Imagine a world of only two dimensions: length and breadth, but no height. Imagine sentient beings living in this world. Everything appears as a horizontal straight line, like looking at coin on table, keeping your eye level with the edge of the table. Now imagine that a sentient sphere, gazing at this Flatland from above, decides to venture down and communicate with a square. From his vantage point, he can see everything. The walls of Flatland are no barrier to his all-seeing gaze. He speaks to the square, but the square cannot see him, so he physically descends into Flatland. As his girth intersects with the dimension, he appears to the square as a circle which widens as he descends. The poor square has never seen anything like this, and believes that he is experiencing a paranormal visitation. Things become even more alarming for the square when the sphere pulls him up into Spaceland. But the sphere is shortly in for a suprise when the square questions him about the logical possibility of a fourth dimension of which the sphere is not privy, just as the square was not privy to the third.
Now, you either love this sort of a mindfuck or you don’t. I’m a great believer (for philosophical reasons that I won’t go into just now) that there is more to the universe than material reality. This charming fiction provides a mathematical basis for such a notion. It behoves us to try and conceptualise a fouth dimension which sees into the third in much the same way that the third can see into the second. It’s impossible to wrap your head around, just as in the story it’s impossible for the square, once returned to Flatland, to describe his experience to his companions, or even to accurately remember it. I’m someone who has an appreciation for things of a magical or psychic nature, so I know that there’s something to the idea that Abbott presents, although I would hasten to add that his presentation is an approximation, not a factual description, of a higher reality than the physical dimension.
Concurrent with a discourse on dimensionality, the story also provides a satirical commentary on social customs of the Victorian era in which it was written, especially as it concerns the abuses of religious authority in preventing the free speech of those who think different. Although this book is classified as fiction, because it is first and foremost a story, I believe that a reader seeking entertainment will find much less pleasure in it than the philosopher-at-heart. To the latter, I thoroughly recommend this little volume.