Flatland: A Romance of Many Dimensions

by Edwin A. Abbott

Overview

This masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square, a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.
Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.

Product Details

ISBN-13:	9780486272634
Publisher:	Dover Publications
Publication date:	09/21/1992
Series:	Dover Thrift Editions: Classic Novels
Edition description:	REV
Pages:	96
Product dimensions:	4.90(w) x 7.80(h) x 0.30(d)
Age Range:	14 - 18 Years

About the Author

Fifty Years in the Flatland
2012 will mark the 50th anniversary in print with Dover of one of the most significant and influential books of the past century and a half. The mathematical, satirical, and religious allegory Flatland by a little-known but immensely prolific Victorian English schoolmaster and theologian Edwin Abbott Abbott, was first published anonymously in England in 1884 — Abbott wrote it under the name "A Square." The unique geometrical romance which is Flatland posited a world and its inhabitants that exist in only two dimensions and forces the reader captivated by the originality of this central idea to think deeply about the meaning of such a world. Generations of readers and students swept into the romance and fascination of geometry and other branches of mathematics and philosophy owe their introduction to this world to Flatland, which continues to entertain and stimulate new readers today, still going strong 126 years after the first edition was launched. Abbott revised the text somewhat for a second edition published just a few months after the first. Dover's 1952 edition was the first American reprinting of the amended second English edition and was published with a new Introduction by physicist Banesh Hoffmann.

From the Book:
"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."

Read an Excerpt

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.

Table of Contents

Section 1: Of the Nature of Flatland ..... 3
Section 2: Of the Climate and Houses in Flatland ..... 5
Section 3: Concerning the Inhabitants of Flatland ..... 7
Section 4: Concerning the Women ..... 10
Section 5: Of Our Methods of Recognizing One Another ..... 14
Section 6: Of Recognition by Sight ..... 18
Section 7: Concerning Irregular Figures ..... 22
Section 8: Of the Ancient Practice of Painting ..... 25
Section 9: Of the Universal Colour Bill ..... 28
Section 10: Of the Suppression of the Chromatic Sedition ..... 31
Section 11: Concerning Our Priests ..... 34
Section 12: Of the Doctrine of Our Priests ..... 37

Part II: Other Worlds ..... 41

Section 13: How I Had a Vision of Lineland ..... 43
Section 14: How I Vainly Tried to Explain the Nature of Flatland ..... 47
Section 15: Concerning a Stranger from Spaceland ..... 52
Section 16: How the Stranger Vainly Endeavoured to Reveal to Me in Words the Mysteries of Spaceland ..... 55
Section 17: How the Sphere, Having Vain Tried Words, Resorted to Deeds ..... 62
Section 18: How I Came to Spaceland, and What I Saw There ..... 64
Section 19: How, Though the Sphere Shewed Me Other Mysteries of Spaceland, I Still Desired More; and What Came of it ..... 68
Section 20: How the Sphere Encouraged Me in a Vision ..... 74
Section 21: How I Tried to Teach the Theory of Three Dimensions to My Grandson, and with What Success ..... 77
Section 22: How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result ..... 79

What People are Saying About This

Isaac Asimov

The best introduction one can find into the manner of perceiving dimensions. (From the Forward)

Editorial Reviews

The best introduction one can find into the manner of perceiving dimensions.
— The Forward

Asimov

"This pre-Einstein geometrical fantasy is one of the best things of its kind that has ever been written, for it is more than an ingeniously sustained fantasy: it is a social satire, with wit as sharp as the sub-lutrous end of a Flatland woman; it is an easy philosophical introduction to the Fourth Dimension; and it is a rebuke to everyone who holds that there is no reality beyond what is perceptible by human senses."

Saturday Review

The best introduction one can find into the manner of perceiving dimensions.
— The Forward

Isaac Asimov

[An] attractive little book…It throws a light on the question of the nature of space, which will be eagerly welcomed by seekers after a Fourth Dimension; and it proves that the institutions and failings of the race which inhabits the strangest countries bear a curiously perverted resemblance to those of our own.”

Spectator (UK)

With so much wit and grace of style is this clever satire on the limits of our knowledge wrought out that we shall not be surprised to see it take a permanent place in literature.”

Literary World (London)

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 Database

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

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

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

"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

From the Publisher