The Marvelous Misadventures of Walter Guilman: The Witch House

Tesseract

Guilman sat studying intently at the improvised desk in the large attic room. There was very little furniture, only a creaky bed and dusty dresser to speak of, so Guilman had to pull the dresser from the wall and place a borrowed chair behind it to use as a desk. The room itself was very queer, since it took up almost the entire northern half of the third floor.  It had 5 walls, with an odd five-panel door in the center of the south wall, and a strange platform, with dimensions of 1x4x9, on the northern side of the room. The floor curved up at a shallow angle like the crest of a small hill, with the platform being the only level place in the room. The ceiling was filled with angles that Guilman couldn't justify for the life of him. At some parts it angled steeply down, or up, and at others it curved smoothly toward the north or south. The only place that was logical was above the platform, where it appeared a trapdoor had been sealed. The only reason Guilman had chosen this room was because he fancied it connected somewhat with his studies of higher dimensions. He had read the old accounts of Keziah Mason, the old witch who had lived in the house up until her disappearance in 1692. The records of her trial show that she spoke of angles that, if followed properly, could lead one out of the universe we inhabit into a kind of limbo, where one could reemerge into any other part of our universe they pleased. After the trial, she vanished from her cell with a flash of violet light. This had exited Guilman, because he was studying four-dimensional calculus and geometry, and living in a room where someone who had allegedly mastered this might have practiced and perfected her method might give him the insights he needed to complete his studies. He was trying to memorize a particularly complex figure, when he heard a knock at the door behind him. Thinking it was the landlord, he stood and walked to the door. But when he opened it, he saw a very distraught looking Daniella Elwood. "Hey, are you alright?" Guilman asked. "Yeah." she said, her voice breaking. "Just been sulking in my room all day, and thought talking to someone might help to take my mind off things." She sighed deeply, regaining her composure. She looked behind Guilman at the dresser covered in papers. "Say, you never did tell me what you were studying." she said slyly. "Oh." Guilman said awkwardly. "Well, uh, I'm studying shapes in the fourth and higher dimensions." There was a long pause. Elwood stared at him blankly and made a rolling motion with her fingers. "Um, well, uh, see..." Guilman stuttered. "Here, itle' be easier of I just show you." Guilman walked over to the dresser and sat down. Elwood stood beside him, looking down at the stack of books and notes. Guilman grabbed his pen and a blank piece of paper, and made a small dot in the middle. "This is a point." he explained. "It is a theoretical area of space that is infinity small, with no length, height or width. However, if you have two points," Guilman placed another dot just next to the first, drawing a line between the two. "you get the first dimension. Length." Elwood crossed her arms thoughtfully. "If you add two more points, you get the second dimension. Height." He added two more points, connecting all of them into square. "If you double that number, you get the third dimension. Width." He added four more points, connecting them all into a cube. "In mathematics, we use the variables X, Y, and Z to represent these three core dimensions-" Elwood interrupted him. "I'm not an idiot," she said defensively. "I understand basic geometry." "I didn't intend to imply you didn't,"  Guilman replied. "Sorry." He turned back to his paper and continued his explanation. "These three dimensions are seen by most to be all there is," He continued, "But recent mathematical revolutions have made it clear that isn't the case. There is, indeed, a fourth dimension." Elwood narrowed her eyes. "How could you possible be sure of that?" She asked. Guilman chuckled to himself. "Highly advanced math, relativity to be precise. Albert Einstein proved that time is not a force, but a fourth physical dimension." Elwood gaped. Guilman continued to speak. "I'm currently studying how shapes would appear in this higher plane. Using various formula, we can simulate what a four-dimensional cube would look like." "But if that kind of shape could only exist in four dimensions," Elwood interrupted again, "How could we make it?" Guilman's face had a beaming smile that Elwood didn't think was possible on such a gloomy person. "Simple." He said, clearly giddy with excitement. "Shadows." Elwood was even more confused than ever. "Here," Guilman said, stumbling over the slanted floor to the window. Sunlight was streaming in, and Guilman place his hand in the beam. "A shadow is a perfect example of moving shapes between dimensions. Rather than representing the shapes with their true angles, they improvise by making a shape that resembles the original, but has very few of the shape's characteristics." Guilman wriggled his fingers, and Elwood saw he was right. On close inspection, the shadow looked like just an abstract shape, but with the context of it being a projection from three dimensions into two, her mind filled in the gaps. "Using this method, we can construct a kind of three-dimensional shadow to represent these shapes." He beamed up at Elwood. "Would you like to see one?" They both hurried back to the desk, nearly tripping on the odd curve of the floor. Guilman grabbed his pen, and drew a larger cube around the smaller one he had drawn earlier, connecting the two at the corners. "This" he said, filled with barely controlled laughter, "Is called a Tesseract! In a perfect, four-dimensional environment, this all of its vertices would be at right angles to each other, and all of the sides would be the same length!" He then lost control, giggling with excitement, as if he had just won the lottery. "Isn't it brilliant?" he continued. "Using this kind of math, we may be able to find a way to break out of the third dimension. And then, oh and then!" he stood from his chair and jumped up onto the platform at the front of the room. "We could find a way to fold space itself, and travel to any point in the universe instantly! Think of it, Elwood! The Earth would truly become one community, cities could be built on the moon, and perhaps people could be sent beyond the sun itself, off to explore any star, or even galaxy that caught their eye!" His smile faded slightly and he stepped down and stumbled back to the desk. "Sorry." He mumbled. "I can get a bit exited sometimes." But Elwood wan't the least bit annoyed. "Guilman," She said, placing a hand on his shoulder, as if she was his father. "I've been through enough stuff to know that apologizing for your interests is a one way ticket to deep depression. It's far easier to persue those interests to the fullest, and keep away from anyone who wants to bring you down. I wouldn't be here if I was ashamed of my interests." She chuckled weakly. "Hell, you have even more reason to be proud than I do. You could uncover the next step to leading humanity to the stars, but I'm just reading about how badly Europe screwed up the world." She took her hand off his shoulder. "To make a long story short, just get good at something you love, and stick with it. You'll be a lot happier that way." She turned and began to leave. "Wait," Guilman said. Elwood turned. "When does the term start?" he asked. "Three days." Elwood replied. Guilman sank down into the chair in utter defeat, and placed his head it his hands. He thought it started in a week.