The power of Knowledge

After placing Carl's dead body into a random bag to throw out later, Beatrice closed the experimental room's door.

She sat down on the bed, completely satisfied with her progress in the past two weeks in regard to the Dark Bolt spell.

Although she had to create a string to control her spell, since she was not yet able to control it without any link, she wasted a lot of mana due to the increased cost that her string added. But this wasn't hopeless, after all, she already managed to reduce the amount of mana spent to around 4.6, which was a large improvement.

Another good news was when she got out her measurement stone and placed it on her forehead to inspect her mana pool's new capacity.

'14.41'

This means her reserve of mana increased about an average of 0.1 per day. Satisfied with her performance, she smiled brightly.

"In five or six months I will be considered a High Ranking Mage Apprentice," mumbled Beatrice as her increase in power brought untold joy to her.

Mage apprentices are divided into three levels, namely Lower Apprentices High, Apprentices and Peak Apprentices.

While the boundary between Low and High Apprentices was rather arbitrary, being thirty points of mana, to be considered a Peak Apprentice, one has to reach the maximum capacity of mana the human body can hold.

Although this fluctuates between people, it mostly varies by a few points, being around 78 to 82 points of mana.

When she was done with evaluating her progression, Beatrice decided to change subject and pulled a thick book from under her bed.

The size of the book was headache inducing, but it's subject, mainly Physics, was elemental to a lot of Beatrice's spell so she couldn't skip it. As laborious the task would be, she started reading with attention.

Other than some extremely rare and esoteric types of magic, the main use of physics for mages was the manipulation of speed and gravity around their spell, which would impact greatly its efficiency. Beatrice's dark bolt were both lacking in speed and efficiency and to understand the reason for this, she must first know one critical part of her spell: the Mana coefficient.

A mana coefficient is the maximum amount of mana at which the spell still operates efficiently. As an example: the Dark Bolt spell, it has a coefficient of around 4 so if we increase the mana output into the spell (use more mana than necessary) this will only destabilise the casting and make it fizzle out instead of empowering it.

The reason for the existence of the mana coefficient is very simple: simplification, as increasing the amount of mana that can be used efficiently by the spell is exceedingly difficult for apprentice mages.

For example, the original form of the Dark Bolt spell, the Rank 1 Dark Arrow, has a Mana Coefficient of 15, and as such, is tens of times more complicated than its Rank 0 counterpart.

Physics can be used as a way for mages to increase the power of their spells without increasing their mana cost.

...

Somewhere, into the forest...

A silhouette was observing three large tent containing trolls that were mostly asleep. The observer smiled, and pulled out a small device from his pocket.

"Your hearing will not save you," thought Leylin before looking at the device in his hands.

After sending a tiny amount of mana into it, a screen flashed, writings detailing multiple metrics like the atmospheric pressure, wind speed, the humidity, the elemental energy level and even the spatial stability of the region were now available to Leylin.

After analysing every factors, Leylin fell in deep thoughts, as a wave of calculations were taking place inside his mind. Being in such a confortable setting, and having no direct threat, he took his time.

Thirty minutes later,

A transparent barrier appeared in an instant around Leylin, and before a leaf falling from a tree could touch the ground, an extremely uncanny Dark Bolt appeared in front of him.

If we had to compare it to Beatrice's Dark Bolt, this one was very distorted, some regions of it being flat, while others curved. Despite it's shape the bolt's weight was balanced to perfection, making it perfect for reaching higher speed when launched.

Instantly, the Dark Bolt was no longer in front of Leylin, as the barrier that was protecting him was suddenly impacted by three sonic booms.

As the Bolt was faster than sound, the Troll's supernatural hearing could not save them of something they didn't even have the time to process. By the time the "pop" of Leylin's spell woke them up, their camp, trolls included, when blown into smithereens.

As unbelievable as it is, the three powerful trolls, which could each crush Leylin into meat paste in a straight-up fight, were all dead without any resistance.

The commotion got for answer the howls of multiples giant wolves, local inhabitants of the forest. They were approaching rapidly to inspect the cause of the explosion. 

Hearing the howls nearing his position, Leylin silently fled the scene, not wanting to fight an unnecessary fight unprepared. His mission already finished he had nothing left to do here.

Although the speed of the bolt was incredibly fast, three times faster than the speed of sound, Leylin could still do better. He recalled when he had to kill a troll warlord, whose hearing and magic sense was extremely sensitive accompanied with an inhuman reaction time that even speed of sound wouldn't be enough for spell to hit it by surprise. This prompted Leylin to spend over half a month creating the perfect dark bolt, the same one he used today against the three trolls and prepare the terrain.

Given enough time, any mage would become a menace. The more knowledgeable they were of their environment, the harder it was for any unsuspecting foe walking into their domain to fight efficiently. And some mage, to avoid the hassle of always having to do all these calculations, made their own tower, thus establishing a zone where every factor that usually degraded their spell to be under their control.