That offer from Evenstar was, without a doubt, the most important thing that had ever been given to me. I was going to have a true look into the inner workings of magic. Evenstar gestured for Amethyst and me to follow him as he walked through the rows of books.
“As you know, Starswirl,” Evenstar started as he stepped through the rows of shelves. “I am a researcher of sorts. I have a few publications in print at the current time, ones that stem back to the very roots of what makes magic function.”
We reached the end of the bookshelves and trotted to the corner where an unassuming door stood in the wall. “This world around us takes so much for granted, it has so many assumptions about the nature of our reality that it believes them to be steadfast, true, and easily understandable.” He looked at me with that same spark in his eye. “However, that simply isn’t the case.”
He unlocked the door and entered the cramped spiral staircase. “You see,” he said as he pocketed his key. “This world isn’t really as steadfast as we want to believe. We want to think things are easy to understand and that solutions to our problems are simple. They’re right, to a degree, but getting to those solutions is a highly complicated game of mental chess.”
We came to another door and Evenstar withdrew another key from his bag. “This mindset of simplicity is basically correct. However,” he said as he pushed the door open, “Finding that simplicity is a much more complicated task.”
My eyes grew wide as we entered into the massive laboratory beneath the library. Everything inside was a sight to behold. Scrolls, books, quills, and strange devices littered the dozens of tables around the closer half of the room. Three of the walls were filled with chalkboards from floor to ceiling. Those boards were, in turn, filled with equations and proofs that stretched across the entire wall. Bookshelves occupied the other half of the room in perfect rows. The books that filled them ranged from newly printed to falling apart. The fourth wall was a massive frameless glass pane that stretched from the floor to the ceiling. It provided enough light to illuminate the entire room, but more importantly it had that same spectacular view over the world as Evenstar’s office had.
Across the top of the ceiling ran several lanterns, their bases connected in a network of pipes to supply a near endless flame from each. On the division between the shelves and tables, a massive fireplace resided. Its embers were glowing ever so slightly, evident of the blaze that had roared through the night. A bunk bed sat in the farthest corner from the fireplace, hiding itself in the shadows to offer its occupants a relief from the light of day.
“Welcome to my laboratory,” Evenstar said with a smile.
I was speechless to say the least. Everything in the room was exactly how I had imagined a magical laboratory to be. I must have sat there for quite some time because I didn’t notice Amethyst and Evenstar beside one of the tables in the side of the room.
“Are you just going to stand there?” Evenstar asked, pulling me out of my wondrous trance.
“What?”
“Do you want to see what we’ve been working on?”
I obviously did, and I immediately raced to the table. There, nearly covering the surface, was a large piece of parchment. On it were several equations and formulas revolving around one singular image. In the center was a group of about 100 shapes. Each one with one more side than the last. The very final one was a perfect circle.
“What is this?” I asked as I tried to understand the equations on the page.
“This,” Evenstar started as he pointed toward the page, “I’ve spent the decade researching.”
“You’re researching shapes? Is it for making magic barriers without lines?”
“It’s a lot more complicated than that,” Amethyst started as she stepped to one of the rolling chalk boards and lifted a piece of chalk from the tray. “How well do you understand math?”
“I’m alright at it,” I said with a shrug. I wasn’t being humble; I was being honest. Math may have been one of my stronger suits in elementary school but I hadn’t excelled beyond complex multiplication.
“So you’re familiar with algebraic equations?”
“Uhhh…”
Evenstar looked to Amethyst with a cocked eyebrow. “He’s smart. Just show him and I’m sure he’ll start picking it up right away.”
Amethyst shrugged and drew two perpendicular lines on the board. “Alright, these are our axes.”
My head bobbed as I focused my wandering mind on the lines. She then drew lighter lines, equidistant and parallel from the first. Within a few seconds, a grid had formed with two thick lines cutting it into 4 parts. “And here’s our grid. Now, this is where the fun starts.” She drew a straight line through several of the grid’s intersections and placed the chalk back in the tray. “Now, what do we know about this line?”
“It’s straight,” I said. It seemed like a simple question.
“Yes, but what else?”
I examined the board more closely, as though it was whispering the answer. “Well… I’m not sure…”
“It has a quality known as slope,” she said as she began writing an equation on the board. “That slope can be calculated by figuring out how high the line goes on the vertical axis divided by how far it goes on the horizontal.”
“So the slope is…” I paused as I counted the squares on the board. “The slope is two!”
“Correct!” Amethyst said as she jotted the number down. “It’s just that simple.”
I was pleased that I understood such a seemingly advanced concept. “That makes a lot of sense!”
“It does indeed,” she said as she carefully erased the line from the board and drew another one as straight as the last. “So can you tell me the slope of this one?”
It goes 3 high and 6 wide. “One half?” I asked, not completely sure that my mental mathematics were sound.
“Yup!” She said as she erased the line again. “So, now that you know that basic piece of information, how do you calculate this?” she asked as she plotted several points on the grid and drew a curving line through them all.
“Uhhh…” I muttered as I tried to find the trick to solving that equation. “It changes all over the place. There isn’t one.”
“Oh there is, Starswirl,” Amethyst said, “Any line has a slope unless it’s straight up and down.”
“But this one curves, how—”
“And now you see the problem,” Evenstar said with a smile. “It’s not hard to understand, but it is definitely difficult to figure out. As of right now, we’re not sure how we’re supposed to get the slope of that line, but we know it’s there.”
“And you’ve spent ten years on this?”
“That and a few other things.” Evenstar shrugged. To him, his work was as nonchalant as walking, but there was something about developing the next level of mathematics that satisfied my soul deep to its core.
“But what does this have to do with magic?” I asked as I looked to Amethyst. “This is just math.”
“Math is the language that magic can be written in,” Evenstar said as he looked to Amethyst. “Would you mind showing him what we’ve been working on?”
Amethyst nodded and stepped to the empty table beside Evenstar and quickly cast the spell to make the blocky blob of shells. “See how the shell itself is made of individual blocks?”
Evenstar took the conversation from there. He approached the shell and looked at my dissatisfied gaze. “I see something is on your mind.”
“Yeah… I always kind of thought that a shell would be… you know… curved a bit.”
Evenstar smiled. “We have a lot in common. The blocky structure is impressive to say the least, and I can’t commend Amethyst enough for her hard work, but there is something about that shell that just isn’t right. I feel like it can be a circle but the only thing that is stopping it is the way we think about those curves.” He pointed back to the chalkboard. “A circle is a curve, a very specific one, but we’re not sure where to go from there.”
Evenstar motioned for the chalkboard and for Amethyst to begin drawing. “So, what we have here is a classic problem: How do we find the slope of the top half of a circle?” Amethyst quickly drew a circle centered on the two axes. “There has to be a way but we’re just not quite there.”
By now my mind was working in overdrive to come up with a solution to the problem at hand. However, I wasn’t able to give an explanation. I wanted to make a good impression on Evenstar, but all I could do was sit there in silence along with the other two. No doubt they were doing the same, but I could feel they were on the verge of a discovery.
Several minutes later, Evenstar broke the silence and turned his attention back to the page on the desk. “This is the way the ancients used to describe, very accurately, a number known as pi.”
“Pie? Like the food?” I asked.
Evenstar chuckled, “I’m fairly certain every pony to ever hear of pi has asked that question. No, it’s not like the food, but it describes the food’s shape. Have you ever wondered how far around a circle is?”
“Uhh…” I couldn’t say that I had.
“Well, pi allows us to know that number just from knowing how far the circle is from its center,” Amethyst said as she pointed to the different shapes. “They were able to calculate pi to an incredibly accurate number, but we are more interested in their method of finding that number.”
“If you look here, Starswirl,” Evenstar said as he pointed to one of the polygons. “With every addition of a new side to the shape, the accuracy increases. By the 96th side, we can see that the shape is almost perfectly identical to a circle. Well I’m looking a step further. I want to know the exact value, but the method they used, despite getting extremely close, will not render the actual number. There is still some ambiguity to its nature. Pi, as far as we know, lies in between two very similar numbers.”
“Somewhere between 3.1408 and 3.148,”Amethyst said as she pointed to the two numbers on the bottom of the page. “But we’re not exactly sure where it is between them. It could be anywhere, we simply don’t know.”
“Right,” Evenstar said with a determined nod. “So all we can do now is either continue the method they used, which will never get us the exact answer, it will only get us close, or we can choose to develop a new method to finding that actual distance.”
I looked back at the board where the curve still sat. It was all beginning to come together in some strange way in my mind. The math made sense with the images it represented, and now I was gnawing on that question Evenstar had been looking at for years.
“So what are you doing to find it?”
“The unthinkable,” Evenstar declared. “We have to find math that is accurate to the most infinite degree. Doing that requires us to redefine math as we know it. We’re working in a world of digits, a system where we can look at chunks of data, but not the individual datum.” Evenstar’s smile grew as he turned toward the massive equation on the wall.
“I tried that equation for a while, but it proved my previous statement. We can’t look at the world the way we always have, in singular digits. No, we need to look at the world as one continuous stream of infinitely small pieces of data. We need to look at it as though it were analog, not digital.”
At the time, little of what he was saying made sense to me, but I was fascinated all the same. It seemed like they were almost there, that only a small equation or piece of information was holding them back.
“Wow…” I whispered as I looked around the room. “And all of this stuff is just for figuring out this one problem?”
Evenstar furrowed his brow as he surveyed the room. “About half of the things in this room are dedicated to that topic. The other half are musings of mine and Amethyst’s.”
“Oh?” I said as looked to Amethyst, “Are you doing research yourself?”
She shrugged as she trotted to her table. “Not really, I’m just kind of tinkering with things. Mainly things that relate to my sphere. I’ve been trying to work on making it look like a sphere without the analog equation that Evenstar is dreaming up.”
“It’s going to happen,” he said without looking up from the page. “Just you wait.”
“But until then, I’ll stick with my algebra,” Amethyst retorted with a smile.
“So, Starswirl,” Evenstar said, “Are you interested in helping figure out the why?”
“You bet I would!” I declared.
Evenstar snickered. “Remember, we are under a library,” he said as he pointed to the ceiling. “We have to be quiet too.”
“Oh, right,” I whispered as a slight heat rose to my cheeks. “So where do I start?”
“Mail.”
“What?”
“That’s right!” Amethyst said with a laugh. “You’re the new mailpony!”
“You’ve got to be kidding me,” I muttered. “How is this supposed to help further magic?”
“Oh that’s right!” Evenstar said as he knocked his forehead with his hoof. “The mail is how we correspond with Challenger, the anonymous group that proposes several challenges for proofs. We are in a war of sorts.”
“A war?” I asked. I never thought magic could be violent.
“Yes. You see, many other researchers all over the world are looking at many of the same questions we are. One, in fact, seems to be working on a similar series of equations to my analog research. I fear we may not have much more time to complete it.”
“So you’re trying to get there first?”
“In a manner of speaking, yes,” Evenstar said as he tapped on the parchment. “This information that we’re using is mostly available to the other researchers in the world. The only advantage we have is my work that I’ve completed thus far.”
“So what do you gain for completing the challenge?”
“Fame.” The statement was so shameless it struck me as rather peculiar. “We’re vying for having the greatest discoveries on the planet, the person whose name is attached to those discoveries… well, he goes down in history.”
“Just fame?”
“Not just fame,” Amethyst said from her table. “Fame is the direct result, but increased funding allows for researchers to get their hooves on the greatest materials available for study.”
“Right,” Evenstar said without skipping a beat. “Look around the room, how much do you figure this all costed?”
I took a moment to take in the sheer volume of the items in the room. Some of the books appeared to be antiques, and the strange devices that precariously tipped off of the shelves must have been each more than my tuition.
“I’ll give you a hint: Those apparatuses total close to a million bits,” Amethyst said nonchalantly.
“You’re kidding me. How did you get that much money?” I asked as I looked to evenstar in bewilderment.
Evenstar looked up from the page and smirked. “Have you ever read any of the magic publications in our library?”
“A few. Why, did you write them?”
“Not all of them,” Evenstar said. “However, I did have one very important publication about a decade ago.”
“Which one was that?”
Amethyst spoke up once more. “Evenstar was the stallion to discover the magic mass unit. You remember, that thing I used when I showed you the shell a few months ago?”
“No…” I started as I looked to Evenstar. “You did that?”
Evenstar simply nodded in response. “Now that you’ve been brought up to speed with the problem at hand, would you retrieve the mail?”
“Sure!” I said as I eagerly started toward the door.
“You aren’t going to get very far without the keys,” Evenstar said as he withdrew the keys from his saddlebag and swung them from the tip of his hoof. “There’s going to be a lot of it and be careful, I frequently get sensitive instruments sent to me via mail, I’d rather them not be damaged.”
“I understand,” I said confidently as I took the keys in my mouth and trotted to the door.
I was excited to work with Evenstar, and having amethyst there was more than I could have dreamed. I had come into the library that morning expecting to grind through several books only to come to the same conclusion that I had before. It was time for me to truly begin my education into the world of magic, and I was the mail pony for one of the greatest magical researchers alive. That thought alone put a spring in my step and a determination to pursue the life that I had dreamed of for so long. I was going to change the world.