Chapter 32 The Germination of Infinite Scale (Part 2)
in the house.
Looking at Mavericks with an annoyed look on his face, Xu Yun couldn't help but be filled with emotion:
Although this guy's character is really slim, his brain is really awesome!
Take a look at what he mentioned:
I won’t talk about calculus, but 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.
This kind of thinking span of 150 to 200 years... I wonder who can do it?
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' study, and the basic theories at that time had been summarized quite perfectly.
It's like the era of controlled nuclear fusion, when you can build a 200cc engine with your eyes closed.
But what about Mavericks?
He belongs 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, the Han Li expansion you mentioned must be used."
After finishing speaking, Mavericks continued to lower his head and quickly listed another line of formula:
Then Mavericks underlined this line of formula, frowned and said:
"If Han Li expansion is used, 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?
Let us assume that there is a mathematical approaching posture, that is... approaching 0 infinitely?"
"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 an idea:
Although there is a gap between the two quantities, as long as the gap can be reduced 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 this mistake of thinking backward.
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 take it one step further, and think of it as something that transcends the real number frame... and is always on?"
"Approaching 0, series variable? Constant?"
Hearing Xu Yun's words, Mavericks was stunned.
The concept of infinitesimals is a problem 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 when you go to college to study mathematical analysis or advanced mathematics. At this time, infinitesimal is a variable, that is, infinitesimal is as small as it needs 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. At this time, 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 second type of limit thinking 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.
And what is the practical significance of the third stage’s understanding of infinitesimals?
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.
Xu Yun then took the pen and continued to write:
The coefficient of the linear term of association is zero at the equilibrium position, so the minimum can only be retained to the quadratic approximation. Naturally, the form of 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 it 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 tiptoe and gently closed the door.
Mavericks had no idea about this. He just stared blankly at Xu Yun's formula, especially the equation 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, the calf rushed out of the door.
Well, in the physical sense, he rushed out of the door - he knocked down the door 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 glance 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 show elastic behavior near the steady state!
This is a formula that has not been discovered, a theorem in a steady state. I bet that Hooke didn’t even derive it himself, because the function he gave actually has a zero-order term!”
Mavericks muttered to Xu Yun as he ran. When he came to the fire, he discovered that Xu Yun was tinkering with something at this time:
"Fat Fish, are you...?"
"Mr. Newton, you are here at the right 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 the sauce."
"Sauce? What sauce?"
"ketchup."
.......
Note:
Do you still remember the tomato mentioned when introducing the tableware? Hehehe...
