Chapter 15 Vectors

“Welcome, Jake.”

A chocolate skin goddess said to Jake with a smile.

“Yeah, I think we might have to be with each other for a long time to come.”

Jake replied with a sigh.

“Please don’t be too hard on her. She just wants to make sure that you are normal or if you in this case a mutant like her. We can help you as quickly as possible.”

“Help me? This immortal—Ahem I don’t think I need any help thank you.”

“What about math? I heard that you have power to control vectors. If you are not good at calculation. You might end up destroying everything around you.”

Jake wanted to refute because he knew a way to seal his power but if he sealed his mutant power. His other power would be sealed as well.

Jake narrowed his eyes. "What do you mean, 'not good at calculation'?"

The goddess chuckled, her smile widening.

"Vectors, Jake. They're all about direction and force. Imagine you want to push a box across a room. You need to know how much to push, and exactly which way. If your numbers are off, that box might fly through a wall instead!"

She gestured around the room.

"Your power to control vectors is incredible. You could move things, redirect energy, even fly. But without precise calculations, it's like trying to hit a tiny target in the dark. You might accidentally send a teacup through the ceiling, or worse, cause a lot of damage."

Jake thought about it. He did know a way to turn off his mutant abilities, which would also seal his other powers.

But then he'd be helpless. He watched the goddess, a flicker of worry in his eyes.

"So, you're saying I need to be a math whiz to use my powers safely?" he asked, a hint of frustration in his voice.

"Not a whiz, exactly," she replied kindly. "But a good understanding. We can teach you. Think of it as learning the language of your power. Once you understand the words – the numbers, the directions – you can truly control it. And we can help you learn, Jake."

“What kind of math are we talking about?” Jake asked, still skeptical.

He wasn't exactly a fan of numbers. School had been more about staying alive during class.

The goddess — who still hadn't introduced herself, he realized — tilted her head.

“Well, for vectors, you’ll need to understand things like addition and subtraction of vectors. Imagine you’re pushing that box again. If someone else is pushing it too, but from a different angle, you need to add your pushes together to see where the box actually goes. It’s not just 2 + 2 = 4 in a straight line; it’s about how forces combine when they’re going in different directions.”

She paused, seeing his slightly glazed expression.

“Let’s try a simpler way to put it. Think of it like a treasure map. If the map says ‘go five steps north,’ that’s one vector. If it then says ‘go three steps east,’ that’s another. To find the treasure, you need to know how those two directions combine to get you to the final spot. That’s what vector addition helps you figure out.”

Jake nodded slowly, picturing the treasure map.

That made a little more sense than just ‘addition and subtraction of vectors.’

“Then there’s scaling vectors,” she continued. “That sounds fancy, but it just means making a vector stronger or weaker. If you want to push that box harder in the same direction, you’re scaling your push. Or if you want to push it only half as hard, you’re scaling it down. It’s like turning the volume up or down on a radio – you’re just changing the intensity without changing the song.”

“So, if I want to fly faster, I scale my ‘flying’ vector up?” Jake asked, a flicker of interest in his eyes.

“Exactly!” she beamed. “And if you want to slow down, you scale it down. It’s all about precise control. You wouldn't want to accidentally go from a gentle float to smashing through the roof because you scaled your flight vector too much.”

Jake grimaced at the thought. L

“Okay, so addition and scaling. What else?”

The goddess led him over to a large, empty table in the center of the room. She picked up two small, identical stones.

“Imagine these stones are objects you want to move. Or maybe they’re just points in space you want to affect. To do that, you need to understand their position vectors. This just means figuring out where they are, relative to you, or relative to some starting point.”

She placed one stone at one end of the table and the other at the opposite end.

“If I want to move this stone,” she tapped the first one, “to that stone,” she tapped the second, “I need to know the vector that connects them. It’s like drawing an arrow from one to the other. That arrow tells me both the distance and the direction.”

“And how do I know that?” Jake asked, frowning. “Do I need a ruler and a compass?”

She chuckled. “Not with your powers, no. But your mind needs to be able to calculate it. This leads us to dot products and cross products. Don’t worry, they sound scarier than they are. Think of the dot product as a way to understand how much two vectors are pointing in the same general direction. It helps you figure out things like how much work you’re doing if you’re pushing something at an angle, or how much one force is helping or hindering another.”

She picked up a long, thin stick and laid it diagonally across the table.

“If this stick is one force, and I’m pushing the box along the table in a different direction, the dot product helps me see how much of my push is actually going into moving the box forward, and how much is just pushing it sideways uselessly.”

“And the cross product is different. While the dot product tells you about ‘sameness’ in direction, the cross product tells you about ‘perpendicularity’ or how much two vectors are pointing away from each other. It’s super important for things like figuring out how much something will spin if you apply a force to it, or if you’re trying to generate a turning motion. Imagine you’re trying to open a stubborn jar lid. The force you apply with your hand and the distance from the center of the lid create a turning effect, right? The cross product helps you calculate that turning effect, which we call ‘torque.’ For you, with your powers, this could mean creating incredibly precise rotations, or even stopping something from spinning altogether.”

Jake was starting to get a headache.

“So, dot product for things moving in the same direction, and cross product for spinning things?” he summarized, trying to simplify it for himself.

“That’s a very good way to think about it for now!” she praised. “It’s about understanding the relationship between different forces and movements.”

“Beyond those basics,” she continued, moving back to stand opposite him, “you’ll also need to understand vector fields. This is where your power really gets exciting. A vector field is like a map where at every single point, there’s an arrow showing a direction and a strength. Think of a weather map with wind arrows everywhere. Each arrow tells you the wind’s direction and how strong it is at that particular spot.”
She swept her hand across the air.

“Your power to control vectors means you could, in theory, create or manipulate these fields. You could make the air in this room flow in a specific pattern, or create a force field that pushes things away from you. But to do that safely and effectively, you need to understand the math that describes these fields.”

“Imagine you want to create a gentle current of air to lift a feather. If you don’t understand the math of the vector field, you might accidentally create a gale-force wind that rips the feather to shreds and blows out all the windows! Or, if you want to create a protective shield, you need to make sure every point in that shield has the right force and direction to deflect whatever is coming at it.”

“And then there’s calculus related to vectors.” She saw his eyes widen with dread. “Don’t worry, Jake. We’re not talking about advanced university-level stuff right away. But eventually, to truly master your power, you’ll need to understand how vectors change over time or space. That’s what calculus helps with. How does a force change as you get closer to something? How does the speed of something change as you apply more force? These are questions calculus answers, and they’re incredibly important for controlling your powers with precision.”

“For example, if you want to slow down a falling object gradually and gently, you need to understand how the force you apply changes as the object gets closer to the ground. If you just apply a constant force, you might stop it too suddenly, or not enough. Calculus gives you the tools to calculate the perfect, smooth application of force.”

“It sounds like a lot,” Jake admitted, running a hand through his hair. “I was never good at math.”

“That’s okay,” she said kindly, her smile unwavering. “You don’t need to be a math genius from day one. You have a unique ability, and like any powerful tool, it requires understanding to wield it safely and effectively. We’re here to help you learn. Think of it as learning to drive a very powerful car. You wouldn't just jump in and race down the highway without lessons, would you? You’d learn about the accelerator, the brakes, the steering, the rules of the road. This is the same, but for your incredible, unique powers.”

She paused, looking directly into his eyes. “We’ll start with the basics, Jake. We’ll use examples that make sense for you, things you can visualize and relate to your own abilities. We’ll go at your pace. And remember, the goal isn't just to make you a math whiz. The goal is to give you the control you need to live a full life, to use your powers to help yourself and others, without fear of accidental harm. It’s about empowering you, truly empowering you, to master what you can do.”

“So, you’re not going to just throw a textbook at me and tell me to get on with it?” he asked, a small, hopeful smile forming on his face.

“Absolutely not,” she laughed. “We’ll make it practical, Jake. We’ll show you how the math applies directly to your power. We’ll start with simple exercises, maybe moving a feather from one side of the room to the other with precise control. Then maybe something a little heavier. You’ll feel the math working in your hands, in your mind. It won't just be abstract numbers on a page; it will be the language of your own unique abilities.”

She stepped closer, her expression warm and reassuring.

“Think of it as training. Just like an athlete trains their body, you’ll be training your mind to understand and direct your power. And we have some of the best teachers here, people who understand both mutant abilities and the science behind them. You won't be alone in this, Jake.”

Jake considered her words. The idea of "training" his mind, rather than just "studying math," made it sound less daunting.

And the thought of being able to control his powers, truly control them, without the fear of causing chaos, was incredibly appealing.

He’d always felt like his powers were a ticking time bomb, something that could go off at any moment with disastrous results.

The idea of taming them, of making them an extension of his will, was a powerful motivator.

“Okay,” he said, a new resolve in his voice. “Okay, I’ll try. Where do we start?”

The goddess’s smile widened, a genuine warmth radiating from her.

“Excellent, Jake. That’s the spirit. We’ll start with something simple, something that will show you the immediate connection between your power and the basics of vectors. How about we try moving that teacup over there to this spot, with absolute precision?” She pointed to a delicate ceramic teacup on a nearby shelf and then to a marked spot on the table.

“Just a few inches, but perfectly controlled. No accidental flights through the ceiling, I promise.”

Jake looked at the teacup, then at his hands, then back at the goddess.

For the first time since he’d arrived, he felt a flicker of excitement mixed with apprehension.

Maybe, just maybe, this wouldn't be so bad after all. Maybe he could actually learn to master this incredible, terrifying gift.

The path ahead seemed long, but with this “chocolate skin goddess” and her promise of practical, understandable lessons, it no longer felt impossible.

He took a deep breath, ready to face his first math lesson, a lesson that promised to unlock the true potential of his powers. He was ready to learn the language of vectors.