It is a shame that the wonderful book that is Flatland is primarily appreciated by mathematicians and physicists and virtually unknown among those who read and study literature. In addition to its interesting mathematical insights, Flatland is an ingenious socio political satire, an amazing treatment of the issues of faith and reason, a brilliant examination of prophets and revelation and how our limitations make it nearly impossible for us to comprehend things that are, nevertheless, true. It also is a discussion of the nature of God and upon what merits he is worshiped. Flatland accomplishes all of this in a fascinating fictional narrative of less than one hundred pages.
Despite the fact that it has been primarily valued for its mathematical insight, its author was not a mathematician. Edwin A. Abbot was educated at Saint John’s College, Cambridge where he took the highest honors in classics and theology. Of the forty-five books Abbott authored, Flatland is the only one that deals at all with math and geometry. Abbott’s specialty was Shakespeare and his primary concern was theology. Among his many books, he published a Shakespearian Grammar that is still considered a significant contribution to English philology.
In my view, the brilliant mathematical analogies of Flatland are only incidental to Abbott’s primary subjects: social satire and theological insight.
Flatland is written from the point of view of A. Square, a lawyer in a land that exists only in two dimensions: length and width. The two dimensional people of the land are shapes of various numbered sides. For the first half of the book, A. Square explains the social structure and history of this land in what amounts to a brilliant satire of our own society.
In the second half of the book, the protagonist relates how he received a visit from a being from the three dimensional world (a Sphere), how he was called as a prophet to preach the gospel of three dimensions, and his rejection by the people of flatland who cannot comprehend what he means by a “third” dimension. In the preface to the second edition, even the fictional author laments:
Even I—who have been in Spaceland, and have had the privilege of understanding for twenty-four hours the meaning of ‘height’—even I cannot now comprehend it, nor realize it by the sense of sight or by any process of reason; I can but apprehend it by faith.
This concept of apprehending some things by faith because they cannot be realized by reason is a fascinating theme of the book. Flatland vividly illustrates the limitations placed on our ability to reason by our mortal world.
Another theme that emerges is a discussion of what attributes qualify God as divine. The Sphere asks A. Square:
This omnividence, as you call it … does it make you more just, more merciful, less selfish, more loving? Not in the least. Then how does it make you more divine?
This is an important theme. Abbot asserts that miraculous power alone does not equate to divinity. It is perfect justice, perfect mercy, perfect selflessness, and perfect love that are divine, not omnipotence or omnividence alone. We worship God not only because he is powerful, but because he is perfectly good.
It is interesting to me that the books by Abbott’s contemporary, Charles Lutwidge Dodgson (better known as Lewis Carroll) are often studied in Victorian English Literature courses while Abbott’s book is not. Unlike Abbott, Dodgson was a mathematician and his Alice in Wonderland stories are rife with mathematical jokes and puzzles which, thanks to our sad compartmentalization of knowledge, most literature students as well as professors are completely oblivious to.
Perhaps it is due to this same compartmentalization of knowledge that Flatland, with its overt mathematical setting, is neglected by Literaturemongers.
If you haven’t read Flatland, don’t let the mathematics of it scare you away. The author’s geometrical explanations are well written and should be easily grasped by even the most math-adverse.
If you have read Flatland, but only for its mathematical analogies, read it again for the satire and theology. The whole thing can be read in a few hours and it is well worth your time.