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PREFACE TO THE
SECOND AND REVISED
EDITION, 1884.
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, fully, to
return his thanks to his readers and critics in Spaceland, whose
appreciation has, with unexpected celerity, required a second edition
of this work; secondly, to apologize for certain errors and misprints
(for which, however, he is not entirely responsible); and, thirdly, to
explain on or two misconceptions. But he is not the Square he once
was. Years of inprisonment, and the still heavier burden of general
incredulity and mockery, have combined with 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 friend's
answer appears to me completely to meet it.
"I admit," said he -- when I mentioned to him this objection -- "I
admit the truth 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 also is 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 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 implied direction, implies
measurement, implies the more and the less. Now, all our lines are
_equally_ and _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.