“The concept of elemental compatibility is not too complicated. It’s essentially just how elemental mana interacts with other elemental mana, be it normally or in spells,” Curiosity began as she shifted the topic.

“As for how it works…” her voice trailed off as she considered how to best explain it. After a short pause, she lifted the ominous black rock and placed it on the ground between the desks. “So… imagine you have this piece of obsidian. What do you think will happen if I cast a spell to push it?”

“It will… move in the direction it’s pushed in?” Chara answered dubiously, clearly puzzled about where this was leading.

“Let’s see~!” Rather than giving a direct answer, the swirling teacher decided to let the result speak for itself.

Without hesitation, she conjured up a swirling ball of water mana and launched it at the motionless piece of obsidian. Upon collision, the mana burst into a shower of illusory water droplets and the rock was sent tumbling forward. When it finally came to a stop, as anticipated, it had indeed moved in the direction it was pushed in.

“Wow~! It looks like you were right~!” exclaimed Curiosity. Unbothered by her student’s unusual look, she returned the piece of obsidian to its original position.

“As we’ve just verified, when a single force is applied to an object, it simply moves in the direction it’s pushed in. Now, consider this: what do you think will happen if I use two spells instead of one? In other words, two forces pushing on one object,” she restated in a curious voice.

“Umm, I think it depends,” Chara belatedly answered.

“Oh~? Depends on what?”

The little spirit hesitated. After mulling it over in her mind, she said, “It depends on which direction the forces from the spells are pushing. If both spells push in the same direction, then the rock will naturally be propelled much farther. If they push in different directions, then uh… I guess it will depend on the exact angles. And if they push in exact opposite directions, the forces will cancel each other out, and the rock will remain motionless… Um, are you okay?”

Midway through her reply, the greater spirit’s mana had begun to ripple in increasingly peculiar ways.

Curiosity, no longer able to hold back her feelings, did a little spin before releasing a magnificent shower of illusory water droplets that shimmered before fading.

“Wow~! How can you be sooo brilliant~? What a stellar intuition~!” she complimented with heartfelt sincerity.

Me, brilliant? I guess you could say so… The little spirit’s mana swelled slightly, her little form overflowing with confidence and pride.

Curiosity chuckled lightly before continuing, “As we discussed previously, each individual mana particle has a direction from reality, its identity. Similarly, the force acting on the piece of obsidian also has a direction, the direction its pushing in. So, bringing things back to elemental compatibility, what do you think will happen if elemental mana, which has a direction, interacts with other elemental mana?”

The little spirit’s swirling slowed before she pulsed in realization.

“It will depend on the mana’s identity!”

“Pretty much,” chuckled the greater spirit.

Having made her point, she retrieved the piece of obsidian and positioned herself to the left of the whiteboard, giving Chara a full, unrestricted view of the elemental diagram.

“Now then, as you have probably started to suspect, this diagram organizes elements according to their compatibility,” the swirling teacher boasted, as if the chart were her own invention.

The little spirit perked up.

This pictogram was one of the things she’d been curious about for some time now. After all, if Curiosity simply needed to verify whether Chara knew all the elements, then it would have been much easier to make a list, or even forego writing altogether. Yet, not only did she go out of her way to construct such an elaborate graph, but she also meticulously placed each element in a specific slot. It was too conspicuous.

Furthermore, as a devoted player of a certain monster-catching game, Chara was already quite familiar with the idea of elemental compatibility. Despite this, she had never seen an element diagram quite like this one, leading to her increased interest.

I wonder if the elements are balanced. Too bad I can’t become a fairy-type—or else I would have surely gone to go bully some dragons~!

The little spirit giggled inwardly. Chara, lost in her thoughts, didn’t notice as her attention was quietly whisked away, her gaze unconsciously fixed on the greater spirit. The moment she resurfaced from her thoughts; their gazes met.

“Baby, you need to pay attention.”

“…”

Feeling self-conscious, she averted her gaze to the side, opting to look at the circular element diagram instead.

Curiosity, picking up where she left off, said, “When elemental mana goes near other elemental mana, it generally results in one of three reactions.

“The first kind of reaction is attraction. Mana particles with similar identities tend to attract. This is especially true for mana of the same element,” she explained meticulously.

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The little spirit’s mind sparked in recognition. The swirling teacher had actually briefly touched on this during her explanation of normal mana, but hadn’t gone into much detail. Thinking back, Chara realized it was probably because she hadn’t yet learned about identity.

“In addition to itself, each element also attracts three other elements. On the diagram, these are the ones sharing a border. For instance, the element of water is bordered by the ice, dark, and wind elements, indicating their mutual attraction,” explained Curiosity, as she pointed to one element after another using the ominous black rock.

Water Attraction Diagram [https://1drv.ms/i/s!AgpGMi0K-XJMlZJutRB7xx7If_SaoA?embed=1&width=600&height=600]

The little spirit’s gaze wandered from one pictogram to the next, studying each element and its neighbors, until it settled on the division between the glowing sun and the sea of black.

Light and darkness? Why are these two touching borders? These two can’t possibly have a similar identity… right?

Sensing her little student’s curiousness, the swirling teacher hummed approvingly. “Well spotted~. Alas, it’s an exception—! Please treat the border between the light and darkness element like it doesn’t exist. Unfortunately, there isn’t really a better way to display this information. At least, not on a flat surface and not without using dozens of arrows.”

I see… Chara could tell that there was a story there, but she decided not to ask.

“The second type of interaction is repulsion. Mana particles whose identity is too different—really can’t stand each other! Run away! Each element repels four other elements. On the diagram, these are the ones not sharing borders. For example, the element of earth is separated from fire, wind, light, and darkness elements, indicating their mutual repulsion,” summarized the greater spirit.

Earth Repulsion Diagram [https://1drv.ms/i/s!AgpGMi0K-XJMlZJv4c3l9nHTOOK66A?embed=1&width=600&height=600]

“Oh, and don’t you point at the tiny corner between earth and darkness. Corners don’t count~!” Curiosity chided, not even giving her student the chance to voice her question.

The little spirit lowered her mana tendril dejectedly.

“The last type of interaction is cancellation! This occurs between elements whose identities are polar opposites! Each element has exactly one opposite. Needless to say, these pairs of elements experience the strongest repulsion and hate each other the most. But in the unlikely event that they actually meet, their opposing potentials cancel each other out, leading to the elimination of both!”

Curiosity thrusted out the piece of obsidian mercilessly, as if striking against some unseen enemy.

Swish!

“On the diagram, these destined enemies are positioned directly opposite each other. For example, earth and wind, or fire and ice. Additionally, while the light and darkness elements are placed right next to each other, these two are also opposites,” she clarified, finally clearing Chara’s doubts.

“While on the subject, the elemental compatibility of essences is the same as its parent element,” Curiosity briefly mentioned.

Oh, I guess that makes sense…

Chara didn’t ask any questions.

“The last thing I wanted to go over is actually the elements themselves—or rather, what they represent,” Curiosity whispered conspiratorially, as if she was divulging some kind of great secret.

Taken by the mysterious atmosphere, Chara unconsciously floated a bit closer.

“Up until now, I’ve been describing elements as ‘directions of possibility’ to make my explanations more intuitive. However, in their truest sense, they are closer to aspects of reality, with each element embodying the principles that define and govern that aspect,” Curiosity narrated mysteriously.

The little spirit briefly pictured eight colossal beings, their gaze cast from a plane far beyond.

“But in that case, you might be left wondering: why do I continue describing them as ‘directions of reality’ when I know full well that that isn’t entirely correct? And the key to this mystery lies in the concept of principles~!” Curiosity asserted confidently.

Principles… It occurred to Chara that the second step of spell casting, invocation, also involved principles.

“Think back. When I first changed the lesson to be about mana, what was the first thing I talked about?” asked the swirling teacher.

“Errm… that things exist?” responded Chara.

“Precisely! In this world, there exists countless things, and all things that exist can experience change. The potential outcomes of these changes are what we call possibilities,” reminded Curiosity.

Chara bobbed up and down cutely.

“However, the fact of the matter is: that things cannot happen without a good reason! For example, why do rocks fall? Gravity! Why does ice melt? Heat! Why does water flow? Fluidity! Without these principles serving as a basis, none of these things could have happened.

“Now, the reason I mention all of this is because this same logic applies to magic too. You see, while mana can be used to satisfy the conditions for any given possibility, we still need to create a solid basis for it to occur. That: is role of invocations.

“By performing an action that reflects a specific principle, we provide the basis for the spell to activate. However, there's a catch! The principles of the mana used to fuel the spell will not necessarily align with those of the invocation. In such cases, well… let’s just say that the chances of something unusual happening rise dramatically.

“Obviously, while not every spell’s outcome will align perfectly with the principles of the mana fueling it, the more closely it does match them, the easier it is to cast,” the curiosity spirit concluded spiritedly.

The little spirit’s swirling slowed, and her mana rippled thoughtfully as she digested the teacher’s explanation. After a moment of contemplation, she asked the pivotal question.

“So, what aspects of reality do the eight elements represent?”

Curiosity swished cheerfully before explaining, “They are solids, liquids, gases, heat, the loss of heat, electromagnetism, light, and the absence of light.

“I think you should be able to guess which elements they correspond to,” she added playfully.

As a matter of fact, I can~!

The little spirit swished confidently. Since she was already familiar with the concepts, she could memorize them without almost any effort.

Unfortunately, directing interest at a curiosity spirit was simply giving them permission to keep sharing. Curiosity, not one to neglect her students, did not miss this opportunity!

“Actually, while we’re on the subject, I might as well tell you the primary principles of each element. For earth, this is solidification, the process of becoming solid. Water is liquification and wind is dispersion. Fire is chemical reaction, ice is freezing, and lightning is electricity. And light is radiation while dark is absorption.

“Keep in mind that these are only their primary principles. While they hold a lot of weight, they are not their only principles,” the curiosity spirit reminded playfully.

“Um, do you have any more questions?”

The little spirit stared blankly.

“No!”

Feeling dejected by her student’s adverse reaction, the swirling teacher decided to bring the lesson to a close.

“Welp, that’s pretty much all the learning material I had planned for today. However, don’t think you can go off and play just yet~. To ensure you have a solid grasp of the concepts I’ve taught you, I am giving you an assignment!” announced Curiosity.