Book Notes: Flatland

18 May

There have been few books which have been as innately challenging, yet as incredibly fascinating as Edwin Abbott’s classic novel Flatland. Part satire, part treatise on multi-dimensional perception, this book both entertains and illuminates readers to multiple complexities commonly glossed over in rudimentary geometry classes.

The premise of the book at first appears to be for jest and humor using simple mathematics as its premise. Divided into two distinct parts, the first matter-of-factly describes the physics, laws, and idiosyncracies of a two-dimensional reality. The tale is directed by a sentient square who inhabits a position of moderate power and merit within his society. Here the speaker discusses what is seen and perceived within the metaphysical bounds of his world. To be frank, it’s a real head scratcher. For starters, since they exist within a two-dimensional plane, they are forced to see everything as a single line. As Abbott skillfully describes, imagine taking a penny and looking at it directly from above. Your vision will perceive it to be a single line. Thus is how all of Flatland is seen by its inhabitants.

Not all who exist here live as perfect squares. Indeed, Abbott used a system of generational ascension to describe the multitudinous shapes which also picks fun at the rigid social movement found within the reader’s world. In Flatland, “humans” begin as simple triangles. Servants, slaves, and career soldiers occupy this class of polygon with individual types of triangles being reserved for specific sects. However, like in reality, upwards mobilization in this society is damn near impossible. In Flatland, merit does not improve one’s shape, although execrated action can degrade it. The shape can only be improved by subsequent generations. I.e., a square and his wife (we’ll get to the women in a moment) will foster a pentagon. A pentagon’s offspring will be a hexagon. Eventually, after roughly “300-400” generations, the near-innumerable angles within the figure will be close enough to resemble a circle. But escaping the burden of triangular limitations is insanely difficult. Each generation of triangle will only increase their angular proportions not their angular counts. And this increase is minimal at best; the immediate posterity of a triangle with a 30 degree angle will be a triangle with an angle of 30 degrees and 30 minutes (or 30.5 degrees). The ultimate goal being the perfect 60 degree rating of an equilateral triangle, which upon being reached finally opens the door to actual improvement.

Women are also satirized in conjunction to social mobility. In the novel, women are single lines (which are thus perceived as points). This “of course” leaves no room for any organs deemed non-vital for proper women. Amongst these includes, ironically enough, a brain. That’s right. Flatland includes women without an actual brain. Thus women are highly emotional, irrational, and stupid. Education is given to them as a means of convention and it frankly goes in one “ear” and out the other. But because of their violent nature and pointed nature, they are extremely dangerous to cross. Apparently Hell hath no fury transcends all dimensions of space. Being assaulted by a woman in Flatland is comparable to being shot by a bullet here in reality. Except that the bullet doesn’t constantly scream, rage, and murder your children. It’s almost impossible not to laugh at this scathingly bitter satire which barely tries to hide its condemnation at the discriminatory practices of society here in reality.

However, the book makes a ready transition from social commentary to a thought-provoking essay on multi-dimensional perception. Keep in mind, this book not only came out before string theory, but before relativity! Yet, some of the concepts postulated would strike anyone reading the book as well-developed and exceptionally modern.

I wish I had read this book when I was writing The Dimensional Constant; many of the concepts of appearances at differing dimensions are strikingly similar. It’s one of those moments where you realize with pride that an idea that originated between your own ears is featured prominently within a verifiably brilliant cult classic. It’s also one of those moments where you sit back and think “son of a bitch, I thought I came up with this idea!”

Ultimately, our square speaker tires to pass off the wisdom of his two-dimensional universe to a universe limited to lines and points. (Points, again, being women. It seems like no matter in which dimension you live in, if it’s before the 1920’s, ladies don’t seem like they’re able to catch a break.) The book shows the difficulty in discussing things which supersede certain realities. When a three-dimensional creature then comes to discuss the higher dimension with the square, his mind is sufficiently blown. Or, whatever passes for a mind within the rigid parameters of four points.

Ultimately, Flatland is a scathingly funny social commentary with profound intellectual content hidden in plain sight… I had to seriously defeat the urge to use say plane sight. You’re welcome.

This novel will come of great use when I’m presented with the need to avoid conventional ways to describe the contours and nuances of the physical world. Furthermore, I’m always happy to snag a book dealing primarily with perception (especially since my next novel will deal with that. But shhh. Sorry. No spoilers yet).

I would strongly insist that anyone read this book, especially someone with a strong background in geometry read the book. Or anyone who knows the difference between a square and hexagon. The language is seriously that inclusive. You may have to Wikipedia a couple of unfamiliar concepts or a bit of outdated vernacular. But ultimately, the book provides a read that was so far ahead of its time, it feels right at home within our own.


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