Flatland is a book about our perceptions of the world and the beliefs that arise from them. Or is that the other way about? It is also a satire about Victorian society and, possibly, an allegorical discussion about the merits of social improvement through evolution, plastic surgery or even eugenics.
The narrator of Flatland is a square that lives in a two-dimensional world. The citizens of Flatland know two dimensions of movement only: northwards/southwards and side to side. In their world rain falls from north to south, so they build their houses with the roof facing north.
In the first part of the book, the narrator tells us about the social structure and social history of Flatland. The inhabitants come in many shapes and sizes. Most are regular polygons, such as triangles, squares and pentagons. The more sides, the higher the social rank. Climbing the social ladder is achieved on a generational basis: triangles father squares, squares father pentagons, and so on. Circles occupy the highest social niche. A minority of inhabitants are irregularly shaped, and they tend to have an abnormal psychology. It is therefore necessary to constrain them either through incarceration or military service.
War has played a prominent part in Flatland history. Indeed, the most destructive war in their history came about when women became warriors. Because women are considered irrational, and because they are by far the most lethal warriors, their social behaviour is severely curtailed in order to preserve an orderly society.
In the second part, the narrator relates a vision he had when he travelled to Lineland, where the inhabitants are one-dimensional and can only travel north/south. He tries to explain to the monarch the concept of a second dimension and, consequently, side-to-side movement. The king will have none of this kind of mad talk as it strikes against both his perceptions and his reason. But the narrator persists and only succeeds in infuriating the Linelanders to the point of war.
Later, the narrator receives a visitor who claims to be from a three-dimensional world. The narrator in his turn becomes angered by his guest's insistence about the possibility of moving upwards and downwards. In the end, the visitor lifts the narrator out of Flatland and grants him a vision of three-dimensional space. They speculate about the possibility of four dimensions. This vision has disastrous consequences for the narrator.
In a short eighty page tract, Abbott has given us a lively and imaginative challenge to our assumptions about the world. The narrator's visions are very reminiscent of Plato's parable of the cave - there may be another world which we can experience if only we could screw our perceptions through 180 degrees, metaphorically speaking. What is very interesting is that the inhabitants of the various dimensional worlds become angry when their notions of reality are challenged. It is an all too common phenomenon in our own world, and one which it is the philosopher's duty to transcend wherever possible.
Flatland is very worthwhile reading and, being mercifully short, can be tackled in an afternoon. I read the Penguin ebook edition which is very well produced and is still text-to-speech enabled.
