Chapter 210: The Dimension of Numbers
210.
In the field of space, the study of high-dimensional projection on low dimensions is a research direction in physics, and it is also an important research field of modern mathematical geometry.
However, people's research on dimensions has always been limited to space.
The study of dimensions in the field of mathematics has also been limited to the field of geometry.
Few people have thought that 'number' is also a concept that has an actual objective concept, and can also have a concept of dimensions.
And after Cheng Li figured out this key link, he felt as if he had opened a new door and entered a new field!
Cheng Li calls this new field "digital dimension"!
The number dimension, that is, the dimension of numbers!
Of course, the point, line, and surface just mentioned are just a simple example for me to give a simple example, and the dimension of the number is by no means because of the different units, which leads to the inclusion relationship before the different numbers.
"It's not because 1 kilometer can contain 1,000 1 meters, it's because the units are different. ”
"It's not the same as 1 kilometer, which is an artificially defined unit. ”
"'Number' is a concept that does not need to be artificially defined, and objectively exists. ”
"Therefore, the dimension of number is a highly abstract concept, even more abstract than the dimension of space!"
"I can't think of a good example to illustrate, so let's use a mathematical formula to describe it. ”
Cheng Li wrote down a lot of mathematical formulas on the light sand.
In mathematics, everything ultimately speaks in terms of formulas and calculations!
According to his own understanding of the dimension of numbers, after figuring out this key link, with his mathematical level, it is easy to derive through formulas at this time, and strictly prove that 'number' is indeed the concept of existence dimension!
"That's right! 'Numbers' really have a highly abstract dimensional concept!"
Cheng Li was extremely excited and couldn't wait to start researching it.
However, after researching for a while, Cheng Li found that in the new field of digital dimension, every step is extremely difficult!
Because he found that in the field of numerical dimensions, there is too much mathematical knowledge that needs to be used!
Topology, Differential Geometry, High-Dimensional Geometry, Projective Geometry, Number Theory, Partial Differential Equations, Functional Analysis, Fractal Geometry......
In the end, Cheng Li found that it seems that as long as it has something to do with mathematics, it can be used to study in the field of mathematics. So after just a little research, Cheng Li found that there is an incomparably broad prospect in this digital dimension!
This is a new and untapped ocean of mathematics!
If a person does not have a deep and comprehensive knowledge of mathematics, even if one day he has the whimsical idea that the bold YY 'number' has the concept of dimension, then it will not be of much use.
Without rigorous proof, no impeccable logical deduction, and no detailed data calculation support, then it is useless to simply put forward an idea. If someone thinks that they have made great achievements because of this, they will end up being reduced to some kind of "civil science" that can only talk about it.
Fortunately, after the baptism of the 2999th floor of this arithmetic monument, and under the nourishment of so much mysterious information, the level of mathematical knowledge has already reached a stage of accumulation.
At this time, he was like a martial arts man who was suddenly taught by a master, and the meridians of his whole body were jammed with a lot of power, and suddenly after the meridians were opened, his cultivation was advancing by leaps and bounds, and he felt like a thousand miles a day.
After entering the field of "digital dimension", Cheng Li began to use all the mathematical knowledge he had learned in the past.
Because he found that almost all the knowledge of most branches of mathematics in the field of mathematics can be used in the field of mathematics!
"Wow, studying the dimensions of topology feels completely different.
"And the combination of topology and fractal geometry is simply the best tool for studying numerical dimensions!"
"It turns out that non-Euclidean geometry still has such a performance and application in the field of number dimensions? This is simply a perfect combination of number theory and geometry!"
"Projective geometry and affine geometry, in the field of digital dimensions, are simply reborn! God, in the field of digital dimensions, to study the projection relationship between high-dimensional and low-dimensional numbers, it is completely possible to make a direct leap forward in projective geometry!"
Cheng Li felt a little incoherent, really excited.
He had only studied the field of numerary dimensions for a while, and he actually had the feeling that many branches of mathematics that were rarely related to each other were closely combined through the realm of numerical dimensions!
The unified development of mathematics is the direction that mathematicians of all generations have been striving for.
Just as physics has been pursuing the theory of great unification, the mathematical community also has the habit and idea of pursuing great unification.
It's just that some branches of mathematics are really related to each other from the current point of view, and it's hard to see any correlation.
However, after Cheng Li entered the field of digital dimension and looked at the essence of mathematics from a high-dimensional perspective.
He found that those branches of mathematics that were rarely related to each other could be so naturally and harmoniously linked together to study the same problem!
For example, topology and number theory are perfectly combined, and even fractal geometry and number theory have various close connections.
Unconsciously, Cheng Li found that he had a vague tendency to unify most branches of mathematics through the field of digital dimensions!
Gradually, Cheng Li was about to fall into a wonderful state of epiphany.
However, at the most critical moment, Cheng Li forcibly cut off this epiphany process.
Cheng Li glanced at the time and found that 40 minutes had passed at this time, and there were only 10 minutes left before the 50-minute countdown he had set for himself.
"No, I don't have time to delve into all aspects of the digital dimension now, this digital dimension is too broad and profound, let alone give me 10 minutes, even if I give it ten years, I'm afraid I may not be able to fully understand it!
"Time is running out now, and I can't forget my primary purpose, which is to solve the Riemann conjecture!"
Cheng Li turned his gaze back to the question of the Riemann conjecture.
After a preliminary study of the multidimensional field, Cheng Li had a completely different feeling when he looked at the Riemann conjecture.
If before that, the problem he looked at Riemann's conjecture was that he was confused and felt clueless.
Now, when he looked at the Riemann conjecture again, he had a feeling of seeing through the fog and finally seeing his true body!
There is no longer that feeling of having no clue, but there is a feeling of seeing the bright moon through the clouds and mist, and it is extremely clear that the broad road that can truly solve the Riemann conjecture is found!
Now countless inspirations and countless wonderful ideas are constantly emerging, making Cheng Li quickly think about the way to truly solve the Riemann conjecture.
With the deepening of Cheng Li's thinking, a clear and direct solution idea gradually took shape in Cheng Li's mind and matured rapidly!