Into the Immortal Cultivation

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The path to the truth is not unique.

This is what mathematics itself told Wang Qi.

In the eyes of ordinary people, the space is straight. For them, European geometry is the geometry that naturally arises in this material world.

But in fact, there is no "straight line" in nature. There are no less artificial traces in the concept of "straight line" than "circular arc" and "hyperbola". The European geometry is also not naturally generated. It just simulates nature and space according to human senses.

If there is a wise race, the main senses are completely different from humans, then their geometrical concepts will be completely different from humans.

Just like Poseidon. The geometry they first developed was not Euclidean geometry, but Li's geometry with positive curvature. This is because they have no so-called "eyesight" at all, and the most important perception is the senses similar to spiritual consciousness. On the other hand, their bodies are too large, which makes them aware of the curvature of the planet early.

And Wang Qi only recently learned that in fact, there is a known race, and the natural concept of space is Roche geometry with a negative curvature.

That is the dragon family.

In the past history, there has been very little dialogue between the human race and the dragon race. . Even if there are occasional people with the same smell and the Dragon clan together, the first thing they do is fight and exchange practices. The strange thing is to eat and drink and experience the experience of foreign ethnic customs. Occasionally there are some rare things. But, sit down and talk about geometry ... it's really rare.

That is Wang Qi. In the past few days, in addition to the step-by-step development of data-based practice, he is preparing to teach Gou Dabao at home. During this period, he and everyone who could discuss had discussed similar issues-mainly Chen Youjia and Mi. If it were n’t for Yueluo Liuli, he was really bored, and Wang Qi did n’t even want to talk to her.

However, in this talk, Wang Qi knew the magic of creation.

The dragon race is almost omnipotent today, free from the shackles of the innate blood, and the cultivation system has multiplied to its peak. However, such a strong ethnic group also has a weak age.

In the Mesozoic generation more than one billion years ago, the Dragon tribe was just an ordinary ethnic group in the ocean. At that time, they were not as innately spiritual as they are now. Like many reptiles, the eyes of the ancient dragons are weak. And in the sea, there are too many factors that affect the propagation of light.

At that time, the future overlord of China could only rely on voice. They rely on sound for communication, and sound for positioning their prey.

For ancient dragons, sound is equivalent to light for humans.

The problem is that light always travels in a straight line. The propagation of sound waves in seawater does not always go straight. At a certain depth, the speed of sound propagation is proportional to the water pressure-in a sense, it is also proportional to the distance from the water surface. In other words, the sound travels in an arc in the water.

If the arc is accurately described, then it is-"the arc whose center is on the surface of the ocean".

In the dragon world, the curvature is always negative.

In their conception, the inner angle of the triangle is always less than 180 degrees, there is no rectangle, and the right-angle pentagon is the most easily understood concept.

After hundreds of millions of years of evolution, the sonar that the Dragon Clan depended on for survival had long been transformed into a majestic Dragon Yin that was not like marine life. However, some concepts of the past have always been maintained to the present.

For example, in Dragon Martial Arts, it is difficult to find the "stabs" that go straight.

For the Dragons, non-European geometry is called "meta painting", while European geometry is called "highland painting", and Li's geometry is "dome painting".

Back then, Junjun joked that there might be alien creatures, looking at the world from the perspective of non-European geometry. When he said this, he never thought that in fact there is such a species above the Divine Land.

In this respect, whales that also use sonar localization do not have the perspective of the dragon. This is because most of the practice of the demon clan is stolen from the human clan, and many ideas come from the human clan. In terms of civilization, they belong to the assimilated part of human civilization.

Gou Dabao was deeply shocked again about Wang Qi's exposition.

And then, it is the key to Wang Qi's story.

"So, do you think that the human race, the dragon race, and the huge alien [referring to the sea gods] I said before can't understand each other?"

Gou Dabao took a deep breath: "No ... Mr. also said that my human race can already understand the so-called Roche geometry and Lai geometry ..."

"Actually, in mathematics, Roche, Lai, and Euclidean are all equivalent. This is like Shinto, Martial, and Ghost. Although the methods are different, they are all monks, and the ultimate goal is to live for a long time. "Wang Qidao said:" This illustrates two points: First of all, the real "geometry" is beyond the conventional perception and conventional thinking of ordinary creatures. Even if it is as strong as the dragon, it can not only be under this heavy "rule". Can't perceive directly. The second point is that the road is the same. Whether it is from European geometry with zero curvature, or from Lewis geometry with positive curvature and Roche geometry with negative curvature, we can finally reach that final state. 'Geometry'. "

"Three thousand avenues, the same way ..." Gou Dabao just felt inexplicably moved. He almost fell to the ground and worshipped Wang Qiding.

At this moment, he had no qualms about the cultivation of Wan Famen.

Wang Qi nodded slightly. He never thought that science was the only truth in the world. However, the greatest advantage of science is that it is the path of "one way is the way of ten thousand people." One person can present the results of his own thinking to another person without reservation, and he can work together. In addition, it can also constantly overthrow itself, rebuild itself freely, and keep on nirvana. Therefore, science has an almost eternal vitality that no one can beat.

Wang Qi is very satisfied with the change of Gou Dabao's thinking.

He stood up and instructed Gou Dabao, saying: "You then practice Yi Jiu Shujing, and then practice for three more days. After you have a certain understanding of the practice of mathematics, you will abolish the current mana and rebuild it again!"

"Yes." Gou Dabao nodded solemnly. Seeing Wang Qi leaving, he hurriedly shouted: "Mr. Wang! Wait a minute! Students still have questions to ask!"

Seeing Wang Qi stop, Gou Dabao held a discipleship and asked, "The disciples heard that the fortune teller produced a book, this is a fortune-telling book. And there are 500 pages in this fortune-telling book. I am talking about 'One Plus One'. The disciple begged my husband to come and tell me about this one plus one. "

Wang Qi frowned: "Your current level, it seems too early to read that scripture."

Gou Dabao's mathematics level is full of junior high school, and will never reach high school. And theoretical monographs are often things that college students can't move.

This is like building a foundation period and challenging the infancy. Although there is a special foundation period such as Wang Qi in the world, Yuanying's crushing foundation is the norm.

"The disciples did not dare to seek extravagance, but only the truth."

Wang Qi thought for a while, this should be the first time Gou Dabao showed interest in mathematics, it is really not good to refuse this request, and then said: "Okay, then I will tell you about it."

The two sat down again. Wang Qi started from set theory again and gave Gou Dabao the definition of "when a set containing one element is merged with another set that also contains one element, the resulting union will always have two elements", which is extended. Go and talk about many others.

Instead Gou Dabao was confused: "One plus one equals two ... one plus one equals two ... this ... there is so much to say ..."

Wang Qi chuckled: "That's it."

"It's amazing!"

Wang Qi shook his head: "It's a pity, for now, this is just a loft in the sky, it looks beautiful."

Gou Dabao puzzled: "Why?"

"Because of its foundation, it has not been confirmed yet." Wang Qi said here, adding in his heart: And it is impossible to confirm.

Gou Dabao's eyes widened: "Why? This is not self-evident ... ah ..."

Wang Qi once said to him that "self-explanatory" is a taboo to seek the way. Everything must ultimately fall on the text.

Gou Dabao's collapse of his worldview: "Could it be said that one plus one may be equal to three? Is it equal to zero?"

"You cannot deny this possibility logically." Wang Qi said: "We have not proved that set theory is completely self-consistent, so logically, there is really no way to assert that one plus one equals three cannot be proved ... "

"How can this be……"

Wang Qi asked back: "Can you find out" one "and" two "?"

What is "one"? What is "two"?

This is also a simple and complex problem. Say it is simple, and children who can't speak can distinguish it. Saying that it is difficult, even a mathematician of the rank of Pang Jialai will be bothered by it.

Gou Dabao first wrote a "one" on the ground, but Wang Qi drew a circle, saying: "Now, I stipulate that this circle means" one "," single "," one "."

Gou Dabao suddenly realized. He held out another finger. Wang Qi still shook his head: "This is 'a finger', not 'one'."

What is "one"?

"One" is a concept, an objective fact that transcends human thinking.

In front of this Zen machine, Gou Dabao shivered. He said: "Also ask the teacher to solve the puzzle."

"The 'number' itself is self-contained, people just extract it from the natural world. This does not only mean integers, but also includes delusions and transcendental numbers. It comes from the square. And the typical transcendental number of pi is to get the circle. "Wang Qi said lightly:" We never invented numbers. We found numbers. We know numbers, not by rational thinking, but Innate feelings. "

"This is the essence of" number "?"

Wang Qi nodded and then said: "The numbers are the natural product of the world. They don't need to follow the concept of people. However, from beginning to end, no one is worried about 'one plus one equals three', why do you think?"

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