the advertising fee, which is very cost-effective. For such users, you can try to guide offline purchases. After all, they have been buying on the platform, and merchants need to continue to give the platform money. The users and the platform's money need to be paid by themselves, which is not cost-effective.
does it feel interesting? Let’s take a look at the classification.
classification
classification is usually to help us find solutions. A "known category" allows us to quickly refer to the solutions of experts in unfamiliar fields. For example, in WeChat mini programs, some people think that text pops up too quickly, and some people think it is too slow to affect reading. This problem can be classified as a text reading experience problem. For such questions, you can find reference answers on "novel reader".
Novel readers are basically a whole page. The presentation of a whole page does not “pop up a piece of text” to allow the eyes to adapt to the ever-changing screen problems.
decomposition and classification are a pair of tools to solve problems. When we encounter problems, we first decompose them one by one, and then classify each specific problem to find the corresponding solution.
collection
For sets, what we usually think of is that the real number satisfying X²+5=0 does not exist, so this is an empty set . The set of odd numbers and the set of even numbers do not intersect. Combining the classification mentioned above, each category can be regarded as a collection, and a collection can be regarded as an algorithm for classification. In work, a collection is suitable to help us discover directions, which directions can be tried, which directions should be stopped, and using the collection can help us save a lot of time. For example, a company that makes teaching equipment, the target user is a school teacher, but the teacher does not have a strong desire to use the product to teach, so he does not pay much attention to the functions and characteristics of the product. How to promote products to achieve good sales in this situation?
We can divide users into a collection of users who need products and a collection of users who do not need products. To make the product good sales, we must open up more doctor markets, that is, we need to develop in the collection of users who do not need products. Users who do not need products, complement is users who need products. Users who purchase products in the collection of products are a subset of them. One set and complement tandem have no intersection, that is, there is no intersection between the collection of users who need products and the collection of users who do not need products, and complement and subset have no intersection, so this product cannot find a way to obtain good sales. Through such analysis, we can quickly stop losses in the wrong direction.
sequence
Next, we look at the sequence. We are very familiar with sequences such as 12345. Sequences can play a deduction tool in work and life. For example, in the past few years, there were many P2P companies in Shenzhen, which gave investors more than ten percent of their returns. Many formal third-party financial management companies cannot do it. How should we compete at this time?
Using sequence thinking, we can deduce it. When giving double-digit returns, it attracts more investors, and the returns decline, and many investors withdraw their investments and become fewer investors, and the market share gradually declines. In other words, if the deduction is based on this return, the other party's market share will continue to decline, which is an opportunity for formal third-party financial companies. Sequence is one of the manifestations of deduction. It is a deduction in a single dimension of time. With time as the axis, things are deduced item by item in the order of occurrence, and to a certain extent, the future can be foreseeable. Looking back at the present from the future can help us make a decision and see things that cannot be seen clearly in the present.
Extreme
In terms of geometry, the limit is a very desperate curve. No matter how much you invest, you can only get close forever, but you cannot reach the final point. In real life, term is a very valuable thinking, which can tell us where you can go along the current road at the farthest. For example, the fitness app takes exercise and let users move as the medium and long-term goal. The monitoring indicators can be course click rate, course learning time, etc. Through AI's machine algorithms, it can be distributed well, reach users, and improve course click-through rates. Should we tilt more resources to allow AI to intelligently sort and display courses and reduce work related to operational activities? The core of the problem of
is to manually use activities to increase the limit of course click-through rate? After all, using AI also requires investment in relevant personnel for development, which also requires a certain cost. At this time, you need to compare and try to find the limit of manual processing to find a more reasonable solution.
Conversion
Finally, let’s talk about the transformation thinking in mathematics, such as seven color boards , different shapes, if you want to calculate the area, it will be very difficult, but if you put it into a square or rectangle, you can solve it immediately. Among all transformation methods, expressing the problem through graphical means can instantly simplify it. For example, a person walks from the foot of the mountain to the top of the mountain on the first day, and from the top of the mountain to the foot of the mountain the next day, is there a moment when the person stays in the same place? You can find the answer quickly through the picture below.
Picture from Qiming Business School
This case seems to be relatively simple. Let’s take a look at another case in Qiming Business School. In a real estate development, there is a situation in the development of a certain real estate property that develops the collective retention land of villagers. Such land cannot transfer property rights, but can only transfer the right of use. Therefore, the developer cannot obtain a development loan from the bank, resulting in high initial investment capital cost, and the built property cannot sell property rights, but can only rent and use rights. cash flow land recycling cycle is relatively long. How to find a better development model and business model to change the status quo in response to this situation?
picture from Qiming Business School
This requires the transformation of this problem. The above problems can be transformed into two problems: how to reduce investment and how to obtain income in advance. It seems that it is still far from finding a solution, so continue to convert. For a normal developer, realizing early income is to sell the property rights to the buyer at one time, thereby obtaining large amounts of funds.
Picture from Qiming Business School
Since the company cannot provide the product, it cannot exchange it for one-time cash flow. At this time, you can use the company's right to exchange it. Naturally, the right to use cannot be sold to previous buyers. At this time, for buyers, you can think about replacing the funds of the charitable fund by taking the rights to collect rent, and using rent to create profits for the fund. Through several transformations of the problem, we found a solution.
Image from Qiming Business School
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