FLATLAND - A Romance of Many Dimensions (The Distinguished Chiron Edition)

By Edwin Abbott Abbott

This special edition is a distinguished vintage reproduction, of the 1884 satirical novella Flatland, by the English schoolmaster Edwin Abbott. Meticulously elaborated by the editorial team of Chiron Academic Press in collaboration with the renowned literature publisher Edition l'Aleph (www.l-aleph.com), this special edition, pays particular attention to the very authentic details of the editorial of text and images, fine type setting, mise-en-page, production, and print. The result is a revival of the vintage for the 21st century's reader. Thus a unique reading experience for the book lovers and collectors of this genre. A recommended edition to libraries.

Writing pseudonymously as "A Square", the book used the fictional two-dimensional world of Flatland to comment on the hierarchy of Victorian culture, but the novella's more enduring contribution is its examination of dimensions. The story describes a two-dimensional world occupied by geometric figures, whereof women are simple line-segments, while men are polygons with various numbers of sides. The narrator is a square, a member of the caste of gentlemen and professionals, who guides the readers through some of the implications of life in two dimensions. The Square dreams about a visit to a one-dimensional world (Lineland) inhabited by "lustrous points", and attempts to convince the realm's monarch of a second dimension; but is unable to do so. . .

"One of the most imaginative, delightful and, yes, touching works of mathematics, this slender 1884 book purports to be the memoir of A. Square, a citizen of an entirely two-dimensional world." -The Washington Post Book World

"Flatland has remained of interest for over a century precisely because of its ability to engage its readers on so many different planes in so many different dimensions."-Victorian Studies "This reprint of Abbott's Flatland adventures contains an Intro¬duction by Thomas Banchoff which is worth reading on its own. So if you don't have yet this book at home, go ahead and buy this edition."-Zentralblatt MATH

In 1884, Edwin Abbott wrote a strange and enchanting novella called Flatland, in which a square who lives in a two-dimensional world comes to comprehend the existence of a third dimension but is unable to persuade his compatriots of his discovery. Through the book, Abbott skewered hierarchical Victorian values while simul¬taneously giving a glimpse of the mathematics of higher dimensions.-Science News

• Language: English
• Publisher: Chiron Academic Press
• Release date: Mar 26, 2015
• ISBN: 9789176370247

Edwin Abbott Abbott

Edwin Abbott (1838–1926) was an English educator and theologian best known for his 1884 novella Flatland: A Romance of Many Dimensions, a forerunner of modern science fiction. 

Book preview

PART I

THIS WORLD

Be patient, for the world is broad and wide.

PART 1

THIS WORLD

§ 1.—Of the Nature of Flatland

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.

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard and with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said my universe: but now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there should be anything of what you call a solid kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate.

Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle.

But now, drawing back to the edge of the table, gradually lower your eye (thus bringing yourself more and more into the condition of the inhabitants of Flatland), and you will find the penny becoming more and more oval to your view; and at last when you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatland citizen) the penny will then have ceased to appear oval at all, and will have become, so far as you can see, a straight line.

The same thing would happen if you were to treat in the same way a Triangle, or Square, or any other figure cut out of pasteboard. As soon as you look at it with your eye on the edge of the table, you will find that it ceases to appear to you a figure, and that it becomes in appearance a straight line. Take for example an equilateral Triangle—who represents with us a Tradesman of the respectable class. Fig. 1 represents the Tradesman as you would see him while you were bending over him from above; figs. 2 and 3 represent the Tradesman, as you would see him if your eye were close to the level, or all but on the level of the table; and if your eye were quite on the level of the table (and that is how we see him in Flatland) you would see nothing but a straight line.

When I was in Spaceland I heard that your sailors have very similar experiences while they traverse your seas and discern some distant island or coast lying on the horizon. The far-off land may have bays, forelands, angles in and out to any number and extent; yet at a distance you see none of these (unless indeed your sun shines bright upon them revealing the projections and retirements by means of light and shade), nothing but a grey unbroken line upon the water.

Well, that is just what we see when one of our triangular or other acquaintances comes toward us in Flatland. As there is neither sun with us, nor any light of such a kind as to make shadows, we have none of the helps to the sight that you have in Spaceland. If our friend comes close to us we see his line becomes larger; if he leaves us it becomes smaller: but still he looks like a straight line; be he a Triangle, Square, Pentagon, Hexagon, Circle, what you will—a straight Line he looks and nothing else.

You may perhaps ask how under these disadvantageous circumstances we are able to distinguish our friends from one another: but the answer to this very natural question will be more fitly and easily given when I come to describe the inhabitants of Flatland. For the present let me defer this subject, and say a word or two about the climate and houses in our country.

§ 2.—Of the Climate and Houses in Flatland

AS WITH YOU, SO ALSO with us, there are four points of the compass North, South, East, and West.

There being no sun nor other heavenly bodies, it is impossible for us to determine the North in the usual way; but we have a method of our own. By a Law of Nature with us, there is a constant attraction to the South; and, although in temperate climates this is very slight—so that even a Woman in reasonable health can journey several furlongs northward without much difficulty—yet the hampering effect of the southward attraction is quite sufficient to serve as a compass in most parts of our earth. Moreover, the rain (which falls at stated intervals) coming always from the North, is an additional assistance; and in the towns we have the guidance of the houses, which of course have their side-walls running for the most part North and South, so that the roofs may keep off the rain from the North. In the country, where there are no houses, the trunks of the trees serve as some sort of guide. Altogether, we have not so much difficulty as might be expected in determining our bearings.

Yet in our more temperate regions, in which the southward attraction is hardly felt, walking sometimes in a perfectly desolate plain where there have been no houses nor trees to guide me, I have been occasionally compelled to remain stationary for hours together, waiting till the rain came before continuing my journey. On the weak and aged, and especially on delicate Females, the force of attraction tells much more heavily than on the robust of the Male Sex, so that it is a point of breeding, if you meet a Lady in the street, always to give her the North side of the way—by no means an easy thing to do always at short notice when you are in rude health and in a climate where it is difficult to tell your North from your South.

Windows there are none in our houses: for the light comes to us alike in our homes and out of them, by day and by night, equally at all times and in all places, whence we know not. It was in old days, with our learned men, an interesting and oft-investigated question, What is the origin of light? And the solution of it has been repeatedly attempted, with no other result than to crowd our lunatic asylums with the would-be solvers. Hence, after fruitless attempts to suppress such investigations indirectly by making them liable to a heavy tax, the Legislature, in comparatively recent times, absolutely prohibited them. I—alas, I alone in Flatland—know now only too well the true solution of this mysterious problem; but my knowledge cannot be made intelligible to a single one of my countrymen; and I am mocked at—I, the sole possessor of the truths of Space and of the theory of the introduction of Light from the world of Three Dimensions—as if I were the maddest of the mad! But a truce to these painful digressions: let me return to our houses.

The most common form for the construction of a house is five-sided or pentagonal, as in the annexed figure. The two Northern sides RO, OF, constitute the roof, and for the most part have no doors; on the East is a small door for the Women; on the West a much larger one for the Men; the South side or floor is usually doorless.

Square and triangular houses are not allowed, and for this reason. The angles of a Square (and still more those of an equilateral Triangle) being much more pointed than those of a Pentagon, and the lines of inanimate objects (such as houses) being dimmer than the lines of Men and Women, it follows that there is no little danger lest the points of a square or triangular house residence might do serious injury to an inconsiderate or perhaps absent-minded traveller suddenly running against them: and therefore as early as the eleventh century of our era, triangular houses were universally forbidden by Law, the only exceptions being fortifications, powder-magazines, barracks, and other state buildings, which it is not desirable that the general public should approach without circumspection.

At this period, square houses were still everywhere permitted, though discouraged by a special tax. But, about three centuries afterwards, the Law decided that in all towns containing a population above ten thousand, the angle of a Pentagon was the smallest house-angle that could be allowed consistently with the public safety. The good sense of the community has seconded the efforts of the Legislature; and now, even in the country, the pentagonal construction has superseded every other. It is only now and then in some very remote and backward agricultural district that an antiquarian may still discover a square

Reviews for FLATLAND - A Romance of Many Dimensions (The Distinguished Chiron Edition)

[kittycunningh-815148 · Rating: 4 out of 5 stars]

This was fascinating.

[drardavis · Rating: 5 out of 5 stars]

As one interested in mathematics in sci-fi, this book has been on my to read list for some time. I’m glad I finally got around to reading it. It is unique and a bit difficult to describe. Partly it is a satire of English culture in 1884. Partly it is anthropomorphizing geometric figures, with surprisingly convincing results. That’s the sci-fi, Abbott’s imagined universe. But basically it is a very clever mathematical proof of the existence of God. Having recently read Frankenstein, I was delighted at the main character’s, A. Square, description of himself as “a second Prometheus.”

[danielstj · Rating: 3 out of 5 stars]

Very strange, unique, and interesting.

[adam.currey · Rating: 1 out of 5 stars]

I suspect it's an effect of this book having been written in the 1880's with language having changed quite a bit in the intervening time, but I found this book completely impenetrable - I only made it through 17 pages before giving up. Quite disappointing, as I was looking forward to it and was expecting it to be interesting.

[rex_lui-1 · Rating: 2 out of 5 stars]

Quite disappointed. Clever analog with Math? Sure. Any productive suggestion? No. Cynism is not the answer, curiosity and compassion are. But then, it's written from 135 years ago. Society progresses, human evolves. We are currently in the best zeitgeist on human period. The function of cynism declines.

[andycyca-1 · Rating: 3 out of 5 stars]

The life and times of a nobleman in 2d, a very interesting view of how dimensions work and how life could work out in a flat sheet

[dandelionroots · Rating: 4 out of 5 stars]

I read the annotated version, which I think was a poor decision. Many of Stewart's side notes weren't terribly interesting or illuminating, and much of the explanation was unnecessary (although parts of it I did appreciate). Abbott's work however is brilliant. I love the satire. The journey through Pointland, Lineland, Flatland, Spaceland and beyond (nonsense!) is epic-ly amazing.

[bryndahlquis · Rating: 5 out of 5 stars]

A short, surreal trip that makes me very curious and almost suspicious about life. Never before have I enjoyed geometry so much, and I'll probably never look at it the same way again.

[theoclarke · Rating: 4 out of 5 stars]

A two-dimensional being discovers the third dimension.

[heptonj · Rating: 2 out of 5 stars]

Very imaginative but very boring. I was waiting for the story to reach a conclusion or at least a revelation which gave a meaning to it. I think, perhaps, I've missed the underlying meaning of the book, as there only seemed a slight parallel with our own past society. Then again, I doubt that was what the author was aiming at.

[pondlife_1 · Rating: 2 out of 5 stars]

The first half of this book appears to be an allegory of victorian class and gender discrimination, with some additional political things thrown in that went over my head but probably made sense to contemporary readers. For example, was the thing about colors and equality talking about the French revolution?The second half is a comparison of worlds of different dimensions from the viewpoint of someone living in a two-dimensional world. This part is easier to understand, but it's a bit overdone. I got the concept after a few pages, and after a while it felt repetitive.

[hemlokgang · Rating: 2 out of 5 stars]

.I get it that this story of a two dimensional world is a metaphor for the superficiality and the divisiveness of the social structure of our three dimensional world. Did not like it at all.

[darthdeverell · Rating: 3 out of 5 stars]

In Flatland, Edwin A. Abbot uses fiction to provide a unique understanding of dimensions. Rather than start with a three-dimensional subject and descend "downward," he starts in the "middle," with a two-dimensional square in Flatland that first visits a one-dimensional world called Lineland before "ascending" to the three-dimensional world of Spaceland. Abbot's narrative technique is quite effective in setting up his explanation of spatial geometry, though the first part of his story suffers from many of the biases and prejudices of his day. The first half of the book, and much of the second half, is replete with blatant misogyny and an approving portrayal of eugenics. Though Abbot's work plays a significant role in speculative fiction, he could not escape the views of his own time even as he invented new worlds. This work will interest fans of speculative fiction and those looking at the history of science fiction, but is unpalatable to modern sensibilities.

[lee7mervin · Rating: 4 out of 5 stars]

A wonderful mixture of science fiction and satire

[chris_el-1 · Rating: 5 out of 5 stars]

One of the most important book I've ever read. It was written a long time ago but still remains one of the best mind stretching ways to open you mind up to understanding the dimensionality of reality. The implications are not merely scientific. The theological implications are significant as well. For instance, if God exists outside of the dimension of time (I believe he is both within and without) then for Him there is no predestination or foreknowledge. Only knowledge of all things.

I am adding this note on this book in Jan 2011. I read this book in 2003 (borrowed from Jonathan Jessup) and it is still shaping the way I see the world. I need to re-read for a refresher. :)

[antt-4 · Rating: 4 out of 5 stars]

This classic should be a must-read! Need I say more?

[starcat-1 · Rating: 4 out of 5 stars]

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 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.

[paulagraph · Rating: 3 out of 5 stars]

An amusing and petite (82 pp)mathematical fantasy written over a century ago, Flatland proves to be a gentle social satire a la Gulliver's Travels that doesn't quite manage to rise above the sexism and classism of its time (even while poking fun at such social prejudices). Flatland's Gulliver is a Professional Man Square (for comparison, Middle Class Men are Equilateral Triangles, all Women are Straight Lines & Lower Class Males are Isosceles Triangles of varying angles, the more acute, the lower the class) in a two-dimensional world where the ultimate goal is to engender a Circle. He visits the one-dimensional world of the line in a dream, the no-dimensional world of the point in his imagination and the three-dimensional world of the cube and the sphere with the assistance of a guide from Spaceland. He is ultimately imprisoned (what else could be his fate?) as a heretic (his heresy, the news of 3-dimensional Space).

[meriwetherr-1 · Rating: 4 out of 5 stars]

Impressed with how the author uses fiction to explain a complex concept and provoke thought.

[kimmarie1 · Rating: 5 out of 5 stars]

Absolutely brilliant - a true masterpiece. The premise is so simple - just the basics of elementary school mathematics. Abbott makes characters out of basic shapes with such diversity and far reaching social commentaries that are as relevant today as it was in the time in which he wrote it.

[nmarun-1 · Rating: 2 out of 5 stars]

I heard the audio book of Flatland and I found it very basic in terms of Geometry. I did like the author's creativity in creating the 1- and 2-dimensional world.

[john257hopper · Rating: 4 out of 5 stars]

This is a short late 19th century concept novel, based on the imaginary thoughts of an inhabitant (a Square) of a land of two dimensions and the conversations he has with the Sphere, a being from Spaceland, a world of three dimensions. Lineland and Pointland also make appearances. I appreciated the author's intent in trying to show how the concept of dimension entirely governs one's notion of the universe; at the same time, I was amused by how the author's natural assumptions of nineteenth century middle class life governed even these other dimensional worlds; so, the Square's household (his wife is a line, his sons pentagons and his grandsons hexagons) has servants (triangles) and there is a criminal underclass of isosceles triangles. Even Lineland has a King. Pointland is (naturally) just a single being unaware of the existence of any other being. Simultaneously interesting and amusing little book.

[lyndatrue · Rating: 5 out of 5 stars]

From the Introduction:Here is a stirring adventure in pure mathematics, a fantasy of strange spaces peopled by geometric figures; geometric figures that think and speak and have all too human emotions. This is no trifling tale of science fiction. Its aim is to instruct, and it is written with subtle artistry...

[mrgan-2 · Rating: 3 out of 5 stars]

Deservedly a classic of popular mathematics, Flatland makes the problem of multiple dimensions into a comprehensible adventure of sorts. It's a great concept and something everyone should read about at some point.

However, there are much better books today from which you could learn the basics of Flatland. Being a product of the late 19th century, the book is saddled with stuffy, annoying prose; outdated and distracting satire; and only a marginally interesting "plot".

If you've heard about the book in the context of a work which covered the same ideas of how to think about dimensionality and other presumably unthinkable concepts, you can probably skip Flatland, as not much else about it is worthwhile.

[akblanchard_1 · Rating: 4 out of 5 stars]

A prolix quadrilateral named A. Square explains how things are done in Flatland, a two dimensional space where one's role in society is determined by the number of sides one has. Isosceles triangles are at the bottom of the rigid hierarchy and circles (which are regarded as having a large number of "sides") are at the top. Women, who are lines (or, more accurately, very thin parallelograms) are beneath contempt. Square also describes his visions of Lineland and Pointland, and his experiences learning from a mysterious being (a Sphere) about three-dimensional Spaceland. When he tries to share his newfound knowledge of multiple dimensions with the inhabitants of Flatland, he finds that he is treated as a heretic.As prior commentators on Flatland have observed, the book combines geometric observations with a satire on Victorian ideas of social hierarchy. I found this novella to be surprisingly entertaining and on-target, even for me as a non-geometrically inclined reader.

[solitaryfossil · Rating: 3 out of 5 stars]

It was a fun re-read, I read it first about 100 years ago while in high school. Published in 1884, it usually gets categorized as Science Fiction, but it’s a social satire that skewers Victorian mores, especially how women were viewed by that society. And it examines dimensions. The main character is a 2 dimensional square who has a glimpse of the 3rd dimension, which sets him thinking in a new way.

It’s a pleasant little story.

[nx74defiant · Rating: 3 out of 5 stars]

A two-dimensional being records his journeys throughout various dimensions.Given his experience with the line I would have thought he would be more open to the possibility of a 3rd dimension.

[theboylatham_1 · Rating: 2 out of 5 stars]

Six out of ten.

Flatland is a two-dimensional world with a strict hierarchy of shapes and rules. The first half of the book is 'A Square' explaining in detail how the world of Flatland works. However, in the second half of the book his understanding of the world is ripped apart by trips to Lineland, Pointland and a possible world of three-dimension.Amazingly innovative. The book is meant as a parody of Victorian society that believed it had reached the edge of all human knowledge.

[occassionalread · Rating: 4 out of 5 stars]

Flatland is a delightful book, the only that I know of that is narrarated by a two dimensional square. It provides a lesson in geometry and understanding dimensions. But it also operates, subtly, on another level, providing perhaps a tongue in cheek commentary on the British class system and social/sexual relations. It's politically incorrect at times, if taken seriously and not as a satire, but it's a lot of fun.

[lauriebrown54 · Rating: 3 out of 5 stars]

This slim book is a book of geometry made simple, in a sort of Sophie’s World style, but it’s a lot more than that. While the story is about an inhabitant of a 2 dimensional universe (A Square is what he goes by) who is shown how a one dimensional and a non-dimensional world would work, and then shown the 3 dimensional world of solids, it’s also a social satire. Written during the Victorian era, he mocks the class system & government through is description of 2-D Flatland. The author has been called a misogynist, but I’m not sure if he really was, or if he was satirizing the view, commonly held in his day, of women as emotional, brainless idiots. Given that he also describes military men as stupid and violent, and has the Square hold the upper classes (the more oblique your angles, the higher your class- circles are the top caste) in unwonted awe, I’m going to guess that the misogyny was part of the satire. The actual purpose of the book seems to be to get people’s heads around the idea of a 4th dimension. I’m not sure he accomplished that, but it was a good read and not dated by being over a hundred years old.