"Flatland" nitpick

Flatland. A. Square, as a two-dimensional being in a two-dimensional world, can only see in one dimension – that is, he sees nothing but line segments. Then the Sphere lifts him out of Flatland into Spaceland, and suddenly he can see in two dimensions, he can see planar shapes like we can.

Only, A. Square, in or out of Flatland, remains a two-dimensional creature with a two-dimensional eye that is adapted to see nothing but line segments. How can he see in two dimensions? Wouldn’t he just see a lot of confusing, incomprehensible one-dimensional images?

Why? Because it would be dull, would keep Abbott from making the points he was trying to make, and because it was irrelevant to anything else: the biology of the flatlanders has nothing to do with the novel.

You’re right, of course, but then, pulling a two-dimensional being out of his two-dimensional world would probably have all sorts of other consequences, as well. Since there is nothing to keep his guts from escaping around the edges of his skin, he’d probably come completely apart, for instance. Better not to think about it. And refuse all offers of travel to higher dimensions by the beings there.

As observed above, it’s just a tool to give you a flavor for higher dimensions, through the eyes of a 2D being.
I strongly recommend a sequel, Sphereland by Dionys Burger written in 1965. (There are many other sequels, as well)


But even more fun is A.K. Dewdney’s The Planiverse, an examination of 2D life in a more realistic 2D universe with its own physics, chemistry, and biology. Not limited to “ideal” forms like triangles, Dewdney and the people who contributed to his newletter (which eventually evolved into this book) tried to come up with workable biology for 2D beings, and realistic 2D technology. Well worth the read.


Seconded. A very entertaining and thought-provoking exercise.

I wasn’t aware it evolved as a semi-collaborative project, though.

Other than that, the book is completely realistic.

One of the points of Flatland is to make the reader aware of the possibility of more spatial dimensions than the three we’re aware of. I think the book succeeds at this. I doubt that the author was trying to describe a world that could actually exist.

His vision (presumably) would remain a line, and he could see only one linear cross-section of 3D reality at any time. He would see that cross-section filled with line segments of varying lenghts, just as in Flatland.

But, assuming he could move or rotate, or be moved or rotated, he could be exposed to a gradually shifting line-panorama that would make the higher-dimensional reality of Spaceland apparent. By analogy, we can grasp the 4D nature of a tesseract through simulations exposing us to different 3D cross-sections over time.

Or so I’m told. I’ve never actually seen one.

There’s also all the social commentary in the book, about things like women being inferior to men, and criminals being inherently criminal by their nature. I’m not sure if it was meant sincerely or if it’s meant to be satire, but either way, it distracts from the main focus of the book.

It was meant as satire of contemporary England.

Here’s a recent Wired article on an interesting looking video game under development (by one person, apparently) that’s a 4-D game, called Miegakure. It shows you a 3-D slice of a 4-D world, and allows you to rotate the slice you see, analogous to what the OP expects A Square to see in Flatland. There’s a YouTube video at that link showing what you see.

It looks interesting, but since it’s one person making it, it will probably be done somewhere between a couple years and never. If it does come out, I think I’ll pick it up.

BTW, here’s an animated film loosely based on Abbott’s book.

It’s a lovely book.

For a good many years, I planned to be reading it when… “It was the last day but one of the 1999th year of our era.” And, in fact, I did.

I hope you guys caught the Flatland sequence in Futurama. (I have no idea if it was a recent episode or a re-run.) It was fun, anyway!

Like this? (Advance to the 5-minute mark.)

Like that, yeah! Might work better as virtual reality, where we could use three-dimensional tactile sense in addition to two-dimensional vision. Likewise for the Flatlander–2D virtual reality would be better than 1D vision.

But obviously, this takes practice. You don’t just get introduced to another dimension and immediately grasp it.

They used to run that at the Museum of Science in Boston. There’s also an episode of the original Outer Limits based on it, entitled Behold … Eck!, but you need sensitive instruments to see the relation to Abbott’s book.