Sunday, October 9, 2016

Book Review: Flatland

Flatland by Edwin Abbott is a book that I have known about since I was in high school, but only got around to actually reading this Summer. It was first published in 1884, ostensibly by A Square, a denizen of a world of only two dimensions. It begins like this,

1. -- Of the Nature of Flatland 
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.

In this way, A Square begins his amazingly detailed description of the economy, social structure, class divisions, climate, methods of social interaction, differences between males and females, religion, and politics of his world. Flatland is intricate beyond what those of us in Space would think possible prior to hearing of its wonderful sophistication and consistency. 

Our author is a solidly middle-class four-sided man: a square. He has a wife and a number of regular five-sided children. The way that genetics works in Flatland is that the vast majority of men are common irregular (unequal sides) three-sided people. Eventually, after generations of slow improvement and progress, a three-sided family will bear a child with three equal sides and that genetic line will then begin to advance in society. From then on, being a regular polygon, the male offspring will always possess one additional side from his father. Equilateral triangles produce Squares, which produce regular Pentagons, which produce regular Hexagons, and so on. Eventually, a family line may produce a polygon of so many sides that its number is incalculable and it is declared to be a Circle, and admitted to the priestly class.

A Square's quiet existence is interrupted one day when he is visited by a being from Space, a three-dimensional world which can communicate with Flatland. The visitor is a Sphere, and as he dips into Flatland, his manifestation in that world is essentially a cross-section of himself, and so appears to A Square as a Circle which suddenly appears out of nowhere.

To the beings of Flatland, everything about the reality of two-dimensional existence is not only taken for granted as the-way-things-are, but it is exclusively and necessarily so. Because of this, much reasoning and proof is required of the Sphere before he is able to get A Square to comprehend and actually believe in a realm of three dimensions. The simple concept of there being a direction that is "up above" and "down below", being different from the Northward and Southward that were so familiar and conceptually obvious to him, is nearly impossible for his geometric mind to fathom.

Eventually, the Sphere succeeds in his endeavor, but only as the result of an experience in which A Square is somehow granted a vision of a one-dimensional world, which he called Lineland. Through A Square's difficulty in expressing to the King of Lineland the nature of Flatland, A Square has an intellectual epiphany, by analogical extension, of the nature of Space.

Sadly, our happy protagonist's life is made very unpleasant by his new understanding of the nature of the universe. His fellow Flatlanders have a difficult time understanding the wonderful new truths that he attempts to share with them, even though he lacks a vocabulary to do so, and he experiences no little degree of persecution.

I will leave it to you to discover how it all turns out for him.

What I find fascinating and insightful about the story is the analogy of existence as one progresses from the single dimension of Lineland, to two dimensions in Flatland, and, finally, three dimensions in Space, our familiar reality. I say "finally", but that is really just an assumption on our part, like two-dimensional reality being an assumption made by A Square and his fellows. The analogy can be extended out yet another level to a four-dimensional reality with which we have no regular discourse and no way to directly comprehend.

The ability to conceptualize a new direction that is "away from" any of our three dimensions is as impossible for us as it was for A Square. We can only comprehend the possibility of such a thing by analogy.

Another intriguing thought is that when the beings of Flatland look at one another they only see a particular side at any given time. Their methods of distinguishing between the shapes are effective, but are obviously clumsy and incomplete to those of us who can simply look down from "above" and see, all at once, the full shape of the individual. No Flatlander truly knows what any other Flatlander, including himself, looks like, for they can only see each other in parts.

Likewise, we can only see each other in Space incompletely. It would take a Being of at least four dimensions to fully know the form of a three-dimensional person.

What do I look like to God, who undoubtedly can see me in full?

How far off and in error am I from understanding, even a little, God's true nature when I conceive of Him as a being that inhabits space, just like me? I know that He created the three-dimensional universe, and I know in theory that He transcends it, but in my everyday thinking do I drag Him into it, and diminish Him?

I can no more comprehend the majestic totality of God's nature than the King of Lineland can comprehend a Sphere.

Flatland is a mind-bending tale that will keep you turning the pages compulsively for its utter originality and the fascination brought about by the descriptions of worlds that might just be right under our noses.

It has also taught me to be very careful about what I say and think about the nature of God that falls outside of what He has explicitly revealed to us.

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