Flatland: The film that can take you into a new dimension?

There’s a popular meme going round right now, Which Science-Fiction writer are you? The one I would like to be like is Edwin A. Abbot. Hopefully he’ll get a new spur of popularity with the release of Flatland as a movie.

The novel is initially about a two dimensional world, utterly flat. In it live men and women. The men are polygons and the women lines. The story explains the class system and satirises the Victorian attitudes of Abbot’s time. There are a variety of restrictions on women for instance. Being a line a woman is only visible as a point if moving towards a man. This is dangerous because a line could penetrate a polygon and kill it, so women are forced to waggle as they walk and issue a peace-cry to let men know there are women around.

Into this world of order comes a point which grows into an expanding circle and then shrinks back to a point before leaving. This is befriended by a square who learns that the circle is in fact a sphere passing through Flatland. The sphere attempts to explain the concept of a third dimension to the square – but the square cannot grasp this. The sphere decides to pull the square up into the three-dimensional Spaceland.

Together they see Lineland and Pointland where the inhabitants simple cannot grasp that there could be higher dimensions. The tragedy comes when the square asks how to visit a four-dimensional space. Logically if a two dimensional shape can be drawn up into a third dimension, surely a three dimensional shape can be drawn into the fourth dimension? The square begs to be taken to the four-dimensional Thoughtland, but the Sphere will have none of it and gets annoyed at the square for thinking such nonsense:

How long I should have continued I know not. In vain did the Sphere, in his voice of thunder, reiterate his command of silence, and threaten me with the direst penalties if I persisted. Nothing could stem the flood of my ecstatic aspirations. Perhaps I was to blame; but indeed I was intoxicated with the recent draughts of Truth to which he himself had introduced me. However, the end was not long in coming. My words were cut short by a crash outside, and a simultaneous crash inside me, which impelled me through space with a velocity that precluded speech. Down! down! down! I was rapidly descending; and I knew that return to Flatland was my doom. One glimpse, one last and never-to-be-forgotten glimpse I had of that dull level wilderness — which was now to become my Universe again — spread out before my eye. Then a darkness. Then a final, all- consummating thunder-peal; and, when I came to myself, I was once more a common creeping Square, in my Study at home, listening to the Peace- Cry of my approaching Wife.

It isn’t just about spatiality, but also about how to react to what appear to be nonsensical conclusions. The novel follows the attempts of the square to educate his fellow citizens, but his arguments run utterly against the received wisdom of the land.

You can read it yourself. The writing is a little dated, but not too badly. The idea behind the novel remains stunning. Perhaps the highest compliment is that it is used in some mathematical courses today to introduce the concept of higher dimensions. Sadly its social commentary also has relevance today. Abbot wasn’t just good at the science, he was also visionary at thinking about how it would be received. It should be essential reading for Science Studies courses too. Hopefully they’ll get both sides of the novel in the film.

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