Ciencia

Flatland
A romance of many dimensions
With Illustrations by the Author, A SQUARE
(Edwin A. Abbott 1838-1926)

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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 ofthat 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

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PREFACE TO THE SECOND AND REVISED EDITION,
1884. BY THE EDITOR
If my poor Flatland friend retainedthe 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 forcertain errors and misprints (for which, however, he isnot 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 thathis countrymen are not only long
and broad, but also (though doubtless in a very slight degree) thick or high. His 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 friend's answer appears to me completely to meet it.
"I admit," said he - when I mentioned to him this objection - "I admit thetruth of your critic's
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' then you can of your `extra-height'.Even I - who
have been in Spaceland, and have had the privilege of understanding for twenty-four hours the
meaning of `height' - even I cannot now comprehend it, nor realize 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 equallyand infinitesimally thick (or high, whichever you like);
consequently, there is nothing in them to lead our minds to the conception of that Dimension. No
`delicate micrometer' - as has been suggested by one too hasty Spaceland critic - would 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
friends - when I talk to them about the unrecognized Dimension which is somehow visible in a
Line - say, `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...