Today, I read two articles by Mr. Lin Xinhao, combining life and programming to make a summary.
Rational & Sensual && Abstract & Discrete
1. How did ancient ape-men count?
At the beginning, he gestured to estimate the number of objects, which represented perceptual thinking. But this count is imprecise and cannot be quantified. At this time, it is necessary to use rational thinking to solve the problem of accuracy, so the concept of "discrete" can be accurate to "one by one", and this counting method represents rational thinking.
As we all know, the computer uses binary, and the binary has only two values of 0 and 1. It can be said that computer hardware counting methods are also discrete, such as full adders. Therefore, the courses of computer-related majors include a special mathematics course-discrete mathematics.
Next, think further, what is the basis for counting by discretization? i.e. what consensus do we have to reach to count like this?
Look at the math problem like this: "Xiao Ming originally had a one-dollar coin, and Xiao Ming's mother gave him another one-dollar coin. How many dollars does Xiao Ming have in total at this time?"
Ha ha laugh, in seconds, the answer is two dollars. The calculation process in our brain is roughly "1 + 1 = 2". What is the precondition for "1 + 1 = 2"? The two coins are "the same" in your mind, that is, you don't care about the properties of the two coins, such as luster, wear level, etc., if you think of the coin as an object, you only care about the "quantity" property . In fact, this process can be understood as "abstract". Only caring about what you want to care about is "consensus".
In computer science, abstraction is everywhere. Why abstract? Abstraction is to shield complex details and provide convenience for users. Users only need to care about what they need to care about. For example, the Hardware Abstraction Layer (HAL) proposed by Microsoft, which belongs to the interface layer between the operating system kernel and the hardware. interface layer? Is it familiar? In the object-oriented design idea, we are all interface-oriented programming, which is also conducive to the separation of front and back ends.
Abstractions and interfaces often come in pairs. So what are the benefits of abstraction? Decoupling.
2. Mathematical thinking in "equal sign ="
Before equating two things, we did a "comparison". The concept of comparison is the basis of rational thinking. The equal sign is the result of the comparison, and the process of this judgment is abstract.
Once you equate two things, you indirectly indicate the basis of your judgment, that is, what you value.
不仅仅是数学，生活中我们也经常“划等号”。父母认为“好孩子”等价于“好好学习”；领导认为“好员工”等价于“能解决实际问题”。理解了等号背后更深层次的含义，有助于我们理解别人“划等号”时隐藏的信息。
比如有些年纪稍大一点的长辈就很难理解年轻人花好几千块钱买一个手机，因为在他们看来手机只是通话工具而已，而年轻人更看重的是手机的智能性等属性。双方对手机“划等号”的结果不一致，导致了矛盾的产生。
因此，当我们和别人交流的时候，可以关注那些“划等号”的信息，以便抓住对方的关注点，这样有利于提高沟通效率，以免出现“对牛弹琴”。