Chapter 49: Doing the Math (Patreon)

https://docs.google.com/document/d/1aGE_hemvYtmx58D8WNGpwikncQ77MPDQm3O-Fe3RL_Q/edit?usp=sharing

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“Is this seat taken?”

Cayden looked over his shoulder at the person who’d walked up behind him and did a double-take.

Seeing a race he had never before encountered was unusual for Cayden, but still happened on occasion. Avernon wasn’t the largest of cities, and the vast majority of the populace was one of two dozen or so of the most common races.

Seeing a race that he had never heard of, however, after his and Elise’s years of experimentation and research, was much rarer.

The boy behind him was an insectoid-looking creature with an almost-black carapace in place of skin, two sets of three eyes on either side of his oblong head, and two small nubs of antennae on his forehead. He had no hair on his head at all, and Cayden took a moment to simply stare at his alien-looking visage before he shook himself from his stupor.

“No, have a seat,” he answered the ant-man’s question, gesturing to the empty spot on the bench next to him, and the ant-man smiled – somewhat unsettling in how normal it looked in contrast to the rest of his body.

“You here for the Delver’s Academy trials?” he asked after settling down on the bench.

“No, those aren’t until later, I thought. These are the trials for the affiliate school.”

“Yeah, that’s right, but I guessed you might just be scoping out the arena,” the man replied, and then gestured to Cayden. “You’ve got the look of an adventurer about you.”

Cayden glanced down at himself before shrugging. “I’ll be attending the academy this coming semester, but I’m not here for the trials. My friend is planning on going to the affiliate academy, though. I’m here to watch her.” He paused as the ant-man nodded. “Is that why you’re here? For the trials?”

“Yep! Hoping to get into the Delver’s Academy – my trial is in a few hours. Nerves were getting the better of me just sitting around waiting, so I figured a distraction might help,” he smiled again at Cayden. “The name’s Jeremy.”

“Cayden,” Cayden replied, nodding at the man. Although, Cayden was starting to realize Jeremy was likely a bit younger than Cayden had originally thought. It was impossible to gauge his age from how he looked, not with such an alien-looking race, but his mannerisms, coupled with the fact he was trying to get into the academy, suggested to Cayden they were a lot closer in age than he had first suspected.

“What’s your friend planning on studying in the affiliate academy? I’ve heard there’s all different sorts of options there,” Jeremy asked a moment later.

Cayden had been planning on listening to the presentations of the trial-takers, but he was bored enough after the first one that he didn’t mind being the distraction Jeremy was clearly looking for. And the arena was big enough that their quiet conversation wouldn’t bother the presenters or judges. “She’s an enchanter, and makes potions as well. But primarily enchanting.”

Jeremy gave a low whistle, something Cayden wasn’t sure how he managed with his strange lips. “That’s impressive. I heard they were thinking of increasing the age limit for students at the affiliate academy to accommodate more enchanters.”

“Really? Why would they need to do that?”

“Apparently, enchanting is hard enough that few are able to become enchanters in their own right before passing the current age limit. Master enchanters don’t want to give up their apprentices mid-apprenticeship, and the academy of course doesn’t want to take on an ‘enchanter’ who hasn’t proven themselves. Those people are more than likely to be completely useless. Increasing the age limit would give new enchanters time to finish their apprenticeships and then join the academy, which would hopefully increase the number of enchanted items available for delving students.”

“Ah, and the real reason comes out,” Cayden replied with a smile.

Jeremy chuckled back. “Hey, I’m not against it if it means getting a good enchanted item for less than half my life savings.” He nodded towards the arena. “That’s why Basura is so famous.”

“Basura?”

“The gnome judge. He teaches for the affiliate school, but he’s well-known and respected even among the delvers. One of the youngest enchanters ever, and his enchantments are some of the best you can get.”

They chatted good-naturedly for the next few minutes, Jeremy doing most of the talking, until they were interrupted by enhanced yelling coming from the arena.

“...and you think you can cheat your way into the academy??” the intelle yelled, his voice slicing through the silence of the arena. Across from him, a young leprechaun stared at his feet, holding a somewhat familiar-looking necklace in his hands.

The gnome put a hand on the forearm of the half-raised intelle, who settled back into his chair with a huff.

“If you can give us any evidence as to how you created your enchantment,” the judge named Basura stated in an even tone as he hefted a strange-looking bar of metal in his left hand. “We will continue this interview. Otherwise…”

The leprechaun glanced up from the ground to look the gnome in the eye. He glanced at the bar, and then after hesitating, turned and sprinted from the arena.

The intelle laughed evilly while Basura sighed and then spoke with his amplified voice. “Guards, please apprehend applicant Jesse’s enchanted necklace as payment for attempting to cheat this application process, and then send in the next applicant.”

“Hah, guessed something like that would happen,” Jeremy said as the judges turned off whatever was enhancing their voices and talked among themselves.

“Really? How so?” Cayden asked.

“With all those potion-making enchantments that’ve been flooding the market, I figured someone would try to take advantage.” Upon seeing Cayden’s confused look, he continued. “You’re not from the capital, I take it?”

Cayden shook his head.

“It’s been a topic of conversation in the adventurer’s guild recently, as everyone’s always looking to add an enchanter to their team if they can, but no one’s been able to find them.”

“Find who?”

“Whoever’s been making the potion-boosters. Over the last few months, there’s been a bit of a flood of enchanted items that boost the effects of created potions. Not an insane amount of them, but enough that people have started to notice. The real unusual thing about them, though, is that none of them have a maker’s mark. That, coupled with the cheaper price compared to most enchanted items due to the abundant supply – at least compared to normal enchanted items – all but guaranteed someone would try and use one of them to sneak into the affiliate school.”

Cayden smirked to himself, realizing a bit of what was going on.

“Why would they want to do that? Wouldn’t it come out when they weren’t able to enchant something?” he asked.

Jeremy shrugged. “Maybe they thought they’d be able to figure it out after they got admitted. Maybe they just wanted the chance to build some connections with nobility. Plenty of possible reasons, but I agree that none of them are really smart.” He nodded towards the judges’ table. “That rod Basura is holding is reportedly a lie detector. And if I was able to guess someone would try and use one of the potion-boosters to sneak their way in, you gotta believe the judges were expecting it.”

They settled into silence as the next applicant entered the arena and began their presentation, occasionally making remarks and chatting back and forth. Cayden was even more looking forward to Elise’s turn, though he couldn’t help a flutter of nervousness for his friend after seeing the way the previous applicant had been treated. But he trusted in Elise’s competence and ability to present her own case. She would be accepted.

Finally, it was time.

Cayden applauded loudly, standing to his feet as Elise walked across the sand to the center of the arena and waved back at Cayden with her free hand. The stands were a little more occupied than they had been for the earlier presentations but were still extremely sparse, so Elise had no trouble picking out Cayden. Beside him, Jeremy applauded politely with less enthusiasm.

“Judges, my name is Elise, and I would like to apply for acceptance to the affiliate academy as an enchanter, with a subspecialty as an alchemist.”

“Do you have an enchanted item you have produced as a show of competence?” the intelle asked.

“Yes. Here I have a necklace that boosts the effectiveness of potions created by twenty percent.”

There was a beat of silence, and before the intelle could react in another yell, Basura put his hand on his fellow judge’s arm. “Can you give any evidence as to how you created the enchantment?” he asked, his voice tired. Jeremy glanced at Cayden with a sad look.

“Of course,” Elise replied with confidence, and Jeremy’s look of commiseration changed to one of surprise. “This was my first enchanted item created, made from the stalks of verdant grass, infused with mana in a reversed-helix pattern as they were woven around a mundane necklace I had prepared for the occasion. It’s only a twenty-percent boost – helpful, but nothing impressive overall. This, on the other hand,” she pulled a second necklace out of her pocket, one that, on the surface, looked almost identical to the first. “Is a necklace that boosts the effectiveness of potions created by sixty-four percent.”

The audience murmured.

“This second necklace I made two days ago, also from verdant grass, also using the same pattern of mana infusion. My magic control and magic power, along with my skills, have all increased in months between the two enchantments,” Jeremy startled next to Cayden when Elise used the word ‘months’. “But a larger portion of the improvement can be attributed to this.” Then, reaching into her other pocket, she pulled out a small vial. “This is a potion of boost enchanting. Normally, it only offers a twenty-percent boost to the effectiveness of created enchanting items, which, while helpful, isn’t much compared to what many skills offer. This specific potion of boost enchanting, however, gives a sixty-eight percent increase to the effectiveness of created enchanting items.”

She paused, clearly having the full and undivided attention of all three judges.

“This percentage increase is much higher than what typical potion-boosting enchanting items could offer, even when multiple are used at once. My potion-boosting items are able to achieve this result due to the iterative creation of increasingly strong potions and then potion-boosting enchanting items. And I hypothesize that this process can be scaled infinitely.”

Basura stared at Elise with laser focus and said a single word: “Explain.”

“I have gone through twenty-one different iterations of potion-boosting enchanted items, each time creating a stronger potion of boost enchanting using those items,” Elise said. “Some of those were created using non-optimal enchanting materials, unfortunately, which sets off some of the numbers. But from graphing my rate of improvement, it seems that the increase in the effectiveness of potion-boosting enchanting items does not converge to a specific asymptote. Though it does have diminishing returns with each iteration.”

“What’s she saying?” Jeremy asked Cayden, and he nodded. He’d been confused enough by Elise’s experiment at first, but over the months he’d grown to understand most of her jargon.

“Basically, she’s been alternating using potions to improve her enchanted items and using her enchanted items to improve her potions, and each side gets stronger every time she does it. The big deal is that it doesn’t seem to have a hard limit on how much of a boost she can get using this method, though the soft limit is that the increase is less and less after each time. Theoretically, after enough repetitions, she could create a potion that boosts the power of a created enchanted item by one hundred times or more, and then use that to make whatever other enchanted item she wants or needs.”

Jeremy’s mouth hung open at the possibilities.

Cayden was proud of Elise, that her experiment was finally getting the recognition it deserved after spending so long working in anonymity. Nearly every enchanted item she’d created had been toward this goal, the only exceptions being the BFG and her portable shield that Cayden insisted she make before he was willing to bring her with him on his solo delves.

In practice, the benefits Elise had found weren’t quite as impressive as Cayden was presenting them as. Diminishing returns quickly lowered the effectiveness of each repetition, and while it had only taken twenty-one iterations to get a potion that boosted enchanted items by sixty-eight percent (up from the initial twenty percent), Elise theorized that it would take at least another hundred iterations to get a potion that boosted enchanted items by one hundred percent, and then another thousand iterations to get to two hundred percent.

The benefit of her experiment, though, was in her evidence that, while the improvement would slow, it would never completely stop. And that the improvement wasn’t dependent on a single enchanter: the potions and items could be carried over between enchanters and generations of enchanters.

A boost of one-hundred times effectiveness to an enchanted item was not something that could ever be achieved in Cayden’s lifetime using Elise’s method, not even with non-stop delves of hundreds of dungeons specifically for that purpose. But ten or twenty generations down the line of incremental enchanting? For a kingdom which thought in the long-term? Elise’s ideas were a potential manifestation of pure power.

And if the judges were half as smart as the reputation of the academy made them out to be, Cayden was sure they’d see the benefits.

“Thank you, Elise, for your presentation,” the intelle said a few minutes later as Elise answered the last of the judges’ quick questions. “We will be in touch.” It was the same final statement the man had given to all the applicants, save the fake enchanter, but from the almost desperate gaze of the gnome which followed Elise as she walked out of the arena, Cayden was confident in the results.

Elise had made it into the academy!

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Might have to modify a few of the exact numbers used here as I double-check some of my math -- but we finally get to see what Elise has been working on for the last year!

Also...yeah, I played Skyrim, why do you ask?