Abbott Edwin Abbott - Flatland: a romance of many dimensions

Fie, fie, how franticly I square my talk!

Flatland

A Romance of Many Dimensions

EDWIN ABBOTT ABBOTT (18381926)

With an introduction by THOMAS BANCHOFF

PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD

Introduction copyright 1991 by Princeton University Press
Published by Princeton University Press,
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New Princeton Science Library paperback printing, 2015

New Paperback ISBN 978-0-691-16555-4

The Library of Congress Control cataloged the 1991 edition as follows

Abbott, Edwin Abbott, 18381926.

Flatland : a romance of many dimensions / Edwin Abbott Abbott ; with a new introduction by Thomas Banchoff.

p. cm.-(Princeton science library)

Reprint. Originally published:

6th ed. New York : Dover Publications, 1953.

ISBN: 978-0-691-12366-0

1. Fourth dimension. I. Title. II. Series.

[QA699.A13 1991] 530.11-dc20 9028266

British Library Cataloging-in-Publication Data is available

This book has been composed in Adobe Garamond Pro
Printed on acid-free paper.
Printed in the United States of America

1 3 5 7 9 10 8 6 4 2

To

The Inhabitants of SPACE IN GENERAL

And H. C. IN PARTICULAR

This Work is Dedicated

By a Humble Native of Flatland

In the Hope that

Even as he was Initiated into the Mysteries

Of THREE Dimensions

Having been previously conversant

With ONLY Two

So the Citizens of that Celestial Region

May aspire yet higher and higher

To the Secrets of FOUR FIVE OR EVEN SIX Dimensions

Thereby contributing

To the Enlargement of THE IMAGINATION

And the possible Development

Of that most rare and excellent Gift of MODESTY

Among the Superior Races

Of SOLID HUMANITY

PREFACE to the Second and Revised Edition By the Editor

If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these Memoirs, I should not now need to represent him in this Preface, in which he desires, firstly, to return his thanks to his readers and critics in Spaceland, whose appreciation has, with unexpected celerity, required a second edition of his work; secondly, to apologize for certain errors and misprints (for which, however, he is not entirely responsible); and, thirdly, to explain one or two misconceptions. But he is not the Square he once was. Years of imprisonment, and the still heavier burden of general incredulity and mockery, have combined with the natural decay of old age to erase from his mind many of the thoughts and notions, and much also of the terminology, which he acquired during his short stay in Spaceland. He has, therefore, requested me to reply in his behalf to two special objections, one of an intellectual, the other of a moral nature.

The first objection is, that a Flatlander, seeing a Line, sees something that must be thick to the eye as well as long to the eye (otherwise it would not be visible, if it had not some thickness); and consequently he ought (it is argued) to acknowledge that his countrymen are not only long and broad, but also (though doubtless to a very slight degree) thick or high. This objection is plausible, and, to Spacelanders, almost irresistible, so that, I confess, when I first heard it, I knew not what to reply. But my poor old friends answer appears to me completely to meet it.

I admit, said hewhen I mentioned to him this objectionI admit the truth of your critics facts, but I deny his conclusions. It is true that we have really in Flatland a Third unrecognized Dimension called height, just as it is also true that you have really in Spaceland a Fourth unrecognized Dimension, called by no name at present, but which I will call extra-height. But we can no more take cognizance of our height than you can of your extra-height. Even Iwho have been in Spaceland, and have had the privilege of understanding for twenty-four hours the meaning of heighteven I cannot now comprehend it, nor realise it by the sense of sight or by any process of reason: I can but apprehend it by faith.

The reason is obvious. Dimension implies direction, implies measurement, implies the more and the less. Now, all our lines are equally and infinitestimally thick (or high, whichever you like); consequently, there is nothing in them to lead our minds to the conception of that Dimension. No delicate micrometeras has been suggested by one too hasty Spaceland criticwould in the least avail us; for we should not know what to measure, nor in what direction. When we see a Line, we see something that is long and bright; brightness, as well as length, is necessary to the existence of a Line; if the brightness vanishes, the Line is extinguished. Hence, all my Flatland friendswhen I talk to them about the unrecognized Dimension which is somehow visible in a Linesay, Ah, you mean brightness: and when I reply, No, I mean a real Dimension, they at once retort, Then measure it, or tell us in what direction it extends: and this silences me, for I can do neither. Only yesterday, when the Chief Circle (in other words our High Priest) came to inspect the State Prison and paid me his seventh annual visit, and when for the seventh time he put me the question, Was I any better? I tried to prove to him that he was high, as well as long and broad, although he did not know it. But what was his reply? You say I am high; measure my high-ness and I will believe you. What could I do? How could I meet his challenge? I was crushed; and he left the room triumphant.

Does this still seem strange to you? Then put yourself in a similar position. Suppose a person of the Fourth Dimension, condescending to visit you, were to say, Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you infer a Solid (which is of Three); but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it! What would you say to such a visitor? Would not you have him locked up? Well, that is my fate: and it is as natural for us Flatlanders to lock up a Square for preaching the Third Dimension, as it is for you Spacelanders to lock up a Cube for preaching the Fourth. Alas, how strong a family likeness runs through blind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubeswe are all liable to the same errors, all alike the Slaves of our respective Dimensional prejudices, as one of our Spaceland poets has said

One touch of Nature makes all worlds akin.

On this point the defense of the Square seems to me to be impregnable. I wish I could say that his answer to the second (or moral) objection was equally clear and cogent. It has been objected that he is a woman-hater, and as this objection has been vehemently urged by those whom Natures decree has constituted the somewhat larger half of the Spaceland race, I should like to remove it, so far as I can honestly do so. But the Square is so unaccustomed to the use of the moral terminology of Spaceland that I should be doing him an injustice if I were literally to transcribe his defense against this charge. Acting, therefore, as his interpreter and summarizer, I gather that in the course of an imprisonment of seven years he has himself modified his own personal views, both as regards Women and as regards the Isosceles or Lower Classes. Personally, he now inclines to the opinion of the Sphere that the Straight Lines are in many important respects superior to the Circles. But, writing as a Historian, he has identified himself (perhaps too closely) with the views generally adopted by Flatland, and (as he has been informed) even by Spaceland, Historians; in whose pages (until very recent times) the destinies of Women and of the masses of mankind have seldom been deemed worthy of mention and never of careful consideration.