Flatland: A Romance of Many Dimensions

This book was recommended to me more than fifty years ago. I finally read it. The basic approach is a challenge. Abbott wants you to imagine what if. He pushes us to realize how things would look if there were only two dimensions. Everything would appear flat. Beyond that different shapes in a two dimensional world would have slight differences visible from only certain ways one would come upon them. It points out how a circle would appear as opposed to how a triangle would appear and that would depend on which direction you approached it, approaching the base or one on the angles. And then there's a square with more bases, and then hexagons, etc. More bases, larger angles, seen from the inside and less severe when approached from the show more outside. Interesting. This approach is taken to another level when one shape is considered superior to another and combined with increased or decreased likelihood of progeny being shaped like the more superior shape. Yikes, sounds like eugenics. Put that aside for a moment.

Abbott takes us in two different directions, fewer and more dimensions. If the world had only one dimension shapes would disappear, things could only be dots or lines. Fascinating. Even more fascinating is what happens when the world has a third dimension. Not just north and south but actually up and down. Now we get even more interesting objects. The concept of volume becomes important. Inside and outside even have deeper, richer meaning. Abbott then speculates about what if there are more dimensions. Wow. What would that look like? We don't even have language rich enough to handle that.

If this was all this book contained that would be great. But introducing hierarchy and it's corollary, caste, begins to show us the darker side. Eugenics seems....normal. But this goes off the rails with misogyny. Woman are worthless according to Abbott, They can't comprehend the richness of any of these worlds. Really? I have to stop and realize this book was written in a very different world, the 1880s. Women did not even have the right to vote and were treated more like property than people. This is a problem with many classics. They have aspects we no longer consider appropriate. I would love if someone would rewrite this classic without the negative baggage. That would be a much better book. show less

ORIGINALLY POSTED AT Fantasy Literature.

Flatland: A Romance of Many Dimensions, published in 1884, is Edwin A. Abbott's social satire and Christian apologetic. As a Cambridge mathematician, theologian, and schoolmaster, Abbott had a lot to say about his Victorian society and about being open-minded to the supernatural. He does this from the point of view of a humble square that lives in Flatland, a world of only two dimensions.

For the first half of the book ("This World"), the square explains the demography of Flatland, all the while offering hilarious social satire. He begins at the lowest social stratum (women, who are straight lines) and ends with the king, who has so many sides that he's indistinguishable from a circle. Low-class show more men, such as soldiers, are isosceles triangles with sharp acute angles. Since the brain is the size of the smallest angle, these men are stupid, but their sharp angles provide offensive weapons. Anyone who has an angle under 60?� is a serf. Women, of course, have no angles, which means they are brainless and irrational (and Abbot provides plenty of tongue-in-cheek evidence for this fact). But women have a mouth on one end, and it can effectively be used as a dagger. When viewed from the back, a woman is hard to notice since she is seen only as a point, thus she must sway her bottom back and forth to alert others of her dangerous presence.

Pretending that he's merely explaining Flatland society to his readers in "Spaceland," Abbot mercilessly mocks his era's class structure, fashion, aristocratic marriage and parenting practices, the education system and school board politics, and government. All of this is done in a reasonable-sounding lecturing tone:

"Obviously then a Woman is not to be irritated as long as she is in a position where she can turn round. When you have them in their apartments -- which are constructed with a view to denying them that power -- you can say and do what you like; for they are then wholly impotent for mischief, and will not remember a few minutes hence the incident for which they may be at this moment threatening you with death, nor the promises which you may have found it necessary to make in order to pacify their fury."

In the second half of the book ("Other Worlds") the square explains his vision of a one-dimensional realm called "Lineland" where he meets the king of Lineland who can't imagine Flatland, a world of two dimensions. The square thinks this is amusing, so he torments the belligerent king by using the second dimension to speak to the king from above, to magically pop in and out of the King's view, and to offer predictions about who is approaching the king from afar (image below). With his omniscience and omnipresence, the square bewilders the king of Lineland.



Upon his return to Flatland, the square is confronted by a sphere from our Spaceland of three dimensions who, poised in the third dimension, can view all of Flatland. To the Flatlanders the sphere looks like a circle of changing diameter, and to Linelanders he seems to be only two lines. The sphere can pop in and out of Flatland and Lineland as he wills, can see inside (and even manipulate) houses and bodies, and can make predictions about the future based on what he sees from his viewpoint.



Our square, who harassed the king of Lineland for his inability to imagine Flatland, is now flummoxed at the thought of a dimension he can't perceive, but he believes it because he has witnessed the sphere's power and he remembers his analogous encounter in one-dimensional Lineland. When the square tries to preach this new teaching, though, he meets resistance from unbelievers.

The metaphor, of course, is that we in Spaceland, being confined to only the dimensions we are able to perceive, can't imagine more dimensions in which other beings exist and may be able to visit, view, or manipulate us. This idea isn't at all new to me, but I found Abbott's explanation to be a very convincing line of reasoning and, perhaps, a way to imagine what it must be like to be God. Flatland is best known, by the way, as a treatise on dimensionality and is considered by scientists to be prophetic in its use of unseen dimensions to explain physical phenomena.

Flatland is available in the public domain, but I chose to listen to Blackstone Audio's recent version which is four hours long and read by Robin Field. The audiobook does not come with Edwin Abbott's drawings, but I had no trouble imagining them because they're thoroughly described by Abbott in the text. However, it's easy to refer to them in public domain sources if you wish. I loved Robin Field's narration and, even though the material seems heavy, I didn't have any problem following along. I did, however, have to maintain constant focus just to translate all of the geometric metaphors into social analogies during the first section of the book. For that reason, Flatland is hard work, but immensely rewarding. I thought it was brilliant.

ORIGINALLY POSTED AT Fantasy Literature. show less

En haut, en bas... Voilà deux expressions qui n'ont pas cours à Flatland. A les employer, on risque de perdre la tête, au propre comme au figuré. Car si les habitants de cet univers qui ne connaît que Deux Dimensions n'ont pas à craindre que le ciel leur tombe sur la tête, ils détestent les illuminés et les faux prophètes qui prêchent l'évangile de la Troisième dimension. Pourtant, le narrateur de cette étrange aventure, un très raisonnable Carré, est certain d'avoir été visité par une Sphère, chose impossible pour ses concitoyens qui ne peuvent y voir qu'un Cercle... Mais ne riez pas de leur aveuglement. Comment réagissez-vous quand on vous parie de la Quatrième dimension ?

I'm not sure why the subtitle contains the word 'romance'.
This book reminded me of Star Maker, but luckily Flatland is much shorter and consists of beautiful English prose. Flatland is a monologue describing an epiphany concerning the Nature of the Universe. I also see connections with thought experiments such as Plato's allegory of the cave. It invites the reader to extend the analogy to our own experience.
The tone of the narrator is scientific and slightly sad, which makes it (despite its short length) a bit of a heavy read. There's also a distopian tinge to the story.
The Flatland States are conservative and very woman-unfriendly. Can't tell if the writer is a bigot or a satirist. ;)

Flatland is a clever book. It may be about two dimensions, but it works on more than one. Like a lot of the best science fiction, it allows us to imagine a world unlike ours while telling us something about the world like ours. At the same time Abbott through his obtuse (lol) narrator, A. Square, is telling us about this fantastic two-dimensional world he's constructed, he's also telling us something about our world; there's a lot of commentary on Victorian gender packed in here, for example. For example, the greatest men actually have what are technically feminine characteristics-- so a law has to be passed to make it clear that that characteristic is good in a man, but bad in a woman (55). Oddly, like in Bulwer's The Coming show more Race from a decade prior, women in the world of Flatland have enormous destructive power (27-8). There must be some kind of metaphor going on that I can't quite unpack; in Flatland, apartments are designed to prevent women from exercising their power (31), and that has to be some kind of commentary on the Victorian home, surely?

The best part of the book in my mind is surely the story of the Sphere who lords his extra dimension over A. Square, but cannot conceive of a four-dimensional world where he himself is less powerful. A. Square can extrapolate by analogy even though he has never seen such a world, but the Sphere cannot. To draw a connection to another late Victorian science fiction work, it puts me in mind of what Wells did in The War of the Worlds: the Martians were to the English as the English were to the Tasmanians, but until the Martians came, no one could conceive of a power with that relationship to us. By giving us a world with fewer dimensions than our own, Flatland prompts us to imagine that there must be a world out there with more, and that is its greatest cleverness. show less

"Estar satisfecho de sí mismo es ser ruin e ignorante, y [tener] algo a que aspirar es mejor que ser ciega e impotentemente feliz"

Este libro ha significado para mi una grata sorpresa. Lo comencé con incredulidad, dada su fama de libro didáctico de matemáticas, con lo cuál cumple en aspectos que son muy sencillos de entender, pero al mismo tiempo cuenta con una historia que bien podría pasar, en parte, como una muy rara distopía (aunque tampoco podría simplemente embolsarlo en ese genero).

"Todos somos proclives a los mismo errores, todos igual de esclavos de nuestros respectivos prejuicios"

La historia va narrada por un cuadrado que nos cuenta la vida y los habitantes, así como la jerarquía social, de Planilandia, una show more "ciudad/país/universo" de 2 dimensiones, cuya estructura es una muestra muy representativa de como se regia la sociedad hacia finales de los 1800, muy inteligente la forma en que,sin resultar políticamente incorrecto, Abbott ofreció una buena crítica a la actitud de los gobernantes, el relegado papel de la mujer y la imposibilidad de lograr alcanza una vida mejor.

"Os creéis la perfección de la existencia y sois en realidad el más imperfecto y estúpido de los seres"

La vida de este cuadrado da un giro dramático la noche del cambio de milenio, cuando tiene un sueño acerca de un universo completamente diferente al suyo. Tras este revelación (y otras posteriores) la vida del cuadrado, y su percepción de ella, cambia completamente hasta que finalmente es llevado a la cárcel por revelar una verdad que los gobernantes de Planilandia no creen, y no desean que sea difundida. A partir de este punto Abbott comienza a dar mayor interés a la historia.

El final es simplemente la realidad de lo que sucede cuando un individuo, aunque tenga razón, se contrapone y desobedece los designio de quienes están en el poder, pero al mismo tiempo muestra que a pesar de la adversidad uno debe mantener su ideología y su esencia. show less

I don't remember how I stumbled across Flatland for the category A Book With Non-Human Characters—most search results list books with animals—but I'm glad I did. The first-person narrator of Edwin A. Abbott's short novel first explains the physical mechanics and societal organization of his two-dimensional space, which he calls Flatland for his readers' benefit, then relays his "personal" story of leaving Flatland for the three-dimensional world with the assistance of an alien visitor, Sphere. The quotes around the word personal reflect the fact that our narrator is a square, rather than a human, who occupies the respectable position of attorney due to his four sides. In Flatland, the more sides an individual has, the higher his show more position in society. Sphere has a third dimension previously unknown and unimagined in two-dimensional Flatland, a dimension which confers status far beyond that of any shape living in Flatland. Eventually, the square comes to treat Sphere as a god.

In some ways Flatland is reflective of its time (1884) and place (England). Flatland is a patriarchal society, where women are the simplest geometric shape (straight lines) and are restricted from education. It's telling that, when viewed head-on, women are essentially invisible. Owing to the sharpness of their terminal ends, they are also extremely dangerous physically to the other inhabitants of Flatland and are required to emit a Peace-cry to warn those around them of their presence. The highest societal position is that of Priests, who are circles.

In other ways, it is still relatable decades after its initial publication. The conflict between the various shapes is analogous to today's world. The upper shapes look down on and use the lower shapes for their own benefit. The lower shapes resent the upper shapes. Their attempt to overthrow the societal hierarchy employs color, rather than weapons, to eliminate the cognitive differences between the shapes.

Flatland is an interesting thought experiment about the universality of human nature, regardless of physical reality. show less