Tonight on Twilight Time
In a basement filled with fluorescent white light, a somewhat-innocuous parabolic lens sat well inside a plastic frame, its contents including a motherboard connecting it to a computer below its plastic table. On a very sunny spring morning, a lavender hand covered by the sleeve of a white lab coat adjusted knobs and buttons on a fan-enabled dehumidifier behind the black case of her computer to aid her breathing, despite the mountains of dank, older books and old schoolwork starting with her days in kindergarten off in the corner. With her computer glowing green, operating at optimal performance, and the record button waiting to be pressed on the program on her screen, her shot included the props laid out before the camera, her phone connected by a matted wire to the front of her machine, and the basement as clean as she could get it for her dealings in the sciences. Twilight Sparkle of Canterlot High School took to the airwaves and to the clouds, as the first video she played for everyone out in the land of the Internet introduced them to Twilight Sparkle’s Twilight Time. Filling the screen was a 3D rendering of her logo that she designed with an art student at school, complete with a twirling six-pointed star that served as the dots of the “I” in Twilight, accompanied by a song from a very obscure video game. It was from a game, but far as anyone knew, no one really cared about the state of video game music copyrights.
“Hello and welcome to another edition of Twilight Time with me, Twilight Sparkle.” Twilight greeted. “As usual, this is a show dedicated to the joy of learning for its own sake. Today, I am—“
Twilight’s speech was promptly and appropriately interrupted by the sound of pinging and vibrations coming from her phone within its pink and purple case. Twilight then looked onto another open program that featured an image of a math problem, from a user named “likehermAne.”
“Well, looks like Twilight is going to be doing a math problem sent in by ‘likehermAne’. The question is:
WORKING ALONE, THE RED WATER PUMP CAN EMPTY A POOL IN 4 HOURS. WORKING ALONE, THE BLUE WATER PUMP CAN EMPTY THE SAME POOL IN 3 HOURS. WORKING TOGETHER, HOW MANY MINUTES WILL IT TAKE THE RED AND BLUE PUMPS TO EMPTY THE POOL?”
“Well,” Twilight ruminated, “this is actually quite easy if you think about fractions and rates.” Twilight quickly sketched out on a piece of paper with her blue ink pen a circle as she continued to explain. “We have a red pump that can do the job in 4 hours, and then we have a blue pump that can do the job in three hours. What we can do is look at how far either pump gets after only one of those hours.”
Twilight then shifted the camera to bring her circle and paper into view, only offset with the colors by the lights. “You see, if the red pump can do the job in 4 hours, we can split the job into four equal parts, fourths, to represent each hour of the job.” She then proceeded to draw four equal parts with just two extra lines within the paper, write out the fraction, ¼, on each part, and then use a pair of scissors to cut them to size. “Meanwhile, the blue pump can do the same pool job in three hours, so I’ll draw another circle and split this one into three equal parts, one for each hour.” She then went on to draw a second circle with three equal parts with the camera on the paper. Inside each third, she wrote out the fraction, 1/3, and cut them out with a pair of scissors. “Now here’s the kicker. We can now assess how far the pumps get by taking only one hour’s worth of work from each pump.”
Twilight took a piece from each of the pies to show that they had a quarter and a third. “So now, we have a third of the pool and a quarter of a pool after two hours of work respectively. We can now add them up to see their total efforts together. However, a third plus a quarter can’t be immediately added together; don’t expect an answer of one-seventh, that’s way too small. You have to change the fractions in such a way where the denominators both match by multiplying based on the lowest common multiples between them.”
Twilight then went on to bring into focus another piece of paper and started to scribble her mathematics notes, as well as display a chart of the multiplication table. “We can start with 3 on this column, and we see that 3 can multiply to give us 3, 6, 9, 12, and 15. Then, we can see that 4’s multiples include 4, 8, 12, 16, and 20. Between them, we have the lowest common multiple of 12.” Twilight brought back her math scrap paper to focus. “So, let’s start with one-third. We know that 3 times 4 is 12, so we have to multiply both the numerator and denominator by 4 to give us 4 over 12. With that sorted out, we can continue to do the same with one-fourth and multiply each part by 3 to get 3 over 12.”
Twilight continued to scribble her mathematics on screen. “Now, we can add with our denominators being the exact same. We just do the math where 3/12 + 4/12 = 7/12. Therefore, after an hour, both pumps will have drained 7/12 of the pool. They’re asking us how many minutes it would take to drain the whole pool, so what we want to do is divide 60 minutes from the hour by 7 for the 7/12ths of the job done within the hour. With your calculator,” Twilight continued bringing her calculator into view, keying in as she talked, “we’ll divide 60 by 7 to give us about 8.57. This means that both pumps will have done 1/12th of the job in 8.57 minutes, which is about 8 minutes and thirty five seconds, but let’s not talk about that. Anyway, all that’s left is to multiply the 8.57 minutes by 12 to get approximately 102.86 minutes, a bit over an hour and a half.”
With all labors completed, Twilight moved the camera back to bring her face into view.
“Well, ‘likehermAne’, I hoped you enjoyed how playing with fractions doesn’t have to tear you apart.” Twilight chuckled. “Well, my next message came in from ‘8vamel,’ and she asks: ‘Twilight, I noticed that the same pitch tends to sound different when I go up eight keys. Why does this happen?’
“Well,” Twilight started with her face in view, “that’s because you are going up one octave, one set of eight major pitches. In the C major scale, it starts with C, then D, and then E, F, G, A, B, and ending in C. All matter in the universe vibrates in its own way, and the sound is generated by those vibrations on the air. These vibrations are picked up by our ears in different ways, as each sound vibrates with its own frequency and amplitude. The frequency usually governs the kind of pitch it is—every time the frequency doubles, the octave goes up—while the amplitude usually governs how loud it is.”
Twilight took a quick look at her pocket watch and realized that she was late for her science club meeting at the school. Though it was a Saturday, she was not without her obligations in her quest for a scholarship to the university where her brother, Shining Armor, was waiting for her while he was dating her old babysitter, Cadance. Seeing the time, Twilight made a mad dash to wrap up the show.
“That’s all the time we have on Twilight Time. Until next time, my faithful students.” Twilight then moved to cue up another video that displayed her name prominently, alongside that of Spike, with even more of the synthesized music.
With that, Twilight navigated her mouse pointer to end the broadcast, knowing that countless viewers, within the Canterlot High School viewing public and otherwise, will have been a little more enlightened. As she dashed out the house, Twilight was greeted by a transient Octavia who had been en-route with some tuning forks for her next program. She hastily carried them all from her as she moved in the general direction of the school, and knowing that her physics grade was once again safe.