Flatland By Edwin Abbott Essay, Research Paper

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 its aspects. 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. All

inhabitants of Flatland are geometrical figures, regular or irregular. A

Flatlander with a regular shape (i.e. a polygon) automatically belongs to the

upper social class; the more sides he has, the higher his position. At the top

of this structure stand the priests, who are circles, and whose judgement cannot

be fought. The lower class consists of triangles with two equal sides (the so

called isosceles), who form the "plebs". 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. Polygons, by having a

good marriage, can have offspring with one additional side (thus automatically

of higher class); women, however, can never be more than lines. In the second

part of the book the Square tells the story of his own life. On the forenight of

a new millennium, the peaceful life he lived with his wife and children is

disturbed by the arrival of a Sphere. The Sphere tries to convince the Square

that there are THREE dimensions by drawing analogies between the different

dimensions. 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). 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. The Square is

then placed back into his two dimensions, and decides to spread the word about

the existence of multiple dimensions among the people of Flatland. Naturally, in

Victorian Flatland these "unholy" theories give him eventually more

trouble than he wished himself. What makes "Flatland" fun to read, is

that it is a popular scientific work and a social satire at the same time.

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). 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?