Top critical review
Interesting exploration of dimensions
on 18 April 2016
I have wanted to read Flatland since I read the reference to it in Gödel Escher Bach: An Eternal Golden Braid which was a set text at university. As the book is out of copyright it was one of the first that I downloaded to my eReader.
The book (although really a novella rather than a full novel at only 88 pages) works on two levels; firstly the story revolves around A Square, an inhabitant of the two dimensional space that is Flatland. Most of the book describes the rigid social hierarchy of the regular polygons that make up the people - the more sides a person has the higher their social standing. Irregular shapes are despised and usually executed. The second half involves investigation into the nature of dimensions when A Square first of all dreams of a one dimensional land, then is shown three dimensions and zero dimensions by a spherical person from the three dimensional land.
The first half is a satire on the rigid class system of Victorian society - it is particularly disparaging of women, who being lines rather than shapes are very much second class citizens, even having their own doors into and out of houses. This half shows the book's age, it was written in a different time and looking at it from more than 100 years later a lot of the discussion is overlong and unengaging. This part has not aged at all well.
The book only comes into its own when A Square has a dream about a land of one dimension, populated by lines of varying length, the longest line being the King of Lineland. The two dimensional dreamer attempts to persuade the King that is he could step sideways he would be able to see that his land of a single line was limited. Of course the King can conceive of no such direction as 'sideways' and rejects the suggestion as ridiculous.
A sphere from the 3 dimensional land of Space then visits Flatland, appearing as a circle of varying size as he passes through the two dimensional space. He tries to persuade Square that if he could move 'up' or 'down' he would be able to move beyond the rigid plane of his existence. Obviously the square cannot understand a direction which doesn't fall into two dimensions, until the sphere pulls him up and then he can look down to see Flatland spread out below him. He has an epiphany and is determined to spread the word on three dimensional space. The sphere also visits a zero dimensional land. However when the square suggests that if the sphere could somehow move in a new direction he might be able to enter four dimensional space the sphere is very quick to say how ridiculous such a notion is.
In this way the ideas behind dimensions are communicated quite effectively, including being able to deduce the properties of a four dimensional regular shape by extrapolating the properties of lines, squares and cubes. It is then clear how properties of higher dimensions can be calculated without our poor three dimensional minds actually being able to perceive of it.
Flatland is regarded as one of the very first science fiction novels. So is Gulliver's Travels but that has very little science and to my mind is more of a fantasy book. Despite Flatland having very little in the way of story and plot (although there are twists in the story) and the first half isn't really story at all but social commentary, it definitely describes fantastic worlds and imagines what the results would be of living in such places. This seems to me to be the very concept behind science fiction.
In conclusion, I would not recommend this to everyone as I think its appeal is quite limited. But for anyone of a mathematical bent who likes science fiction, it's always good to see where it all started.