Volume 4: Spacetime Singularity Chapter 31: Miscellaneous Manifolds
When the last monster they had found was destroyed, Fang Cheng found that there was a mountain range covered with pine forests under his feet. The dark green treetops extended towards the plains under his feet, like emeralds scattered all over the ground from a cloth bag.
Time was frozen in the morning. At this moment, the morning mist in the mountains had not yet dissipated. There was still a layer of gauze between the two people and the green carpet under their feet. They could only see the birds flying vaguely between the treetops.
There was still no one in Fang Cheng's sight, as if all human beings had disappeared overnight, and there was only mottled green on the empty land.
The flat forest is covered with misty smoke, and the cold mountains are sad and green.
"This should be the last one. Didn't you see any others just now?"
As Fang Cheng spoke, he folded up the umbrella that had shrunk back into a cylinder, and reached out to touch the forest owl that was flying beside him, although of course he touched nothing in the end.
"That should be it. When we reached the highest point, I counted twelve of them, so I plucked out twelve hairs and threw away one for each one I killed. Now I have thrown away all of them."
Hundreds of years had passed since humans last used silk to record events, and the first time humans used knotted cords to record events was hundreds of thousands of years ago.
Perhaps as long as humans exist, natural or artificial silk threads will always be used as notepads.
"Thank you for your hard work, but pulling out my hair... doesn't it hurt?"
"It's okay. Just gently pull the bangs down. It won't hurt too much."
After hearing what she said, Fang Cheng naturally reached out to touch the bangs of the girl opposite him, but she slapped him down.
"Actually, based on my life experience, if your hair gets caught it really hurts, but it's better to just pull it..."
As she spoke, she pulled out a hair from behind her ear, which was much longer than the hair on her bangs. She smoothed it in her hand and handed it to Fang Cheng.
The hair was dark brown in color and felt weightless when held in the hand. It stretched from the base of the left hand to the wrist of the right hand, and it seemed to reflect a little under the sunlight.
Fang Cheng carefully looked at the hair in his hand, and suddenly an old question popped up in his mind:
Photons cannot come to this world, so he cannot see the color of his hair under the sunlight. Is the sunlight in front of him still brought by those new particles?
"What are you thinking about?"
A familiar voice sounded in my mind.
It seemed that it was because the surroundings were too quiet. The timbre of this voice was completely different from the one he had heard before. Fang Cheng did not recognize who this voice belonged to at first.
"You are...Keats?"
"Yes, you just contacted me."
A few minutes ago, Fang Cheng and Observer No. 1 sent a contact signal, and after a slight delay, I was able to talk to Fang Cheng directly.
But now Fang Cheng has another question in his mind. The aliens said before that their observatory was tied to the sun. Now the sun has been moved away, so where did their observatory go?
Observer No. 1 had previously said that it would take several hours for their observatory to reach the original location of the Earth by "walking", but this time it only took them a few minutes from the beginning of contact to the conversation, which means that their base has been moved, or the aliens were not at the base just now.
"Do you need me to transfer the Earth back?"
"You mean... restart time?"
"That's probably what I mean, but once a space weapon is activated, it's not easy to stop. If you ask me to shut it down now, I'll need some operations to deal with the newly generated space."
In fact, Fang Cheng envied the aliens for being able to describe their manipulation of space itself so lightly, as if stimulating a higher-dimensional space or destroying a higher-dimensional space was as easy as building blocks.
"Based on your current perception of time, this process should take several days."
However, without the alternation of day and night, there would be no concept of day, and it would be the same whether you talk about time or not.
Fang Cheng lowered his head thoughtfully, but did not say anything.
"Then if you have no problem, I will send the Earth back to your universe. But as I said before, it will take you a few days to return to your original world."
"I have a question."
Each time Observer One flew over a new biome, he patiently taught the natives everything that their scientific paradigm could understand.
The prerequisite is that the other party is interested in asking questions.
Moreover, the interest of indigenous species in natural science and understanding the universe is a very important indicator for , which is directly related to the threat level of different species.
Although they have many more sophisticated measurement methods to quantitatively analyze this "curiosity index", directly asking the natives is undoubtedly the fastest and most intuitive sampling method.
In fact, they have this consideration when choosing the people they want to contact, and they always find the most curious group of people within a species.
On Earth, these people are called "physicists."
"I wanted to ask from the beginning, why can space have speed? In human understanding, the universe is a compact differential manifold, which cannot define speed itself."
Ning Yu'an watched Fang Cheng talking to himself in the air, and she was wondering whether he was really talking to aliens or if there was something wrong with his brain.
But what is a manifold? I only know that the heaven and earth have righteousness, which is endowed with manifolds...
She remembered what Fang Cheng had told her: if we think of Euclidean space as a piece of white paper and the coordinate system as the arrows drawn on it, then the manifold is a piece of curved paper. Although the coordinate system drawn on it can still be straight, they are just tangent to the white paper.
"Your understanding is correct. The space near the Earth is indeed independent of the coordinate system and is homeomorphic to a Euclidean space. From a human perspective, describing the movement of matter in it depends on an additionally defined differential structure."
This is like reading the cosmology textbook again.
"However, your three-dimensional manifold can be defined as moving from a higher-dimensional perspective. This higher dimension is not the microscopic space curled up in your theory, but the low-dimensional manifold itself is regarded as the differential structure in the high-dimensional manifold. It's just that human mathematics still cannot understand this."
"Then... when you constructed the rotating space, wasn't the universe you defined a single-connected one? Would a non-single-connected universe cause any problems..."
"Your universe is not simply connected either. I thought you had already discovered this. If it is not simply connected, why would there be wormholes?"
Fang Cheng nodded, but he had not previously connected .
"The linear universe and circular universe I just told you about are approximations for the sake of intuition. In fact, we just cut out two pieces of space near you and copied them into the pocket we constructed."
