FLATLAND - A Romance of Many Dimensions: the distinguished Chiron edition

By Edwin A. 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 (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. . .

• Language: English
• Publisher: Chiron Academic
• Release date: Dec 23, 2019
• ISBN: 9789176370247

Book preview

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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

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

This was fascinating.

[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

[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.”

[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.

[jorgecardoso_1 · Rating: 5 out of 5 stars]

Flatland: A Romance of Many Dimensions is a great little book by Edwin Abbott. Flatland is a mathematical adventure on geometry. It takes place on a two-dimensional world with a strict hierarchical society based on the shape of its individuals and it describes the consequences of the adventure of one of those individuals (a square) through the realms of three-dimensions. It's a great book that makes us think about more-than-three-dimensional spaces and objects through analogy with two- and one- and even zero-dimensional worlds. As I read this, I thought it would be interesting to see an animation version of this book, but it turns out there are already some movies on Flatland. There is even a recent one with Martin Sheen (voice).

[pratchettfan · Rating: 5 out of 5 stars]

A fascinating allegory on Victorian society told with two and three dimensional geographical figures. Even though written in the late 19th century, aspects of the story about people's sometimes limited world views are still relevant today and the moralities of the book shouldn't be lightly dismissed. At only 80 pages it is a quick read which you shouldn't miss.

[fieldri1 · Rating: 3 out of 5 stars]

Imagine a world where things exist on a plane of two dimensions. There is no up and down at all. People this world with polygons whose social position is ruled by the number of sides they have (triangles are the plebs, circles are the priests) and the class structure is rigidly adhered to.Then imagine of young person in this world who is contacted by a three dimensional sphere and who offers to take her out of her plane world and show her how the universe really is! This is the concept behind Flatland.Part satire on the class structure of Victorian Britain, part teaching aid for teaching euclidian space, this is a classic book, aimed at children, but powerful and thought provoking enough for adults.Its a very slim volume, but the content and its ideas will sit with you for a very long time.

[juanjux_1 · Rating: 5 out of 5 stars]

Very interesting fantasy about worlds of one and two dimmensions and its inhabitants.

[millsge_1 · Rating: 4 out of 5 stars]

Who thought that Euclidean Geometry could be so much fun? This is a book that I have read many times since I first read it in the 9th grade; when we believed it was an esoteric work whose real meaning was about the reality of life in other dimensions. I even found myself in a long discussion with a retired Air Force colonel about the possibility and significance of multiple dimensions with multiple life-forms. The colonel was a kind and patient provocateur who gently brought me back to earth and in an almost Socratic manner helped me put the book and my thoughts about it in a more realistic perspective and one that was more in line with the intentions of the author. So, for me, the book is very special as it gave me a special friend who helped me through the many terrible things young boys with new-step fathers go through.

[jmattas_1 · Rating: 3 out of 5 stars]

The first part of this book, where the specifics of life in Flatland are explained, is boring and a bit awkward. It does give "life" to the inhabitants of that flat world and perhaps the rest of the book wouldn't be as captivating without it, but it feels like a kid ranting on about his cool new fantasy. Or perhaps I'm too informed in math to be thrilled by it. Actually I was disappointed by the "fog", I was expecting some motion-related means of identification.What strikes out from the description is of course the stiff class society. The idea of relating world views and actual worlds is great. I mean, how can one make a better point of someone's narrow-mindedness than exposing him to an infinitely larger world.The sphere refusing to understand or accept the possibility of higher dimensions is also a very strong scene. It can be viewed as a student questioning his mentor, who becomes aggressive, or as a reminder that although one has a reason to criticize another society, one's own is not perfect.

[aethercowboy · Rating: 5 out of 5 stars]

Set in a two-dimensional world that could be represented on a large sheet of paper, we meet A. Square, a free thinker in a land ruled by oppressive religious zealots who will hear nothing other than "the world is flat."One day, however, Square meets Sphere, and is bumped out of Flatland and sent on a multidimensional journey.If you've ever been interested in the mathematical concept of dimensions, and want any reason to believe that the fourth dimension is not time, per se, I suggest you read this book, as it will open your eyes to a whole new perspective by likening yourself to Square.

[lmichet_1 · Rating: 3 out of 5 stars]

This book was given an overview in a silly book from the 1960s which my father once gave to me-- it was a book of math puzzles and the like. That book, however, did not hint to me that Flatland is really more of a Victorian social commentary than a book about math. I enjoy creative books about math, like 'The Math Devil'. The Math Devil is one fine book.Anyway, Flatland is interesting, yes, but-- well-- it's Victorian social commentary! Not something I enjoy reading for the sake of itself. Victorian social commentary is fine when there's an interesting plot to be had, but using MATH to make Victorian social commentary more interesting? Hmm. Not exactly the best decision. But it's still good, and it's very easy to see why this is a classic. Everyone should get around to reading it at least once-- and it's so short that this shouldn't be a problem for anyone, really.

[wendyrey · Rating: 3 out of 5 stars]

Interesting novella, a sort of mixture of science fiction/social commentary and a Dummy's guide to dimensions and relativity.Very , very clever.

[csixty4 · Rating: 3 out of 5 stars]

I had such high hopes for this book. I figured any speculative fiction that stood the test of time so well must be something really special. Instead, I got porn for math geeks. The whole first half of the book, a description of the inhabitants of Flatland, might have been more interesting if the details were revealed through narrative, but the explanations and diagrams would make a good cure for insomnia. The second half was more interesting, and indeed the last bits were exciting. But the cost to get there was too much.

[antt-4 · Rating: 4 out of 5 stars]

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

[liberuno · Rating: 4 out of 5 stars]

I started reading this book thinking that I was just going to get a quick humorous read on geometry. I didn't expect a short story told from the point of view of a square in a plane to hold so many interesting questions ranging in subject: from metaphysics and religion to discrimination.This short book is definitely worth reading.

[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.

[hansel714_1 · Rating: 4 out of 5 stars]

Science fiction meets geometry meets fairy tale. It gets odder. Published in 1884, this has to be one of the first book that uses a story to illustrate principles of geometry. Part I describes the world of Flatland where all its inhabitants are shapes on a flat and very large piece of paper. Part II tells of a messiah, a 3D sphere, descending into Flatland and appearing to a Square. When the Square wants to spread the gospel of 3D, no one believes him. It's a political satire, social parody, philosophical argument, and scientific enlightment. How odd can that be.

[bratfarrar_1 · Rating: 4 out of 5 stars]

A bit dry, but an excellent way to get interested in geometry. Goes well with Euclid.

[masyukun · Rating: 5 out of 5 stars]

Have you ever had trouble visualizing what a high-dimensional space would look like? Have you considered what possibilities such a space would offer, and what it would be like to encounter a higher dimensional being?Abbott's Victorian age novel explores these questions through analogy. This is the story of the two-dimensional world of Flatland, and its inhabitants' encounters with a mysterious and powerful three-dimensional being. Humorous and entertaining, this is one math text everyone can enjoy.

[cuviper · Rating: 4 out of 5 stars]

The first part of Flatland is a little dry, but in Part II it gets into the exploration of dimensions and perceptions. The blatant sexism and classism seem ridiculous -- perhaps they are meant to show how limited thought can hold you back. By opening your mind to more liberal thoughts, new dimensions may be revealed to you. Or something. At any rate, it's a quick read, and carries amusing thoughts to ponder.

[psiloiordinary_1 · Rating: 4 out of 5 stars]

Political satire mixed with philosophical and scientific enlightenment.Interesting, thought provoking and very quick read

[thebooknerd · Rating: 2 out of 5 stars]

A classic--all fans of science fiction should read this book.

[legendaryneo · Rating: 4 out of 5 stars]

This is a short easy read, but within this simple work are ideas that are almost beyond our comprehension. A majority of this story takes place in a 2D world, but there is so much explanation as to how everything works in this world that you feel as if you are in this world. Putting yourself in a smaller dimension the 3 Dimensional world seems impossible, but we know its there. Therefore it makes you think...are there more dimensions?

[stormraven_1 · Rating: 3 out of 5 stars]

This short work is rooted in the English tradition of political dissent and social commentary through satire (see, for example, Swift). In this book, Abbott describes a two-dimensional world in which various shapes exist, living their two-dimensional lives. The status of a shape is determined by how many sides it has - the more sides, the more important a shape is. Females, who are simply straight lines, are of lowest status. Slightly higher than females are triangles, the lowest status male. As shapes get progressively more sides, they are also supposed to get progressively smarter and thus, those with 50 or 100 sides are the elite, and rule the others. Oddly, those with fewest sides (and thus sharp points) are the most lethal - to such an extent that houses are constructed so that females have their own door to enter and females are required to waggle back and forth and cry out to warn others of their approach (so they don't puncture anyone else with their sharp point).The book is a satire of class politics, gender, and social status in 19th century England. While it makes numerous insightful points, the weakness of the work is that its social commentary is so very heavy-handed. It is so blunt that it overwhelms any kind of story at times, and so obvious that it mutes its own effectiveness with a kind of shrillness. A little more subtlety would have made this work much more effective.

[optinik · Rating: 5 out of 5 stars]

i really enjoyed this book.It is about a two dimensional world, aptly named Flatland. A particularly intelligent square, called A. Square (known as Albert in Flatterland; like Flatland, but more so), atracts the intelligents of a sphere. The sad truth is that Flatland is two dimensional, but, with the right amount of effort, one can raise oneself up, and become three-dimensional. None of the Flatlanders ever achieved this demigod-like position, until A. Square does, with the help of the Sphere. However, he upsets the sphere, and the book ends with a tragedy; A. imprisoned, and his story dismissed as a hoax, ubtil he himself can only remember the mantra 'Upwards, not Northwards.'As interesting as a plot this is, the main reaon for the book being written is because it is a parody of Victorian society, with such concepts as sexism, blind pigheadedness in ignoring the third dimension and the superiority of the ruling classes are also present in Flatland.

[randulf-3 · Rating: 5 out of 5 stars]

A story told using simple geometry, brilliant! This is a journey of a 2D man into a 3D world and conveys much of the firm arrogance of Victorian society towards its scientific views, where to interrupt the set way of scientific thinking at that time, was tantamount to heresy. Perhaps not quite as an accessible subject as Alice in Wonderland, but this a fable of the same proprtions - elightening us to endless worlds of possibilities.