Klein Bottle

It must be said that this viewpoint makes a lot of sense. In the absence of direct experimental evidence, people are very willing to believe that the real universe is as it is, and that real Two-Dimensional Space and Four-Dimensional Space are as they are.

In fact, this concept of spatial dimension did not just come to light at this time; it existed as early as Earth Era. However, when the experiments were first conducted, scientists were focused on exploring the entire universe, so no one thought about this aspect.

Of course, this concept of dimensional space lacks actual data, but it has a rigorous mathematical derivation process. Although mathematicians don't need to consider the feelings of physicists, and rigorous mathematical statements aren't necessarily absolute truths in the real physical world, they always feel convincing.

Therefore, once this concept of dimensional space was brought back from history, it was immediately recognized by many scientists. At that time, on the Research Ship, many physicists with MAX mathematical ability directly demonstrated its correctness from a mathematical perspective.

With no progress in the search for the existence of hyperspace, physicists have been forced to seriously consider the possibility of this spatial dimension concept.

Against this backdrop, many scientists began to shift their focus, devoting their efforts to exploring Three-Dimensional Warped Space. The form of this Three-Dimensional Warped Space naturally became a key consideration for the next few research teams.

In fact, human understanding of spatial distortion is quite accurate. After discussing this issue, scientists easily came up with a spatial structure, namely the Klein Bottle.

In mathematics, Klein Bottle refers to a non-orientable plane; in topology, it is a non-orientable topological space.

Its structure can generally be described as follows: a bottle has a hole at the bottom, the neck of the bottle is extended and twisted into the inside of the bottle, and then connects to the hole at the bottom.

Scientists who insist that this space is not hyperspace have long held the idea that the entire space, or parts thereof, is composed of Klein Bottle or similar twisted spatial structures, which are combined or arranged together to form the boundary of this entire space.

The experimental spacecraft's unnoticed change of direction can be explained as a natural consequence of its movement along the distorted space of the Klein Bottle. Obviously, the experimental spacecraft itself would not be aware of the so-called change in spatial direction, because for it, the direction had not changed.

Based on the theory of Klein Bottle, scientists have reason to believe that the phenomenon of the experimental spacecraft changing direction unexpectedly is one of the examples of space distortion.

However, one thing puzzles scientists: in their view, the spatial structure of the Klein Bottle does have a reasonable explanation for its existence, but for such a structure to exist, it must be possible in Four-Dimensional Space, because the situation of 'the bottleneck extending into the interior of the bottle' does not exist in Three-Dimensional Space.

Just as Möbius Strip cannot exist in a space with only two dimensions, it must undergo a process of flipping into a third spatial dimension, although it is still a two-dimensional structure.

Humans are, after all, creatures that live in Three-Dimensional Space and Four-Dimensional Space-time. Using the Möbius Strip as an analogy is indeed easier than simply imagining the flipped structure of Klein Bottle in one's mind.

Imagine a strip of paper. If you want to connect its ends in the shape of Möbius Strip, it will inevitably have areas that are flipped and twisted. It is through this flipping and twisting that the paper becomes a strip with only one side.

The so-called twisting and flipping is actually the paper passing through a third dimension. Imagine you flip a piece of paper over and then join the ends together, then flatten the paper. You'll find that part of the paper overlaps, and the thickness of the overlapping part increases. Two-Dimensional Space doesn't have the concept of thickness, let alone an increase in thickness.

Therefore, the Möbius Strip cannot be represented in Two-Dimensional Space; it can only be represented in Three-Dimensional Space. Similarly, the Klein Bottle is a curved surface that can only be truly represented in Four-Dimensional Space.

This is why scientists who insist that this space is Three-Dimensional Space distortion or exists in the form of Klein Bottle space are very confused, because if they can prove that the structure of the Klein Bottle space can be manifested in this space, then it is equivalent to proving the existence of Four-Dimensional Space in this space.

In other words, the scientists who insisted on the hyperspace concept have actually won this time. Of course, who wins and who loses is not important; what is important is that hyperspace would cause all three-dimensional things to lose the physical laws that support them, which is quite contradictory.

In order to resolve the unavoidable contradiction, some scientists have even proposed that this space is in the form of Möbius Strip. However, this theory faces the same contradiction as the Klein Bottle: three-dimensional objects entering Two-Dimensional Space will be subjected to Dimensional Reduction Strike, but the experimental spacecraft was unharmed.

Moreover, how could a Three-Dimensional Space spaceship possibly go to two dimensions, flip itself, and then return to Three-Dimensional Space?

Therefore, for scientific research teams, both the Klein Bottle Structure and the Möbius Strip structure present inherent contradictions that they cannot avoid.

Faced with these contradictions, some scientists have said: Is it possible that the Awakeners used some kind of technology unknown to humans to hide the structure of the Klein Bottle that extends to the fourth spatial dimension, or the Four-Dimensional Space anchor point, so that humans cannot discover it?

Of course, this is possible. It's like a creature from a two-dimensional world swimming freely in Möbius Strip structure, but it has no idea why humans could create such a structure in its world.

But when faced with the unknown, explaining it with an even greater unknown is sometimes a kind of contradiction, isn't it? Of course, if that's the case, then it makes sense: a creature living on Möbius Strip completes a left-right flip after walking around the Möbius Strip once, but it will never realize that it has already traveled in Two-Dimensional Space towards a third dimension that does not exist for it.

The reason he didn't die from the spatial dimension upgrade is because he flipped along with the Two-Dimensional Space to the third spatial dimension. The Two-Dimensional Space did not change its physical laws because of the flipping to the three-dimensional space; the Two-Dimensional Space is still Two-Dimensional Space, and he is bound to the space he is in.

Similarly, a human spaceship moving on the Klein Bottle Structure walls without an inside or outside can also be explained by the Klein Bottle Structure of this space. However, this view has a flaw: it requires that the Awakeners possess such powerful means.

Humans, of course, cannot guarantee whether the Awakeners has or does not possess this ability.