"Today, the 10th, seems to be the time when the Journal of Tsinghua University will be published. I wonder if mechanical drawing will be published at the same time... Forget it, no matter, there is still some progress before establishing the thinking finite element analysis system. Try to make it within this week.
Done." Yu Hua put down his pen and thought silently.
Luo Geng had three math classes today and would not come back until the afternoon. After finishing his homework, Yu Hua got up and went to his desk to study and review the Lagrangian mean theorem explained by his master Hua Luogeng.
Learn while practicing. Learning is the stage of contact with knowledge, and practice is the stage of transforming knowledge into oneself.
Review the knowledge points explained in today's number lesson, break them down, reconstruct the knowledge, understand it deeply from multiple angles and aspects, and only then can it be considered complete.
Immediately afterwards, Yu Hua opened the book on fractions and previewed Rolle's theorem and Cauchy's mean value theorem that were about to be discussed.
In essence, many mean theorems are special cases, generalizations, and even extensions of Lagrange's mean theorem. However, Rolle's theorem is very special. It is expressed in language as a function of Lagrange's mean theorem.
The function values at both endpoints are equal.
What are the practical benefits of learning this?
It seems not.
But it is an important tool for studying specific functions, and it is extremely important to Yu Hua.
Yu Hua looked serious and his eyes were focused, and he carefully studied the proof process of Rolle's theorem and related knowledge points.
Nowadays, as the level of knowledge and knowledge information entropy are getting higher and higher, and the extent of brain evolution is lower than the increase in information entropy of advanced knowledge, Yu Hua's overall learning efficiency has gradually shown a downward trend. For mathematical knowledge points containing high information entropy
, it is no longer as simple and easy as when learning elementary mathematics before.
Information entropy is the average amount of information in a certain piece of information. The higher the information entropy, the higher the amount of information contained in it. This is the concept of the information field that Shannon, the father of information theory, will officially announce in 1948. Shannon doesn’t know yet
where.
From the perspective of information theory, every knowledge point and every theory in mathematical analysis is a typical example of high information entropy.
If you want to ask how high it is specifically?
Assuming that the information entropy value of the quadratic equation of the elementary mathematics system is 5, then the information entropy of Rolle's theorem that we are studying now is 20. The information entropy that has troubled the mathematics community for more than two hundred years may be as high as 500, or even exceed a thousand.
.
Looking at it this way, it seems to be extremely prudent, but just having numerical values is not rigorous.
Because, there is also difficulty in understanding the information.
This concept is easy to understand. A typical example is when the teacher teaches trigonometric functions in class. The top students understand it easily, but the poor students are confused. Until the get out of class ends forty minutes later, they still don’t understand what trigonometric functions are.
The difficulty of understanding information is fixed, and the speed of understanding depends on the overall efficiency of human acceptance of information entropy.
The total efficiency of ordinary people receiving information entropy is generally in the range of 0.05-1 per day, and geniuses are generally in the range of 1-5 per day, and this is often the gap between scumbags and top academics.
It takes ten days and a half for a scumbag student to learn a quadratic equation, but a eugenic student only needs to look at it to understand it, which is incomparable.
0——10, 11——20, 21——30, 31——40, etc. all belong to the difficulty level of understanding information entropy. The difficulty of understanding information entropy across each level is no longer addition, but multiplication, that is
Information and understanding difficulty with an information entropy of 10 will even double when the information entropy level breaks from two digits to three digits.
There is no upper limit on the value of information entropy, because knowledge has no limit, it only gets harder and harder.
For Yu Hua, repetitive and large-scale calculations are not a problem at all, because the information entropy of these things is extremely low, but learning and understanding abstract advanced mathematical knowledge with high information entropy requires a lot of time and energy.
Memorizing knowledge does not mean learning it. Mathematics is not about rote memorization, but about understanding.
In the past, Yu Hua could understand the knowledge of the elementary mathematics system at a glance. Now that he has entered the vast sea of fractions, this kind of thing that can be understood at a glance is gone.
Objectively speaking, while learning mathematics is fun, it is also really difficult.
The most important thing is that this is still the advanced mathematics stage, and the real mathematics has not yet begun.
Look at these knowledge monsters with extremely high information entropy, Fourier series, Laplace transform, group theory, complex variable functions, topology, Riemann curves, differential geometry, Hilbert space, Boolean algebra
, algebraic geometry, algebraic number theory...
The information entropy is higher than the previous one, and the difficulty of understanding is exaggerated. Especially the various conjectures and theories at the forefront of mathematics. For ordinary people, let alone thinking about them, they feel dizzy just by looking at them.
After the evolution of the brain, Yu Hua has almost reached the limit of human beings. The current total information entropy acceptance efficiency is about 15 per day.
Of course, despite the downward trend in learning efficiency, Yu Hua still surpasses the efficiency of any ordinary person in accepting new knowledge.
One morning passed, Yu Hua's preview progress was considerable, and he had reached the node of Cauchy's mean value theorem. On the other hand, the progress of the thinking finite element analysis system had increased from 89% to 94.5%.
There is still 5.5% left to reach the 100% target.
At noon, lunch was simple steamed buns and pickles. Yu Hua ate it with his wife, Wu Xiaoyuan, and then returned to the study to study, striving to improve the progress to about 97% today.
In the editorial office, the wall clock hanging on the wall shows the time - 12:50.
The atmosphere in the office was serious. Editor-in-chief Wen Yiduo, deputy editor-in-chief Chen Yinke, editor Tian Qi, director of the Department of Mechanical Engineering Zhuang Qianding, and reviewer Ye Qisun gathered here, and everyone waited quietly.
Today is the publication date of the Tsinghua Journal. It will be officially published at one o'clock in the afternoon.
For Wen Yiduo, Chen Yinke, Zhuang Qianding and others who have been waiting for a long time, today is particularly important.
Because today is also the day when "Chinese Mechanical Drawing" is published. After keeping it confidential in the early stages, "Chinese Mechanical Drawing" has been printed in large quantities, with nearly 10,000 copies covering areas including Peking, Tianjin and Shanghai.
We just have to wait for the publication date to be officially announced.
The atmosphere was quite solemn. Zhuang Qianding, who was well aware of the significance of this book, walked back and forth, looking at the clock on the wall from time to time, like a student waiting for his final grades, completely losing the demeanor that a Tsinghua professor and senior scholar should have.
The rest of the people did not laugh at Zhuang Qianding. Everyone knew the importance and significance of this book.
Since ancient times, literati have looked down upon each other and looked down on each other's achievements and works. However, all the 'literati' present could not and did not dare to look down on this book compiled by Mr. Zhang San.
In terms of importance, this work far exceeds the other articles published in this issue.
"Heshou, I heard that there was a draft article in the Department of Mathematics this time, written by a high school student, right?" The atmosphere in the office was too solemn, Ye Qisun spoke softly, without persuading Zhuang Qianding who was walking back and forth.
, looked at Chen Yinke who was sitting beside him, and asked.
"Yes, this article is called "Reconstructing the Lebesgue Integral". The first author is Yu Hua, a student of Peking No. 4 Middle School. The manuscript was submitted by the school professor Hua Luogeng. Brother Di and Brother Wu reviewed the manuscript and it was included in the journal library.
"Chen Yinke, who has good Qi-nurturing skills, seemed calm and calm. He tapped the table with his right index finger in a regular manner. He smiled at Ye Qisun and slowly explained.
When Ye Qisun heard this, he was surprised: "Oh? I didn't expect that today's high school students have reached the academic level of reconstructing Lebesgue integrals. It's really interesting."
As the dean of the School of Science, Ye Qisun is naturally also a mathematician, but his achievements and reputation in the field of physics are much higher than those in the field of mathematics.
Reconstructing the Lebesgue integral is an operation that not even a sophomore in arithmetic can do.
However, now a high school student has done it.
Really interesting.
"This is the genius we are waiting for in China. It's a pity that he was born at the wrong time..." Chen Yinke sighed.
In a time of national crisis and turbulent times, there is no time for a student to grow from a seedling to a towering tree.
Ye Qisun heard this, nodded silently, and said softly: "This book can at least enhance the power of my Chinese industry."
The two chatted, Wen Yiduo sat and sipped tea, not participating in the conversation, and occasionally looking at the wall clock.
Under the gaze of Zhuang Qianding and everyone, the time on the wall clock seems to have slowed down a lot, making people feel anxious and irritable.
wait.
Waiting silently.
"Click!" The second hand that keeps moving forward makes a subtle sound. As the second hand completes a circle and finally reaches the twelve o'clock position, the minute hand suddenly moves forward one step and points to 12.