Chapter 32 The sprout of infinite magnitude (Part 2)
inside the house.
Looking at Mavericks with an annoyed look on his face, Xu Yun couldn't help but be filled with emotion:
Although this person's character is really slim, his brain is too good!
Take a look at what he mentioned:
Not to mention calculus, we also mentioned the concepts of normal vector, potential energy, net moment and the assumption of small deformation.
Each of the above concepts was officially made public as a theory at the earliest after 1807.
Who can achieve this kind of thinking span of 150 to 200 years?
True.
The problem raised by Hooke was actually very simple. It was so simple that Xu Yun immediately thought of nearly twenty solutions. The fastest method could be solved by establishing a covariant derivative in a non-Cartesian coordinate system.
But don't forget that Xu Yun's knowledge was acquired through later generations, and the basic theories at that time had been summarized quite well.
Just like the era of controlled nuclear fusion, you can build a 200cc engine with your eyes closed.
But what about the Mavericks?
He belonged to the era of drilling wood to make fire, but his eyes saw that the cetane number calculation formula of an internal combustion engine was so outrageous!
Thinking of this, Xu Yun felt inexplicably want to laugh:
He once wrote a novel, but as a result, not to mention Newton, even Maxwell was dissed by some comments as "I looked it up, it's just a system of equations."
Then he took a deep breath and turned his mind back to the scene:
"Mr. Newton, I very much agree with your idea, but there are many unknown mathematical tools that need to be used, and the current research progress in the mathematics community seems a bit weak."
Mavericks nodded and admitted this generously:
"That's right, but other than that, we must use the Han Li expansion you mentioned."
After finishing speaking, Maverick continued to lower his head and quickly listed another line of formula:
V(r)=V(re)+V'(re)(r-e)+[V''(re)/2!](r-re)^2+[V'''(re)/3!] (r-re)^3
Then Mavericks underlined this line of formula, frowned and said:
"If Han Li is used to expand, what should be the properties of the pinball near the stable position? This should be a series, but dividing it is another problem."
Xu Yun looked up at him and said:
"Mr. Newton, what if the stable position is calculated as a minimum value?
We assume that there is a mathematical approaching posture, that is, infinitely approaching 0?"
"Infinitely approaching 0?"
For some reason, a strange emotion suddenly appeared in Maverick's heart, as if he saw Lisa coming out of the bedroom arm in arm with someone else.
But he soon put this emotion behind him and thought about it for a while:
"Isn't that the principle of cutting a circle?"
The circle-cutting method is an early idea for calculating pi. Anyone who has attended elementary school should know this method.
It actually implies such a thought:
Although there is a gap between the two quantities, as long as the gap can be narrowed infinitely, it can be considered that the two quantities will eventually be equal.
The circle secant method has been regarded as an abandoned mathematical tool in this era. Xu Yun can casually talk about Han Li's mathematical attainments. In theory, he should not make the mistake of regressing in thinking.
Facing Mavericks' question, Xu Yun shook his head gently and said:
"Mr. Newton, the concept you are talking about is a non-series variable, but what if we go one step further and understand it as a series variable?
Or even go one step further and treat it as a constant that transcends the real number framework? ”
"Approaching 0, series variable? Constant?"
Hearing Xu Yun's words, Mavericks was stunned.
The concept of infinitesimals is a question that has caused countless university fishermen to hang on trees.
Generally speaking.
From a college student to a Ph.D., a person's understanding of infinitesimals must go through three stages.
The infinitesimals in the first and second stages are variables. When you realize the third stage, all infinitesimals become constants, and each infinitesimal corresponds to a constant.
These constants are not in the framework of real numbers, but are generated by the axioms of the non-standard analytical model.
The first stage is the understanding gained when studying mathematical analysis or advanced mathematics in college, that is, infinitesimals are as small as they need to be.
That is, the absolute value of positive or negative infinitesimal is smaller than any given positive real number.
The second stage is when learning non-standard analysis. Many calculus formulas introduce infinitesimal quantities, and concepts such as order appear.
The third stage is when understanding mathematical model theory, when infinitesimal quantities can become constants.
Once you realize that infinitesimal quantities are constants, you will find that there is a broader mathematical world. This mathematical world is wider, deeper and more complex than the mathematical world known today. The second type of limit thought and its geometric structure appears. The quasi-limit idea is given by infinite space, and the limit idea of standard analysis is given by infinitesimal space.
Then the compatibility phenomenon of Euclidean geometry and non-Euclidean geometry appeared, and the coordinates of parallel intersections can be accurately expressed.
The above situation has derived a lot of unconventional geometries, which are neither Euclidean geometry nor non-Euclidean geometry, but belong to the third type of geometry (Chinese geometry) and so on.
What is the practical significance of the third stage of understanding the infinitesimal?
The most straightforward thing to say is that you can build a supercomputer.
At present, the most in-depth research on the third stage in China is the University of Science and Technology of China. The quantum computer of Academician Pan Jianwei and Professor Lu Chaoyang is also one of the intuitive manifestations of this convenience.
Friends who have participated in supercomputer algorithm research and development interviews should all know that infinitesimal third-order cognition is a required interview question.
Although Mavericks' theoretical knowledge was not that complete at this time, as the proposer and founder of calculus - especially the concept of infinitesimals, he was vaguely able to provide feedback on this information.
Then Xu Yun took the pen and continued to write:
Assuming that the coefficient of the linear term is zero at the equilibrium position, then the minimum can only be retained to the quadratic approximation, and naturally the form of the quadratic correlation between potential energy and equilibrium deviation is obtained:
V(r)≈[V’’(re)/2!](r-re)^2
V(r)≈k/2(r-re)^2.
Write here.
Xu Yun stopped writing, glanced at Mavericks who was in a daze, and quietly turned around and left.
Before going out, he took a small bag of sugar, a little salt, half a spoonful of butter, an unused crucible and two potatoes from the table - the first few are commonly used condiments for breakfast and dinner, and the latter two are for emergencies. grain reserves.
Then he stood on tiptoes and gently closed the door.
Mavericks didn't express anything about this. He just stared blankly at Xu Yun's formula, especially the equal sign.
A few minutes passed.
His Adam's apple suddenly slid up and down a few times, and several gurgling sounds came out of his mouth.
After a moment, he rushed back to his seat and started writing quickly.
Three hours later.
Just hearing a clang, Maverick rushed out of the door.
Well, in the physical sense, he ran out of the door - he knocked the door down and held it directly in his hand.
There is no way, the house is too old.
It was past eight o'clock in the evening, so Mavericks saw at first sight a cluster of fire not far away, and Xu Yun's face illuminated by the fire.
Mavericks walked quickly to him and said excitedly:
"Fat Fish, I figured it out, it's a force that changes linearly with distance, an elastic force!
There are no requirements for its specific form. In other words, any system will exhibit elastic behavior near the steady state!
This is a formula that has not been discovered, a theorem in steady state. I bet that Hooke didn't even derive it himself, because the function he gave actually has a 0th order term! ”
Mavericks muttered to Xu Yun as he ran. When he came to the fire, he discovered that Xu Yun was lowering his head and tinkering with something:
"Fat Fish, what are you...?"
"Mr. Newton, you are here just in time."
Looking at the calf in front of him, Xu Yun picked up a dinner plate and smiled brightly:
"Freshly baked potatoes are delicious with sauce."
"Sauce? What sauce?"
"Ketchup."(End of Chapter)