"One by one gets two, one two gets three, addition, in the mathematical system, is the result. ”

"But math is never for math. There is not much point in talking about mathematics in isolation from concrete things. ”

There is a record in Wang Yangming's "Biography". Wang Yangming traveled with his friends, and one of them pointed to the flowers and trees in the mountains and said: "Lao Wang, what you said, there is nothing outside the heart in the world. But what does it have to do with this flower and plant, which blooms and falls in the mountains, to my heart?'"

"Wang Yangming's answer is?" Mr. Chen paused.

Xu Guangling answered: "When you don't look at this flower, this flower and your heart will die together." When you look at this flower, the color of this flower is immediately understood. ”

Mr. Chen smiled and nodded, "This is from the standpoint of people, to look at all things in the world, emphasizing the uniqueness and centrality of people, people are the main and all things are guests, and guests are as they are the masters." ”

"The flowers and plants in the mountains bloom and fall spontaneously, 'the plants and trees have their own hearts, why ask the beauty to fold', which is from the standpoint of the grass and trees, and also from the standpoint of all things in the world. ”

"But we are human beings, and we cannot talk about all things without people. What is good, what is bad, what is useful and what is not useful, all of these all require a preset premise, that is, the position of the person. ”

"Without a position, there is no good or bad, no useful and useless. ”

"It is also meaningless to go from us to me, to leave 'me' and talk about all things in the world. ”

"Just like the old man, if the old man is braided now, then the next moment, tomorrow, and later, I will say that what good trees you plant, what delicious food you make, and how good things you are, it has nothing to do with the old man. ”

"Radiating outward, China, the whole world, the whole earth, the entire solar system, the whole universe...... Everything has nothing to do with the old man anymore. ”

"So the world is big and it's small. ”

"The big is them, they and theirs, all things in the world and other human beings, and the small is the old man's own, and at the moment, the old man's world is only this mountain, and the two of you. ”

"Trees need roots, and people have their roots. The tree is ten thousand feet high, do not leave its roots, and people are glorious, do not forget its roots. No matter how much flowers bloom and the fire cooks oil, if you cut off the roots, you will soon step towards apoptosis.

"Only by understanding the fundamentals can we have stable survival and further development. ”

"In the mathematical system, this is a coordinate system, the establishment of the coordinate origin. ”

Xu Guangling nodded solemnly.

"It doesn't make sense to leave me and talk about us, about humanity, about the whole world. Many sentient beings in this world do not understand the difference between 'me' and 'us', and often regard 'our' as 'mine', and fall into a kind of false satisfaction and fancy eyes. ”

"In the modern society, knowledge is exploding, the economy is developed, and science is prosperous. ”

"How trillion is the GDP. ”

"A new generation of satellites has risen into the sky again. ”

"The telescope's detection has been many light years beyond the Earth. ”

"These, from the standpoint of 'me', are all flowers and embellishments. With mathematical thinking, we can strip away this background, fly back from the far point of the world's coordinate system, return to the origin from the far point, return to the original point from the colorful back, know the white, but keep the black, in order to purify the body and mind, stick to and develop the fundamentals. ”

Xu Guangling nodded again.

This is exactly what he is doing at the moment. The achievement of knowledge requires him to return to simplicity, to abandon white and black, and to abandon all kinds of things in the world to come here and be a nameless hermit in the nameless mountain.

"It is vain to talk about all things without me, and to talk about mathematics without all things. ”

"The fundamental meaning of mathematics is to measure and construct other systems as quantitatives and variables. ”

"One, two, three, four, is the foundation, addition, subtraction, multiplication and division, is change. Quantification and variables are the two major elements of mathematics. To express it in our culture, it is yin and yang. Yin is quantitative and unchanging, while yang is variable and is in constant flux. ”

"Constant is not really constant, it's gradual. ”

"Change is not really a change, but changes according to certain quantifiable rules, and on the basis of mastering the rules, it can be regarded as unchanged. ”

"It's like the rotation of several great rows of the solar system. ”

"They're in flux, but from another point of view, we can see them as constant, and we can quantify their position at any time, even if we don't need to observe it. ”

Xu Guangling nodded.

"This orange. Mr. Chen weighed the orange in his hand, "If you put it here, it will slowly rot." ”

"In this process, the change of the date is addition, one plus one plus one plus one, and it goes on and on. ”

"But the speed at which this orange rots, not addition. Decay is due to the breeding of microorganisms, and the reproduction of microorganisms is explosive, so the speed of orange decay cannot be a simple addition, but must introduce other algorithms, such as multiplication, such as power. ”

Xu Guangling nodded.

"So, mathematics is out of necessity. ”

"There is a phenomenon in our world, and if we extract this phenomenon and map it to mathematics, it becomes the 'addition' in mathematics, and there is another phenomenon in our world, and if we extract this phenomenon and map it to mathematics, it becomes 'multiplication' in mathematics. ”

"So, what is mathematics? Mathematics is a reflection of the world. ”

"The more we know about the world, the more and more we need to build the arithmetic of numbers, and the more and more complex it becomes. ”

"So, mathematics, too, is an indicator of world civilization, like a thermometer. Where there is civilization, there must be mathematics, and the height of the development of mathematics usually represents the height of people's understanding and application of the world. ”

"Suppose in the future, we travel the universe and encounter another civilization. ”

"How can we recognize, analyze, position, and measure this civilization?"

"The best, the fastest, and the easiest way to do this is to study the math of it. All kinds of formulas, all kinds of algorithms, correspond to all kinds of phenomena. ”

Xu Guangling nodded again, and because of the old man's remarks, he decided to include mathematics in his study and research projects.

In addition to medicine and food, he wants to become a master of mathematics.

"What is mathematics? Mathematics is a mapping of the world. ”

"What's in math?"

"The first is the number, and the second is the shape. Mathematics before the seventeenth century was simple numbers and shapes. It can be perfectly applied to the static world. ”

"But the world is not static, but dynamic. ”

"The rotting of an orange is dynamic, and if I throw the orange, from the time it is thrown to the time it hits, the whole process is dynamic. Simple numbers and shapes cannot describe this phenomenon. ”

"Mathematics starts here, from the mathematics of constants to the mathematics of variables. ”

"Whether it is constant mathematics or variable mathematics, they describe inevitable and definite phenomena. However, there are still some phenomena in this world that cannot be described by necessity and certainty. ”

"Or is this orange rotten, if a box of oranges is placed there, how many days will it rot, will it rot? How many days after it will rot, will it all rot?"

"From a purely mathematical point of view, it is inevitable, there are definite numbers. ”

"But in terms of actual phenomena, it is uncertain, the size and texture of this box of oranges, the location and time of storage of this box of oranges, the factors of this box of oranges, etc., all form a lot of complex 'numbers' that cannot be simply quantified. ”

So in this case, even the mathematics of variables is not enough to describe this phenomenon, and things like probability must be introduced, and mathematics goes from here to the mathematics of probabilities and fuzzy mathematics. ”

Xu Guangling still nodded.

"Constant mathematics, variable mathematics, contingent mathematics, and fuzzy mathematics are also the four stages of the development of mathematics in our world, from ancient times to modern times. ”

"In today's first lesson, we'll start with constant math. ”

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