Flatland: A Romance of Many Dimensions

A satire of Victorian cultural norms, it's the story of a denizen of a two dimensional world, a square by the name A. Square. The first half skewers the class system and the deplorable condition of women. Going into this book, I thought it was only a satire of the class system, so I initially believed the misogyny was merely background noise. After a few pages though, it became so outrageous that I realized it was also satirical. Bravo, M Abbot. At the end there's some stuff about art, science, and individual expression, but I'm not sure how successful that was/is.
The second half concerns A Square's dream of a one dimensional world, and a forced journey to 3D world wherein he can see the nature of his own world. This forms the show more background into some pointed questions about political authority and religious veracity, especially when Square attempts to get a 3D Sphere to contemplate a 4th dimension. It's a bit forced, and is less satire and more questioning, but I think it still works.
4 stars oc, 3.5 for the book, and an extra .5 because my copy smells fantastic. show less

What struck me most, when I read this years ago, was the author's plea for keeping an open mind: we should accept the idea that there may be four or more dimensions. (see p. 88 and p. 95) Similarly, we should accept the idea that we don't know everything knowable. And of course, thanks to Godel, we have to accept that there are things we can never know.

Rereading it now, the author has constructed an interesting society where polygons that are most like circles run society and have instilled some convenient ideas in everyone else: For example, when a sphere manages to talk the narrator, the square explains: "'More merciful, more loving!' But these are the qualities of women! And as we know that a Circle is a higher Being than a Straight show more Line [a woman], in so far as knowledge and wisdom are more to be esteemed than mere affection." [p. 83]. Women, being straight lines and not even polygons, are clearly inferior. show less

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

This is a fascinating little book. Written in the latish 19th century, it is a despatch from a very simple two-dimensional world by one of its inhabitants, the supposed author: A Square. The first part of the book simply describes the society of Flatland for the benefit of we three-dimensional creatures, its intended audience. The second describes how the square came to learn of our three-dimensional world, as well as other zero- and one-dimensional worlds, and his efforts to educate his fellow bi-dimensional fellows about the higher dimensions.

Both sections are very different (the first has little plot, and more of the maths; the second is much more philosophical), but both are packed with allusions and layers of meaning. For example, show more the society shows antediluvian, barely qualified, attitudes to women and class - this is a little off-putting initially, until it becomes clear that this is social satire, of a Swiftian level. In describing his attempts to educate people about the higher-dimensions, Abbott is explicitly imploring the reader to be open-minded about radical abstract ideas, by way of making us consider that there are higher-dimensions of which we are not aware. And ultimately the story contains elements of traditional tragedy, of transformation - apotheosis even - and of attaining knowledge from a state of ignorance and of the resultant fall from grace.

On top of that, the book is crammed with references to Shakespeare and the classics. (And through all that it is written in beguilingly simple language (although in a slightly archaic style - even for the 19th century - to give it a timeless quality).

It is a deceptively simple, towering achievement.

This edition in particular is to be recommended. I found the notes on the maths, and Abbott's literary references very useful (although the ones explaining some of the language far less so). And almost more fascinating than Abbott's fable of abstract thought is the man that emerges in the other material in the book.

From the main text you discern a clever, thorough, drily witty and whimsical man; and the basic notes clearly illustrate through their detailing of classical and literary allusions, a highly - and widely - learned man; but that barely scratches the many surfaces of Abbott. Fortunately there is considerable back material in the appendices to fill in some of the detail. His accomplishments include

Legendary headmaster (Prime Minister Asquith attended the City of London School while Abbott was in charge)
An award-winning Cambridge scholar (top in his year in Classics)
A renowned preacher
A bible scholar and leading progressive thinker on the non-miraculous Jesus (reminiscent of Thomas Jefferson's 'The Life and Morals of Jesus of Nazare')
Shakespearean scholar
A biographer and critic of Cardinal Newman
Educational reformer (an early proponent of formal teacher training; promoting teaching for lower classes)
Active Proponent of women's education and suffrage
Admiree (reciprocated) of George Eliot
Author of numerous books and essays, on a range of topics encompassing most of the above

And, of course, a writer of whimsical mathematical fiction, which - along with beautifully communicated (and occasionally entertainingly illustrated) higher mathematical concepts - incorporates existentialism, social criticism, and a plea for scientific rigour and open-mindedness.

I have a new hero. 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

"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 was dubious starting this, as it's written in a high Victorian style that can be a bit of a slog, and the introduction, which is mercifully short, did not exactly make my heart leap up like an eagle at the thought of continuing. But once I got into the book proper, it turned out to be a delight on a lot of levels -- for example, as a satire of stratified Victorian society (and our own, too); as a commentary on the dangers of bucking conventional wisdom; and on the difficulty of pushing our minds past their accustomed boundaries. The book also gives the reader a good review of geometry and physics, and if it's been years since you gave much though to those things (since a few years after college, in my case), you'll enjoy the mental show more gymnastics you'll have to do to follow the narrator's explanations of the various geometrical principles. I was quite sorry when this one ended. show less