Shu Qinghou nodded, shook his head again, and asked with a smile: "In ancient times, it was called the universe, and the four directions were called the universe. Time and space are the universe, and in the real material world, they cannot exist alone, and in the imaginary completely unrealistic world, we have no way to imagine that there is only space and no time. ”

"Take this flying arrow not moving, or the famous family called the bird does not move, the shadow does not move. Let's start with the flying arrow. ”

"Since it's a flying arrow, it must have speed, right?"

The students below nodded one after another, and Shu Qinghou said, "What's the speed?" It is distance divided by time, that is to say, for the existence of a flying arrow, there must be a universe and a universe, and there must be time and space at the same time, so that it can be a flying arrow. Even if the arrow does not move, then you can say that the speed of the arrow is zero. ”

"Suppose time stands still now, then time is zero. Does a number divided by zero exist? Can you compare the size? Or can you think that a number divided by zero is zero? When time stands still, space doesn't exist, then space doesn't exist, and you say you can know if the arrow is moving or not? ”

"It's like the imaginary number I just said, does it exist? Doesn't it exist? In the real material world, there is no such thing as an imaginary number that can be concrete, so can you draw me an imaginary root number minus two now? Needless to say, imaginary numbers, can you now draw me a line segment with a length of minus one? ”

"It's something that can only exist in another universe, but it can't exist in our material world. If the immovable arrow exists, then our physical universe does not exist, and we do not exist, so we don't know whether it is moving or not. ”

"Didn't you learn that too? Consciousness arises from objective reality, which is matter. ”

Students seem to understand the saying that objective reality determines consciousness, and they have learned it, but it is only slightly exposed.

Shu Qinghou had been prepared for a long time, and he had also asked a similar question, so he said: "Zi Mo Zi Yan is thick and big. We are in reality that things must be high, so the thinnest and thinnest thing is also high, and infinitesimal is not zero. ”

"Now, suppose we all live in a world without heights, it's like a painting you make on paper."

"Then, close one of your eyes."

After all the students closed their eyes, Shu Qinghou took out a cube for teaching, rotated it in his hand, and asked, "What if your world has no height, only length and width. So what should you look like when you see the rotation of this cube? ”

"What you see is the shadow of the cube on the paper under the light, a strange change from one on the side to two on the side. One will be a square and the other will be a rectangle, but can you imagine a cube that is not tall? ”

"This cube exists in reality for us, and in our consciousness, it is a cube."

"But for people who don't have a world of heights, in their consciousness, this is a strange existence that will be square and square."

"They are right, and we are right, because the objective world is different, so there is a huge difference in consciousness. Consciousness originates from objective reality, and that's what it means. ”

At this, a knowing smile appeared on his lips, and he continued to pick up the cube as he remembered the answer he had heard when he first heard someone explain the question.

"If there were people in that universe without height, and they also had priests and star officials, one day they observed the starry sky and found this rotating cube in my hand. They will use their own consciousness to summarize the rules. ”

What is this law? The 'moon' in the sky would change in the form of a triangular sine table, and at its largest would be a rectangle, twice the length of the side of the square, and this change might go on and on and on as we would with the moon, so their priests came up with the calendar and used it to guide the people there. ”

"If I put some food into that world every time I turn to the sine maximum, they will think that the food has something to do with the sine table of the moon."

"Are you saying they're wrong? Nor can it be said that they are wrong, they are only conscious according to the objective laws of their world. ”

"Their consciousness is right in their world, and it is wrong and ridiculed in ours."

"So our Mo family said 'in', Yao's policy at that time was good governance, that was for the time, and now let Yao's policy be put now, that is bad government, and it can't govern the world."

"Is it because the people of the Yao Shun era have changed? Or has the material basis of the Yao Shun era changed? What caused Yao Zheng to be good in the past and evil now? ”

"It's like when we observe the moon in the sky, we find the moon's waxing and waning, and we find the cycle of cloudy and sunny and waxing, and determine the month, which is called respecting the objective law."

"On the basis of respecting the objective law, we use this law to choose the middle of the month instead of the end of the month or the beginning of the month when we rush to the night, which is called giving full play to subjective initiative."

"Heaven and earth are not benevolent, and all things are used as dogs, and objective laws will not take the initiative to meet people's needs, which requires us to use the laws and conditions to create a better life after mastering the objective laws."

"The difference between us and the Taoists of Chu State is also here, they believe that all things are self-transformed, deny the role of subjective initiative, and believe that the natural evolution of objective laws will make the world naturally govern, which we call mechanistic. They recognized the existence of the Tao and the existence of objective laws, but they did not give full play to the role of human consciousness, did not recognize the difference between heaven and humanity, and did not realize that after people have obtained consciousness from matter, they can use consciousness to use objective laws for profit. ”

Speaking of these, all the students below laughed, and Shu Qinghou himself also laughed, and said with a smile: "Don't laugh, that's what the giant said." I'm what kind of dates he fed me to eat, I'll spit it out and feed it to you, you really want to think about this, and after answering all the arithmetic questions I assigned correctly, go to the next door to listen. ”

When the student heard this, he immediately looked bitter, there are so many problems assigned by Mr. Xindao, and the daily calculus cannot be completed, where can he have time to go next door to listen?

After laughing, another student raised his hand and asked, "Sir, you must have heard what Achilles and the turtle said." I've tried to answer this question, but I've come to a strange conclusion. ”

"If the speed is fixed, and the distance is halved each time, then the time each time is one plus one-half, plus one-quarter, plus one-eighth, plus one-sixteenth ......"

"And so it adds up, and it is endless, until at last it is almost infinitely small."

"If infinitesimal is not zero, then the time when Achilles catches up with the turtle in the end is certainly not an integer, but it is obviously an integer when calculated by arithmetic."

"Also, it is the same thing to take an infinite half of a wood, which is inexhaustible for generations. That time is halved each time, but the number is infinite. Why isn't the sum of the time of each halving of this infinity infinite, but just a fixed value? ”

"There is also half of the wood, which is inexhaustible for many years, and after an infinite number of times, the sum of these infinite amounts of wood is still less than the length of that wood. Since they are already infinite, how can they be less than the length of that log? ”

"Another example is a line segment, one foot long, with an infinite number of dots on it. A line segment is two feet long, and there are also infinite number of points on it. So, is the infinite number of a two-foot-long line twice as much as the infinite number of a one-foot-long line? ”

For another example, Juzi said that he knew the algorithm of the volume of the ball, which was calculated by the two gentlemen, and said that he used the infinite division method. If a ball is infinitely cut, then the thickness of each piece is infinitely small. Zi Mo Ziyan said that thick can be big. Only if there is a height can the volume be calculated, so why is the infinitely small addition of infinite size the fixed value of the volume of the sphere? ”

"How is infinity and infinity small?"

"Is infinity a number? The sum of an infinite number of numbers that gradually approach infinitesimal is not infinitely large, and both the Achilles tortoise and the taki half-cut can prove to be a fixed value, can this be calculated? ”

Shu Qinghou patted his forehead and said with a smile: "I think of a sentence from the giant back then. I also asked a similar question, and he said that he couldn't, and said that if he knew everything himself and could answer all the Heavenly Wills, then why would he accept disciples? ”

"Take care of these questions yourself, don't give up. I remember the words in the "Persuasion of Learning", blue is better than blue, ice water is cold for it, I hope that after you finish your studies, you will one day be able to find me and tell me how to calculate this infinite and infinitely small. As the saying goes, knowing is knowing, not knowing is not knowing, and now I still use the words of the giant back then to tell you. “

"If I understand everything and comprehend all the heavenly aspirations in heaven and earth, then what else do you want to do? I want you to be better than the blue. ”

"Now! Class! ”

After the class ended, the disciples got up one after another, and after Shu Qinghou left, the student who asked the question wrote down this incomprehensible question on the paper, thinking about the words that the blue is better than the blue, and the heart said that one day, I must know how to calculate this infinite and infinitely small.

Shu Qinghou got rid of these students who he liked, but often came up with many answers that he couldn't get an answer even if he racked his brain.

When I returned to my dormitory, I received two letters.

One is living not far from him, but because he hid in the Xuan Xuan Intensive Study of Arithmetic and did not ask about the affairs of the world, the two of them hardly spoke, and studied astronomy.

The two have been communicating by letter for many years, because once they meet, they will quarrel about what the policy of benefiting the world should be, so they simply do not meet.

Shu Qinghou opened the letter very happily, looking at the thin font on it, he didn't care much about the content of the letter.

The letter said a big thing, they really saw the "moon" of the Tai Sui Star, and for the time being, they only saw one, revolving around the Tai Sui Star, even if the multiple of the clairvoyant mirror was not large enough, they could still see them revolving around the Tai Sui Star, which was the same as the hypothesis of the moon and the earth.

He also thought that if those craftsmen who sharpened the mirror could make the clairvoyant mirror better, perhaps they could really use the cloudy and sunny days of the Tai Sui star "moon" to map the entire Kyushu with an accurate map of latitude and longitude.

In addition, they also observed the phase change of the morning star, or Chang Gung star, which is enough to prove that the morning star does not revolve around the earth, but around the sun, and in any case the statement that the sky is round and the place cannot explain these two problems.

At the end of the letter, he was asked some questions about ellipses, asking him a lot about the focus of the ellipse, but he did not say what it was used for.

The second letter was unfolded, written by his elder brother, King Shuqing, and the content of this letter was much simpler.

Tell him that his nephew is married in Takayanagi and will be transferred back to Sishang soon, so that he can go home after the New Year and get together as a family.

Nothing else was said.

Shu Qinghou looked at the second letter, finally picked up the pen, took a piece of paper, and wrote a reply to the first letter.

"The knowledge of elliptical focus originates from Zimozi's eight optical methods for the reflection of concave-convex mirrors, and whether the dot is an extension of the focus discussion is not something that can be clearly explained in one sentence or two."

"I'm figuring out how to solve a cubic equation, my students are asking me for answers to infinitesimal accumulation problems, and I'm afraid I don't have time to write a whole set of questions about ellipses in my cabin."

"My nephew is getting married, and he wants to go back to Sishang, and he wants to hold a wedding in Sishang. When the time comes, I'm going to go back, and then I'll not have to think about the problem of unary cubic equations and infinitesimal superpositions for a while. If we go up the canal and then take the post road back, it's an elliptical shape, and the line connecting the two focal points is the shortest distance from here to my house, but there is no road. ”

"That would be the best opportunity to talk about the ellipse together, if you will."

After writing a short reply, Shu Qinghou opened his daily notepad and recorded everything that happened in class today.

And at the end of this daily account, Shu Qinghou wrote.

"imaginary numbers and three-power equations; a discussion of the focus of ellipses and curved surfaces left by the eight methods of sub-Mozi optics; the needs of artillery on curve operations; whether infinitesimal is zero; The ball volume is calculated by accumulating the ball method; whether infinitesimal can be calculated; Can infinitesimal in an operation be regarded as zero......"

"It is foreseeable that within a hundred years, chaos is coming. A hundred years can be described as two lifetimes for people, but in the vastness of the universe is just a moment, its way is endless, I have an end to life, it is really the first regret in life. ”

Before closing the notepad, he took a note two fingers wide and wrote down the words "chaos is coming" in heavy strokes, and sandwiched it on the page of the diary recorded today about whether the infinitesimal is zero and whether the operation containing the infinitesimal is reasonable.