Zou Rong has a bad temper: "Let's put it bluntly! Revolution is necessary, otherwise there will be no future."
Cai Yuanpei held him down and said, "I've told you many times not to be so impulsive. You have to do things step by step. You are too young. If you are anxious, you will easily suffer big losses and be used as cannon fodder by others."
Fortunately, Cai Yuanpei can control him.
Lin Baishui also said helplessly: "I really don't know how it will develop in the future."
Cai Yuanpei is considered to be middle-aged and has already made a certain judgment on the situation: "I am afraid that the Qing court will not be in power for a long time. Even their hometown in the Northeast will have to be taken care of by ordinary Han people like us. But even if the Qing court dies, it will
It is not enough to make us strong. As Mr. Li Yu said, politics, law and science must be connected."
Li Yu said with a smile: "What the principal said is very reasonable. Pure revolution is only destructive. How to break and rebuild is the most difficult and most important thing."
Lin Baishui wrote down the conversation between the two: "I want to think about the content of the next issue, and I have another idea."
Cai Yuanpei said to Li Yu again: "Shucai, I still have some questions to ask you. Although Jing'an (characterized by Wang Guowei) has been mentioned in the article, there are some very successful scientific achievements in the history of our country, as written in the article.
Zu Chongzhi’s calculation of pi. I’m very curious, how is such a subtle and delicate thing calculated?”
Li Yu said: "I didn't expect that the principal is also interested in mathematics."
Cai Yuanpei said: "As for Western learning, the most basic thing is mathematics. I heard that pi is a common sense content. I feel a bit ashamed to ask this question."
Let’s review the story first:
There was a man in the state of Qi. He was worried that the sky would collapse and the earth would sink. He would not have a safe place to live. He was so worried that he could not sleep well or eat.
The person who comforted him said: 'The sun, moon and stars are also made of gas. They are just glowing things in the gas. Even if they fall, they will not cause harm to people.'
Everyone has regained a little confidence through him: Yes, we were able to lead Europe in the past, why can't we do it now?
Seeing how interested everyone was, Cai Yuanpei once again recommended Li Yu to write an article about why China was lagging behind in science and how to break the situation.
"Really?" Cai Yuanpei said, "I just said it casually."
Of course, I am not saying that everyone should do so-called useless things. Because science not only has a scientific spirit, but also has two other elements, that is, science has three elements: scientific purpose, scientific spirit, and scientific method.
.
Lin Baishui was a little disappointed: "Isn't it enough?"
And this issue is very worthy of discussion for China's current situation.
The purpose is easy to explain, which is to discover the laws hidden in nature or society. Note that it is not just for practicality. As long as it is a law, it is the purpose.
Lin Baishui enthusiastically submitted his vote to the newspaper the next day.
In fact, in later generations, for many people, even for top students in non-mathematics majors in science and engineering, slightly more advanced mathematics is still a bible. After all, it is a subject that depends entirely on talent.
We are complacent and think we have the truth, but in fact we are just deceiving ourselves.
I would also like to clarify to you that science is science and technology is technology, and the two are completely different.
Not long after, he and several students threw it five thousand times in coordination.
Cai Yuanpei said: "I think science must be about strict hepatic control."
Science is about discovering the unknown and creating new knowledge, and it is about answering "what" and "why".
He is also patient enough.
Scientific discovery is the theoretical basis of technological invention; science proposes the possibility of development, and technology turns "possibility" into "reality".
Li Yu found a piece of paper, a ruler and a needle, then drew a few parallel lines on the paper, and said: "Throw this needle on this piece of paper at will, and remember the total number of times.
And the number of times the needle intersects the parallel line, divide the two, and the result is the value of pi.
Li Yu said with a smile: "If you want to be precise, the data must be multiplied many times. If you throw it all day long, twenty or thirty thousand times, you might get a more accurate number."
What’s even more sad is that this word is actually positioned as a negative idiom, which has been taught to the world for thousands of years! It is used to ridicule those who worry about things that they don’t need to worry about, and to persuade people that there is no need to worry too much about unknown things.
No need to look for trouble.
Because we focus on practicality, we can see that these four great inventions are of great practical value.
What Li Yu is talking about is the famous Buffon needle problem, which uses the classic probability theory model to calculate pi.
This is the power of culture, this is the gene of tradition, and this is the epitome of the development of science in ancient China. When Western sages encounter problems, they delve into the reasons; when our sages encounter problems, they only focus on whether it is useful.
Li Yu had no choice but to give him a general explanation of the probability model, but the trigonometric function sin was still used in it anyway. Even though it was only about high school mathematics, Cai Yuanpei still couldn't understand it.
What is science? Science is about asking the fundamentals, rather than focusing on whether it is useful.
Someone went to comfort him and said: "The sky is just accumulated gas. There is no air anywhere. Every move you make, every breath you take, you are active in the sky all day long. Why are you worried that the sky will collapse?"
?'
Lin Baishui was actually very interested and took the initiative to start experiments.
The spirit of science is what I just mentioned, the spirit of questioning everything and the spirit of inquiring into questions.
Of course, the explanation of the theory must be made by Li Yu.
Li Yuben said that throwing it two thousand times was enough and he could almost get 3.14, but Lin Baishui insisted on "surpassing" the famous Zu Chongzhi.
But after five thousand times, the result is still around 3.1418. The fourth place is far off, which means it is only accurate to the third place.
The person who comforted him said: "The earth is just piled up clods of soil, filling up the emptiness in all directions. There is no place without clods of soil. You are walking and jumping, and you are active on the ground all day long. How can you worry about sinking?"
Where are you going?'
Technology lies in the application of unknown and existing knowledge, answering "what to do" and "how to do it".
But I want to say that the real mediocrity is actually everyone who laughs at Qi people!
Everyone was astonished: "How can it still be like this?!"
Therefore, people are not mediocre, it is us in the past who are mediocre.
Cai Yuanpei said: "I would like to hear the details."
The Liezi that contains this fable is a classic written more than 2,000 years ago. After so many years, how many ancient Chinese sages have not seriously thought about why the sky cannot fall? Why cannot the earth collapse?
In fact, I think Qi Ren is a person who loves to think. He thinks about scientific issues: atmospheric science issues, earth science issues, mechanics issues, astronomy issues, etc. If our sages study carefully, modern science can even start from
If it were studied here, there might not have been the rise of modern science in Europe.
Our ancestors did not ask these questions thoroughly. Since it has not collapsed, there is no need to worry or delve into it.
"I think everyone has heard a story about unfounded worries. It comes from a fable in the Taoist classic "Lieh Zi" during the Warring States Period.
And this is the spirit of science.
This kind of simple model in life that contains mathematical principles is more popular. Through Li Yu's fame, readers can get to know Zu Chongzhi again.
However, this is not the case with Western scientific spirit.
That is to say, our ancient times only had technology and no science. Or to be more strictly accurate, we had science in ancient times, but it was very rudimentary and weak.
We have been ahead of the world for almost most of our history, but unfortunately, this lead is limited to technology.
Qi Ren asked again: 'What will happen if the land collapses?'
This is an evocative story that has lasted for more than two thousand years, and it is also why we have gradually gone from being scientifically ahead of the Western powers to the current situation where we are being beaten everywhere.
However, technological inventions do not necessarily need to be supported by scientific theories and can also rely on experience.
Qi people said: 'The sky is really filled with accumulated gas, so won't the sun, moon and stars fall down?'
For example, conic sections were of no use at that time. Thousands of years later, when Western scientists Kepler, Newton and others were studying the motion of celestial bodies, they realized that this mathematical knowledge had to be used.
However, although it has been more than a hundred years since Buffon proposed this experimental method, until now, many people even in the mathematical community still find it difficult to accept it.
Lin Baishui was not willing to give in. He actually threw the needle nearly 20,000 times that day. Although the result was only about 3.14151, the error in the last digit was quite large. But it was still considered a "small achievement" and the result was able to reach four decimal places.
Cai Yuanpei was very surprised when he saw the data was 3.14: "Why is this?"
It can be said that if there is science, there must be technology, but if there is technology, there may not be science.
Li Yu smiled and said: "If you don't believe it, just try it."
Cai Yuanpei sighed: "From this little thing, I finally understood what science is. Although I can't know its principles, from the explanations given by Brother Shucai, I can also feel that mathematics is ingenious and can use such ingenious ideas to solve practical problems."
"
Since it was the future principal himself who requested the manuscript, Li Yu certainly could not refuse.
Because in the eyes of most mathematicians, the calculation of pi is a very rigorous matter, and finding it through experiments is really jaw-dropping.
"If you drop the needle enough times, it will be very close to the pi ratio. If you want to achieve what Zu Chongzhi achieved in half his life, it may only take a few days."
Even the four most famous inventions in ancient times: papermaking, compass, gunpowder and printing, etc., are strictly speaking technological inventions, not scientific discoveries.
Therefore, many historians have been busy for a long time with the research on the lives of ancient Chinese scientists such as Zu Chongzhi.
Li Yu smiled and said: "Your statement is very consistent with the relationship between mathematics and science."
"There is nothing to be ashamed of," Li Yu said. "Actually, the inscription method used by Zu Chongzhi is still relatively complicated in calculation, but in fact there are many interesting and simple algorithms about pi."
For him, mathematics is a book of difficulty, but who can't throw a pin or count?
Although Li Yu is not good at writing, he can still tell stories to a certain extent and knows how to cut into the story. He wrote this:
Li Yu said: "Mathematical models can handle a lot of problems, so they are the queen of science."
Li Yu said: "That's it. What limits the upper limit of science is often mathematics."
Cai Yuanpei thought thoughtfully: "In this way, the new school's emphasis on mathematics is on the right track."
Everyone must also know that this fable mocks the kind of mediocre people who spend their days with unnecessary worries and endless sorrows, disturbing themselves and others.
If you can study ancient Greece, you will find that the Western scientific sages have studied many things that are of no use at all.
As for the scientific method, one is logical, just like the "Elements of Geometry" written by the Greek sages two thousand years ago, which is clear and deductive; the other is empirical, that is, experimental verification.
This is the essence of science.
It is precisely because we lack this kind of scientific literacy that we will gradually lag behind the great powers!"
Although Li Yu didn't know much about writing political commentary between the revolutionary party and the constitutionalists, when it came to science, he was really familiar with it, and he wrote it eloquently and well-founded.
This question is very famous in history, that is, the famous "Needham problem" raised by Chinese technology history expert Joseph Needham: Why did ancient China, which was both culturally and technologically advanced, not develop modern science?
Regarding this question, Einstein once answered: The reason why modern science in Europe can develop is because of two things. One is formal logic that originated in the ancient Greek period, and its representative figure is Aristotle;
Experimental science originated in the Renaissance, and its representative figure is Galileo. The ancient Chinese sages neither understood formal logic nor experimental science. Therefore, it is not surprising that modern science did not develop.