Amethyst and I were well acquainted by the time Evenstar returned about a week later. We had made some minor progress on the proofs as we had spent most of our time stargazing. Astronomy was something that fascinated me, but that wasn’t why I was so profoundly interested in it. No, in a way, I feigned my interest so Amethyst would come alive like she did that one night. It was something I was rather fond of.
When he first entered the room, Evenstar didn’t say a word. There was no authoritative direction that we had been accustomed to, not that there was any need at this point. We had come to operate as automata in the lab with our morning duties, so everything was as it should be as he stumbled into the room that morning.
After surveying the room and seeing that all was in order, he spoke. “My apologies for my absence. I had some matters to attend to.” His voice was harsh, notably so
“Is everything alright?” Amethyst asked.
“Everything will be fine,” Evenstar mumbled as he stepped to one of the tables and gave it a hearty push. We cringed at the shrill scream of wood as it scraped across the floor.
“Will?” Amethyst asked as Evenstar brought the table came to rest beneath the chalkboard.
“Yes,” he said with a rather irritated glance at us. “It will take some time to get things working again, but it will be alright.” He turned his attention to the cracked slate and frowned. A silence filled the room as we all struggled to keep our gaze from tracing the cracks that marred its surface. It was a reminder to the threat of Constance that had ruptured our routine.
“Amethyst,” Evenstar started as he walked toward the bookshelves. “I’m sorry to say this, but your shell development will have to be put on hold. We have lots of work to do, and I need your magical expertise focused on the analog equations.”
“I understand,” she said with a sigh.
“Good.” Evenstar turned to address me. His eyes were filled with a wild determination that made me shrink just a bit. “Starswirl, I need your mind.”
“My… mind?”
“Yes. You’ve been in the laboratory for several weeks now. It’s time you start contributing.”
“Haven’t I?” I asked, shocked that Evenstar had failed to see my help thus far.
His stare hardened. “No. Getting mail, organizing books, and grunt work is not contributing to the research, it’s aiding it.”
“Isn’t that the same thing though?
“Semantics do not become you, Starswirl!” Evenstar growled. “It’s time you start blazing paths, not following them.”
Evenstar’s tone made me shrink further as I nodded. I didn’t want to cross him, now more than ever. Evenstar turned from me and looked back to the chalkboards. Nearly a decade of work was scribbled on the black slate, and the analog equations took up a decent portion of them. Proofs, formulae, and a mess of numbers and symbols were squeezed between others in a chaotic network of research.
“Erase it.”
“What!?” Amethyst and I both shouted. Before I could begin my protest, she started hers. “You’ve been working on this for years! You’re just going to throw it away?”
“And where are we now?” He didn’t turn to face us. “The analog equations are nowhere near completion and everything on that board is a testament to my failure.”
Now it was my turn to stop his madness. “That’s not failure, what you’re doing is failure! You can’t just give up on the analog equations!”
Evenstar’s head started to turn toward us. “Who said anything about giving up on the analog equations? We’re starting over, from scratch, taking the years of missing the mark and putting it behind us.”
I felt my head nodding halfway through his discourse. Behind his harsh words, he had a sense of understanding, hope, and determination that filled his spirit. It pushed him, forced him to make changes to his life so that he could finally reach his goals. It was inspiring, in a way, to see him like that. There wasn’t anything that he would dare overcome, but that made him much harsher than he had been before.
Amethyst lifted an eraser from the cradle and turned to Evenstar. Her gaze asked the question that I dared not speak. We both feared him losing his work, but he was more determined now than ever before.
Evenstar gave a single firm nod.
As the eraser began to smear the notes into a chaotic mess of chalkdust, I couldn’t help but twinge. I never wanted to see work destroyed like this, but Evenstar was convinced that this was the only way to his goal. I watched helplessly as the decades of work disappeared from the board. Nopony spoke, and the soft rhythmic scratching of the eraser on the board roared with every stroke.
As Amethyst continued down the board, traveling back through the years of research, the room seemed to grow dark. That was when a low rumble of thunder reverberated through the rafters above our heads. Nopony spoke as the three of us turned to the window to see a towering cloud approaching the mountain in protest of Evenstar’s decision. I believe Amethyst was the first to return to the board, and Evenstar soon after her, but my gaze lingered on the brewing tempest.
It was terrifyingly beautiful, like standing on the edge of a cliff and looking out over an ocean of clouds. On one side, you are admiring something much more grand than yourself, but on the other, there is an inner feeling of danger that makes you respect the scene all the more. At any given moment you could cease to exist. Your life would hang so threateningly in the balance that your own mind begins to beg you to back away to save yourself, but your fascination with the scene before you keeps you firmly planted in place. I suppose what I’m trying to say is that the storm marked me in a way I would never forget.
Despite the looming threat, the work continued, the room growing darker still as the wind began to stir outside. It wasn’t until the last equation was erased that the light sound of rain began tapping on the window.
Even with the newly prepared board awaiting our first proof, the room remained motionless as the storm began to demand our attention. It was early spring, so storms would become rather commonplace, but their intensity never ceased to inspire. Distant flickers of lightning dimly lit the room with a pale flash of white, easily outshining the network of lamps above our heads.
“So,” Evenstar said, snapping my attention back to the lab. “Where shall we start?”
“Well...” Amethyst started as she brought her hoof to her muzzle. “The analog equations have proven to be difficult to setup with typical math…”
“Right, and I thought we had something with that proof we solved a week ago, but that seemed to dead end as well. It was promising, but it lacked a mathematical backbone,” Evenstar muttered as a distant roll of thunder underlined his words.
“A backbone?” I asked as my mind began to recalling the day searching for the proof of the windows. “What do you mean?”
“Always with the questions,” Evenstar muttered as he instinctively looked toward the board. As his eyes caught its blank surface, the spark within flickered. It was subtle, but it was then when I realized how much he had given up and how hard he was trying to mask it. “Math doesn’t bode well when infinity is involved. You can’t do anything to infinity, it just is.”
“So…” Amethyst said as she lifted a piece of chalk from the holder. “Does infinity mean something to the analog equations?”
“I’ve toyed with the idea of using infinity for years now,” Evenstar muttered as he watched Amethyst draw the symbol on the board. “But I was never able to employ it. Amethyst, draw a grid with an arbitrary curve on it, I want to start from the beginning.”
Amethyst did as she was told, and I was finally beginning to catch onto why the analog equations had been so elusive. Neither Amethyst nor Evenstar had a way of dissecting the concept of the infinite with anything they thought to use.
“So…” I started as Amethyst’s line came to an end, “Where did this graph come from?”
Amethyst glanced at the piece of chalk. “Ummm… what?”
“Who came up with it? It hasn’t just always been, has it?”
Evenstar spoke first, “The idea of mapping functions on a coordinate plane like this dates back several hundred years. Why do you ask?”
“Well, how did they figure out how to use it?”
“Why does that even matter?” Amethyst interjected as a frown spread across her lips. “I think we should focus on the analog equations, not how we’re graphing them.”
“One moment, Amethyst,” Evenstar said as he held a hoof to her response. “What are you getting at, Starswirl?”
“Well…” I paused as I noticed Evenstar’s face, he wasn’t worried, but that’s the expression it bore. He was concerned about something. “They had to build a framework to allow functions to be mapped like this.”
“Go on…”
“What if we have been forgetting that framework for the analog equations? You said yourself that there wasn’t any mathematical backbone, so why not make one?” Either I had just displayed my ignorance in its entirety, or I had swept them off their feet, because neither of them made a sound. Amethyst looked to Evenstar, who returned the gaze, and then they both looked back to me. “Is something wrong?”
“Many things are,” Evenstar said as he started toward the bookshelves. “Developing a new method of mathematics is easier said than done, and if we’re already doing it with the analog equations, then adding another might make things even more difficult to finish in time.”
“In time for what?” Amethyst asked.
“In time to stay ahead of my competition… Ah, here it is.” Evenstar said before motioning for Amethyst to come to his side. “I have a book on the development of algebra and it’s graphing, maybe there are some clues in it that would speed up our research.”
Amethyst lifted the thick book from the shelf and began to read. “It’s pretty long,” she said as she rifled through the pages. It’d take at least a week to read it if I was scanning.
“That’s fine, I’m sure Starswirl is up for the task.”
I never really appreciated being volunteered to do something as monotonous as reading, but with everything changing so quickly, I only nodded in reply.
“Excellent, Amethyst, you and I will start from the opposite end. Hopefully our research will connect in the middle.”
“The opposite end?” She asked while laying the book at the table before me.
“You see,” Evenstar started as a deep rumble filled the room, “I’ve spent a lot of my life fantasizing about what these equations could unlock. What we’re doing could change mathematics forever. We live in an analog world, Amethyst. Everything around us exists in a world without boundaries, a world of infinity.” He waved his hoof through the air in a slow arc. “Math has always been in search of a way to describe the world we live in. Everything from addition and subtraction to the fundamental understandings of algebra are all things that we have made to look at the world around us.” He paused as a particularly loud clap of thunder echoed through the storm outside. “We’re taking the next step in math, and we’re starting now.”