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 a very intriguing question. One of those people was Edwin A. Abbott, a nineteenth-century schoolmaster and clergyman who was fond of mathematics and literature. In 1884 he wrote "Flatland", a small but very amusing book which is not only about spatial dimensions, but also houses an entire Victorian society of two-dimensional creatures. "Flatland" is divided in two parts. In the first part a Square, inhabitant of Flatland, gives a very amusing overview of Flatland society in all it . . .
What makes "Flatland" fun to read, is that it is a popular scientific work and a social satire at the same time. The lower class consists of triangles with two equal sides (the so called isosceles), who form the "plebs". This is particularly interesting because truly imagining higher spatial dimensions seems to be an almost impossible business. The Sphere tries to convince the Square that there are THREE dimensions by drawing analogies between the different dimensions. Being a woman means that you are no more than a single line, and you continuously have to beware of severely wounding a Flatlander with your sharp, needle-like end. The Square, failing to imagine the existence of such a thing, makes an effort to chase the Sphere away, but the Sphere lifts him out of his two-dimensional world into the third dimension! At first horribly frightened, the Square becomes more and more enthusiastic about the beautiful things he sees (and could never have imagined possible). All inhabitants of Flatland are geometrical figures, regular or irregular. A Flatlander with a regular shape (i. Amusing, because Flatland society reveals itself to the careful reader as a subtle satire of the Victorian society in which Abbott lived: it is, for example, clearly hierarchically organized. In the second part of the book the Square tells the story of his own life. When, however, he concludes that there should be even more dimensions than these, he runs into an argument with the Sphere, who appears to be very short-sighted in these matters. Abbott succeeded in wrapping these themes in an entertaining story, which seems incapable of aging, even after more than a hundred years! Naturally, there have been many who tried to 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).
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