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We use high-dimensional objects to test low-dimensional, and the specific experimental objects used are high-dimensional objects.

Objects that exist in higher dimensions are invisible and intangible.

Just like a two-dimensional circular pattern for example, in one-dimensional space, it can only see points, not lines.

So it can't understand what exactly a circle is.

In the same way, if a sphere passes through a plane, you can't see the sphere in two-dimensional space, and you can't understand what the sphere is.

In three-dimensional space, if we want to do an experiment of a four-dimensional space "sphere" through three-dimensional space, it is extremely difficult to understand.

Because we've never seen anything like this, how can we imagine it?

We've tried to explain it, and we've come up with a lot of conjectures, is it true that the fourth dimension is time?

No, Xiao Hao can be sure of this.

Because the unit of measuring time is completely different from the length, width and height.

One-dimensional, two-dimensional, and three-dimensional space, length, width, and height are all units of length, and the measurement of four-dimensional space should also be units of length.

In 3D, we can understand front and back, left and right, up and down, and can use the spatial Cartesian coordinate system to understand with three lines perpendicular to each other.

But the fourth dimension, we can't understand, the fourth line that is perpendicular to the length, width and height at the same time, we don't have the perspective of the four-dimensional space, so we can't imagine it.

Although it is unimaginable, it can conceive of a four-dimensional space through rational deduction.

In a one-dimensional space, what only exists in this space?

Either it's nothingness or it's a point, and there is no line.

Its perspective can only see the dots, either the dots or the nothingness, how do you ask it to imagine the pattern?

It has an extremely limited viewing angle and can only see the dots.

It can't understand that in this world, there are ever-changing patterns.

Its mind is dead, and it can only understand what the color of the dot is.

The pattern composed of lines is so complex that it bursts with limited thinking, and it fails to understand the essence of the pattern.

In the same way, creatures in two-dimensional space can only see patterns, but do not see the "vision" of concrete substances.

Its mind is dead, and it can't see the strange concrete substance.

And all matter, in the eyes of two-dimensional beings, can only be patterns, and they can only see patterns.

Matter, on the other hand, exists in three-dimensional space.

Therefore, two-dimensional beings can understand the front and back, the left and right, and can faintly perceive the direction of "up and down", and the things contained in this direction are so complex that they cannot understand them.

Now, we're in three-dimensional space.

By analogy, we can faintly perceive the "direction" of the fourth dimension, which is equally complex beyond our comprehension.

Miraculously, the Taiji diagram, in Xiao Hao's understanding, may correspond to a four-dimensional space sphere.

He could not be sure that his understanding was absolutely correct, so he could only try to explain this mysterious state with a shallow cognition.

It is still necessary to make an analogy between a sphere passing through a plane and a circle passing through a straight line to make it easier to understand.

A two-dimensional circular pattern crosses a one-dimensional straight line, has two cases, and is exactly perpendicular to each other.

It is assumed that the xy axis is used as a plane, and the x-axis and y-axis are respectively used as two experimental straight lines in one-dimensional space.

The x-axis alone and the y-axis alone have a "front and back" direction, and the xy straight lines perpendicular to each other may be analogous to the concept of "yin and yang".

Xiao Hao simply understands that this is the "world of the outside and the inside" that is exclusive to the one-dimensional space.

Assuming that one-dimensional organisms live on the x-axis, then the x-axis is the "surface world" of one-dimensional organisms.

Perpendicular to the x-axis, such as the y-axis or the z-axis, it can be the "inner world" of the x-axis, depending on which plane the "circle" is located in.

When the circle is in the xy plane, the y-axis is the "inner world" of the x-axis.

Thus, when a circle located in the xy plane crosses the x-axis, a ()... co

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The dimension was amazed to discover why a point would suddenly split into two points, and then the two points would move "back and forth", and when they moved to the vertex, the distance between the two points was exactly the diameter of the circle.

After the maximum distance, that is, the diameter of the circle, the two points on the x-axis will come close to each other until they are restored and merged into one point.

This is a peculiar phenomenon on the x-axis, and the reason why it is so peculiar is because the things that travel on the x-axis are lines or patterns that are unique to the two-dimensional axis.

See, one-dimensional beings can't understand it, but if it's a living creature in two dimensions, they can understand it, it's just a circular pattern, moving in the xy plane.

This explanation is much clearer.

Note, however, that although the points split and merge and do not seem to change at all on the x-axis, in fact, the coordinates of the center of the circle have already moved on the y-axis.

The Y-axis alone, even the "inner world", cannot interpret a higher-dimensional circular pattern, and it can only show the movement of two points at the same distance at most.

Similarly, 3D takes the xy-z axis as an example.

Suppose something unique to 3D - a sphere, the center of the sphere is on the z-axis, the sphere passes through the xy plane, and the two-dimensional organisms live in the xy plane.

So, what happens to two-dimensional creatures, but I won't go into too much detail: dots → circles → dots.

It should be noted that the center of the sphere moves on the z-axis.

The "surface world" is naturally the xy plane, and the "inner world" is the plane where the "direction" of the z-axis is located, that is, the xz and yz planes, which are perpendicular to each other and all perpendicular to the xy plane.

Each dimension builds on the previous one, and the fourth dimension is no exception.

If a two-dimensional space is decomposed into one-dimensional space, there must be at least 2 one-dimensional spaces to form a two-dimensional space.

Then, the three-dimensional space is decomposed into two-dimensional space, and at least three two-dimensional space bodies can form a three-dimensional space body.

For example, the xy, yz, and xz planes have the same diameter, and the center of the circle is all located in the circle of the dots, which can form a sphere.

Similarly, a four-dimensional sphere is composed of at least four three-dimensional spheres, and it just so happens that the Taiji diagram is the epitome of the four-dimensional space sphere.

When we reach the four-dimensional space, we need the "sphere" on the four-dimensional space to travel through the three-dimensional space.

Assuming that the "sphere center" in four-dimensional space is located on the axis, the four-dimensional coordinates are naturally the xy-z axis.

Then it needs to pass through the space of xy-z, and the center of the test subject moves on the axis.

So, what happens?

The peculiarity of the one-dimensional "surface world" is manifested in the splitting into two points, then the distance is extended, and then shortened and resynthesized.

The peculiarity of the two-dimensionality is manifested in the fact that the dots widen into circles and then turn back into dots.

Can you deduce the peculiarity of three-dimensional? Yes, the process by which a point expands into a sphere and then recompresses it into a point is the process by which a four-dimensional "sphere" travels through three-dimensional space.

But the problem is that what the creatures in three-dimensional space, that is, us, see from the "perspective" is not real.

Just like the change of a sphere when it passes through a plane, there are only dots→ circles → points, and only a very superficial "side" can be seen. ... co