One of my favorite books is Flatland, by Edwin A. Abbott (writing pseudonymously as A. Square). Originally published in 1884, the book is typically plugged as an early science fiction work or as some kind of mathematical fantasy intended to open people's eyes to the beauty of geometry and the possibility of a fourth spacial dimension. Before I talk about a different interpretation, I'd like to recap the story. [Spoiler alert: If you want to read the book, you might want to do so before continuing.]
The narrator, A. Square, lives in Flatland, a world of just two dimensions. Things in Flatland— including its inhabitants, their dwellings, and all the accoutrements of their society—have no height or depth. Women are lines. They have length but no width. Men, who have both length and width, exist as various sorts of triangles, squares, and polygons. Their social status is determined by their shape. As polygons gain an increasing number of sides, they rise in status. Circles are at the pinnacle of Flatland's social order.
Because Flatland lacks a third dimension, its citizens can see only the presenting side of an approaching person. There is no way to stand over a scene to determine someone's true shape. To help in this effort, the inhabitants have developed the custom of feeling each other's angles. This practice gives the Flatlanders clues from which complete forms can be deduced. Some in the higher social orders learn how to visually distinguish between what may appear to be a straight line from one with ends that curve away from a leading edge.
In this two-dimensional world, the residents of Flatland scurry around in the same manner as shadows on a piece of paper. They move north or south or east or west, but they do not have any frame of reference for considering notions like up and down.
One night Mr. Square has a dream in which he visits Lineland, a realm of just one dimension, inhabited by a population of points and lines. As a two-dimensional being, Mr. Square is able to stand to the side of the inhabitants of Lineland, but they exist only along the length of their line. He moves part of himself onto the line so he can become visible to them, but when he moves off the line, he becomes invisible because they can't look to the side. He tries in vain to explain the concept of width.
Mr. Square's dream serves as a prelude for a visitation he later receives from a mysterious entity called a Sphere, which arrives in his own two-dimensional Flatland from a three-dimensional realm called Spaceland. The Sphere takes the dramatic step of pulling the Square into the previously unknown, unexperienced dimension of height by tugging Mr. Square's insides upward. During his adventure, Mr. Square learns the difference between a square and a cube.
The story doesn't end happily. The revelation transforms Mr. Square, but in his excitement he offends the Sphere by asking about fourth, fifth, and sixth dimensions. Furthermore, when Mr. Square returns to Flatland and tries to teach the Theory of the Third Dimension, authorities outlaw his perspective. He ends up in prison.
The book works as science fiction and mathematical fantasy because it takes the rules of geometry and builds an entire society based on principles of reality that differ from our own. It also works as a social satire that wrangles with the prejudices of its era, highlighting the absurdities of gender and aristocratic discrimination. But at a more fundamental level, I believe the author wrote it as a religious text.
Abbott was an ordained minister, theologian, and schoolmaster. His Mr. Square learned about the nature of another dimension when his insides were moved in a direction that was impossible to explain to his fellow Flatlanders. People who have had spiritual experiences can relate to this difficulty of articulating whether the spiritual dimension is above them or within them.
Reliance on scientific methods expanded during the late nineteenth century and attained prestige among the educated. As this prominence grew and new angles were considered, the new knowledge continued to stretch. Ultimately its vast expanse obscured a profound reality: Scientific knowledge was limited. Its reach extended only to the material plane its principles were designed to measure. Information about what might exist in other planes or dimensions was rejected. Within certain scientific circles, religious opinions were held in contempt. Furthermore, even among groups aware of a spiritual dimension, the practice of asking questions about other possibilities was seen as an offense.
Perhaps we should acknowledge that we are just as limited as the Flatlanders. We cannot see each other's true shapes. We are unable to get an accurate perspective on reality and how all of its pieces fit together because we remain locked within a physical dimension without the means to measure all the dimensions of existence. We try in vain to explain concepts that fall outside the plane of measureable dimensions, and we are frustrated when evidence becomes visible and then fades to invisibility.
For all these reasons, Abbott's tale still rings true—even 130 years after he wrote it. His work illustrates the absurdity of denying the existence of realms beyond our experience, and it realistically documents the intolerance with which those who claim a spiritual experience are often met.