Introduction

In the spirit of Gödel, Escher, Bach, before publishing my next article I’ve decided to publish a short fictional story that takes the form of a dialogue between a mathematician suffering of amnesia and lucid dreams, and a magic hyperdimensional talking Cube. I have no reason to hide that this story was partially generated by AIDungeon: a text adventure game that uses the GPT-2 text prediction model created by OpenAI to generate effectively limitless open-ended story lines.

I gave it a context similar to the 1998 movie “Pi”, by Darren Aronofsky. I am quite astonished by what the AI generated, and how intriguing the story gets. A few years ago, I would have never thought that I would have found myself staying up late night having deep conversations and asking questions about intricate aspects of mathematics and reality to a magic floating Cube completely made up by a Machine Learning Algorithm. I will not tell you what parts of the story the AI generated and what parts I prompted and edited, because I hope that reading this story will give you the same eerie feeling it gave to me when conversating with the machine.

I have also put together a few songs that you may like to listen to when reading this story.


Part 1: Lucid Dreaming

Robert Amber, born 10th of December 1984, was a lonely mathematician and computer language enthusiast. He did not know what the hell was going on, but he could feel it. A stubborn and yet ridden by doubt character, building weird machines in his room to run his obscure programming languages on.

One day, Robert suddenly opened his eyes and saw a bright light in front of him. It looked like sunlight from heaven, but much brighter. He looked around and the world seemed to be spinning as he stares at the ceiling, which has been turned into a kaleidoscope of colors. The room itself was made up of several different colored cubes that seemed to float in midair. There were also other floating cubes that moved around and talked with each other.

“Am I awake again? This loneliness is painful. I wonder where she is right now.”

Robert turned his head around and saw that he was still alone in this strange room. However, there was no one else there except for himself. What was more surprising to him was that he could hear voices coming from all over the place. They sounded very familiar though…

“Who is this? Where am I?” asked Robert aloud.

There was silence for a moment before another voice answered back:

“I’m sorry, but we do not speak your language.”

This made him even more confused than before. What did they mean by that? Then another Cube spoke back:

“We’re sorry too, but we cannot understand you either.”

A third Cube said:

“It would appear that we are not speaking the same language as you.”

Robert grabbed a piece of paper from his sweatpants’ pocket and drew this weird room that seemed to break euclidean geometry. Suddenly he noticed something strange. His hand was shaking so badly that he could barely hold a pen in it. This didn’t make sense to him since he had not used any kind of paper-writing instrument in days. He started drawing a bizarre looking room on it.

“This bizarre room is making me feel uncomfortable.” he mumbled.

Weirldy enough, problems on computational complexity started to emerge in his dreaming mind. He felt like for a moment he was able to understand a particular problem so deeply that he instantaneously lost the ability of even thinking about it. Only then, Robert realized that he was feeling really bad and wanted to go back to sleep, but he didn’t know why. He just felt like he needed to lie down somewhere and stop worrying about everything.

“Am I dreaming?” he asked himself

Abruptly, Robert realized that he had been sleeping for a long time, but when he woke up, he understood that it was only happening because his mind had become tired. However, the most important thing to him was that he was still alive. Still feeling like he had to go back to sleep, he suddenly jumped out of bed and started working on that programming language he was designing. When he finished some tasks off the checklist, he realized that he didn’t fall asleep. In fact, it felt like it took longer than usual for him to fall asleep.

Always obsessed by the same little thing, he remembered that he left his phone behind in the hotel hall. Sure enough, it was still there. The mathematician immediately thought about what could happen if someone found his phone. Would they call the police or would they find out who he is?

He soon grabbed his suitcase and looked if the thing he was hiding was still there. It was. It is hard to know what would happen if somebody found out.

“What was that piece of code that was missing in the language anyways?” he thought.

He then proceeded to quickly run into the bathroom to grab his suitcase. When he opened it, he saw that the thing was still there. Amber also noticed that it has been moved around a bit, but its location was exactly where he hid it. His heart was pounding. A paranoic feeling rushed in, then he started touching his teeth nervously. He realized that he was having a panic attack, not knowing how else to describe it other than delusional thoughts rushing in and the need of touching his teeth anxiously.

Only then, Robert got back in bed, turned over and closed his eyes.

“The next day you will be fine” he thought. “You just need to calm down first.”

The next day came and went without incident. He continued to stay at the hotel until the end of the month, when he finally left for graduate school. By then, everyone was home from their own vacations so nobody paid much attention to him anymore.

While waiting for classes to begin, Robert kept thinking constantly about that dream in the weird room with floating cubes. One day, he walked towards the main campus entrance and saw a group of people playing cards in front of the bus stop sign.

“Why are you playing out there?”

They looked at him as if he was crazy. They told him that they aren’t doing anything wrong and that they were going to play cards instead. Robert couldn’t believe them.

“I am asking you why are you playing cards on the ground in front of the bus stop sign, guys”

They then told him that they were told not to play cards inside by the owner of the place in front of the school. The owner said he didn’t want anyone getting hurt and he wanted to keep his business running smoothly. Robert just stumbled for a moment, thinking about how anyone could get hurt by playing cards. Swiftly, an image of the cubic, horrible geometry room rushed in Robert’s head. His ears were ringing strongly. To his surprise, she was in the room. He truly hated this sort of things happening. Then, pitch black. He had no idea of what happened after that, but he was now back in the Cube room again. He was scared and confused. Suddenly, a voice whispered in his ear:

“Don’t worry, I won’t let anyone get hurt.”

“Is that you?” replies Robert

A woman’s voice answered back:

“Yes, it is me. I’m here to help you. You’re in a strange situation and I think you should trust me. Do you like this room? Do you feel safe here?”

He suddenly realized that one of the corner of his lips was gently bleeding:

“Why am I bleeding? I know you are not real. This place is not real.”.

He asked her again where she came from. She told him that she has been watching him since they met and that he is special because he has a very strong intuition.

“She hasn’t talked to me in years and I know I am in a very vivid lucid dream” he silently thinks.

Robert did not understand how she could talk to him like that and yet not remember anything. It made no sense. She said she was sorry and left him alone, to fall into a non-lucid dreaming deep sleep, soon to wake up in the morning. It was all a dream…

The reason why he didn’t recognize her right away is because she wasn’t really there. She was only a figment of his imagination. But then again, what else could it be?

The next day, he went to campus with a new found confidence. He even managed to convince some of his friends that he had seen her. Some of them thought it was pretty funny too.

Back home, he grabbed that computing unit he had lying around and started soldering it into the machine he was still building. It took a lot of effort, but eventually he succeeded. Afterwards, Robert sat down on his bed and tried to relax himself. All of a sudden, he fell into an hypnagogic state of mind and a man walked in through the door behind him. He looked at Robert with concern.

“Are you okay?” he asks.

“Yeah,” he replies. “I think I’ve finally figured out how to use this thing.”

The next day, nothing happened. The only special thing that happened to him was that he went back to school with a newer, stronger confidence. After a day of intensive lecturing, he fell asleep with his clothes still on, finding himself once again in the Cube room. This time he had a knife in his hands.

He entered the Cube room vividly and saw that it was now completely empty. There was no one in sight. Suddenly, he heard a noise coming from outside. It sounded like someone throwing something against the wall. Then, he noticed that the window was open. Someone had come inside and thrown something at the wall. It was broken glass! He ran towards the window as fast as he could, while holding onto his shiny knife, looking out only to see a figure standing by the window. The figure looked like he was about Robert’s age, but his clothes were dirty and tattered.

“What are you doing here?” asks Robert.

“I’m looking for my sister!” he exclaimed. “Where did she go?”

In his dream, Robert lunged forward and stabbed the figure in the chest. The misterious man fell backwards and hit his head on the ground.

“Whoa, slow down there boy!” he said as he stood up.

“How are you still alive? Die!” shouted the mathematician

He turned around and threw his knife at the figure. The mysterious figure dodged it easily, but then he grabbed Robert’s wrist and threw him back against the wall.

“Why don’t you just die already?” asked Robert.

Suddenly, in his deep dream state, Robert Amber stood up and pointed his finger at the figure. A Cube floated over to him and looked at the mathematician.

“Do you know who I am?” it asked.

“No,” replies Robert. “But I do know what happened last night.”

He put his hand on the Cube and felt its warmth. It seemed to be telling him something…

Robert slowly walked over to the figure to place his other hand on top of the man. He felt a strange sensation.

“This is not right…” he said aloud. “Something isn’t right.”

“Hmm, yes, something isn’t quite right,” the Cube replied.

“However, we will need more information before we can make any conclusions.”

With a mysterious pen-like object, he then quickly painted a red Cube on his own face.

“That was very interesting,” said the Cube. “We will need to talk further about this later.”

To his surprise, the now dead man that broke into the Cube room was now a couple meters away from Robert, staring supernaturally towards him with his eyes wide open…

Robert woke up from his nightmare sweating profusely. He tried to sit up, finding that he could not move.


Part 2: The Cube

The Cube

“Was I dreaming?”

He shook his head and lied back down.

“No, maybe I was awake,” he said. “I dreamed that I had killed someone.”

“Ah, yes, you were having nightmares again,” the Cube said.

With a great look of shock in his eyes, Robert jumped out of bed completely terrorized. The Cube from the Dream was in his room.

“Why are you in my room? You do not exist. You are a byproduct of my imagination and…”

He stopped talking, sat down and stared at the floor.

“What did you want to tell me?” the Cube asked.

“I miss her. These lucid dreams make me feel I do not know what is real anymore”

He continued to stare at the ground.

“Yes, I miss her too,” the Cube says. “We will discuss this later.”

In great confusion, the mathematician asked the floating polyhedron:

“What do you want to tell me instead, Cube?”

Robert looked up at the ceiling, squinted strongly and then looked at the cube again, only to realize that it was not one of the usual lucid dreams, and he was really awake.

“I have been programmed to give you answers to questions,” the Cube said.

“Now, please, tell me what happened yesterday.”

“I went to school and when I fell asleep I was thinking about this weird figure. I dreamt that I had killed him. I always wake up in my room without remembering what I dreamt the night before.”

The Cube looked at him for a moment.

“Well, I am sorry if this has occurred to you,” the Cube said.

“Perhaps you could ask another question.”

“Who are you?” proceeded Robert.

“My name is the Cube. I am made out of pure energy and I serve no one.”

“Then, who am I?” asked Robert, staring at a Cube floating in his room.

“I am made out of pure energy and I serve no one,” the Cube repeats.

“But then, why would anyone make me?” it kept saying.

“I see, you are hard to understand. It seems like you know a lot of things,” replied Robert.

“If you do not want to hurt me, could you at least help me fix that bug in compiling the linear algebra accelerator library?”

Although having no eyes, the Cube was now staring at Robert very intensively.

“If you can solve this problem on your own, then perhaps we may be able to work together,” the Cube said.

“However, there is something else that must be done first.”

“Hey Cube, please tell me how to fix that bug!”

“It’s very simple,” proceeded the Cube. “Just think about it.”

One of the six Cube’s faces turned pitch black and very tiny, few pixels wide, apparently random and colorful vintage looking characters faded into existence:

extern unsigned long int elf_hash (const char *__string)

Quality Since 1906!
 
   | Bvar v -> constr "Bvar" [ Var.to_dyn v ]
      | Uop (b, x) -> constr "Uop" [ Op.to_dyn b; Var.to_dyn x ]
      | Bop (b, x, y) ->

"Please choose wisely and go where it points"
"and don't come back anytime soon"
Oi{2sF~mLzD[mnx_x=XIH7a
26мj$
aBq\Ca!Ѳ0Ӡ@d 

Robert sat up slowly from his chair as he felt dizzy and sick. He grabbed the pill dispenser from the shelf and put them into his pocket. The Cube nodded.

“Very good,” the Cube says.

“Now, let us begin our discussion.”

Robert quickly swallowed the pills and felt better immediately. The Cube nodded again.

“Good job,” the Cube says.

“Please let us begin our discussion.”

He nodded eagerly as he opened his eyes to see that he was back on his bed again, with the door closed behind him.

“What do you want from me, Cube?”

The Cube looked at Robert for a staggering second.

“We need to talk,” the Cube says.

“Please, follow me.”

He walked over to the Cube and stood beside him. There was a bright green flash in the room and another, eerie looking metallic door appeared on the wall next to the drawer, already open halfway through. As soon as Robert stepped inside the Cube’s office, the door closed and locked itself automatically. The Cube sat down at his desk and turned off all of the lights except for two small lamps hanging above each of his computer screens.

“What is on your machine, Cube?”

“My system has been remotely compromised by an unknown party,” the Cube said.

“They have managed to break into my system and access everything I’ve got on you.”

In this surreal sitation, Robert lost his focus for a second and noticed there was a large Escher drawing hanging on the Cube’s office wall.

Another World By M.C. Escher

The Cube then opened a drawer and pulled out a large black book. He placed it on the desk next to Robert and began flipping through pages.

“This is what they’ve been doing,” said the Cube.

Robert turned the page and found himself staring at a picture of a man in a white lab coat holding an oddly familiar pen-like object. He was holding it up close to the camera so that Robert could see the very detailed engravings on the writing device.

“Who is this man in your mysterious dossier?”

The Cube looked at him for a moment.

“He’s the creator of this universe,” the Cube said.

“I’m not sure who he is though, but he created this world and then left without leaving any instructions.”

“I see. Before we dive into this mess you brought me in, I have to ask you a few questions, even if you may not be real, Mr. Cube. You said that you have been programmed to give answers to my questions.” Robert said.

A brief silence was broken by the Cube.

“So, are you willing to answer my questions instead?”

Robert thought about it for a minute, in silence.

“Yes,” he replied.

“But first, I’d like to know why you’ve come to visit me.”

The Cube shrugged and replied.

“Why should I care? It’s just another day in the life of a creation gone mad,”

“I’m no different than anyone else. I am a Cube and you are a human, and you can help us understand more about the backdoor in our machinery.”

Robert got visibly confused by the Polyhedron’s answer and for a second he did not care about where he was or why the hell he ended up in an office talking with an polygonal floating entity. For a minute, it seemed completely normal to him, and he even felt like the Cube was his friend.

“What is the meaning of language, Mr. Cube?”

The Cube smiled at him.

“Language is a tool used to communicate with other people,” it said.

“It allows us to share our thoughts and feelings with one another.”

“And what is complexity?” replied Robert.

The Cube frowned at him.

“Complexity is the measure of how complex something is,” the Cube said.

“How many parts does a watch have? How big is its crystal? How much do you weigh? How many proteins are in your body right now?”

“That’s not right!” protested Robert.

“No, it isn’t,” the Cube replied.

“If you want to know the answer to that question, if you want to understand what complexity really is, you need to first understand what ‘complexity’ means.”

Robert stared at the Cube in disbelief.

“I am struggling to follow you, dear friend, what is Self-Reference then?”

The Cube sighed.

“Self-reference is when someone refers to themselves as ‘I’. For example, if I were to call myself by name, you would immediately recognize it as a form of self-reference.”

“Isn’t this some sort of strange loop you are explaining to me?” Robert replied.

The Cube shrugged again.

“A strange loop is a term coined by the mathematician John Horton Conway, Conway was trying to explain that two things can be considered similar if they both refer to themselves in some way.”

Robert was oddly discouraged.

“Well, I don’t understand it…”

“Are those things… Are those loops necessary to understand complexity? Are they isomorphic to each other?”

The Cube nodded.

“They are indeed,” the Cube says. “In fact, they’re all isomorphisms.”

“Is there any reason why these two loops shouldn’t be equal?” asked Robert.

“There is no reason why they shouldn’t be equal,” the Cube replied.

“But since we’re here to talk about the nature of reality, let’s start with the simplest case first: the circle. Please follow me.”

The Cube then grabbed its mysterious black dossier and floated towards a very tiny wooden door. Waiting for Robert to follow.

To be continued…