Leaning back in the couch, she let her mind relax. Think…

““Leaning back in the couch, she let her mind relax. Think, Heather. Think. She visualized a grid containing the origin of a coordinate system. A perpendicular set of lines labeled “x axis” and “y axis” appeared to float before her. She drew a single point located right three ticks and up four ticks from the origin on the grid, then followed up with another point, connecting the two with a line. It was there, floating perfectly in the air before her. Right, she thought. She added another dimension to the grid to form a cube, and into this cube she drew spheres, ellipsoids, cubes, and pyramids. It was easy. The equations came faster and faster, as if she had fumbled around and found a switch in the dark. A part of her mind turned on, big time. Adding a fourth dimension was easy. She took her three-dimensional grid cube, shrank it to the size of a pinhead, then formed a line of these cubes. Five dimensions formed from a plane of the 3D grid cubes. Six: a cube made of cubes. Seven dimensions: a line made of the new cube of cubes. On and on the mental sequence spun from her mind. Easy. Oh so easy. She no longer had to think about the equations that represented the shapes. Merely visualizing the shape brought the corresponding equations to her mind. She didn’t have to solve them; she just knew them. It was beautiful beyond her wildest imaginings.””

— Richard Phillips