At the outset... the 5 stars are entirely subjective
. I love maths, I love playing mathematical games, I love philosophising about maths. So this book is perfect for me. But if maths is not your cup of tea, you may not enjoy it as much as I did.
I first read about this book in one of Martin Gardner's "Mathematical Games" anthologies, and was enthralled by the concept. (In fact, he discusses two books: Flatland
by Edwin A. Abbot and An Episode of Flatland
by Charles Hinton written with the same premise. He says Hinton's book is better, and I have managed to locate an online version recently, but have not had time to read it so far.)
We live in a world of three dimensions. It is easy for us to deal with one dimension (the line), two dimensions (the plane) and three dimensions (space). But can we conceptualise a fourth dimension? It is well-nigh impossible, for our whole being is tied up on this three-dimensional paradigm.
Abbot's fictional world is two-dimensional. The characters move about on a flat landscape. They cannot imagine a third dimension. The narrator of the story, A. Square, is living the relatively comfortable life of a country gent until he is snatched up into "Spaceland" by a sphere, a three-dimensional being. He has a view of his land from a three-dimensional perspective, and Square is never the same again. He comes back to preach the concept of Space to his fellow countrymen and is promptly incarcerated in an asylum as a lunatic.
There is no story in this short novella: it is more of a mathematical exploration and social commentary. The first part uses the Flatland society to poke fun at Victorian norms, and is quite entertaining. The inhabitants of Flatland are all geometrical figures: social pedigree is conferred by the number of sides one has, the lowliest being the isoceles triangles (the soldiers) and the highest being the cirles (the priests). (The circle is a special instance of a polygon with an infinite number of sides.) The male children of a member of one class are usually born with one more side than the parent, so social climbing is possible. However, the women are all single lines: they can't aspire to be anything other than "women"! There are also irregular polygons, who are social misfits.
Abbot explains at length the geography and history of his society. The "Chromatic Revolution" where an attempt to overthrow the established order by a scheming "irregular" is scuttled by a clever circle, through an inspiring speech in parliament worthy of Mark Antony, is especially hilarious.
In the second part, the story submerges itself in the philosophy of maths. The protagonist has a vision of "Lineland", a world of a single dimension: he tries to explain Flatland to the King of that realm, but with little success. Then, our hero has a visit from a Sphere, an inhabitant of "Spaceland", and he faces the same problem in comprehending the third dimension as the king of Lineland had in comprehending the second (later, the Sphere demonstrates the same shortsight when Square moots the possibility of a fourth dimension).
Square is transported into Spaceland by Sphere, and suddenly he can see Flatland from the outside: including the inside of the houses and the intestines of the inhabitants, all at the same time! He also comprehends that the magical ability of a Spaceland denizen to move in and out of Flatland wherever he/ she wishes is nothing but a question of simple three-dimensional geometry. Square also is witness to a parliarmentary meeting where the Sphere makes a surprise appearance, to try to convince the rulers of Flatland about the existence of space, but to no avail. The preaching of space is a state crime in Flatland, with the penalty of either death or life in confinement(according to the social status of the individual)- the ultimate fate of the narrator of the story.
Yet even though he is destined to spend his remaining life in an asylum, Square is not willing to let go of his vision of Space. Once seen, he is transformed for life.
Abbot, a teacher and theologician, uses his knowledge of philosophy and mathematics not only to create a satire, but also to raise big questions about the limitations of perception in general. It is an extremely enjoyable read, and the issues it raises will stay with you even after you finish it.
Since it is available online free from Gutenberg, I suggest everyone to give it a try.