There is no single path to truth.

This is also what the mathematics itself tells Wang Qi.

In the eyes of the average person, the space is straight. For them, Euclidean geometry is the geometry that comes naturally out of this material world.

But in reality, there is no such thing as a "straight line" in nature. The concept of "straight line" has no less traces of artificial carving than "arc" and "hyperbola". Euclidean geometry, on the other hand, is not spontaneous. It is just according to the human senses, simulating nature, simulating space.

If there is an intelligent race whose primary senses are completely different from those of humans, then their concept of geometry will be completely different from that of humans.

For example, Poseidon class. The geometry they first developed was not Euclidean geometry, but Richter geometry with positive curvature. This is because they have no so-called "vision" at all, and their primary perception is a sense similar to spiritual sense. On the other hand, their bodies are too large, which makes them aware of the curvature of the planet itself early on.

And Wang Qi recently learned that, in fact, there is another known race, born with a spatial concept, which is Roche geometry with negative curvature.

That's the dragons.

In the past, there was very little dialogue between the human race and the dragon race...... Even if there are occasional similar-smelling Terrans and Dragons getting together, the first thing they do is to fight and exchange cultivation, and the strange thing is to eat, drink, and experience the customs of different races, and occasionally trade a little rare things. But sit down and talk about geometry or something...... It's just too little.

That is, Wang Qi. In the past few days, in addition to developing the data-based method step by step, he is preparing a lecture for Gou Dabao at home. During this time, he and everyone who could discuss similar issues – mainly Chen Youjia and Mi. If it weren't for the fact that the moon fell and Liuli was really bored, Wang Qi wouldn't have the idea of talking to her.

But this talk. Wang Qi knew the magic of creation.

The dragon clan is almost omnipotent today, getting rid of the shackles of innate bloodline, and the cultivation system has multiplied to the peak. However, such a strong ethnic group also has weak times.

More than a billion years ago, in the Mesozoic Era, dragons were just an ordinary race in the ocean. At that time. They didn't have the innate spiritual sense they had now. Like many reptiles, the Elder Dragons had weak eyesight. And in the ocean, there are so many factors that affect the propagation of light.

At that time, the future overlord of Shenzhou could only rely on sound. They rely on sound to communicate, and they rely on sound to locate their prey.

Sound is to the ancient dragons what light is to the human race.

The problem is that light always travels in a straight line. The propagation of sound waves in seawater does not always follow a straight line. at a specific depth. The speed at which sound travels is directly proportional to the water pressure – in a sense, it is proportional to the distance from the water. In other words, sound travels in an arc in the water.

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

In the world of dragons, curvature is always negative.

In their conception, the sum of the inner angles of a triangle is always less than 180 degrees, there is no rectangle, and the right angle pentagonal is the easiest concept to understand.

After hundreds of millions of years of evolution. The sonar that the dragon clan relied on for survival back then has long since turned into a dragon roar that is not as majestic as a sea creature. And some of the ideas of the year. But it has always remained until now.

For example, in dragon martial arts, it is difficult to find a straight "stabbing attack".

For the dragons, non-Euclidean geometry is called "meta-painting", while European geometry is called "highland painting", and Lai's geometry is "dome painting".

Shui Jun once joked back then. Maybe there are alien beings who see the world from a non-Euclidean perspective. When he said this, he never thought that in fact, there was such a species above Shenzhou.

In this regard, the same whales are located using sonar. There's no dragon-like perspective. This is because most of the cultivation methods of the demon race are stolen from the human race, and many ideas come from the human race. In terms of civilization, they belong to the part that has been assimilated by human civilization.

Regarding Wang Qi's discussion, Gou Dabao was deeply shocked again.

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

"So, do you think that the human race, the dragon race, and the alien race with a huge body [referring to the sea god class] I mentioned before can't understand each other?"

Gou Dabao took a deep breath: "It's not ...... Sir also said that our human race can already understand the so-called Roche geometry and Li geometry......"

"In fact, in arithmetic, Roche, Lai, and Euclidean are all equivalent. It's like Shinto, martial arts, and ghosts. Although the practice is different, they are all monks, and the ultimate goal is to live forever. Wang Qi said: "This shows two points: first, the real 'geometry' is beyond the conventional perception and conventional thinking of ordinary creatures. Even if it is as strong as the dragon clan, it can't be directly perceived only under this heavy 'rule'. The second point is that the road leads to the same end. Whether we start from Euclidean geometry with zero curvature, or from Rieche's geometry with positive curvature or Roche geometry with negative curvature, we can finally reach that ultimate state, real 'geometry'. ”

"Three thousand avenues, different paths to the same end......" Gou Dabao only felt inexplicably moved. He almost bowed to the ground and bowed to Wang Qi.

At this moment, he no longer had any problems with the cultivation of the Ten Thousand Methods.

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

For the change in Gou Dabao's thinking, Wang Qi is already very satisfied.

He stood up and instructed Gou Dabao, saying, "You continue to practice the Yi Ji Sutra, and practice for another three days, and after you have a certain understanding of the cultivation method of arithmetic, you will abolish the current mana and re-cultivate it again!"

"Yes. Gou Dabao nodded solemnly. Seeing that Wang Qi was leaving, he hurriedly shouted, "Mr. Wang! Wait a minute! The student still has questions to ask!"

Seeing that Wang Qi stopped, Gou Dabao took the disciple salute and asked, "The disciple heard that the master has published a book, which is a sutra. And in this sutra, there are 500 pages of 'one plus one'. The disciple begged the gentleman to come and tell me about this 'one plus one' again. ”

Wang Qi frowned: "Your current level, looking at the scriptures, it seems to be too early." ”

Gou Dabao's math level is only junior high school if he is full, and he will definitely not reach high school. Theoretical monographs, on the other hand, are often things that college students can't chew.

It's like building a foundation and challenging the infancy. Although there is a special foundation building period of Wang Qi in the world, it is the norm for Yuanying to crush the foundation.

"The disciples don't dare to understand it, they just want to understand it. ”

Wang Qi thought about it, this should be the first time Gou Dabao showed interest in mathematics, and it was really difficult to refuse this request, so he said: "Okay, then I'll tell you about it." ”

The two of them sat down again. Wang Qi started with set theory, and gave Gou Dabao the definition of "when a set containing one element is merged with another set that also contains one element, the union obtained always has two elements", and then extended it to many others.

Gou Dabao was confused: "One plus one equals two...... One plus one equals two...... This...... There's really so much to say about this......"

Wang Qi chuckled: "That's it." ”

"That'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 was puzzled: "Why?"

"For its foundation has not yet been proven. Wang Qi said this, adding in his heart: And it is impossible to confirm it.

Gou Dabao's eyes widened......: "Why? Ah......h

Wang Qi once said to him that "self-evident" is a taboo in seeking the truth. In the end, everything has to fall on words.

Gou Dabao looked like his world view was collapsing: "Could it be that one plus one is still equal to three?"

"Logically there is no denying this possibility. Wang Qi said: "We have not yet 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 is this possible......"

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

What is "one" and what is "two"?

Again, this is a simple and complex question. It's so simple that even children who can't speak can tell it. Saying that it is difficult, an arithmetic of the level of Arithmetic Jun Pang Jialai will also be troubled by it.

Gou Dabao first wrote a "one" on the ground, but Wang Qi drew a circle casually and said: "Now, I stipulate that the meaning of this circle is 'one', 'single', 'one'. ”

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

What is "one"?

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

In front of this Zen machine, Gou Dabao trembled. He said, "Please also ask the teacher to solve your doubts." ”

"The 'number' itself is self-contained, and man simply pulls it out of the nature of heaven and earth. This doesn't just mean integers, but also delusions and transcendentals. The typical delusional number, the root number two, is derived from the square. And the typical transcendence of pi is derived from the circle. Wang Qi said lightly: "We have never invented numbers. We found the numbers. We don't rely on rational thinking to understand numbers, but on our own feelings. ”

"This is the essence of 'number'?"

Wang Qi nodded, and continued: "Digital skills are a natural product of heaven and earth, and they don't need to follow human concepts. But, all the while, no one worries about 'one plus one equals three', why do you think?" )

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