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Saturday, December 26, 2009

Analysis of Flatland: A Romance of Many Dimensions by Edwin A. Abbott

Speculative Conceit:
What would it be like to exist in different dimensions?


A number of critics point up the importance of such thematic concerns as social class, gender relations, and religion. These all figure into Abbott's work, certainly. But perhaps these critics are open primarily to seeing through their primary profession. For a number of reasons, Abbott's primary concern may be, first and foremost, the speculation itself.
"I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy* readers, who are privileged to live in Space." [emphasis mine]
Abbott's occupation was as an educator, and one can see his primary drive in the illustrations he uses: diagrams to spell out his meaning. He uses analogies that his readers would be familiar with in order to drive home technical points. His first chapter is devoted to showing us how a Flatlander sees.

His apologia, or modus operandi, is spelled out in the "Preface to the Second Revised Edition, 1884":
"For the rest, he begs his readers not to suppose that every minute detail in the daily life of Flatland must needs correspond to some other detail in Spaceland." ["Spaceland" meaning our world of three dimensions]
He follows the speculations to their ends, not to their allegories. Flatland probably is a corollary to Victorian England; however, that corollary is likely intended to be approximate. English women do not tend to go on blind murderous rampages: This Flatland attribute was necessitated by their being made lines which could be invisible and stab more murderously than soldiers' less sharp angles. Social-climbing may have occured in Victorian times through offspring, but priests were not the top of the pecking order and nobility could not be achieved naturally over time.

He goes on to say,
"...and yet he hopes that taken as a whole, his work may prove suggestive as well as amusing."
By which I take to mean that this is both an entertainment in extrapolation ("amusing") as well as something to be taken to heart ("suggestive").

The suggestive portion--that which critics readily respond to--is summarized in the title: "Flatland: A Romance of Many Dimensions." Also, the narrative itself suggests this by its ordering of dimensions: The point-dimension displays self-love, self-absorption, self-worship as being its folly. The line displays polygamy (this probably would not fly as well today as being a negative although I would submit that, for many Victorians, it would have been grotesque). The second dimension is closer to our dimension's mores of the period, but I suspect these, too, were made grotesque to the Victorian reader, which was why he had some readers call him a "woman-hater." If he had merely described the actual roles of women in society, the protests may not have been so strong.

However, the whole point of traveling up dimensions was to reach higher levels of perfection, which we had not yet attained. A. Square's moments of transcendence are fleeting, though, as he struggles to recall them and their meaning outside his dreams or visions. This is probably why he has no major transformation when he returns to his own dimension--just the minor one of converting people to the possibility of higher dimensions. This goes for religion as well as social conventions, gender and social class. There may be infinite orders of perfection above us, and the third dimension is not all there is.

It is curious to note that Abbott had A. Square readily mend his ways in the revised Preface:
"[I]n the course of an imprisonment of seven years he [A. Square] has himself modified his personal views, both as regards Women and as regards the Isoceles, or the Lower Classes. Personally, he now inclines to the opinion of the Sphere that the Straight Lines are in many aspect superior to the Circles."
Was this really necessary? No. In the text the sphere already suggested that the womanly attributes were superior. The point of the tale was to show the difficulty one had in transcending one's own dimension or limited perspective. What's interesting was how quickly Abbott abandoned this theme in order to appease his more literal readers.

Lori M. Campbell, in her introduction to the Barnes and Noble edition, points out that another purpose was to demonstrate how miracles were unnecessary in multiple dimensions. At least, what appears to be a miracle to one's own dimension with one's limited perception may actually be normal for someone above that person's dimension. This apparently is in keeping with Abbott's other theological tracts.

* = Note that happiness, to some extent within the confines of this work, denotes some degree of failure to aspire. Could it be, rightly or wrongly, that A. Square assumes that we readers do not aspire to higher dimensions? Does the term "privilege"--at least before we have read the work--hint at our contentedness with living merely in our own dimension?

Main character:

A question I have not resolved: Why is A. Square a lawyer? He does not seem to use his occupation whatsoever. It must be useful in some thematic sense. Perhaps it is useful as a position of middling importance from the burgeoning middle class. That he is a square is probably useful in the sense of disinterest in fads and of conventionalism--where even he can be moved to transcendence.

Educational purposes:

How useful would this be to an educator? A teacher in Missouri, Sandy Stuart-Bayer, has put up a lesson on Flatland, for an English Literature class. I do not see it as particularly useful to science, however, unless it were used early on to show how one's scientific perspective can change dramatically over time. This might also be useful for a class in geometry. Possibly, the best use might be a three-way teacher collaboration, in which an English teacher approached the thematic possibilities, the math teacher addressed figures and dimensions, and the science teacher addressed scientific method and the ways scientific perspective can be changed over time.

This might be a challenge to many readers, however, as it is not an incredibly engaging text--however short it may be. Perhaps this might be best reserved as an advanced project for the gifted, precocious student--possibly a voracious reader or one intensely interested in math or science.

Another possibility would be to condense: Read chapter 1, 13-22. Maybe even jettisoning 21 & 22 might help although, then, the text would feel incomplete (not to mention leaving out the important theme that aspiration and transcendence were more necessary than happiness and social stability).

Nonetheless, this may be a text that students were glad they had read it but did not enjoy while reading it. It might be interesting to see how a condensed version went over. Perhaps a condensed version might engage a few to read the other chapters.

On the other hand, in an age of iPods, how can a student complain if you make available the audio version (see below)?

Resources and sequels:
Flatland (wiki)
Flatland (text online)
Flatland (audio -- Librivox)
Flatland (audio -- Podiobooks)
Edwin Abbott Abbott (wiki)
Rudy Rucker's Spaceland (see also wiki)
Ian Stewart's Flatterland (wiki)
Dionys Burger's Sphereland (wiki)A. K. Dewdney's The Planiverse (wiki)
Clifford Pickover's Surfing through Hyperspace