A Man of Science and Engineering in Troubled Times Wandering in the Late Qing Dynasty

Zou Rong has a bad temper: "Just say it! We need a revolution, otherwise there will be no future."

Cai Yuanpei held him down and said, "I've told you many times, don't be so impulsive, and do things step by step. You are too young, and if you are impatient, you will suffer big losses and be used as cannon fodder by others."

Fortunately, there is still Cai Yuanpei who can control him.

Lin Baishui also said helplessly: "I really don't know how it will develop in the future."

Cai Yuanpei can be considered middle-aged, and has already made a certain judgment on the situation: "I am afraid that the Qing court will not be able to sit for a long time, and even their Northeast nest needs us ordinary Han people to worry about it. It’s not enough to make us strong, as Mr. Li Yu said, the two paths of politics, law and science must be smooth.”

Li Yu said with a smile: "The principal is very reasonable. A simple revolution is only destructive. How to break it and rebuild it is the most difficult and most important."

Lin Baishui wrote down the conversation between the two: "I think about the content of the next issue, and I have an idea again."

Cai Yuanpei said to Li Yu again: "Shucai, I still have some questions I want to ask you. Although Jing'an (Wang Guowei's character) has been mentioned in the article, there are some very successful scientific achievements in the history of our country, just like in the article. Zu Chongzhi’s calculation of pi. I’m curious, how is such a delicate thing calculated?”

Li Yu said: "I didn't expect the principal to be interested in mathematics."

Cai Yuanpei said: "Western learning, the most basic thing is mathematics. I heard that pi is a common-sense content. I am really ashamed to ask this question."

"There is nothing to be ashamed of," said Li Yu. "Actually, the inscribed method used by Zu Chongzhi is relatively complicated in calculation, but there are actually many interesting and simple algorithms for pi."

Cai Yuanpei said: "I would like to hear the details."

Li Yu found a piece of paper, a ruler, and a needle, and drew a few parallel lines on the paper, saying: "Throw this needle on this piece of paper at random, and remember the total number of times you throw the needle. And the number of times the needle intersects the parallel line, the two are divided, and the result is the numerical value of pi.

"If the needle is dropped enough times, it will be very close to pi. It may only take a few days to achieve Zu Chongzhi's half-life achievement."

Everyone was stunned: "Can it still be like this?!"

Li Yu smiled and said, "If you don't believe me, try it."

What Li Yu said was the famous Pufeng's needle problem, which used the classical probability theory model to calculate pi.

It's just that although it has been more than 100 years since Buffon proposed this experimental method, until now, even many people in the mathematics community still find it difficult to accept it.

Because in the eyes of most mathematicians, the calculation of pi is a very rigorous matter, and it is really jaw-dropping to find out through experiments.

Lin Baishui was actually very interested and started to experiment on his own initiative.

For him, mathematics is difficult at the bible level, but no one can throw a needle or count numbers.

In fact, in later generations, for many people, even if they are non-mathematical science and engineering students, a little advanced mathematics is still a holy book, after all, it is a subject that depends entirely on talent.

Not long after, he and a few students cooperated to throw [-] times.

It is also patient enough.

Li Yu originally said that throwing 3.14 times would be enough to get [-], but Lin Baishui insisted on "surpassing" the famous Zu Chongzhi.

Only after 3.1418 times, the result is still about [-], and the fourth place is quite different, that is, it is only accurate to the third place.

Lin Baishui was a little disappointed: "Isn't it enough?"

Li Yu said with a smile: "If you want to be accurate, the data must be multiplied many times. If you throw it all day, twenty to thirty thousand times, maybe you will get a more accurate number."

Cai Yuanpei was very surprised when he saw the data was 3.14: "Why is this?"

Li Yu had no choice but to explain the probability model to him in general, but the trigonometric function sin was still used in it anyway, and Cai Yuanpei still couldn't understand it even if it was only about mathematics in the first year of high school.

Cai Yuanpei sighed: "From this little incident, I finally understand what science is. Although I can't know its principles, but from Brother Shucai's explanation, I can also feel that mathematics can be described as ingenious, and can use such ingenious ideas to solve practical problems. "

Li Yu said: "Mathematical models can deal with many problems, so they are the queen of science."

Cai Yuanpei said: "I think science must be strictly controlled by wives."

Li Yu said with a smile: "Your statement is very suitable for the relationship between mathematics and science."

"Really?" Cai Yuanpei said, "I just said it casually."

Li Yu said: "That's it. Mathematics is often what restricts the upper limit of science."

Cai Yuanpei was thoughtful: "In this way, the new school is on the right track to attach importance to mathematics."

Lin Baishui was not quite reconciled, and he actually threw the needle nearly 3.14151 times that day. Although the result was only around [-], the error in the last digit was quite large.However, it can be regarded as a "small achievement" and can reach the result of four decimal places.

Lin Baishui voted for the newspaper with great interest the next day.

Of course, the interpretation of the theory has to be done by Li Yu.

This kind of simple model in life that contains mathematical principles is more popular. With the help of Li Yu's reputation, readers can get to know Zu Chongzhi again.

Since then, many historians have been busy for a long time with the textual research on the lives of ancient Chinese scientists such as Zu Chongzhi.

Everyone has regained a little self-confidence through him: Yes, we were able to lead Europe before, why can't we now?
Seeing that everyone was so interested, Cai Yuanpei strongly recommended Li Yu to write an article on why China lagged behind in science and how to break it.

Since it was the future principal himself who requested the manuscript, Li Yu certainly could not refuse.

Moreover, this issue is very worthy of discussion for China's current situation.

Although Li Yu is not good at writing, he still knows how to tell stories and knows how to cut them in. He wrote:

"I think everyone has heard a worrying story, which comes from a fable in the Taoist classic "Liezi" in the Warring States Period.

You must also know that this fable ridicules the kind of mediocrity who is full of unnecessary worries and endless sorrows, bothering himself and others.

But I want to say that the real mediocrity is actually everyone who laughs at the barbarians!

Let's review the story first:
There was a man in the state of Qi. He was worried that the sky would collapse, the earth would sink, and he would not have a safe place to live. He was so worried that he could not sleep well or eat.

Someone went to comfort him, saying: "The sky is nothing but accumulated gas, there is no place without air."Every move you make, every breath you take, is active in the sky all day long, so why worry about the sky falling down? '

Qi said: "The sky really is the accumulation of gas, won't the sun, moon and stars fall down?" '

The person who comforted him said: "The sun, the moon and the stars are also gas accumulations, but they are just glowing things in the gas. Even if they fall, they will not harm people." '

Qiren said again: "What if the land collapses?" '

Those who comforted him said: "The earth is nothing but accumulated clods, which fill up the emptiness in all directions, and there is no place without clods."You walk, jump, and move on the ground all day, so why worry about sinking? '

The "Liezi" that contains this fable is a classic book more than 2000 years ago. After so many years, how many ancient Chinese sages have not seriously thought about why the sky can't fall?Why can't the ground fall down?
In fact, I think Qiren is a person who likes 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 be studied from here, and perhaps there will be no rise of European modern science.

Therefore, Qiren is not mediocre, but mediocre is us in the past.

This is an evocative story of more than 2000 years, and it is also why we have gradually moved from being ahead of the Western powers in science to being beaten everywhere today.

When we are complacent and think we have the truth, we are only deceiving ourselves.

Our ancestors didn't get to the bottom of these questions, and since they didn't collapse, there's no need to worry and delve into them.

What is even more sad is that this word is positioned as a negative idiom, which has educated the world for thousands of years!It is used to ridicule those who worry about things that they don't need to worry about, to persuade people that there is no need to worry too much about unknown things, and they don't need to worry about themselves.

This is the power of culture, this is the gene of tradition, and this is the epitome of the development of ancient Chinese science.When Western sages encountered problems, they were investigating why; when our sages encountered problems, they only focused on whether it was useful or not.

What is science?Science is to get to the bottom of things, not to focus on whether it is useful or not.

I would like to clarify to you again that science is science and technology is technology, and the two are completely different.

Science lies in discovering the unknown and creating new knowledge, to answer "what" and "why".

And technology lies in the application of unknown and existing knowledge, to answer "what to do" and "how to do it".

It can be said that if there is science, there must be technology, but if there is technology, there may not be science.

Scientific discovery is the theoretical basis of technological invention; science proposes the possibility of development, and technology turns "possibility" into "reality".

However, technical inventions do not necessarily require the support of scientific theories, but can also rely on experience.

We have been ahead of the world almost most of the time in history, but unfortunately, this lead is limited to technology.

In other words, our ancient times only had technology, but no science.Or more strictly speaking, we had science in ancient times, but it was very elementary and weak.

Even the four most famous inventions in our ancient times: papermaking, compass, gunpowder and printing, etc., are strictly speaking technological inventions, not scientific discoveries.

Because we pay attention to practicality, it can be seen that these four great inventions are of great value in practicality.

But the scientific spirit of the West is not like this.

If you can study ancient Greece, you will find that the scientific sages of the West have studied many things that are not useful at all.

For example, the conic curve was useless at the time. Thousands of years later, when Western scientists such as Kepler and Newton were studying the movement of celestial bodies, they realized that they needed to use this mathematical knowledge.

And this is the spirit of science.

Of course, I am not saying that everyone should do so-called useless things.Because science not only has the spirit of science, but also two other elements, that is, science has three elements: the purpose of science, the spirit of science, and the method of science.

The purpose is easy to explain, that is, to discover the laws hidden in nature or society. Note that it is not purely for practicality.As long as there is a law, it is the purpose.

And the spirit of science is what I just mentioned, you must have the spirit of questioning everything, and you must have the spirit of inquiring about doubts.

As for the scientific method, one is logical, just like the "Elements of Geometry" written by the sages in Greece in 2000, which is clear and logical, and the deduction is reasonable; the other is empirical, that is, there is experimental verification.

This is the nature of science.

It is precisely because we lack this kind of scientific literacy that we will gradually fall behind the great powers! "

Although Li Yu didn't know much about writing political theories between the revolutionary party and the constitutionalists, when it came to science, he was really familiar with it, and he wrote it eloquently, with reasons and evidence.

This question is very famous in history, that is, the famous "Needham Dilemma" put forward by Joseph Needham, an expert on the history of Chinese technology: Why did ancient China, which was ahead in culture and technology, not develop modern science?
Regarding this question, Einstein once also answered: The reason why modern science in Europe can develop is because of two things, one is the formal logic originated in ancient Greece, and the representative figure is Aristotle; The experimental science originated in the Renaissance, and the representative figure is Galileo.The ancient Chinese sages knew neither formal logic nor experimental science. Therefore, it is not surprising that modern science has not been developed.