Just like the grading problem of infinity in mathematics, it is also infinity, but there are also differences in Aleph 0, Aleph 1, and Aleph 2. [Note 1]
This is also the reason why Cantor was admitted to a mental hospital.
The theory he developed was too abstract and was not understood by people at the time. It was not until more than ten years after he entered a mental hospital that it gradually began to be taken seriously.
Later, Hilbert proposed the famous hotel paradox in a speech in order to popularize the concept of science. In the famous Hilbert 23 questions, the ultimate question in this area of research is the first-ranked continuum.
Assumption.
In short, any concept, if you want to push it to the extreme, will cause problems of one kind or another.
The simplest and most basic counting in mathematics has such grading problems, and the same goes for fractals.
Although there is infinite self-similarity, it is also hierarchical.
Just like the Mandelbrot Set, the magnificent patterns evolve layer by layer, and it will take a long, long time before they return to their original appearance.
And is the beginning at this time still the beginning? Are the seemingly identical patterns really the same?
Ye Han said no, there is one level at the nanoscale, one at the micron scale, one at the millimeter scale, one at the meter scale... The levels follow self-similarity, but there are some essential differences.
Therefore, there will be differences between hand-drawn spells and giant array spells, as well as differences between two-dimensional spells and three-dimensional spells.
Simply zooming in and out is definitely not enough.
Che Feng said how can you prove it?
You must know that fractals generate self-similar patterns from concise and beautiful functional forms, which are the results of iterations.
The result output of this round becomes the input of the next round, and then it is output again, and then input again, and so on, and the endless pattern gradually emerges.
However, the joint perturbation of the longitudinal scale factor and function terms of the iterative function system will lead to errors...
To put it bluntly, if you use a calculator to press compound interest, anyone who has played a number game will know that such an endless cycle will soon encounter a situation where there are not enough digits to display - when the number reaches a certain number, the calculator will not be able to display it.
It may give you exact results every time, but only approximate values.
Therefore, Feigenbaum's use of a calculator to calculate his own constant was completely accidental. When Lorenz discovered the butterfly effect, the difference in approximation of the data led to unexpected deviations in the results. This is the norm.
Although fractals have order in chaos and are full of strange beauty, the results they obtain are always approximate.
So no matter how Ye Han explained it, Che Feng could just say, "Your calculation is wrong, your result is not accurate yet, there must be something wrong."
It is really difficult to give an answer to such an important question. This is obviously a problem of the century that is as difficult as the continuum hypothesis.
But Ye Han happens to know the answer!
How do you know?
Calculating this by hand is definitely not possible, and if computer simulation does not use methods similar to renormalization, there will definitely be problems, but... that is talking about classical computers with limited computing power.
Ye Han has a quantum computer.
It does not mean that quantum computers are faster and more accurate than classical computers, so they will definitely get accurate results - fractal chaos itself is formed by extremely small deviations from infinite methods. As long as you round off, it will definitely be inaccurate.
The real reason is that classical computers are digital, and no matter what they calculate, there will definitely be approximate results in the end; but quantum computers are not digital, they are analog...
Just like the transition from analog signals to digital signals, mobile phones have also changed from big bricks to small and exquisite ones, achieving a qualitative leap.
It's just the opposite here. As computers tend to become more and more difficult and sophisticated, digital computing with pure code jumps can no longer cope with the chaotic reality, but simulated quantum computers can.
Because it is not calculated, but built to simulate the corresponding model.
Numerical calculations definitely require rounding and approximation, but simulation does not, and it can even work without numbers.
Classic computers need to calculate trillions of years of problems. As long as they find the right model, Jiuzhang and Suzhu can solve it in a few seconds, or even solve it hundreds or thousands of times.
This is not a difference in computing power at all, but a difference in mode.
For Ye Han, asking a quantum computer to calculate something feels almost the same as using a calculator.
After hearing Ye Han's answer, Che Feng's mouth was full of blood: "Pfft!" It was like Wang Lang meeting Zhuge, and like Washington facing each other.
He saw the key and calculated everything, but he never expected that Ye Han still had such a move waiting for him.
We have also taken the lead in the field of quantum computing, and have developed mature prototypes.
It was as if he had tied the most complicated knot in history, and said to others with confidence, "You can solve it. I guarantee that you will never be able to solve it until you die." Then he took out a Heavenly Sword from the other side and cut the knot with one stroke.
Everything is in disarray...
Don’t talk about martial ethics!
He couldn't even refute, because it was him who was answering, and Ye Han only needed to give a reasonable explanation.
This is what is meant by the so-called quick step, step by step. Seize the opportunity and do not give future generations a way to survive.
After vomiting blood for several minutes, the score finally reached 1.5:2.5.
Ye Han, who was behind, completed the overtake, and there was not much time left for Che Feng... No, to be precise, there was no time left.
Because of two rounds of questions and answers and four confrontations, Ye Han's performance had shattered his confidence. His little world began to become unstable, as if it collapsed and disintegrated like Ye Han, and he could no longer hold on.
Vomiting blood for a few minutes is not an exaggeration, it is real.
The small world collapses, the flesh vomits blood, the spiritual world is full of illusions, and the soul is tortured...
Regarding the collapse of Taoist heart, everything is perfectly justified.
In fact, like Ye Han, who is collapsing over there, but can still defend himself as if nothing happened, is an alien, no, he can be called a monster!
If this point hadn't been missed, Che Feng would have won without a fight, and there would be no future.
But why?
For other cultivators, the collapse of the great path is more terrifying than being possessed. How can Ye Han be like a normal person? This is something Che Feng, who fainted on the ground, cannot figure out.
To put it bluntly...well, it's quite complicated.
First of all, Ye Han has a golden body.
The integration of the golden body can directly improve the cultivation level, while the unfitness of the golden body can be slowly infused. During this period, it can also continue to help the body share the damage and reduce the burden from the body to the soul.
Secondly, Ye Han is a pioneer of science.
The person who climbs the mountain at the front will have a difficult and dangerous path, but there will also be some benefits, that is, once you go the wrong way, it will be easier to turn back than others, and you will receive the least punishment from heaven.
Only the people at the front of each road know this, and the people at the back are not clear about it, just like a scumbag can never understand the world of a top student.
But the most important point is the third point, the particularity of scientific method.
For all other roads, everyone climbs from the beginning. The sages left many words, but the words of the sages can only be used as reference. They must be understood, implemented, revised, and tried again... By studying things to gain knowledge, and integrating knowledge and action, only in this way can it truly become one's own.
thing.
To describe it, it's like writing an essay.
You will have a lot of corresponding accumulation and learn a lot of principles of writing essays, but when it comes to the examination room, it is still quite difficult to ensure that you get full marks every time you write essays.
The way of science is clear and distinct, and verified theorems are not references, but answers, which are universally applicable to the universe... Later practitioners stepped on the mountain of truth that will never collapse.
It's like a science exam. Once your IQ and your thinking level are up, it's very difficult to get a perfect score.
Therefore, although Ye Han's world collapsed, it actually only collapsed the layer he built himself. It was not that the entire mountain collapsed. In addition, the burden of the golden body and the welfare of the pioneers were affected to some extent. It was really impossible to do anything.
There are still no big problems with the cannon.
Even the floor he built himself didn't collapse. It was more like... he discovered that there were problems with the structure and the decoration didn't look good. Then he calculated the load-bearing capacity of the frame structure, blasted it at fixed points, and started over.
This kind of self-realization collapse and being pushed to the point of collapse by other people's words are completely different things.
Even if Che Feng missed so much, it was natural for him to be in trouble.
[Congratulations, you have won this mountain gate challenge. From now on, Yemen can be independent from the computer Tao and become its own sect, no longer affected by the old Tao rules. 】
【You can rename the sect.】
[Congratulations, you have obtained the achievement of "Pioneer of the Great Path". The Great Path is not dreamed up, but recognized and fought for!]
Since returning from the battlefield of time, whether it is martial arts, items or attributes, they have become more and more vague, and the labels have become simpler and simpler.
It seems that at this level, the arena system is no longer able to measure the strength of an item very accurately. It has something to do with people's thinking, perception and cognition.
It seems that in the later stages of Dragon Ball, the combat power can reach hundreds of thousands, millions or hundreds of millions, and the numbers below tens of thousands or even below billions are basically omitted.
Ye Han didn't quite understand the specific effect of being a pioneer in the avenue, but he could vaguely feel that it would allow him to maintain a certain advantage in the avenue, support underachieving disciples, or suppress others in the same path.
People like Che Feng may not have the chance to challenge him in the future.
But how exactly it works, I'm afraid no one can tell clearly.
Tsk, is this the end? Randomly scanning the system prompts, looking at Che Feng who was vomiting blood and unconscious and being carried out, Ye Han sighed quietly, why did he faint? There is one last question that has not been discussed...
That’s the real big problem——
In the Dharma-ending world, is the spiritual energy really completely exhausted?
Is the science of the earth real science? Or is it science that is still unknowingly influenced by beliefs and distorted by cluster consciousness?
Which ones are absolute, which ones are relative, and which ones need to be modified?
If it wasn't such a big topic, how could it possibly cause Ye Handao to be so damaged that he had to start over from scratch?
It's a pity that Che Feng didn't hold on. If he had known this, he should have brought it up in the second round... What a pity!