The Dimensional World: A Journey of Discovery and Adventure

Exploring the Two-Dimensional World

It was a portal to another dimension, where Vincent found himself in a vast and beautiful landscape, full of wonders and mysteries. He felt a surge of energy and vitality, as if his illness had vanished. He felt a warm sensation in his hand and saw the grasshopper on his palm, He looked up and saw that the scroll had changed, it now displayed a beautiful painting of a mountain and a river. He felt a connection with the scroll, and realized that he could control it with his mind, he felt he had inherited a legacy of ancient art and wisdom.

Vincent had decided to look at it from the three axioms of the theory of the universe:

Time (T), Space (U), and Matter (M).

Time, space and matter were tightly related to each other one another. The three elements were independent yet inextricably linked. The relationship between space and time was U=U(T), and M=M(U) for matter and space. Time was found in space, and space was filled with matter. Thus, time and space were related to matter.

Among the three elements, matter was the primeval element. If there was no matter, space would never have existed. If space did not exist, time would never have existed. Vincent suspected that this painting was the entrance to a two-dimensional world. As matter did not exist in this two-dimensional world, space and time likewise did not exist.

A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called planes, or, more generally, surfaces. There are different types of two-dimensional spaces, such as Euclidean, elliptic, affine, projective, vector, and topological.

Vincent looked at the painting, finding it inconceivable. He seemed to have found the entrance of a new world. He wondered…

“If I place large amount of matter into the Two-dimensional space, would I create a stable two-dimensional world? A two-dimensional world with time and space, and also be able to sustain lives?”

Vincent felt excited at this thought, so he started to make a plan. He would first try to put a pipeline into the painting space, then transport sand and other things into it. At this moment, someone pressed on the doorbell. He looked down and saw that the courier was there.

“Are you Sir Vincent? Please sign for the parcel!” the courier requested, in a friendly and polite tone.

The parcel contained the camera that he had ordered. After linking it up with his computer, Vincent put the camera into the painting space. He wanted to find out what was inside the painting space instead of observing it from the surface of the painting.

The moment camera was put inside the painting space, the computer screen went dark. Vincent’s heart sank, but he had anticipated this reaction. Firstly, there was no light in the two-dimensional space, so he was prepared to see nothing. Secondly, he had a feeling that most likely the signals could not be sent out from the two-dimensional world, otherwise it would be too inconceivable. Although Vincent felt this way, he still just wanted to give it a shot.

After Vincent clicked on the mouse and turned on the light on the camera, the computer screen brightened. Vincent’s jaw dropped in surprise, then he moved the camera around.

I can’t believe something actually showed on the computer screen!

The images on the screen looked strange. The camera seemed to have captured the images, but what he saw was a flat side-view. The camera had captured its own image.

What angle is this?

There was nothing on the screen except darkness and a straight ray of light. It was like a 2D horizontal animation or a caricature. At this very moment, Vincent saw a shadow flash across the screen.

What was that?

He quickly shifted the focus and found that there was a special sigil on the screen: a horizontal 8. Vincent knew that this symbol meant infinity. However, in the capital city, the mark also represented smog.

The infinity symbol (∞) is a mathematical symbol representing the concept of infinity. This symbol is also called a lemniscate, after the lemniscate curves of a similar shape studied in algebraic geometry, or “lazy eight”, in the terminology of livestock branding. This symbol was first used mathematically by John Wallis in the 17th century, although it has a longer history of other uses.

Vincent was certain that he had seen it correctly. It must mean infinity. The sigil was in the center of the painting space. No matter from which angle Vincent looked, he could only see the front view.

He found the situation in the painting space mysterious. He was certain that it was a two-dimensional space, but from what the camera had captured, it did not seem like a two-dimensional perspective. However, it was definitely not a three-dimensional one.

Vincent had never entered a two-dimensional space, so he did not know exactly what a two-dimensional space should be. He retrieved the camera and saw that the part of the camera that had disappeared into the painting space seemed to be rebuilding itself until it finally re-appeared in the three-dimensional world.

This occurrence was nothing new to Vincent, so he was not surprised. After pondering things for a while, he decided to remove the horizontal 8 to have a closer look!

This was the first time that he had placed his hand inside, and it had required much courage. If he could not pull his hand back out, he would be in deep trouble. He felt strange, when his hand was in the painting space. He seemed to have lost his sense of touch, yet he could still feel his hand. His hand became light, like a piece a paper.

I have caught it!

Vincent was elated, and quickly pulled the thing out. However, when he looked at his hand, it was empty.

What happened? Where is it?

Vincent turned his hand around and saw the silver ∞. It moved between the surface of his skin and his flesh without resistance as if his flesh and blood did not exist. It flopped around on his hand like a fish, then moved up his arm.

F*ck! F*ck! F*ck! F*ck!

Vincent was frightened, so he kept hitting and scratching his arm, but was unable to feel the thing. He saw it crawling up his arm, so he quickly dashed into another room and held up a mirror. The thing had reached his neck, crawled up to his face, and ultimately, entered his brain.

Bang!

Vincent felt as though something in his head had exploded, and he lost consciousness. It was as if he had seen the explosion of the universe, resulting in endless of information being sent to his brain. However, the information was too much for the capacity of his brain. The information passed through his brain but could not be kept. Ultimately, only a small, vital portion remained in his memory.

When Vincent got up from the ground, it was dark. He felt that although he had remained calm to face death, but was still quite terrified by the fact that something so strange had gone into his body. However, after giving it some thought, he was able to shrug it off. It was just like the cancerous cells: worst case, he would die.

The thing that had entered his brain must be the controlling power of the painting it represented the ownership and the control center of that two-dimensional world. Vincent could sense that there were tons of information, such as detailed explanation and operation manual, available to him. He felt the information was as much as what was stored in the National Library of Dragon Kingdom, yet he was unable to load all of it into his brain at the moment. He only learnt some simple operations, but had left the rest behind.

That being said, he now understood how to open and enter the two-dimensional space, and how to set up the internal rules and variants for it.