There are quiet places also in the mind, he said meditatively.
{ Balls in boxes offer a simple system for studying geometry across a series of spatial dimensions. A ball is the solid object bounded by a sphere; the boxes are cubes with sides of length 2, which makes them just large enough to accommodate a ball of radius 1. In one dimension (top left) the ball and the cube have the same shape: a line segment of length 2. In two dimensions (top right) and three dimensions (bottom) the ball and cube are more recognizable. As dimension increases, the ball fills a smaller and smaller fraction of the cube’s internal volume. In three dimensions the filled fraction is about half; in 100-dimensional space, the ball has all but vanished, filling only 1.8 × 10–70 of the cube’s volume. | An Adventure in the Nth Dimension | American Scientist | full story }
