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Low-dimensional prisoner

Plato’s “Utopia” has a cave metaphor. A group of prisoners are locked in dark caves, facing a stone wall. There is a torch behind them. The fire is shining, and the stone walls in front of them appear shadow. The prisoners think this is The truth of light.

Until a prisoner turned and saw the torch, he walked out of the cave and saw the sun, only to understand that the shadow was illuminated by the fire, and the range of the fire was far less than the sun. He finally knew that the real light was the sun .

The prisoner returned to the cave and told his companions that the shadow was not light, the real light was outside, and the vastness was boundless. The prisoners laughed at him and thought he was crazy.

Summer insects can’t speak ice, and that’s the truth. People are limited by the feelings of five senses, the scope of migration, lifestyle, cultural customs, and the knowledge they possess is always far less than the existing things, that is, those with little pity, and it is hard to say the truth.

Most people are prisoners trapped in this world. They cannot see the truth of the world. A small number of people can see the true light and be laughed at by other prisoners.

Ignorance is the eternal dilemma of low-dimensional people and cannot be eliminated . Can the prisoner finally get a reliable truth? Why do many people be prisoners of falsehood?

Because they are trapped in a very low dimension, and never doubt, lack of logic, always think that they are seeing the truth.

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Low-dimensional truth

The truth we see is only the low-dimensional projection of the high-dimensional truth , which is the shadow of the real form.

What is the low-dimensional truth?

A snail continually circulates on the edge of the bowl, thinking that as long as it continues to climb, there will always be an end line. The knowledge of snails is one-dimensional knowledge, it does not know that straight lines can be bent into circles. One-dimensional circles must be visible on a two-dimensional plane.

A seven-spot ladybug crawls on the sphere, it crawls fast, but it never climbs out of the sphere. Its knowledge is two-dimensional knowledge, it does not know that the plane can be curved into a spherical surface. The two-dimensional sphere must be visible in three dimensions.

It depends on “flying” into the three-dimensional space to “crawl” out the two-dimensional sphere

Humans surpass snails and reptiles, knowing that there are spheres and three-dimensional in the world, but in fact, people can not see a complete two-dimensional sphere at one time, but by continuously rotating the stereo spheres, superimposing and splicing into one by the visual segments on the side. Victorian sphere. In fact, we can’t see a complete sphere at all. Similarly, one cannot see any three-dimensional shape at a time.

As a low-dimensional creature, you can only see the low-dimensional truth. What is special about human beings is that he not only sees two-dimensional surfaces, but also superimposes and splices two-dimensional surfaces to form a three-dimensional shape.

So, will this three-dimensional world we live in is just a projection?

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Finite boundless three-dimensional universe

In the universe model of general relativity, our three-dimensional universe is indeed a small projection of a four-dimensional sphere, limited and boundless .

Since ancient times, philosophers have argued whether the universe is limited in space and formed a famous antinomy :

The universe is infinite in space.

Anti-thesis: The universe is limited in space.

The solution to this problem relies on the difficult exploration of mathematicians and geologists. From European straight geometry to Riemann bending geometry, geometricians finally use “curvature” and “circle” to quantify the degree of curvature using curvature and degree, creating an n-dimensional non-Euclidean geometry, size and boundary. The two concepts are separated.

A limited volume geometry may have no boundaries . For example, a one-dimensional circle has a limited length but no starting point and end point; the two-dimensional spherical area is limited but has no boundaries.

Einstein creatively applied n-dimensional non-Euclidean geometry to the universe, explaining the limited boundlessness of the three-dimensional universe .

The universe we live in is a four-dimensional ball. Within this ball, any three-dimensional creature, including humans, cannot perceive the curvature of the universe as a whole, but instead treats the universe as a generally flat three-dimensional space. Large celestial bodies in the universe will partially distort the three-dimensional space, just like a convex or concave surface on a sphere, but it does not affect the overall curvature of the spherical surface.

The volume of the universe is limited. It is expanding and may shrink in the future, but we will never fly this four-dimensional ball. Humans fly in the universe, crawling on the circle with snails, and walking on the two-dimensional sphere of the seven-spotted ladybug. There is no essential difference, they only move in a limited and endless curved circular space. Unless God created multiple universes, we cannot explore the edge of the universe.

What does this mean? If a person has lived long enough, the light from his back will pass into his eyes from the front after several billion years, that is, he can see his back .

The nature of the four-dimensional ball is absolutely impossible to imagine , because it is a high-dimensional truth that transcends the human eye and imagination. It is the truth assembled by humans through the low-dimensional projection visible to the naked eye.

In fact, all human cultural behaviors are assembled and spliced, from low-dimensional to high-dimensional.