The Good Teacher

Chapter 258 Modelling

"The Sect Elders have been asking me why I'm bending over backwards for someone from outside the Sect. They're confused over whether they should kick you out for your insolence or prostrate in front of you in fear," Jace jabbed as he approached a seated Krish.

The recipient, the man seated atop a stone bench with a cross-legged posture and his walking stick resting on his lap, responded without turning. "So, what did you tell them?"

"I played the 'I'm dying, let this be my last wish' card and they acquiesced," Jace said with a snicker.

"You really are squeezing it for all it's worth, huh?"

"Better than sulking over it, anyways. So, why did you ask me to clear up the largest sparring field in our Sect for your Disciple?" Jace redirected. "Do you realise just how much whining I have to subject myself to? This entire Sect is filled with battle maniacs, and you've just asked me to deprive them of an outlet for their 'creativity'!"

"She needed a large chalkboard. Apparently, you troglodytes don't even have a regular-sized chalkboard. So, I decided to think outside the box." Krish waved his hands in front of him, gesturing at the large field with a flat yet textured stone flooring. "The field is basically a chalkboard laid flat on the ground."

Jace nodded contemplatively and said, "What does she need all this space for?"

Krish shrugged noncommittally. "I don't know."

"What a great Master you are..." Jace mocked sarcastically.

Krish scratched his forehead and released a sigh, "Listen, I basically spent a week doing banal scribe work. My mind decayed to a point that it has quite literally shut down. I cannot think nor can I reason. Let me have this moment to cleanse my mental palate. And please, spare me the witty digs, I lack the brain power to come up with an equally witty retort."

"You're no fun," Jace huffed and joined his old friend on the stone bench. The elderly duo then directed their attention towards the only other entity in their vicinity.

At the centre of the massive combat field, Marie was hunched over onto the ground with white chalk in one hand and the other flipping through the pages of the Endless Book her Master used to log the celestial data points. The mental and spiritual decompression she experienced yesterday while gazing listlessly into the vibrant sunset had transitioned into a welcome ten-hour sleep. Upon waking up this morning, her mind was churning up ideas at a feverish pace. It was as though a troublesome stopper inhibiting the free flow of thoughts was dislodged.

Without wasting another moment, she rushed to find her Master and asked for a large enough workspace to jot down her thoughts as they came. The way her mind was working, there were a lot of concepts and lines of reasoning that seemed disjointed, though she could feel that there was a connection if only she could see it all together. However, resources of that kind were found to be lacking in this place. Through some quick thinking, her Master managed to sanction the largest combat field available. The irony of the moment wasn't lost on Marie - to use a haven for combat as a medium for academics - but she didn't have the luxury of dwelling on that. Every second where her hand wasn't actively scribbling out words was another second worth of lost ideas.

Incrementally, a large tapestry started to take shape on the ground of the combat field. Marie's hand danced mechanically while the chalk deposited its residue on the ground. She ran through one stick, then another, then another... very soon she lost track of how many chalks she'd consumed. It all started to blend in together.

A system is another word to describe a dynamic process. A mass attached to a spring is a system. A closed room with an air-conditioner running in it is a system. A pipe to transport fluids from one place to another is a system. Within a system, there is a myriad of interconnected components that elicit a behaviour of some sort, which is the focus of observation. A system can be a complex mechanism, or it can be extremely trivial. To make sense of a system and predict its behaviour, one needs to first identify it and build a working mathematical model of it.

Marie's goal was to identify and build a model of the universe. Needless to say, it is an incomparably complex system and was impossible for her to achieve given her current capabilities. For that reason, she drew a metaphorical dotted line around the Solar System and designated it as her sub-system of interest. The Solar system is in no way simpler to model, but it is inarguably simpler than the Universe as a whole. Another reason why she decided to limit the scope of her model was that she realised that the formulae and theorem she knew that describe the behaviour of celestial bodies were not exhaustive enough to handle complex inter-system interactions and were fairly basic in describing the known behaviours.

For instance, Kepler's Laws of Planetary Motion provide a robust set of rules to define planetary behaviour and orbit. It states that the orbit of planets around the Sun is elliptical with the Sun at the focal point. It also states that the area swept by a line connecting a planet with the Sun is constant per unit of time. These are simple mathematical definitions that produce a palatable model of the Solar System. But only to a certain degree.

First off, the laws are satisfactory in a world where it is just the two masses (the Sun and the planet). The moment the other celestial bodies are added into the fold, things start to go haywire. Each planet is influenced by its neighbours, and even those far away. In fact, Uthea the fifth planet from the Sun is so massive that its influence can be registered from Duenea, the first, and Sacagea, the last. Apart from that, there are also satellites orbiting the planets to take into consideration. Gaea has a single satellite orbiting it, some of the other planets in the Solar System have multiple (or none at all). The introduction of additional masses with their own appreciable gravitational fields starts to skew the base equation, requiring multiple layers of Newton's Laws of Gravitation to replicate the natural behaviour.

This way, the problem started to balloon up much like how she expected it to. Just to model the behaviour of Uthea she had to rely on an equation that spanned the entire width of the combat arena.

Nonetheless, her efforts were slowly starting to bear fruit. For a given initial state, Marie could match the behaviour of the model with that of the real celestial body for a finite time frame. With each new model appended, the time frame started to widen more and more.

Unbeknownst to her, an entire day had passed, yet she was barely halfway through her work. Without pause, Marie continued to scribble away, expending one stick of chalk after another. The moment she depleted one, another would magically levitate itself into her open palm courtesy of her Master. Another day passed, and unwritten real estate was starting to turn scarce. Marie was forced to squeeze equations between other equations - some snaked through the gaps between text. For an outsider, it would be cryptic and indecipherable, but it made complete sense from Marie's perspective.

A third day passed, and Marie was growing sluggish and depleted. She was broken from her trance by her Master who forced her to eat and drink. Following that, he practically restrained her onto a mattress and forced her to fall asleep. She thought the exercise counter-intuitive, but Marie had severely underestimated the fatigue her body had accumulated over the past three days. Within minutes of her body falling into the welcoming embrace of the goose-down mattress, her mind entered hibernation. A day later, she awoke refreshed with her mind just as sharp as it was four days ago.

Without another moment of dalliance, Marie returned to her work, with her Master observing and replenishing her chalk stock. Nearing the end of the fourth day, a pleasant mood started to radiate from her as things started to approach a close. Equations started to balance out, plots started to match, and it was all starting to come together. The entirety of the Solar System was starting to shrink and fit perfectly within the confines of the combat arena.

One final line, and thus concluded the modelling process. Marie took a step back, leapt off the stage and collapsed onto her back. She gazed exuberantly into the sky and pumped her fist in celebration.

"I did it! FINALLY!" She bellowed.

"Congratulations," her Master congratulated.

Krish didn't know what he was seeing. The complexity of the nearly unintelligible scribbles marring every nook and cranny of the combat arena was far beyond anything he had ever seen in his lifetime. But he trusted his Disciple and he was elated to see her excited and satisfied.

"So, what next?" Krish probed.

"Well, all that's left is to merge this with The Heavenly Eye somehow," Marie responded. She stretched out her body to relieve the cramps assaulting her muscles and continued. "Although, there are some... issues I need to lay out that I think will influence the efficacy of the integrated result."

Krish furrowed his brows and gestured for Marie to expound.