Flatland: A Romance of Many Dimensionsby Edwin A. Abbott
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With wry humor and penetrating satire, Flatland takes us on a mind-expanding journey into a different world to give us a new vision of our own. A. Square, the slightly befuddled narrator, is born into a place which is limited to two dimensionsirrevocably flatand peopled by a hierarchy of geometrical forms. In a Gulliver-like tour of his bizarre homeland, A. Square spins a fascinating tale of domestic drama and political turmoil, from sex among consenting triangles to the intentional subjugation of Flatland's females. He tells of visits to Lineland, the world of one dimension, and Pointland, the world of no dimension. But when A. Square dares to speak openly of a third, even a fourth dimension, his tragic fate climaxes a brilliant parody of Victorian society.
An underground favorite since its publication in England in 1884, Flatland is as prophetic a science-fiction classic as the works of H.G. Wells, introducing aspects of relativity and hyperspace years before Einstein's famous theories, and it does so with a wonderful, enduring enchantment.
This reprint of Abbott's Flatland adventures contains an Introduction 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.
"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 Introduction 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
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Part One This World
"Be patient, for the world is broad and wide."
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 you 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 lastwhen you have placed your eye exactly on the edge of the table (so that you are, as it were, actually a Flatlander) 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. I 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 towards 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 closer 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.Flatland. Copyright © by Edwin Abbott. Reprinted by permission of HarperCollins Publishers, Inc. All rights reserved. Available now wherever books are sold.
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Meet the Author
Edwin A. Abbott (1838–1926), a Victorian of great intellect and wit, enjoyed success not only as a writer, but as a scholar, educator, and theologian. Educated at St. John’s College, Cambridge, he was Headmaster of the City of London School from 1865 to 1889. During that time, his progressive belief in the importance of the study of English for every student, even before traditional classic curriculum, led him to write A Shakespearian Grammar (1870) “to help solve most of the difficulties that will present themselves to boys.” It ran to three editions within its first year of publication alone and continues to be a touchstone for Shakespearean scholars. In 1884, he wrote Flatland. First considered by many as merely “a pleasant tonic, and an excellent stimulant for boys,” it was later recognized as a magnificent work of science fiction, as prophetic as those of Jules Verne and H. G. Wells. Retiring to a scholarly life in 1889, he produced numerous other works, including Silanus the Christian (1907), Apologia: An Explanation and Defense (1907), Message of the Son of Man (1909), and Light on the Gospel from an Ancient Poet (Odes of Solomon) (1913).
Valerie M. Smith earned her PhD from the University of Connecticut. An associate professor of English at Quinnipiac University in Hamden, Connecticut, she is currently at work on a manuscript entitled Crossroads: Cultural Autobiography and Imperial Discourse.
John Allen Paulos is a Professor of Mathematics at Temple University and the bestselling author of eight books including Innumeracy, A Mathematician Reads the Newspaper, and Once upon a Number. He has been a columnist for ABCNews.com, Scientific American, and the Guardian, as well as the author of numerous reviews, articles, and op-ed pieces for a variety of publications. Among his many honors are the American Association for the Advancement of Science Award for Promoting Public Understanding of Science and the 2013 Mathematics Communication Award from the Joint Policy Board for Mathematics.
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