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Flatland: A Romance of Many Dimensions (1884)

by Edwin A. Abbott

Other authors: See the other authors section.

MembersReviewsPopularityAverage ratingMentions
8,030157737 (3.75)162
A square, who is a resident of the two-dimensional Flatland, dreams of the one-dimensional Lineland. He attempts to convince the monarch of Lineland of the possibility of another dimension, but the monarch cannot see outside the line. The square is then visited himself by a Sphere from three-dimensional Spaceland, who must show the square Spaceland before he can conceive it. As more dimensions enter the scene, the story's discussion of fixed thought and the kind of inhuman action which accompanies it intensifies.… (more)
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English (144)  Italian (6)  French (2)  Swedish (1)  Portuguese (1)  Dutch (1)  Spanish (1)  All languages (156)
Showing 1-5 of 144 (next | show all)
Sometimes it's the simplest ideas that can be the most striking. We all live in a three-dimensional Universe. All of us. Even amoeba, who only ever show up on the television under a microscope on a flat surface, eating their food by simply encircling it, even these chaps live in a three dimensional world. (It turns out that the natural state of an amoeba is not floating around the oceans in a Petri dish.)

Because we live in a three-dimensional Universe it's tempting to think that life couldn't exist in a Universe with more or fewer dimensions. And there are genuine problems facing life in other dimensions. The laws of physics are pretty robust and work (with occasional tweaks) no matter how many dimensions your Universe has. And so we can tell that:
• In four or more dimensions, planets wouldn't be able to maintain stable orbits around stars. In fact the only Universes where planets can orbit a star for any respectable amount of time are two- and three-dimensional ones.
• If your Universe has more than one dimension then the strength of gravity decreases as you move away from a massive object. In four or more dimensions it tails off so fast that the Universe would quickly drift apart and face heat death. In two dimensions it doesn't fade away quickly enough, so the Universe would quickly collapse in on itself. Although having said that…
• The above points assume that Newtonian mechanics are a good approximation for how gravity really works, i.e. for general relativity. In three or more dimensions this is (probably) true. But 2D general relativity is a curious beastie and differs drastically from 2D Newtonian mechanics. The most startling difference is that if a 2D Universe worked as predicted by 2D general relativity then there would be no action at a distance. Stick two 2D black holes near one another, and they would just kind of sit there, being black and holey. Things wouldn't be attracted to one another, and the whole Universe would just shuffle off in whatever direction space was expanding, never looking back.
• These are some of the physics-y problems in other dimensions, but there are biological issues too. Consider your brain. It's basically millions of little nodes connected by wires. In 3D this kind of neural network is pretty easy to arrange. If I give you a bunch of points in space and tell you to join up certain pairs with wires then you should be able to do it. Sure the wires might be horribly tangled and tied up in knots before you finish, but that's fine. Or at least that's fine in three dimensions. In two dimensions your wires can't go over and under each other. They have to go around. So suddenly wiring up a brain is much more problematic; only neural networks that form a planar graph are allowed. On the other hand, in four dimensions, wiring a brain is even easier since your wires have an extra dimension to slip into, so if brains ever did evolve in a higher dimensional Universe they would have the potential to surpass our own clunky things with ease.


None of these points really preclude life from arising in a 2D or 4D Universe. At worst they say it would have to evolve quickly before the Universe ended; and at best they say that we don't really know what would happen in other Universes. Hell, we're not really sure what's happening in our Universe. There's dark matter holding together galaxies that should spin themselves apart, and dark energy speeding up an expansion of space that should be slowing down, but both dark matter and dark energy are just placeholder names physicists use for whatever is causing these effects. So what might life be like, if it existed, in two dimensions?

Enter Edwin Abbott Abbott, a guy so cool his mother named him twice. He was a nineteenth century theologian, but is best known for writing Flatland. The genre of Flatland is often listed as “mathematical satire”, so it was inevitable I'd like it.

Although it's set in a two dimensional Universe, Flatland doesn't attempt to deal with the physical and biological issues that arise, in fact these are generally brushed under the carpet with some apologetic lampshade hanging. What Abbott Abbott does describe are the societal quirks forced upon a two-dimensional land, and later a one-dimensional one. Depending on who you ask, the result is either a cutting satire of Victorian England or a hundred-odd pages of sexist fluff. But whether it's biting or fluffy, Flatland is undeniably a quaint and fun work. ( )
  imlee | Jul 7, 2020 |
Sometimes it's the simplest ideas that can be the most striking. We all live in a three-dimensional Universe. All of us. Even amoeba, who only ever show up on the television under a microscope on a flat surface, eating their food by simply encircling it, even these chaps live in a three dimensional world. (It turns out that the natural state of an amoeba is not floating around the oceans in a Petri dish.)

Because we live in a three-dimensional Universe it's tempting to think that life couldn't exist in a Universe with more or fewer dimensions. And there are genuine problems facing life in other dimensions. The laws of physics are pretty robust and work (with occasional tweaks) no matter how many dimensions your Universe has. And so we can tell that:
• In four or more dimensions, planets wouldn't be able to maintain stable orbits around stars. In fact the only Universes where planets can orbit a star for any respectable amount of time are two- and three-dimensional ones.
• If your Universe has more than one dimension then the strength of gravity decreases as you move away from a massive object. In four or more dimensions it tails off so fast that the Universe would quickly drift apart and face heat death. In two dimensions it doesn't fade away quickly enough, so the Universe would quickly collapse in on itself. Although having said that…
• The above points assume that Newtonian mechanics are a good approximation for how gravity really works, i.e. for general relativity. In three or more dimensions this is (probably) true. But 2D general relativity is a curious beastie and differs drastically from 2D Newtonian mechanics. The most startling difference is that if a 2D Universe worked as predicted by 2D general relativity then there would be no action at a distance. Stick two 2D black holes near one another, and they would just kind of sit there, being black and holey. Things wouldn't be attracted to one another, and the whole Universe would just shuffle off in whatever direction space was expanding, never looking back.
• These are some of the physics-y problems in other dimensions, but there are biological issues too. Consider your brain. It's basically millions of little nodes connected by wires. In 3D this kind of neural network is pretty easy to arrange. If I give you a bunch of points in space and tell you to join up certain pairs with wires then you should be able to do it. Sure the wires might be horribly tangled and tied up in knots before you finish, but that's fine. Or at least that's fine in three dimensions. In two dimensions your wires can't go over and under each other. They have to go around. So suddenly wiring up a brain is much more problematic; only neural networks that form a planar graph are allowed. On the other hand, in four dimensions, wiring a brain is even easier since your wires have an extra dimension to slip into, so if brains ever did evolve in a higher dimensional Universe they would have the potential to surpass our own clunky things with ease.


None of these points really preclude life from arising in a 2D or 4D Universe. At worst they say it would have to evolve quickly before the Universe ended; and at best they say that we don't really know what would happen in other Universes. Hell, we're not really sure what's happening in our Universe. There's dark matter holding together galaxies that should spin themselves apart, and dark energy speeding up an expansion of space that should be slowing down, but both dark matter and dark energy are just placeholder names physicists use for whatever is causing these effects. So what might life be like, if it existed, in two dimensions?

Enter Edwin Abbott Abbott, a guy so cool his mother named him twice. He was a nineteenth century theologian, but is best known for writing Flatland. The genre of Flatland is often listed as “mathematical satire”, so it was inevitable I'd like it.

Although it's set in a two dimensional Universe, Flatland doesn't attempt to deal with the physical and biological issues that arise, in fact these are generally brushed under the carpet with some apologetic lampshade hanging. What Abbott Abbott does describe are the societal quirks forced upon a two-dimensional land, and later a one-dimensional one. Depending on who you ask, the result is either a cutting satire of Victorian England or a hundred-odd pages of sexist fluff. But whether it's biting or fluffy, Flatland is undeniably a quaint and fun work. ( )
  leezeebee | Jul 6, 2020 |
19th-century Victorian social satire through forward-thinking mathematical study.

Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognisance even if the number Two; joe has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet make his perfect self-contentment, and hence learn this lesson, that to be self-contented is to be vile and ignorant, and they to aspire is better than to be blindly and impotently happy.

Wild. ( )
  piquareste | Jun 3, 2020 |
My first taste of the Hungarian master of bleakness. Will be going back for more soon. ( )
  Aaron.Cohen | May 28, 2020 |
Wikipedia lists three different varieties of literary satire if you're interested in actually learning something, but all I'm interested in is figuring out what stuff I like and what stuff I don't like.

I evaluate satirical writing based on the following two questions:
1. Is it sympathetic to its targets?
2. Is it funny?

If the answer to at least one of those questions is yes, there's a chance I'll like what I'm reading (I still might hate it!). If the answer to both questions is no, I'm going to loathe it no matter what.

Satire that I might enjoy usually entails the author poking fun at a group of people for which he feels affection or maybe toying with some collective failure that's part of the human condition. A good example of this is Nikolai Gogol's Dead Souls, in which the reader is introduced to a multitude of quirky characters that inhabit the Russian countryside. Gogol treats his subjects with dignity, no matter how strange some of their behavior might be. More importantly, he presents his theses directly and sincerely, never talking down to the reader.

Satire that I'm less likely to enjoy but still occasionally do is of a harsher variety. The author feels a deep animosity for his subjects and wants to ridicule them as aggressively as possible, making no attempt to paint a fair picture. Somehow, though, despite all that anger, the author manages to make the book hilarious. Take Mikhail Bulgakov's Heart of a Dog. Bulgakov felt nothing but contempt for Bolshevik leadership in the Soviet Union, but he's such a talented writer that he managed to take that anger and turn it into a funny book about a dog and a mad scientist. These novels are few and far between because they are driven by a fury so fierce that it manages to drown out any trace of smugness in the author. That's pretty impressive, because smugness is the driving force behind almost all satire as well as its worst flaw.

The satire I don't like is focused on reducing life's complexity in order to smile condescendingly and shake your head at all the people who aren't you. Rather than directly confront the world's problems with their writing, some authors prefer to be clever and snipe at caricatures of the figures and institutions they feel are worthy of ridicule. "Wow!" we say. "This stuff you made up is silly. Wait! THIS STUFF IS LIKE SOCIETY. THAT MEANS SOCIETY IS SILLY. GEE YOU REALLY SKEWERED US!" The most prominent modern day example of this is the TV show Black Mirror, and I swear no matter how many times people tell me I'm wrong George Orwell's Animal Farm is in this category too and it's absolute trash.

I've just written far too many words without ever mentioning the book I'm trying to review, when all I really needed to say was that I hated the first half of it. Part One of Flatland is a satire of Victorian England. Let's run it through my test.

Is Flatland sympathetic to its targets? If we take the book's targets to be shapes with lots of sides (representing England's upper classes), then I'd say not really. Our guide through Flatland, a square named A Square, gives us 50 pages worth of explanation on his universe that somehow manages to be too much information while at the same time not the information we need. The social structure of Flatland is based on how many sides each shape has, with squares being better than triangles and so on and so forth. Obviously, you want to have more sides so people will respect you more, but besides that, all this shit is pointless without understanding how this universe works. We have no idea how these things eat or move or have sex or any of that, which is annoying, and A Square says that he has all that information but just won't tell us out of respect for our time, which is very annoying. That means the reader has to fill in a million blanks to fully understand the motivations for these characters, and if we're doing all that work already when we're reading a story parodying Victorian England, we might as well just fucking read about Victorian England. This, as always, is what makes so much satire so stupid. It's a whole lot of work to get to a point that could have been made just as eloquently and far more directly in 2% of the time. Anyway, the answer is no, Abbott's targets are not treated with any charity, because no character in this book is.

I'll answer the second question faster. Is the book funny? No.

So that's the first part of the book. It's bad. The second half is much better, but it just happens to be about a subject that doesn't interest me too much. That part isn't Abbott's fault, and I bet if I cared the slightest bit about math and science, his look at several worlds with different amounts of dimensions would be pretty cool. Also, to give him credit, the writing in the second half seems pretty sharp, given that the book was written in the 1880s.

I can't believe I wrote this much about a book that was barely 100 pages. I really suck. But at least I didn't write Animal Farm. ( )
  bgramman | May 9, 2020 |
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» Add other authors (62 possible)

Author nameRoleType of authorWork?Status
Abbott, Edwin A.primary authorall editionsconfirmed
Bradbury, RayIntroductionsecondary authorsome editionsconfirmed
Dewdney, A. K.Introductionsecondary authorsome editionsconfirmed
Edelmann, HeinzCover designersecondary authorsome editionsconfirmed
Hoffmann, BaneshIntroductionsecondary authorsome editionsconfirmed
Jann, RosemaryEditorsecondary authorsome editionsconfirmed
Kalka, JoachimTranslatorsecondary authorsome editionsconfirmed
Langton, JamesNarratorsecondary authorsome editionsconfirmed
Lightman, Alan P.Introductionsecondary authorsome editionsconfirmed
Smith, ValerieIntroductionsecondary authorsome editionsconfirmed
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Epigraph
Dedication
To
The Inhabitants of SPACE IN GENERAL
And H. C. IN PARTICULAR
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries
Of THREE Dimensions
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE OR EVEN SIX Dimensions
Thereby contributing
To the Enlargement of THE IMAGINATION
And the possible Development
Of that most rare and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY
First words
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.
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Disambiguation notice
The Annotated Flatland has substantial commentary by Ian Stewart and so is a separate work.
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