The current time is actually the winter vacation of the university hall, but the Beiyang Military Preparation Crash Course is an early military school after all, which is unusual, and the vacation is very short in comparison.
That's why Li Yu had time to teach Wu Peifu and Sun Chuanfang in Tianjin, and also learned how to shoot on horseback.
Shooting may sound like a kind of
"Insurance" may not be useful, but riding a horse is a common skill in daily life. Li Yu is now practicing hard to master this early twentieth century
"basic skills". When he returned to the hotel that day, Li Yu saw a young man waiting for him. When he saw Li Yu, he ran over directly.
"Mr. Li Yu! I've finally waited for you!" Li Yu was afraid of hitting someone when he was riding now, so he said quickly: "Be careful!" He pulled the reins from a distance, then turned over and dismounted, and asked: "Who is your Excellency?" Said: "My Majesty is Ma Yuanshan, whose courtesy name is Yinchu. I heard that Mr. Ma is now in Tianjin, so I came here to pay a visit." Ma Yinchu... Isn't this the famous first person in Chinese demography in the future?
His "New Theory of Population" was the first in China to put forward the theory of population control and fewer and better births, which has influenced China's national policy for decades.
The impact is not insignificant. Li Yu said: "Hello!" Ma Yinchu said: "I finally found out the hotel where Mr. was staying from the newspaper office, so I hurried over." Li Yu said: "So you are also in Tianjin?" Li Yu remembered Ma Yinchu He was probably from Zhejiang, and later became the president of Zhejiang University.
"I heard that the university hall was about to start. I rushed here last year, but it hasn't started yet." Ma Yinchu said.
"Beiyang University Hall?" Li Yu asked again. Ma Yinchu said: "Yes, it is helpless to say that I have been admitted to Beiyang University a long time ago. However, because the Eight-Power Allied Forces occupied the school building, the school's equipment, documents, and papers were destroyed and it was forced to close. I have almost taught myself. For two years." Li Yu praised: "It is not easy to study by yourself, sir, your perseverance is amazing! Let's go upstairs and have a cup of tea first." Li Yu rented a suite, which was not small.
After making tea, Li Yu asked: "What major are you studying, sir?" Ma Yinchu said: "It's metallurgy, but I'm more interested in numbers, especially those magical expressions, so I want to study economics in the future." so-called
The "magical expression" is naturally the Arabic numerals, letters, and symbols that are common in later generations.
But economics itself is indeed inseparable from mathematics. Li Yu said: "Why hasn't the Peiyang University School resumed classes yet? The Capital University School where I live had already started school at the end of last year." Ma Yinchu said helplessly: "The previous school building was seriously damaged and can no longer be used. We can only find a new location. The new campus selection In Xigou, it is said that school will start after the new year." This place later became the east campus of the Hongqiao Campus of Hebei University of Technology.
"Speaking of after the new year, won't you return to Zhejiang?" Li Yu asked again.
"I'll be leaving in a few days, but I'll be back soon." Ma Yinchu said,
"From now on, the university will select students to study abroad every year. I have wasted more than two years and want to catch up as soon as possible." Li Yu said, "Yes, time cannot be wasted. Now there is a lot of waste to be done, let alone no one." ." Ma Yinchu said: "I have read your husband's reports before, and I have cut out all kinds of news myself. I am especially interested in the book "Fractals and Chaos" written by him. Unfortunately, I searched Tianjin bookstores and couldn't buy it at all. arrive."
"That's easy! I'll get you a copy." Li Yu took out a copy from the cabinet and handed it to him.
"gave it to you."
"That's not okay!" Ma Yinchu refused.
"It doesn't matter, you may be interested in this knowledge in the future." Li Yu said.
"I was wondering if I couldn't understand..." Ma Yinchu said. Li Yu said: "It's not a big problem. I have made this version progressively more difficult. If you plan to study economics in the future, you will use the theory in fractals."
"Fractal?" Ma Yinchu said,
"To be honest, I just saw reports in the newspaper about Mr.'s unique theory and the magical 'carp effect'. But when it comes to the specific theory, I don't know."
"That being said, you should take a closer look at this book." Li Yu said with a smile. Ma Yinchu was proficient in English and could understand it completely. After flipping through the book, he said, "How about I pay you sir according to the price listed at the back?" Li Yu said, "You don't have to be polite to me! These books were given to me by the publishing house. Yes, it didn’t cost any money, and they even had to pay me royalties." Ma Yinchu said gratefully: "Thank you so much, sir! Well, if possible, can you sign it again..."
"Of course." Li Yu signed and discussed with him for a while the application of fractals in economic theory, especially telling him about a famous typical model in fractals: the logistic equation.
In fact, this equation is very simple. It is just an iteration of the quadratic equation of one variable. The logistic equation discusses the population growth model.
Ma Yinchu also knew a little bit about demography. He said: "I once read Mr. Yan Fu's translation of "The Evolution of Heaven", which mentioned Mr. Darwin's 'natural selection and survival of the fittest'. I also know that Mr. Darwin once Influenced by the scholar Malthus. But later I read Mr. Malthus's book. He mentioned that population will grow exponentially, but food will grow linearly, and terrible disasters will occur. But why is your equation just a quadratic equation? ?” The first person in the world to propose population control was indeed Malthus, but Li Yu didn’t want to discuss it with him.
Is the "Malthusian catastrophe" really a problem?
The problem of "Malthusian Trap" belongs to the category of political economics. Li Yu said: "Although it is a quadratic equation, it is already nonlinear, and there are fractals and chaos hidden in it. Mathematically, even such a simple population growth model, such a rudimentary quadratic equation iteration, also hides Chaos. To put it simply, the conclusion of this model is that when the population growth rate reaches a certain value, the population size is difficult to predict."
"Is there also chaos?" Ma Yinchu was confused. Li Yu said: "Of course, so chaos is everywhere. The population growth model is just a manifestation of chaos in nature." Li Yu found paper and
"Let me calculate it for you." The process is not complicated. As long as you understand quadratic equations, you can understand it completely, but the mathematical ideas embodied in it are very profound.
It's just that Ma Yinchu will have to discover the famous period-doubling bifurcation diagram by himself in the future. How can I put it this way, Li Yu is still very selfish now!
And this selfishness is not only for himself, he also hopes to subtly use various methods to inspire, guide and even cultivate some of his own scientists, so that they can slowly have greater inventions and discoveries.
After all, my own strength is too small. Just like in the library, only by combining as many forces as possible can we form a joint force.
He doesn't just want to have a smooth journey in scientific research, he wants to turn it into a hurricane and lead local scientists to rise!
Ma Yinchu looked at the formulas on the manuscript paper and expressed deep admiration: "It seems that I have learned too little after all! I didn't expect that the ideas in simple mathematical formulas can be so profound. I will study it with concentration in the next few years." Li Yu said: " There is still a lot of time in the future, I hope this book can help you.”
