Chapter 440 Low-Dimensional Expansion
“Ning Chen, there must be no problem here. I don’t need to rest. Where are you, Professor Tao?”
“I have no problem either. In that case, Academician Ning, there is no need to take any more rest. Let’s strike while the iron is hot and try to prove Goldbach’s conjecture as soon as possible.”
Speaking of which, Tao Zhexuan is still a little tired now, but he is still there. Tao Zhexuan would not be so exhausted that he could not work. In previous research, Tao Zhexuan would not easily rest under such circumstances, but would continue to work.
Especially this research, its research significance and research value are so huge that Tao Zhexuan is even less likely to waste even one day. This motivation to crack Goldbach's conjecture is enough to support Tao Zhexuan persisted.
Seeing that neither Song Xiyun nor Tao Zhexuan had any intention of resting, Ning Chen first used Xiaozhi's information perception function to confirm that both Song Xiyun and Tao Zhexuan were in acceptable physical condition before agreeing to their request.
“Okay, since both of you said so, let’s continue working tomorrow. But let’s all take a good rest tonight. The next stage of work will only be more difficult than the previous one. "
Tao Zhexuan and Song Xiyun accepted Ning Chen's request very readily. After all, they both felt a certain amount of fatigue. It was also a good idea to take a good rest today. It’s a matter of “sharpening your sword will never make you chop wood again”.
Early the next morning, Ning Chen, Tao Zhexuan, and Song Xiyun arrived at their workplace on time and started a new stage of work.
In this stage of work, they need to use the prime number four-dimensional space model they have just constructed before to complete the proof process of Goldbach's conjecture.
This work will not be as easy as it seems, because they need to find the connection point between the two problems and try to deduce relevant theoretical formulas that conform to all prime numbers through the four-dimensional space model of prime numbers.
Fortunately, after a night of adequate rest, Ning Chen and the three of them were in relatively good physical and mental condition, and their previous tiredness was gone.
"Professor Tao, Teacher Song, now we will try to simplify the complex four-dimensional space model representation of prime numbers into a formula representation in a conventional sense. This work has never been done in previous mathematical research. have never appeared before, so we need to find a very novel method suitable for such a transformation..."
Listening to Ning Chen's words, Tao Zhexuan and Song Xiyun were also thinking constantly. , try to find a suitable method.
It is difficult to transition from a simple problem to a complex problem, but it is a task to turn a difficult problem into a simple problem while ensuring that the nature of the entire problem remains unchanged. Something more difficult.
"The representation of Goldbach's conjecture itself is very simple. Even a primary school student can easily understand this problem. But it is completely impossible for them to understand the four-dimensional representation of prime numbers... …”
Tao Zhexuan is also well aware of the difficulty of this matter. Normally, if a complex problem is presented in a simplified manner, a lot of important information will be omitted, and it is difficult to strictly analyze the two. equivalent value representation.
At this time, Song Xiyun seemed to have thought of something, and said to Ning Chen and Tao Zhexuan:
“Can we think about this problem in a different way, for example, this is a three-dimensional space? Although the mass and volume of the particles are very small, they actually carry a lot of information, because if you want to describe them in detail, they must be processed in three-dimensional space. Otherwise, it is It is absolutely impossible to describe it accurately..."
Both Ning Chen and Tao Zhexuan listened carefully to Song Xiyun's thoughts and tried to understand what Song Xiyun wanted to express.
"But in fact, if we reduce the dimension, it is still possible for us to describe it in theory. It is like expanding a three-dimensional figure into a flat figure. We can expand the matter in the high-dimensional space into a low-dimensional one. It is described in a lower dimension..."
Song Xiyun's words suddenly opened up the minds of Ning Chen and Tao Zhexuan, which made them both feel that the direction of Song Xiyun's thinking was A very feasible direction.
"So, this method can theoretically achieve the conversion from four-dimensional space to three-dimensional space. But it is not enough to just rely on the expansion of high-dimensional space in low-dimensional space. We We must also set up a conversion method between two different dimensional spaces..."
Ning Chen was thinking based on Song Xiyun's ideas, and soon thought of another important issue.
“It’s like we get a flat expansion of a three-dimensional figure, but if we don’t know how it unfolds, we still can’t restore it in a three-dimensional space. It’s just that we are all used to dealing with this. This kind of problem, subconsciously knows how to deal with such a flat expansion diagram, but the same problem becomes much more complicated with prime numbers.”
"Academician Ning is right, I have the same idea as you. Teacher Song's idea is very novel, but we must also define the transformation conditions of one dimension, so that we only need to use simple formulas in three-dimensional space. Determine its representation in the four-dimensional space, and make the two completely equivalent."
After determining this research idea, Ning Chen, Tao Zhexuan, and Song Xiyun. , began to think about this issue.
Fortunately, until now, the four-dimensional space state of the prime number still exists in Ning Chen's brain, which allows Ning Chen to make comparisons very conveniently.
After some research, the three of them determined their approach to this problem.
They will continue to analyze and calculate this problem by composing the brain biological computer architecture, and Ning Chen will continue to be the core of the entire brain biological computer architecture.
The difference from the last time is that this time they need to try to expand the four-dimensional space form of this prime number. This research method is a very huge test for them.
After the research officially started, Ning Chen and the other three quickly entered a high-intensity brain biocomputer state and formed a connection channel between each other.
Through this special connection method, Tao Zhexuan and Song Xiyun also felt the four-dimensional spatial state of the prime number that existed in Ning Chen's brain.
Ning Chen tried to expand the form of this prime number into a low-dimensional form. However, because Ning Chen had never made the same attempt before, the initial research was not smooth.
With no choice but to do so, Ning Chen had no choice but to start with the local area, and first tried to use projection to search for the projection of the material in the four-dimensional space under the three-dimensional space.
This job was much easier than the previous job. Within a short while, Ning Chen had obtained a large number of projections, and these projections were completely non-repeating.
Ning Chen knew that if he kept searching like this, he could theoretically get countless such projections. Such work would not help Ning Chen achieve their goals, so Ning Chen began to search for these three-dimensional projections. In the projection, we are looking for some internal connection between them. "Academician Ning, the number of three-dimensional space projections that can be used by us must be limited. This specific number... I will calculate it soon..."
Tao Che Xuan seemed to have discovered something important, and after Tao Zhexuan's prompting, Ning Chen immediately realized this problem.
“42...yes 42!”
Shortly after Ning Chen blurted out this number, Tao Zhexuan also nodded quickly.
"Yes, it is indeed 42! Academician Ning, your calculation speed is really too fast. Even though you started calculating after me, you still calculated this result before me."
“This mainly relies on the key ideas provided by Professor Tao. The calculation problems are relatively easy to solve.”
In terms of calculation speed, Ning Chen is definitely much stronger than Tao Zhexuan's, after all, Ning Chen's brain biocomputer ability is unique. The technology produced by the "original" system is still much better than the reproduced technology.
Listening to the conversation between Ning Chen and Tao Zhexuan, Song Xiyun seemed a little confused.
"What are you two talking about? Why can't I understand it at all? Can you let me understand it first?"
Next to Ning Chen and Tao Zhexuan, Song Xiyun still felt it. There was a very obvious gap. Before, she could barely keep up with Ning Chen and Tao Zhexuan's thoughts. This was Song Xiyun's limit.
"It doesn't matter, Song Xiyun, this problem is indeed not that easy to understand. I will explain to you our analysis process..."
After all, Song Xiyun is also the top in the world today. One of the mathematicians, under Ning Chen's explanation, quickly understood the principle.
"That's it. In theory, we only need to obtain 42 valid three-dimensional projections, and through these projections, we can completely determine its representation in the four-dimensional space. It's just Ning Chen, I still I can’t figure it out, how did you calculate so quickly? Even if I were to do it again, I wouldn’t be able to complete all these complex calculations in almost an instant.”
"It's hard for me to explain this. Maybe it's just my instinct. In fact, as long as we can make good use of the brain's biocomputer technology, there won't be much difference in calculation speed between us."
Ning Chen deliberately didn't I stayed on this topic for a long time, but continued to lead Tao Zhexuan and Song Xiyun in follow-up work.
After several days of continuous work, Ning Chen and the others finally found several effective three-dimensional projections, which all fell within the 42 effective projection ranges.
While working these days, Ning Chen, Tao Zhexuan, and Song Xiyun have gradually found some feelings, and they have become more and more comfortable in doing this work.
Now that they look at objects in the four-dimensional space, they can easily accept this existence, as if they themselves also live in the four-dimensional space.
"Ning Chen, do you think there really is such a four-dimensional space in this universe? In this four-dimensional space, are there any four-dimensional creatures? What would they look like? What? "
"I can't be sure about this question, but if these four-dimensional creatures really exist, they may look at us like we look at ants, otherwise they will definitely not care about our existence. It is absolutely impossible for us to survive until now. "
This is just like when humans encounter ants, they will not destroy them all. This is not because humans do not have such abilities. It's just that there is no need to do such a thing.
As for if this kind of four-dimensional creature really wants to attack humans... then humans will not have any ability to resist.
“Now is not the time to think about this kind of problem, let’s finish the work at hand first. When we have enough ability, we can try to build a real science fiction island on the new science fiction island. 'Fourth dimension'," Tao Zhexuan said.
Ning Chen and Song Xiyun didn't have much thought, spending too much time discussing a philosophical issue at this time, but continued to discuss the search for effective projections of prime numbers.
After some research, the three people summarized several previously discovered rules of effective projection and formulated a new plan for finding effective projection.
The new plan indeed has a higher search efficiency. In the same time, they found more than twice the effective projections before, and the final progress is less than half the current progress.
…………
Finally, after a month of work, Ning Chen, Tao Zhexuan, and Song Xiyun found all 42 effective projections and successfully found one of the two different dimensions. conversion method between.
With this research result, it has become much easier to prove Goldbach's conjecture. The problem of infinite workload they encountered before has finally found a solution.
“Academician Ning, we have finally found a new law of prime numbers. With the support of this law, even though the number of prime numbers is still infinite, we can already express them through finite formulas. There will no longer be a situation where the workload can never be completed!”
What also makes Ning Chen happy is that under Xiaozhi’s evaluation, the progress of this research project has suddenly improved! , which is enough to prove how helpful their research results will be in proving Goldbach's conjecture.
"Yes, although the work during this period was very hard, we finally got the results we wanted. If we continue to study at this rate, maybe we will soon be able to give Goldbach's conjecture to The proof came out.”
(End of this chapter)