Math: Part One

Math

It was a nice sunny day in Ponyville; the birds were tweeting, the cloud were few, and puddles from the rain a week before had finally dried up in some of the more shaded areas. Yes, it was a great day, but it was anything but an ordinary one.

“Okay Applejack, I just have to know; why do you need this textbook again?” Twilight asked as she and her farmer friend walked out of the library and in the direction of the orange mare’s farm. “I didn’t take it you were one for learning more a advanced mathematical techniques.”

“It ain’t for me, Twilight; it’s fer Big Macintosh,” Applejack said as the pair walked. “He’s been hidin’ something from the rest of y’all, especially you, Twilight, and I’ve finally convinced him to come clean about it. Mind you, it took a heap o’ convincin’, but I need this book for both his sake, and my own.”

“Both of your sakes?” the purple pony asked. “Just what does big Macintosh need with a book on statistics?” If anything, she thought he'd want something on farming, or maybe dating; she wasn't the only pony who had heard of his so-called "bad luck" with mares. He worked too hard and socialized too little in her opinion, though if she ever bothered to ask anypony else, they'd say the same thing about her.

“Well, you see, bein’ a farmer ain’t just plantin’ seeds, feedin’ hogs and harvestin’ apples,” Applejack replied. “There’s a might more to it than just that. Ya gotta know how to read the weather, ta know what foods will get ya through winter better, and what sorts of supplies make the best barns and such.”

“I still don’t see what that has to do with statistics,” Twilight said, a bit nonplussed by her friend’s statements. "Proxemics, definitely, logistics for sure, and maybe genetics, but statistics? That's a bit... different from what I'd expect a farm pony to need to know."

“I was getting’ to that,” Applejack said, rolling her eyes slightly. “Anyways, when it comes ta farmin’, ya gotta know what’ll give y’all the best sorts of produce. That meanin’, do we plant corn this year in the south field, or alfalfa, dependin' on the fertility of the soil and the expected rainfall each month? Which direction should our rows be facin’ when they get planted, seein' as how some of the field-borderin' trees are a bit taller than last time we had that crop? Has an early rain made the ground too soft fer us to use some of our bigger plows, or is the soil too dry fer us to be plantin' our winter wheat? Do we harvest the last of the cider-makin’ apples two weeks before the frost, or three? What’s the darn ratio of apples in the cider to all the other ingredients, like cinnamon and stuff?”

“Gosh, I didn’t know so much technical and mathematical thinking went into farming,” Twilight said, the implications starting to fully become apparent to her. Sure, reading the weather and knowing the seasonal changes was one thing, but all of this... it just boggled her mind. “I just thought it was... you know...”

“Plantin’ and hopin’ fer the best?” Applejack asked, arching an eyebrow at her friend. "Milkin' cows and balin' hay; is that whatcha thought we did all day?"

“Well, yes, actually,” the purple pony replied. “I never really read up much on farming, except the progression of its technological improvements and methods throughout history.”

“Well then, you’ll finally get to see just how much brain power goes into makin’ a farm successful,” the orange pony said as they walked up to the barn. “Come on now, Big Macintosh should be inside, waitin’ for us.”

The two mares walked inside, and indeed, Big Macintosh was sitting over on a bale of hay, seemingly off in his own little world. The sudden shutting of the barn door behind Twilight seemed to snap him out of his thoughts, causing him to look from Twilight to his sister and back.

“Applejack? Twilight? Why did y’all need me in here?” the big red stallion asked. “Ah got some chores that need doin’ on the north fields, and-,”

“Brother, it’s time you confess to Twilight, of all ponies, your true passion,” Applejack said bluntly, removing the textbook from one of her saddlebags. “Come on now, take this.”

Big Macintsoh, seemingly stunned by his sister’s assertive stance, gingerly took the book from her and lay it down on a bale near his hooves. Flipping it open to a random page, he looked up at his sister. “Y’all sure about this, AJ? Ah mean, we could always do this some other time, since I got mah chores-,”

“No, Big Mac; as much as I know there’s plenty of chores that need a-doin’, yer just gonna have to swallow yer pride on this one and just tell Twilight here the truth,” Applejack said.

“Truth?” Twilight asked, looking from stallion to mare. She had chosen to remain silent until she had an opening in which to speak. “What truth?” Tons upon tons of possibilities flowed through Twilight's brain, some far more insane than others; was Big Macintosh in love with one of the family apple trees? Was he really a unicorn? Were his sisters secretly trying to get him a date for some upcoming festival? Applebloom had learned her lesson about things like that, but maybe Applejack needed to get in in her head that her brother liked to be alone.

“Big Mac here is a cert-i-fiable genius,” her friend said, drawing out the word “certifiable” as if doing so made it more important. To the purple unicorn, it just sounded like Applejack didn’t really know what the word meant, or how it was said. “He’s likely the smartest in our family, and that’s sayin’ somethin’, given all our relatives across the country.”

“A prodigy?” Twilight asked. She wouldn't have picked the stallion in front of her to be something like that; muscular and silent, to be sure, but... a genius?

“Yes siree, he’s a gen-u-ine wiz on them fancy mathematics,” Applejack said, looking back at her brother. “Hey! Get back here, brother, you gotta show her fer yerself!”

The big red stallion, during the conversation, had been silently trying to sneak away, but given the fact he was the biggest stallion in Ponyville, that’d be like Spike trying to disguise the fact he was a dragon by painting himself bright pink. In a resigned nature he made his way back to the book, looking deep into its contents before looking back up at his sister and her friend.

“Okay, I’ll do it, but... don’t think less of me fer it,” he said, flipping to another page.

“Why would I think that?” Twilight asked, taking a step forward. Seriously, what was his secret? Did he guard some sort of magical treasure? Were the Apple stallions tied to some ancient cult of assassins and scholars? Did he have two tails?

“Because... farmin’ ain’t just about the trees and the crops and the animals,” Big Macintosh said. “There’s far more to it than just that. it's just... most ponies don't think it is, and we Apples take pride in what we do fer our communities. i just... never really saw other ponies' knowin' of mah smarts as bein' important is all.”

“I know about the stigma; Applejack told me all about that on the way here,” the purple pony replied. Okay, so maybe some of her guesses were... pretty far-fetched, now that he just kept talking about farming and the community. If it wasn't for Applejack's insistence, Twilight doubted he would have even been talking to her. Not because he didn't like her, but because he was about the shyest pony short of Fluttershy, and that was saying something.

“Did she tell ya that the only correct way to harvest regular apples is to measure the mean ripening period every year and then determine the best time to harvest the largest numbers in the shortest amount of time?” the big pony asked, his voice suddenly taking on a distinctly, and frankly unheard-of (to Twilight, anyway) tone of... intellectualism?

“What? No, I, uh,” Twilight tried to say, but her words failed her as Big Macintosh continued.

“The standard deviation of every year’s mean is how we know just how many cider apples to harvest, somethin’ yer friend Rainbow Dash should think about whenever we run outta cider,” the big pony said. “Within one deviation is just 68 percent of the apples we could have, and within two deviations is 95 percent. We’ve rarely had a harvest year in which we could both harvest and process 95 percent of our good cider apples. We’ve never yet had a year where we were able to harvest more, but someday, when there’s more of us to work the fields and orchards, we just might. I'm not even gonna try and tell y'all about how hard it is to try and find variance among these here samples of our hay," he added, gesturing at the stacks in the barn.

“I, um, uh,” Twilight tried to say again, her brain beginning to lose focus as the large pony continued.

“See, it’s not just these standard deviations, but the overall means as pertainin’ to the total number of individual sites,” the red stallion rattled off. “See here, in this book? It’s all clear as day, right on the printed paper.”

Twilight, almost unbidden, walked over and looked in the book. She saw symbols that were definitely not those of the same language she had grown up speaking, but at the same time, they seemed awfully familiar. It had been a good while since she studied mathematics; friendship had taken over her more "scientific" aspects of her life.

"See? Clear as a bell, I tells ya. And don't get me started on those fancy folk out judgin' us by crop tonnage and not quality; the nerves of some ponies, not knowing the difference on how ta properly calculate a z-test and a t-test..."

Big Macintosh continued for another good thirty five minutes, telling Twilight all about the inter-connectedness of farming, logistical growth equations, variance determination and sustainable harvest. He even went into a small rant about how population dynamics of their pigs were entirely dependent on the goodwill of ponies and the inclination of weather-based phenomena for good rains. Then, with a sudden finality, he closed the book and looked up at his sister, who was almost asleep from all this “fancy mathematical” jargon.

“If y’all need me, I’ll be out doin’ more chores,” he said, walking past her and out of the barn altogether. He didn't sound mad, or even gruff; just... back to business as usual for him, was all. Applejack, startled out of her stupor by his sudden departure, looked over at her friend, who kept looking back and forth between the book and where Big Macintosh had just exited, as if expecting some great secret to emerge from the pages upon his disappearance.

“See? What did I tell ya?” the orange pony asked as she walked over and picked up the book. “He’s a smart one, ain't he?”

“Uh, um, uh... yes,” Twilight said with hushed breath, and then something strange happened. Applejack didn’t believe her eyes, but she could have sworn her friend’s pupils turned into little pink hearts and... was she hovering an inch off the ground? “He’s definitely a smart one.”

Seemingly defying any laws of physics, Twilight almost floated out of the barn after Big Macintosh, her friend just staring at her before she vanished. It might have been her imagination again, but there seemed to be... a small trail of hearts following her friend's path.

Applejack didn’t know what had just happened, but she sure knew how to respond.

“Aw, shucks; can't say I was expectin' that to happen."

Math: Part Two

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Part 2

Twilight followed Big Macintosh as swiftly and with as much stealth as a deaf panther. Tracking skills aside, it wasn’t exactly difficult to follow the great big red stallion through a small section of the apple orchard and onto the edges of the northern fields. Almost immediately she noticed he began to survey each row of pumpkins with an almost machine-like precision. The way he moved just... fascinated her; it was if he were an entirely different pony when he was working than when he was just doing what she would consider regular chores.

After about a half hour of watching him mutter to himself about the pumpkins, the size of which rivaled the wheels on the princess's carriage, she watched as he slowly made his way over to a small orchard; now was her chance to strike. With a speed that would have impressed the Turtle King, the purple unicorn made her way over to where Big Macintosh was and stepped out from some bushes.

“Hello, Big Macintosh,” she said, trying not to let her voice sound dreamy. She wound up sounding congested instead.

“Hello Twilight,” the big stallion said, not looking in her direction; her voice sounded a tad weird to him all of a sudden. Did she somehow get sick on the wat over here? “Did ya follow me from th’ barn?”

“Yes, I did, and I couldn’t help but notice the way you surveyed your pumpkin patch like a machine,” she said, walking up to his side. “Do you really use your gift with statistics and all things mathematical in all of your chores?”

“Mostly,” the red pony replied. “Ta tell you the truth, Twilight, I think this is the longest conversation we’ve ever done had. Mind tellin’ me why you’re so interested in me all of a sudden?” He'd always thought her a tad cute, but never thought of her as a strong pony; she was a bit too small for the kind of work he did. Then again, he was pretty much the biggest stallion in Ponyville, so maybe he was the only one cut out for most of the work he did.

“I... I am just... fascinated by your gift,” Twilight said. “Have you always had it?”

“Y’all could say that, if it makes it easier fer you ta understand when I talk about it,” the Apple stallion replied. “I’ve bin this way fer as long as I could remember, and there’s no shame in that.”

“Of course there isn’t any shame in it!” Twilight said, almost with a tone of indignity. “Why in the world would there be any shame in being so gifted? There are ponies who'd part with many a bit to have such an understanding of the world.”

“I know that, but the reason I feel the need ta hide it is because I ain’t exactly a normal pony, Twilight,” he replied. “I’m a farm-pony, as my family has been fer a very long time. We’re used to our way of life, but the world is constantly wantin’ us to change, to become “newer” and whatnot. Could you imagine if some fancy-pants college found out ‘bout my smarts?”

“Judging from your tone, I’m guessing that’d be a bad thing?” Twilight asked. Here she'd thought somepony would have found out by now about this stallion's gifts, but it seemed it took a mighty deep friendship with this stallion's sister to even get him to confess to such a thing.

“Sure tootin’ it’d be a bad thing; they’d want me in their schools, learnin’ and possibly even teachin’ all about this stuff,” the red stallion huffed. “Even on a scholarship, our family don’t make enough fer me to go someplace like that, even if I got a job there. Besides, my place is on this farm; it’s my family’s farm, and so it’s my responsibility to keep it runnin’ as best I can. That’s why I never told nopony about my smarts before; they might try and convince me ta go to college or summat.”

Twilight blinked in surprise; she had just been thinking along the lines of putting in a good word with Celestia about getting Big Macintosh a lofty teaching position in Canterlot. His explanation and evaluation of the situation, however, made her see things differently almost immediately. He wouldn’t fit in, even less so than she had, and he’d be homesick all the time. His gift was tied to the line of thought associated with running a farm, and not the other things one might use statistics for. Plus, he was the muscle for this farm; without him, there’d just be too many chores for Applejack and Applebloom to do.

Maybe he wasn’t just smart, but wise as well; he certainly knew enough about what he wanted in life. She only wished she could have that same intuition. Her earliest dream, before enrolling in school, had been to become a ballerina.

Then she found out she couldn't dance like they could worth a hoot. The dashing of her brother's dream of becoming a kite had been even harder for him to accept than the failure of her's had.

“So,” the purple pony said as the pair walked over to another apple tree. “Just... what are you doing now? Is this some chore as well?”

“Kinda, but it’s more like a work-related hobby,” the big stallion said, sounding much more relaxed after confessing his worries to his sister’s friend. “I’m just makin’ mental life tables of our trees.”

“Life tables?” Twilight asked. She didn't know tables were alive; technically they were at some point, but until the day hers told Spike to stop spilling his juice every other week, she'd assume they remained inanimate.

“Yes; I use this ta see just how many trees we can expect to survive from year to year in our orchards,” Big Macintosh said. “Ever learn what I life table is?”

“No, I never got around to that part of statistics,” the purple unicorn replied. Okay, this was actually bugging her; Big Macintosh, of all ponies, knew something she didn’t about something she actually knew about. It’d be like Spike knowing more about baking than Pinkie Pie, or Luna schooling Rarity in fashion design. It just... it just seemed ludicrous.

“Well, the thing is, ever since ya plant a tree, there’s always a certain percentage that don’t make it,” the big stallion said. “Weather, varmints, accidents and disease can take their toll on trees, especially young’uns. Plus there’s this whole bit on age classes, which fer our apples trees, I just determine by height and trunk width. Sure, there's a whole lot more too it than just that, but it's easier fer me to remember that way.”

“I see,” Twilight said, her heart fluttering as Big Macintosh’s voice once again became intellectual in nature as he explained trees. Ponyville wasn't exactly the intellectual hotspot, since ponies there didn't need to be on the high end of education. Most would spend their lives happily working family businesses or making their own, though a few, like Rarity, always had their eyes on something bigger and better than what they had then.

So when Big Mac talked about apple trees, Twilight doubted there was another pony in town who knew as much about them as he did. He even made talking about trees sound cool, something her assistant would find impossible.

“Dependin’ on a buncha different factors, with our biggest three bein' size, species and rainfall, every tree produces a different number of apples fer harvest,” Big Macintosh coninuted. “We here pride ourselves in knowin’ how ta treat our trees right, but some years we lose some of our most productiv’ branches to heavy snowfall and ice.”

“I see,” Twilight said. She did know quite a bit about trees, but from the way in which the large stallion beside her was talking, he wasn’t even getting started.

“Now, outside of these here “life tables” I gots in my head, there’s the whole issue of recruitment for these trees,” he said. “We gots ta trim these tree enough so that new growth ain’t hog-wild and erratic, but not so much that we hurt the tree too much. See this here limb right here?” he asked, pointing to a large and sturdy-looking piece of wood.

“Yes; what about it?” Twilight asked.

“Well, this here was once just a tiny little offshoot of another branch, but it grew just fine, seein’ as how we couldn’t reach it at the time with our pruners,” Big Macintosh said. He turned to look at her. “How many apples do ya think we grow every year, Miss Sparkle?”

“I... I don’t quite know,” the smaller unicorn said. “Lots?” She remembered when Applejack had worked herself to exhaustion trying to harvest all the apples one year, and thankfully for her friend, the rest of them had stepped in to help. Twilight didn't know why the Apple family didn't just ask for help more often; she'd picked a good dozen trees clean with her magic in mere moments.

The stallion grinned a bit, as if trying to hold back a laugh for her sake. “We’ve never been able to count ‘em all, ya see, so I learned to use a hoofty-doofty formula that can estimate ‘em to a good degree. It’s all about how many we harvest outta the total number we grow.”

“Okay, but couldn’t you just take the total number you harvest and subtract that from losses to estimate the proper total?” Twilight asked. It would be simple math, to be sure, but there was somehting about his tone that siggested it was anything but simple.

“Shucks Miss Twilight, we would if we could, but we ain’t got the time to do somethin’ as labor-intensive as that with all the other things we gotta do around our farm,” Big Macintosh said. “Instead, we count how many apples we actually manage to process, as in make into pies, jams and such. There’s always a certain number fer each, so with that, we can estimate just how many we harvested without havin’ to count every dern apple.”

“And what of the other ones? The ones you don’t use?” the purple mare asked. She knew not all apples would be used, just like not all of Pinkie's baked goods would be sold.

The bad ones would be given to Spike, the living garbage disposal. She'd even caught him eating a book once, just because he was curious to what it tasted like. Luckily for her, it hadn't been a good book: "Economics in Practice" by some large walrus or something.

“Well, we do count the ones we throw out, but even then, we’ve still got quite a few we lost over the year to bugs and wing and stuff,” the big stallion replied. “What we do is...”

This continued on for another good thirty minutes, the pair of them having no idea that another pony was watching them. Applejack, having finished her chores on the south field, found the two of them sitting and talking away about exponential growth and conditional mortality of apples. She didn’t understand any of it, but in her honest heart, she knew there was something different between the two of them.

“They’re getting’ ta be good friends now, I reckon,” the orange mare said softly to herself as she watched the pair walk off towards the tomatoes. She could hear Big Mac talking about how he could teach Twilight all about the harvesting techniques that brought in the most tomatoes without sacrificing quality. “Maybe someday Twilight’ll get her head outta them books she loves and instead spend some more time on this farm.”

Before she walked off, she took one last look at the pair, both seeming to be having the time of their lives. “Maybe more than just some time, judgin’ from how she’s lookin’ at Big Mac,” she muttered, smiling as she left them to their own devices.