flatland

Dimensions: you keep running into them while reading your books and attending your lectures, and in most computations they are not very difficult to handle. But have you ever tried to imagine what all those more-dimensional spaces and objects look like? For example, the four-dimensional analogon of a cube? There are lots of people who will put this aside as nonsense, not worth spending your time on, but there have been others who found this …

…follow Abbott, however, with only a mathematical goal (indeed, some kind of sequel to "Flatland" exists; it is called "Sphereland", but I have never read it myself). In these much more recent books, higher dimensions are again explored in a popular way; also, some attention is given to "visualizing" these higher dimensions by drawing analogies. This is particularly interesting because truly imagining higher spatial dimensions seems to be an almost impossible business... A challenge awaits?