"One one equals two, one two equals three, addition, in the mathematical system, is the result..."
"But mathematics has never been about mathematics. It doesn't make much sense to talk about mathematics without specific things."
"There is a record in Wang Yangming's "Zhuan Xi Lu". Wang Yangming was traveling with his friends, and one of them pointed to the flowers and trees in the mountains and said: "Old Wang, you said that there are no unintentional things in the world. But flowers and plants like these grow naturally in the deep mountains.
What does opening and falling have to do with my heart?'"
"Wang Yangming's answer?" Mr. Chen paused.
Xu Guangling answered: "When you don't look at this flower, this flower and your heart are silent together. When you look at this flower, the color of this flower becomes clear for a while."
Mr. Chen smiled and nodded, "This is to look at everything in the world from a human perspective, emphasizing the uniqueness and centrality of human beings. Human beings are the master and everything is a guest. The guest does as the master does."
"Flowers and grasses in the mountains bloom and fall on their own. 'The grass and trees have their original intention, so why ask for beauty to break them'? This is said from the standpoint of the plants 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 human beings. What is good, what is bad, what is useful, what is useless, all of these require a preset precondition, which is the human standpoint."
"Without a stance, there is no good or bad, no use or use."
"It is also meaningless to go from us to me, and to leave 'I' and talk about all things in the world."
"Just like me, if I have my hair cut off now, then the next moment, tomorrow, or in the future, no matter what good trees you plant or what delicious food you make, no matter how good the food is, it will have nothing to do with me.
Already."
"Radiating outward, China, the whole world, the entire earth, the entire solar system, the entire universe... everything has nothing to do with me anymore."
"So the world is both big and small."
"The big ones belong to them and theirs, and belong to all things in the world and other human beings; the small ones belong to me. At this moment, my world only consists of this mountain and you two."
"Trees need roots, and people have their roots. As tall as a tree is, never leave its roots. No matter how prosperous a person is, never forget their roots. No matter how prosperous the flowers are, or how vigorous the fire is, if you cut off the roots, they will soon wither.
Death.
“Only by understanding the fundamentals can we have stable survival and further development.”
"In a mathematical system, this is a coordinate system and the establishment of the origin of the coordinates."
Xu Guangling nodded solemnly.
"It is meaningless to talk about us, mankind, and the entire world without me. Many people in this world do not understand the difference between 'I' and 'us', and often regard 'our' as 'mine'
', and fell into a false sense of satisfaction and dazzling eyes."
"We have entered modern society, knowledge is exploding, the economy is developed, and science is prosperous."
"How many trillions is GDP?"
"A new generation of artificial satellites has ascended into the sky again."
"The telescope's detection has reached many light-years beyond the earth."
"These, from the standpoint of 'me', are all flowers and embellishments. Using mathematical thinking, we can peel off this background and fly our physical and mental consciousness back from the far point of the coordinate system of the world, and return from the far point.
Go to the original point, return from color to black and white. Although you know the white, you should keep the black to purify your body and mind, and stick to and develop the fundamentals."
Xu Guangling nodded again.
This is exactly what he is doing at the moment. The achievement of consciousness requires him to return to his basics, to abandon the white and keep the black, to abandon all the things in the world, and come here to be a man in the unknown mountain.
The unknown hermit.
"To talk about all things without me, and to talk about mathematics without me, is all nonsense."
"The fundamental meaning of mathematics is to use quantification and variables to measure and construct other systems."
"One, two, three, four are the basis, addition, subtraction, multiplication and division are changes. Quantity and variables are the two major elements of mathematics. Expressed in our culture, they are Yin and Yang. Yin is quantitative and unchanging, and Yang is variable.
It’s always changing.”
"Constant is not really constant, but gradual change."
"Changes are not real changes, but changes according to certain rules that can be quantified. On the basis of mastering the rules, they can be regarded as unchanged."
"Just like the rotation of several large quantities in the solar system."
"They are changing all the time, but from another perspective, we can regard them as unchanged. Even without observation, we can quantify their position at any time."
Xu Guangling nodded.
"This orange." Mr. Chen weighed the orange in his hand, "If you place it here, it will slowly rot."
"In this process, the change of date is addition, one plus one plus one plus one, and it keeps adding."
"But the speed at which oranges rot is not addition. Rotation is due to the growth of microorganisms, and the reproduction of microorganisms is explosive. Therefore, the speed at which oranges rot cannot be simple addition. Instead, other algorithms must be introduced, such as
Multiplication, such as exponentiation.”
Xu Guangling nodded.
"So, mathematics is born out of necessity."
"There is a phenomenon in our world. Extract this phenomenon and map it to mathematics. It becomes the 'addition' in mathematics. There is another phenomenon in our world. Extract this phenomenon and map it to mathematics.
, it became ‘multiplication’ in mathematics.”
"So, what is mathematics? Mathematics is the mapping of everything in the world."
"Our understanding of this world is getting deeper and deeper, and the number calculation rules we need to establish are becoming more and more complex."
"Therefore, mathematics is also an indicator of world civilization, just like a thermometer. If there is civilization, there must be mathematics, and the degree of development of mathematics usually represents the degree of people's understanding and application of the world."
"What if in the future, we travel across the universe and encounter another civilization."
"How to understand, analyze, locate and measure this civilization?"
"The best, fastest, and simplest way is to study its mathematics. Formulas and algorithms correspond to phenomena."
Xu Guangling nodded again, and because of what the old man said, 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 map of the world."
“What’s in math?”
"Numbers come first, shapes second. Mathematics before the seventeenth century consisted of simple numbers and shapes. It can be perfectly applied to the static world."
"But this world is not static, but dynamic."
"The decay of oranges is dynamic, and if I throw this orange, the entire process from the time it is thrown to before it falls to the ground is dynamic. Simple numbers and shapes cannot describe this phenomenon."
"Mathematics starts here, from constant mathematics to variable mathematics."
"Whether it is constant mathematics or variable mathematics, what they describe are inevitable and certain phenomena. But there are some phenomena in this world that cannot be described by necessity and certainty."
"It's still about the rot of oranges. If a box of oranges is left there, how many days will it take for them to rot? How many days will it take for them to rot?"
"From a purely mathematical point of view, it is inevitable and has a definite number."
"But in 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 the box of this box of oranges, etc., all form many complex problems that cannot be simplified.
Quantitative ‘number’.”
"So in this case, even variable mathematics is not enough to describe this phenomenon, and things such as probability must be introduced. From here, mathematics will enter probability mathematics and fuzzy mathematics."
Xu Guangling still nodded.
"Constant mathematics, variable mathematics, probability mathematics, fuzzy mathematics, these are also the four steps of the development process of mathematics in our world from ancient times to modern times."
"Today's first lesson, we'll start with constant mathematics."
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