Author: Edwin Abbott Abbott
Publisher: Seeley & Co.
Year: 1884
Language: English
Country: England
Number_of_pages: 96
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If I ask you to describe to me a three-dimensional object, none of you will have any trouble doing it, right? “Just look around, dude!” would be a likely response.
And you would be dead right!
Our universe exists in three dimensional space, so we, as part of this universe, are constantly interacting with 3-D objects, and are, ourselves, 3-D objects.
Now, I must warn you that this article will probably stretch your brain like no other. We are going to hop on on a very strange tour in a very strange land with very strange inhabitants…
Dear readers, welcome to Flatland!
Flatland is a story narrated in the first-person perspective of a character called A Square (a literal square), after he had a glimpse of the third dimension.
The novella is split into two parts. In the first part, A Square explains to the reader the different aspects of living in his 2-D world that three-dimensional beings call Flatland: the different shapes that exist, the social hierarchy, particularly meaningful events that occurred, etc.
In the second part of the novella, A Square narrates his (mis-)adventures after a Sphere visits Flatland and takes A Square on a sightseeing tour of Spaceland, allowing A Square to gain an understanding of three-dimensional space.
I find the idea of Flatland spectacular. For a novel written in the late 1800s, Flatland seems impressively contemporary in its ideas and it has managed to remain relevant even to this day.
Indeed, plenty of films and TV shows have direct references to the novel. For example, in the film Interstellar (which is related to the concept of higher-dimensional space), Joseph Cooper accidentally drops the novel Flatland from a bookshelf. In the TV series The Big Bang Theory, Sheldon Cooper mentions that one of his favourite places to visit is Flatland from Abbott’s novel.
Abbott, who had graduated with the highest honors in mathematics, showed that he knew his business. His descriptions of places existing in lower dimensions were picked by the likes of Stephen Hawking and Carl Sagan, who took inspiration from Abbott’s novella and popularised the topic of extra dimensions.
Despite its potential, I do have a few criticisms.
First, the first part of the novella (which comprises half of the book) is purely descriptive of the inhabitants and the world they live in. There is no particular plot to speak of. Even the second section of the novella, which is certainly the most interesting of the two, suffers from an underdeveloped plot, with only sporadic and ephemeral entertaining passages.
Thus, even though I found the topic of dimensionality extremely interesting, it felt more like reading a textbook rather than a novella.
The writing style of the first section in particular was also quite difficult for me to get into. In all honesty, I learnt more about the topic from reading reviews of the book than from the book itself. That might sound unfair, given that we had more than 100 years to dissect Abbott’s novella and apply modern teaching tools to explain dimensionality.
Nevertheless, it could have been written in a more reader-friendly and exciting way, as some science fiction books from some of Abbott’s contemporaries (e.g., Jules Verne, H.G. Wells). Abbott’s descriptions were often convoluted and off-track, and I found myself losing interest quickly (although his explanations improved in the second section).
I did, however, find his drawings amusing, and they did help visualise the second dimension much more than the text descriptions were able to.
I have to say that I have mixed feelings regarding Flatland.
On the one hand, the topic was great. Also, taking into account that the book was written at the end of the 19th century, I do think Abbott was reasonably good at simplifying a very complex topic to non-mathematicians (particularly his drawings).
However, the writing style and the descriptions of the first section were just not my cup of tee, and I think the book could have been improved to be a more interesting read.
Since Flatland is a novella, I was also expecting a relatively interesting plot. However, plot was almost inexistent, with most of the book devoted to explaining dimensionality. The most exciting event was A Square’s interactions with the Sphere, which really took up only two chapters.
Here at Mindlybiz, Flatland gets a rating of 2.5.
Hmmm… I would say Flatland is bizarre, not for the obvious reasons that the all characters are geometric figures (which is kind of weird on its own), but because the novella is highly satirical in tone.
Also, the topic of dimensionality is not an easy one to grasp, although I think the author did a relatively good job simplifying it to the general, non-mathematician reader.
Flatland gets a bizarrometer score of 2.
It is possible that Abbott wrote Flatland with two aims in mind: 1) as a gentle introduction to the concept of spatial dimensionality, and 2) as a criticism of the social stratification that prevailed in the Victorian society of his time.
With respect to spatial dimensionality, Abbott chose to write his novella from the first-person protagonist narrator A Square, an inhabitant of a two-dimensional (2-D) world called Flatland, where 2-D geometric figures are organized in rigid social classes.
After describing the inner properties of Flatland and its inhabitants, A Square visits Lineland (a 1-D world) and has a conversation with its King. The King of Lineland could only see A Square (and everything else) as a single point, and had no understanding of the left-right dimension, since his 1-D world restricted his movements to only North-South directions. Witnessing the simple life of the King of Lineland, A Square pities the King and arrogantly concludes that his 2-D world is the true world.
Later in the novella, A Square meets the Point, the only being in Pointland (a 0-D world), who couldn’t conceive anything existing but his own self. Even when he heard A Square’s voice, the Point thought the voice was coming from his own mind.
With the arrival of the Sphere to Spaceland however, A Square begins to understand the limits of his own existence. The epiphany that there is another world beyond Flatland leads him to drop any previous assumptions that Flatland is all there is. In fact, he goes further and claims that even higher dimensional worlds than Spaceland must exist, something that even the Sphere quickly dismisses.
Abbott was very critical of blindly basing one’s faith on miracles, so perhaps he was pointing out that we should not haste attributing powers to phenomena we cannot understand. The Point, the King of Lineland, A Square and the Sphere all refused to accept the possibility of superior planes of existence, because their restricted dimensionality prevented them from visualizing these extra dimensions. In a twist of irony, when A Square finally becomes aware of the limitations of Flatlanders’ minds, he transforms himself into an almost biblical prophet, preaching the Gospel of the third dimension, even if that meant certain incarceration.
In addition to teaching about spatial dimensions, Flatland appears to have been written as a social satire. Having lived in the mid-late Victorian era, a time of strict class rigidity, pervasive misogyny, sexism, and oppression of the working class, Abbott felt the need for deep societal changes. Flatland was likely his response to these issues.
The appalling descriptions of women as lacking intelligence, sense of justice and reason probably echoed the attitudes of Victorians towards women. The working class was also viewed as simply factory fodder, too easy to manipulate and replace whenever their utility declined. The clergy held an enormous control over people, and remained a powerful influence on state affairs, particularly on education and policymaking. All these aspects of the Victorian society are in some way or another satirized in Abbott’s novella.
So, that’s Flatland in a nutshell. Let’s now go over some really interesting facts about dimensions, because they will come in very handy when discussing Abbott’s book.
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