Flatland

Specifications:

Abbot, Edwin A., Flatland, A Romance of Many Dimensions, Dover Publications, 31 East 2^nd Street, Mineola, NY 11501, First published 1884, this edition 1992. Pseudonym was originally "A. Square," with was part of the satire, as well as protection for the author.

Reading:

This was read from about 07/15/2008 to 07/28/2008. The book is from my private collection, although the text is available from http://www.gutenberg.org/etext/97.

Review:

There are many things that can be said about this story, which is why it has lasted as long as it has. The author postulates a world which is on a plane, and, therefore, two dimensional. The inhabitants of this world are geometric figures.

The story satirizes society, since is was written in England, English society by using the geometric figures to represent the society. Unfortunately, I have not made a study of nineteenth century English society, so much of the satire was lost on me.

It does take a demeaning attitude toward women, which probably is part of that satire, but as I said, I've not studied that time period enough to realize what is satire, and what is not.

Some of the satire did get through, however. For example, at the end the leaders are confronted with the truth - that it is possible to have three dimensions - but rather than accept it, they kill or imprison any being that might be able to attest to the truth.

Some of the satire regarding women is not lost. For example, cases where women have been killed their entire families, then asked where they had gone.

It also shows the distribution of rank and class as being by looks rather than by intelligence. Therefore, someone does something wrong, and rather than ascertaining the facts, and then forming opinions, all that is done is that the figure causing the problem is measured to see how far from a regular polygon they are. This probably satirizes the practice of psychology of the time (pre-Freud) which tried to determine if a person was insane by measuring the bumps on a persons skull.

The first half of the book really doesn't have a plot. That is, a square simply explains how their society works. This has a lot of the un-understood satire, and can be rough reading.

However, it is worth it because the second half has a definite plot. This starts with a dream. The square dreams of a lineland, in which the beings are lines. He enters lineland (in his dream) and talks with the monarch. He has no success explaining to the king what it means to have two dimensions. In lineland, the only motion possible is back and forth, so the square can see the lineland beings, including their insides.

In Lineland, the king doesn't actually see his subjects, since all he can see is two dots representing the two beings closest to him. He communicates with his two wives (one for each side) with sound that travels through the other beings.

After he wakes up, he has an experience where a three dimensional being, a sphere, enters his world. At first, the three dimensional being has a hard time convincing the square that there are three dimensions. He goes through all the gyrations that the square had gone through with the line. He also adds more. For example, he goes into a locked cabinet, and takes out some gold, and gives it to the square, but the square is not convinced. Finally, the sphere takes the square out of his two dimensional world into the third dimension, where he can see the inside locked cabinets, etc. This convinces him. The sphere takes him to the place where laws are made for Lineland, and they catch the passage of a bill to declare that anyone talking about a third dimension is to be put to death, or imprisoned if he is more of an aristocrat.

The square convinces the sphere to make himself known, which he does. All the legislature does is to imprison or kill all who saw the "proof" of three dimensions, including the squares brother.

Later, they visit pointland. Pointland has only one being, a point, who spends all his time praising himself. The square, with the sphere's urging, tells the point that there is a bigger world out there, but it makes no difference, because the point just incorporates the words into his soliloquy. So, there is no progress.

Then the square gets excited about this concept of three dimensions. Having made the leap to three dimensions, he asks about the fourth and fifth dimension, etc. (Out of respect for many movies and stories that get the dimensions mixed up, I will say that when I talk of the fourth dimension, I mean the real fourth dimension, not another three dimensional world. That is, in the fourth dimension, there can be four lines, all mutually perpendicular to each other. If this seems difficult to understand, that's what this book is about.) Unfortunately, the sphere, who had just introduced the square to three dimensional space, won't believe that higher dimensions are possible.

In a part of the satire which is obviously about religion, the square talks of beings coming and going without going through walls, etc. The sphere acknowledges that these types of occurrences have been said to happen, most people just attribute it to hysteria, or something. That is, it doesn't really exist. The square sticks to his guns, and the sphere will not be convinced. After this, the sphere dumps the square back in flatland.

The square tries to tell people about the third dimension, no one believes him. He eventually ends up in jail, where he sees his brother on occasion. But he cannot convince his brother, who has actually seen the third dimension phenomena.

Significance:

This story is significant even if the satire is missing. That is, the discussion of three or more dimensions is very mind stretching to someone who has not seen it before. (My dissertation talked about many dimensions, and I did read the book in high school, so I was already familiar with more than three dimensions.)