In 1880 Charles Hinton (inventor of the baseball gun) turned his attention to the fourth dimension, that unseen world whose behavior seems so baffling to ordinary thinkers. In his 1888 book A New Era of Thought, he announced a unique way to think about it, a set of 81 colored cubes that correspond to the 81 parts of a 3 × 3 × 3 × 3 hypercube. By creating a set of wooden cubes, painting them according to Hinton’s instructions, and working through the prescribed exercises, the reader could learn to visualize the fourth dimension as intuitively as the third:...