A Matter of Perspective: Edwin A. Abbott’s Flatland
One of the greatest gifts offered by books is perspective. Perspective on how others live their lives; on what it means to be different; and on how else it may be possible to see the world. Over a century since it was first published, Edwin Abbott’s Flatland remains a frequently referenced resource for teachers seeking to pry open the minds of their students.
Part of Flatland’s enduring relevance is that at its heart is a simple concept: the story of one A. Square who inhabits the eponymous two dimensional Flatland. Almost half the novella concerns no more than an exploration of how life might be in a two dimensional existence where a person’s entire surroundings, whether filled with people, objects or buildings, would be perceived only as a line of varying brightness. Taken alone this concept would be of some interest, but Abbott was seemingly unwilling to leave the point half made, and flings his protagonist on a short but dramatic adventure; first into universes that exist in only a single dimension (a line) or none (a point), and then most dramatically into a three dimensional universe. Square ridicules the inhabitants of the universities with fewer dimensions than his own for being unable to accept the notion of a second dimension. Yet he himself struggles when his three dimensional counterpart, a sphere, confronts him with ‘the gospel of third dimension’.
Written in large part as a satire on Abbott’s closed minded Victorian contemporaries, Flatland ably demonstrates the absurdity of those unwilling to admit their own ignorances, even when they scoff at the ignorance of others. Flatland is, whether intended or not, more than satire. It is also a very useful thought experiment. Abbott’s novella articulates the challenges, to the point of frustrating impossibility, of trying to explain extra dimensions to people who can’t see them. How do you describe depth, when someone’s only references are width and height? Flatland’s protagonist settles on moving ‘upwards, but not northwards’, which to his fellow two dimensional beings sounds like moving inside themselves while standing still.
The existence of a fourth dimension was proposed and debated in Abbott’s time as a means of explaining the supposed existence of a ‘spirit realm’. This spiritual fourth dimension would be one we moved through without realising it, with beings from this ‘higher’ dimension flitting in and out of our three dimensions in the same strange manner the sphere enters Flatland; presenting only the dimensions that fit at a single point in time.
The Victorians who first read Flatland were in a sense right, of course. We do move through a fourth dimension without perceiving any shift in the first three dimensions: time. Einstein’s work demonstrated that time is our fourth dimension, as real and relevant as width, height, or depth. Flatland’s thought experiment is not irreversibly damaged by this knowledge, it simple shifts the question. If we now know we exist in four dimensions when we previously assumed we existed in three, is it possible we might in fact exist in five? Or six? Or ten?
String theory, which I will not pretend to understand, is a much debated hypothesis that some physicists have argued might reconcile the gap between quantum mechanics and the Theory of Relativity. String theory only works, however, in universes of ten dimensions or more. It’s difficult for most people to conceive of how so many dimensions might work, or even be possible. The blocks to thinking in more dimensions than those we inhabit that face all of Abbott’s characters s, are also within most of us. We might be on board with considering time as a dimension, but the idea of moving in a manner that is not in any of our four dimensions remains elusively inconceivable. In the face of such a challenge in conceptualization, Abbott’s linguistic wrangling of readers’ minds in Flatland remains one of the best places to start.
Flatland continues to sit on our shelves because its commentary on perception remains useful and relevant, almost ageless. Unfortunately other elements of Flatland have not aged quite so well. In Flatland social standing, and intelligence, is determined by the number of sides a person has. The ruling class are circles, the middle class squares, and the working class are triangles. This visible hierarchy reflected the views on and realities of class of the time in which Flatland was written. Sos do the strange evolutionary mechanisms that give a child one more side than their father, so that over generations a family might shift from middle class to upper. Though tellingly the shift from working class to middle class in Flatland is a much slower process.
Abbott’s apparent approach to class and social standings are a curious relic of his age, but can be read today with relative ease. Regrettably his treatment of women is less digestible. In Flatland’s side-segregated society women are presented as lines; they are almost literally one dimensional. This makes women nearly inviable, of lower intelligence, and, because as lines they can pierce other shapes, potentially lethal. Flatland includes several references to women flying into rages and murdering all around them. Yes, the Victorian era in which Abbott was writing included repressive attitudes, but even contemporary reviewers were taken aback by Abbott’s characterisation of women. Perhaps just as galling, the description of women as unintelligent yet dangerous serves very little narrative purpose, and distracts from and undermines the more useful elements of the book.
Flatland is, despite its faults, justifiably described as a classic. As a story, it is easily overshadowed as an example of Victorian science fiction by the contemporary works of HG Wells and others. But as an intellectual challenge, a tool, a thought experiment, to push the reader to consider the very nature of perception, it retains the relevance, social descriptions aside, that that the moniker of ‘classic’ entails.
-H
