Of course, a concrete thing can be expressed intuitively, and an abstract concept is not so easy for people to understand.

"'Recursive' relations only exist in functions because they cannot exist in a physical sense. The essence of 'recursion' is self-invocation, imagining two mirrors A and B facing each other, B has a reflection of A, but A envelops B in its entirety, so that there is another mirror A in mirror B in mirror A, denoted as A′, and in the same way, there is also an A in A′, and so on, there are infinite mirrors in two mirrors facing each other. "This is an example of laxity, because recursion is a logical relationship that occurs by the causal entanglement of an event, rather than between two isolated individuals, as in a mirror." Moreover, the meaning of recursion is change, and all the mirrors in the mirror are exactly the same. ”

This explanation sounds easy to understand, but I think the logic is very reasonable, as you call the causal relationship of self-invocation. ”

Xiao Yifan shook his head and smiled: "Have you ever heard that there is 'recursion' or 'self-invocation' in causality?"

Olivia was slightly stunned, it was true that there had never been.

"It is impossible for a specific thing or event to have a 'self-invoking' relationship with itself, not only because once it happens, just like the mirror in that mirror, the cycle is infinite, and the event will fall into infinity! In the example just now, the mirror images of mirror A and B are infinite!" Xiao Yifan took a deep breath, "It is also because cause and effect are driven by time, and if this cause and effect is fed back from the event to the time level, there will be a recursion of the chronological order." ”

"The ...... of time Recursion?" Olivia frowned, a little confused.

At this time, time is no longer a one-dimensional arrow, at this time time is like a mirror, the mirror is nested with countless mirrors, with the infinite cycle of events, infinite nesting, each mirror is a specific mirror rather than a reflection, so that although time is also eternal, but the inner mirror is all attached to the outermost mirror, and the length of that mirror is the fundamental aspect of all events. If we look at it in terms of one-dimensional time, the initial period of time is finite, but the inner nesting is infinite. And the logic of the function has the condition of jumping out of the loop, otherwise recursion is meaningless, the question is that this is only for the function, whether it can jump out of the loop for the event is not knowable, if it can't jump out of the loop, there will be an infinite number of events in a limited time, is this possible?"

Thinking about it along Xiao Yifan's train of thought, Olivia suddenly felt chills all over her body, which was a fear of things beyond common sense.

As for the possibility that the time dimension of time falls into a nested infinity, I can only say that we can only propose ten dimensions of space, and all space only exists on a one-dimensional timeline. Infinite dimensional time, this is more ridiculous than accomplishing infinite things in a limited time," Xiao Yifan smiled bitterly, "So, the non-existence of time is the most reasonable explanation!"

"But how do we explain why we're not in the loop?"

"You've probably heard of the time paradox and the observer theory, we can't go back to the fact that we killed our parents and changed our births. So the most plausible explanation for time travel is to watch history as an outside 'observer' as if it were a movie, isn't that how we relate to the world right now? ”

"We're observers now?"

"Yes, we are only observers, and in a world where the concept of time is missing, it is not our business how much time has passed in the outside world. Xiao Yifan said, "That is to say, after we come in, no matter how long it takes to go out, our original world may only be a second or hundreds of millions of years have passed." ”

"Hundreds of millions of years?" Olivia's expression froze, "When we go back, is it possible that humans and even the Protoss no longer exist?"

"Yes, and if my guesses are correct, it's very likely. Xiao Yifan stated quietly.

"Well, let's ......" Olivia's voice was not the first time it trembled, only this time, there was a cry of almost despair in this panic.

"Look, I was going to hide it from you, but you have to question it, and now your eyes are going to cry. Xiao Yifan smiled and comforted, "The truth is often more cruel than you think, which is why we explore the unknown with awe." ”

"You're talking about it easy," Olivia gave him a roll of his eyes, but he also calmed down a little under Xiao Yifan's relaxed tone, "You should be more concerned about the world on that side than I am, and you can even laugh." ”

"What can I do if I don't laugh? If crying is useful, I can cry for three days and three nights. Xiao Yifan shrugged.

"Yes, you are no longer a knight Gavin, you are now Xiao Yifan, the god of death, no, Xiao Yifan, the chairman of the God Acting Committee. ”

"It wasn't my choice, you should know that. My change is depraved to some, and sublimation to others. But no matter what they think, these views don't mean much to the world, and when you experience something deeply, it will make your vision not limited to the 'world'. Just like we do now, after we are out of the chess game, everything is none of our business. ”

Xiao Yifan didn't show any emotion when he said this, as if all the sufferings and joys and sorrows in the past were just a floating cloud drifting away with the breeze.

"Are you comforting me?"

"If you need it, you can think so, if you don't, I don't say it. ”

"Hey, if you coax girls, shouldn't you skip the second half of the sentence?"

"No matter your age or experience, you are no longer a little girl," Xiao Yifan said softly, "Of course I hope you will always be innocent and beautiful, but the price of our growth is a bit high, so high that we are a little unacceptable, we can't go back to the past time, and we can't afford to go back." ”

"I see what you mean, Gavin. Olivia put away her coquettish tone and took a deep breath, "What should we do now, I haven't even entered the Courtyard of the Gods, let alone this world that even you find weird." ”

"This cycle allows me to observe two more cycles, and then I'm going to go to the bottom of the deep pool. ”

"You want to go down?" Olivia bit her lip, and the crisp laughter still lingered in her heart for a moment when night and day alternated.

"Didn't we come here for the 'Golden Drum of Africa'?"

Day and night alternate like a precise rule, and the overlapping idols of Anubis and Horus dominate darkness and light, and in a silent cycle, history and years are forgotten......

"You can wait for me here. Xiao Yifan turned his head and smiled at Olivia, "I wasn't going to let you follow up, although this result was caused by your willfulness, but I still affected you." ”

"Hmph!" Olivia didn't appreciate it, "Come on, I'm the only sage in two hundred years who has drawn a sword in a stone, am I a sage, okay! I'm afraid of being the king of Britain?"

"That's ......" Xiao Yifan's smile became even brighter, "But Your Highness, I didn't say that you were scared! ”

"Uh......"

Olivia, who was so anxious that she didn't know what to say, suddenly found that Xiao Yifan didn't continue to tease her, but the sun, moon and stars rose in those amber eyes.

"Let's go. It's 'night' right now, and it's just the right time to see how the drums lead to change. As he spoke, Xiao Yifan's body was once again at the level of the ground.

"Don't say it. ”

Olivia quietly followed.

Indeed, as Xiao Yifan said, they are "foreign objects" in this world, similar to observers, who can only witness but cannot change anything. When they walked towards the bottom of the deep pool with unspoken emphasis, they realized that the feeling of being down-to-earth all along was just an illusion of their own.

In fact, they haven't really stepped on an inch of soil here, and after being released, they are also walking on the mountain wall in their own subconscious. The strongest evidence of this is that the cascading waterfall did not divert after hitting them, but directly passed through their bodies, after all, their common sense can only affect themselves, and cannot affect any of the rules of this world.

Olivia, who was following Xiao Yifan, felt that this situation was a little funny.

"I think now we are like bear children whose lies have been exposed and have to be forced to speak hard, stupid and embarrassed. ”

"Really?" Xiao Yifan was also a little helpless, "But what can we do if we don't descend along the mountain wall?" Although the rules for the two of us here are all built by the subconscious, but you have never been a bird or a pangolin, so there is no way to fly and burrow into the ground for the time being. ”

This section of the road is familiar to Xiao Yifan, including the rock walls, the moss on the rocks, and other detailed scenery are very similar to Zimbabwe. In other words, the scenery here is subtly changing with reference to the real Zimbabwe.

It's just that the scenery of Zimbabwe changes with the seasons, that is, everything goes on a one-dimensional timeline. And there is no concept of time in the changes in the scene, so it is likely that these changes interfered with this place the moment they entered this world.

"The rules of this world are completely different from what we understand, and the only thing that is thankful is that the spatial dimension here is at least three-dimensional. Olivia said.

"Of course, we can't get in without three-dimensional. ”

"Oh? Why?"

"After finishing secondary school mathematics, you will be able to draw inferences, my Highness. Xiao Yifan sighed, "This is a completely independent space, and there is no need to argue about this. Therefore, it is impossible for the two spaces to intersect, otherwise the laws of nature will intervene with each other and cannot be independent. Therefore, if we want to enter this space, we can only make two spaces tangent, the tangent of a one-dimensional line and a line can only be a point, the tangent of a two-dimensional face and a surface may be a point or a line, and so on, the three-dimensional tangent of space may be a point, a line or a surface. As creatures in three-dimensional space, it is theoretically impossible for us to pass through a point or a line alive, so the tangent can only be a surface, and what can form a tangent plane with the three-dimensional space is at least a three-dimensional space. ”

"Can't a face be tangent to three-dimensional space?"

"This surface has a tangent aspect to the three-dimensional space, so doesn't this surface already belong to this space? How can it be independent? And we can't enter the two-dimensional world alive, don't we know that the dimensionality reduction strike in science fiction can destroy all the matter in the high-dimensional space?"

The two chatted and chatted, and soon approached the edge of the deep pool. Since the alternation of day and night here occurs in an instant, they do not know when the "day" will come, but only estimate the time and wait in the deep pool.

A white light gradually emerged, the drum sound at the bottom of the pool became clearer and clearer, and through the hazy mist, the rainbow bridge could be seen hanging in the air, and the colorful glow reflected down.

It's just that what makes both of them extra heavy is that the string of laughter coming from the bottom of the pool has disappeared. You must know that they had observed several cycles before going to the bottom of the pool, and the sound was never late when night alternated into day. But when I got here, there was no way to hear it.