Chapter Forty-Six: The High-Dimensional Creation Klein Bottle
The endless void, the primordial universe.
When Lu Xuan came back to his senses again, he was no longer in the base.
No, Lu Xuan has even broken away from the original space-time now, and has come to the space-time rift located outside the universe.
Here, there is no concept of matter, energy and time, only eternal darkness and loneliness.
The moment a normal person enters here, he will be reduced to a dimension due to the loss of the concept of life, and become an existence infinitely close to "0".
People in this state will be unable to act, unable to think, and even "existence" itself is an impossible thing to exist.
However, it is not true that nothing exists in this void rift in space-time.
Every universe is born and dies, leaving some indestructible traces to a greater or lesser extent.
Or the incredible wonders of the universe itself, or some kind of racial creation that has reached the level of a god-level civilization......
In short, in this endless void, only things that transcend the universe itself can continue to exist in the form of obliterating concepts.
For example, the red ball not far away, which has lost any concept, but can still make the person who sees it realize that it is a red orb at the first sight.
No shape, no color......
But it can make everyone who witnesses this red ball realize that it is a red orb—a red orb that can grant all wishes.
In fact, it only takes one opportunity for this red ball that was "self-disappeared" by Lu Xuan's wish to reappear in an unknown parallel universe.
[I thought you really could do anything! 】
[It turns out that your ability also has a limit......]
There is only one concept left, and this level of red ball is indeed worthy of the supreme creation of the highest civilization.
It's a pity that this level of "disappearance" is obviously not the true realization of Lu Xuan's wish.
Thinking like this, Lu Xuan immediately began to re-examine his current state.
In this endless void of silence, even the Red Ball, the supreme creation of the top human civilization, has been erased from all existence, how can he continue to think?
Not only is it as simple as keeping thinking, Lu Xuan even maintains a complete physical form now.
Not in dark form, not in human form......
Lu Xuan's current appearance is pure Galvin form, the clothes and equipment on his body have been disassembled, and only one watch is still worn on his wrist.
[Is that it?] Does this thing still have this function? 】
Lowering his head slightly, Lu Xuan stared at the Omnitrix on his wrist with some surprise.
This was the first time Lu Xuan had discovered Omnitrix's special ability outside of its normal functions, and it seemed to be an extremely powerful hidden ability.
Obviously, when I made the Omnitrix, I didn't use any special materials.
If you really want to say it, the Ultra armor that Lu Xuan specially tailored for himself is much more demanding than Omnitrix in terms of material selection and use.
As a result, the Otter armor has now been conceptually erased, but the Omnitrix has remained the same.
This can only show that what makes Omnitrix special is not the material, but the technological concept it uses.
To put it simply, there is something mysterious about Omnitrix's design drawings.
It may sound incredible, but it's true.
It's like a geometrically sound, structurally stable architectural plan.
As long as the materials used are not too poor, the building built according to this architectural design drawing can exceed the bearing limit given by the material to a certain extent.
Omnitrix uses a similar principle.
It's just that the level of the Omnitrix is much higher than simple geometry, because it uses a Klein bottle-like structure.
When it comes to the Klein bottle, we have to mention the Möbius ring first.
In everyone's common sense, normal paper has only two sides.
But if you twist a strip of paper by 180 degrees and then connect it head to end, you get a ring structure with only one side.
Suppose there is a bug that has no concept of height, and will only crawl forward forever.
Then this little worm can crawl through the front and back sides of the Möbius ring without climbing over the edge, and return to the original point again.
From this, is it possible to conclude that in a two-dimensional plane world with no height, the Möbius ring is a cyclical, closed surface with no edges?
This is simply an incomprehensible thing for a life living in a two-dimensional world.
Applying this concept to a higher-dimensional three-dimensional world is theoretically valid.
This is known as the "Klein Bottle Theory".
Make a hole in the bottom of a bottle, then extend the neck of the bottle and twist into the inside of the bottle, connecting with the hole at the bottom.
So from the perspective of three-dimensional creatures, this bottle is a bottle with no inside and outside.
A fly can fly directly from the inside of this sealed bottle to the outside of the bottle without passing through the surface of the bottle.
However, the fact is that when the neck of the bottle enters the bottle, certain points on the neck of the bottle and certain points on the wall of the bottle must occupy the same position in three-dimensional space.
Two different points occupy the same position in the three-dimensional world, a phenomenon that is more incredible than piercing walls and overlapping, which is impossible to achieve in the real world with physical rules.
However, if you add another dimension to it outside of three-dimensional space, let the neck and wall of the bottle avoid intersecting places from the other surface.
So is it possible to achieve a "bottle" that can only be seen through the eyes of four-dimensional creatures, just like the Möbius ring?
To put it more plainly.
For creatures in the two-dimensional world, the Möbius ring is a one-way surface that never ends.
For creatures in the three-dimensional world, the Klein Bottle is a bottle that has no distinction between inside and outside, and can never be filled.
The only difference between the Möbius Ring and the Klein Bottle is that human beings can clearly see the two sides of the Möbius Ring, but they can only rely on their own imagination and understanding of the four-dimensional space to imagine the intersection of the Klein Bottle occupying the same position in the three-dimensional world.
Then the problem arises, the creatures of the two-dimensional world can actually perceive the existence of the three-dimensional world through the Möbius ring.
So can the creatures of the three-dimensional world touch the four-dimensional space that is more advanced than themselves through the Klein bottle?
If it was before today, Lu Xuan would definitely feel that this was a fool's dream.
Because this has nothing to do with the level of imagination and technology.
Unless you elevate your dimension and leave this three-dimensional world, the creatures of the lower dimensional world will never be able to reach the creations of the higher dimensions.
It's like a character in a comic book who can never jump out of a comic book and touch something in the real world.
However, at this moment, Lu Xuan felt that he seemed to have underestimated the technological level of the Galvin people again.
The Omnitrix in Lu Xuan's hand is a genuine "Klein bottle" that has appeared in the three-dimensional world.
The most important thing is that this "Klein Bottle" is not something left by a high-dimensional creature in the three-dimensional world, but a creation made by Lu Xuan little by little.
"Is this the real level of technology up to level 20?"
With the technology of low-dimensional creatures, we have created things in the high-dimensional world.
This kind of thing that sounds incredible happened to Lu Xuan so really.
And before that, he didn't even notice this peculiar phenomenon.
"A 'Klein Bottle' that is never satisfied, a real high-dimensional creation ......"
——Commuter/Recommended Ticket——
(End of chapter)