When Arthur saw the triangle, his scalp began to tingle.
He was beginning to see why formation was so difficult to learn. But he was also beginning to understand some of the things he read in the textbook.
He thought to himself, "The expression has transformed from a single dimensional object into a two dimensional object all because of one additional point."
He mummured, "Just one more point!"
He was mummuring to himself when the lecturer pointed to the diagram of the triangle and said, "How many expressions are here?"
Without waiting for anyone to answer, he sneered and said, "If you think there are only three expressions here, you're deadly wrong."
"I meant what I said. Not only are you wrong, you're so wrong that it can get you killed."
He pointed to the triangle and said, "We now have three angles, three edges, a perimeter, and an area. That's eight different expressions. All because of the addition of a single more rule."
Many people in the class were stunned when they realized what the man was saying. The look on their faces made the man laugh.
He slapped his thigh, stomped his feet and bellowed as he laughed.
When he was done laughing, he said, "Now add another point. Add more and more points. Consider the possibilities."
"But take note that this is just a two-dimensional array. In the real world, arrays are at least three-dimensional. Once it becomes three-dimensional, we will have to deal with the expressions of volume, mass, density, etc."
"Imagine what kind of expressions you will be working with then. The same rules will have vastly different outputs. A slight difference in the interaction of rules will make you think you're working with something different."
He patted his chest and said, "I stake it on my life that the rules of formation might be finite, but the expressions of formation are infinite."
Arthur was amazed by this. He groaned to himself and said, "It is not even certain if the rules of formation are finite? What the hell?"
Then he wondered to himself, "Can a supercomputer help in simulating expressions?"
He gave up on that idea because he didn't know how to build a computer and he wasn't even sure that a computer would help in simulating the language of nature.
He didn't know if the lecturer's claim about infinite expressions was true, but he certainly didn't have the authority to say that it was false. He could only listen in awe.
After staking his life on that claim, the lecturer took out his identity card and showed it to them. He pointed it to them as if they couldn't see what he was holding.
Anyway, everyone focused on the identity card while listening attentively.
He said, "This right here is your goal. It is what you should aim to achieve if you want to achieve a respectable level of mastery of formation. If you can manage to build this, I will respect you."
Some people took out the magical item that they call an identity card. It looked like etched glass. But the etchings on it are colorful and change frequently.
Many of them couldn't even begin to figure out how the identity card works. So they were already daunted by the goal.
The lecturer saw this and shook his head in disapproval. "Don't think it is too difficult. I could accept such a judgment if I had asked you to aim to build teleportation platforms."
"A teleportation platform is the epitome of a four-dimensional array formation. That's from what I can tell. I have spent more than a hundred years studying it, and that's what I can tell. It might very well be a five-dimensional array."
Then he began to laugh. This time, the laughter wasn't because of amusement. It seemed to the onlookers to be a deprecating laugh.
The lecturer sighed and said, "Do you know what makes me dismayed the most? It is that the level of the array doesn't matter to the patriarch that mastered the teleportation platform."
"He can understand and manipulate it intuitively, so he doesn't need to see everything about the array. But if I see everything about the array, the best I can achieve is going mad."
He began to laugh again. But mixed with that laughter was sobbing.
The sight of a grown man crying made Arthur feel strange. He thought to himself, "You're probably already going mad."
Then the man stopped laughing all of a sudden. He resumed his lecture as if nothing had happened.
"The second reason why you can't say that this goal is too difficult is because you're an ignorant fool. Do you even know what exactly I am asking you to achieve? When you know, you can tell me it is too difficult. Until then, you shut up and do what I tell you to do."
Arthur nodded and said, "Yeah. You're losing it, man."
The lecturer turned to the board and wrote down two words.
He pointed to them and said, "The language of formation is divided into rules and expressions. But the ultimate goal of a formation is enhancement or enchantment."
"Enhancement is the process of amplifying a property or attribute of a material. Enchantment is the process of granting a property or attribute that a material doesn't have."
"So one is amplifying innate properties. The other is bestowing properties. The combination of the two can produce a myriad of outcomes."
"Rules fall into these two categories. As for expressions, god knows what those are."
The lecturer stopped here and looked lost. He stood there frozen in his thoughts. It wasn't until someone coughed that he recovered and began teaching the class again.
Eventually, the class ended. It ended with a lot of homework and a recommended reading list.
Arthur acquired the knowledge crystals containing the information that was in the recommended reading list. Then he went home to work on the assignments.
No one was going to mark his assignment. He wouldn't be graded for doing it, but he went ahead to do them because they were beneficial to him.