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How I Then Tried To Diffuse The Theory Of Three Dimensions By Other Means And Of The Result

From: Flatland

My failure with my Grandson did not encourage me to communicate my
secret to others of my household; yet neither was I led by it to
despair of success. Only I saw that I must not wholly rely on the
catch-phrase, "Upward, not Northward," but must rather endeavour to
seek a demonstration by setting before the public a clear view of the
whole subject; and for this purpose it seemed necessary to resort to

So I devoted several months in privacy to the composition of a treatise
on the mysteries of Three Dimensions. Only, with the view of evading
the Law, if possible, I spoke not of a physical Dimension, but of a
Thoughtland whence, in theory, a Figure could look down upon Flatland
and see simultaneously the insides of all things, and where it was
possible that there might be supposed to exist a Figure environed, as
it were, with six Squares, and containing eight terminal Points. But
in writing this book I found myself sadly hampered by the impossibility
of drawing such diagrams as were necessary for my purpose: for of
course, in our country of Flatland, there are no tablets but Lines, and
no diagrams but Lines, all in one straight Line and only
distinguishable by difference of size and brightness; so that, when I
had finished my treatise (which I entitled, "Through Flatland to
Thoughtland") I could not feel certain that many would understand my

Meanwhile my wife was under a cloud. All pleasures palled upon me; all
sights tantalized and tempted me to outspoken treason, because I could
not compare what I saw in Two Dimensions with what it really was if
seen in Three, and could hardly refrain from making my comparisons
aloud. I neglected my clients and my own business to give myself to
the contemplation of the mysteries which I had once beheld, yet which I
could impart to no one, and found daily more difficult to reproduce
even before my own mental vision. One day, about eleven months after
my return from Spaceland, I tried to see a Cube with my eye closed, but
failed; and though I succeeded afterwards, I was not then quite certain
(nor have I been ever afterwards) that I had exactly realized the
original. This made me more melancholy than before, and determined me
to take some step; yet what, I knew not. I felt that I would have been
willing to sacrifice my life for the Cause, if thereby I could have
produced conviction. But if I could not convince my Grandson, how
could I convince the highest and most developed Circles in the land?

And yet at times my spirit was too strong for me, and I gave vent to
dangerous utterances. Already I was considered heterodox if not
treasonable, and I was keenly alive to the danger of my position;
nevertheless I could not at times refrain from bursting out into
suspicious or half-seditious utterances, even among the highest
Polygonal or Circular society. When, for example, the question arose
about the treatment of those lunatics who said that they had received
the power of seeing the insides of things, I would quote the saying of
an ancient Circle, who declared that prophets and inspired people are
always considered by the majority to be mad; and I could not help
occasionally dropping such expressions as "the eye that discerns the
interiors of things," and "the all-seeing land"; once or twice I even
let fall the forbidden terms "the Third and Fourth Dimensions." At
last, to complete a series of minor indiscretions, at a meeting of our
Local Speculative Society held at the palace of the Prefect
himself,--some extremely silly person having read an elaborate paper
exhibiting the precise reasons why Providence has limited the number of
Dimensions to Two, and why the attribute of omnividence is assigned to
the Supreme alone--I so far forgot myself as to give an exact account
of the whole of my voyage with the Sphere into Space, and to the
Assembly Hall in our Metropolis, and then to Space again, and of my
return home, and of everything that I had seen and heard in fact or
vision. At first, indeed, I pretended that I was describing the
imaginary experiences of a fictitious person; but my enthusiasm soon
forced me to throw off all disguise, and finally, in a fervent
peroration, I exhorted all my hearers to divest themselves of prejudice
and to become believers in the Third Dimension.

Need I say that I was at once arrested and taken before the Council?

Next morning, standing in the very place where but a very few months
ago the Sphere had stood in my company, I was allowed to begin and to
continue my narration unquestioned and uninterrupted. But from the
first I foresaw my fate; for the President, noting that a guard of the
better sort of Policemen was in attendance, of angularity little, if at
all, under 55 degrees, ordered them to be relieved before I began my
defence, by an inferior class of 2 or 3 degrees. I knew only too well
what that meant. I was to be executed or imprisoned, and my story was
to be kept secret from the world by the simultaneous destruction of the
officials who had heard it; and, this being the case, the President
desired to substitute the cheaper for the more expensive victims.

After I had concluded my defence, the President, perhaps perceiving
that some of the junior Circles had been moved by evident earnestness,
asked me two questions:--

1. Whether I could indicate the direction which I meant when I used
the words "Upward, not Northward"?

2. Whether I could by any diagrams or descriptions (other than the
enumeration of imaginary sides and angles) indicate the Figure I was
pleased to call a Cube?

I declared that I could say nothing more, and that I must commit myself
to the Truth, whose cause would surely prevail in the end.

The President replied that he quite concurred in my sentiment, and that
I could not do better. I must be sentenced to perpetual imprisonment;
but if the Truth intended that I should emerge from prison and
evangelize the world, the Truth might be trusted to bring that result
to pass. Meanwhile I should be subjected to no discomfort that was not
necessary to preclude escape, and, unless I forfeited the privilege by
misconduct, I should be occasionally permitted to see my brother who
had preceded me to my prison.

Seven years have elapsed and I am still a prisoner, and--if I except
the occasional visits of my brother--debarred from all companionship
save that of my jailers. My brother is one of the best of Squares,
just sensible, cheerful, and not without fraternal affection; yet I
confess that my weekly interviews, at least in one respect, cause me
the bitterest pain. He was present when the Sphere manifested himself
in the Council Chamber; he saw the Sphere's changing sections; he heard
the explanation of the phenomena then give to the Circles. Since that
time, scarcely a week has passed during seven whole years, without his
hearing from me a repetition of the part I played in that
manifestation, together with ample descriptions of all the phenomena in
Spaceland, and the arguments for the existence of Solid things
derivable from Analogy. Yet--I take shame to be forced to confess
it--my brother has not yet grasped the nature of Three Dimensions, and
frankly avows his disbelief in the existence of a Sphere.

Hence I am absolutely destitute of converts, and, for aught that I can
see, the millennial Revelation has been made to me for nothing.
Prometheus up in Spaceland was bound for bringing down fire for
mortals, but I--poor Flatland Prometheus--lie here in prison for
bringing down nothing to my countrymen. Yet I existing the hope that
these memoirs, in some manner, I know not how, may find their way to
the minds of humanity in Some Dimension, and may stir up a race of
rebels who shall refuse to be confined to limited Dimensionality.

That is the hope of my brighter moments. Alas, it is not always so.
Heavily weights on me at times the burdensome reflection that I cannot
honestly say I am confident as to the exact shape of the once-seen,
oft-regretted Cube; and in my nightly visions the mysterious precept,
"Upward, not Northward," haunts me like a soul-devouring Sphinx. It is
part of the martyrdom which I endure for the cause of Truth that there
are seasons of mental weakness, when Cubes and Spheres flit away into
the background of scarce-possible existences; when the Land of Three
Dimensions seems almost as visionary as the Land of One or None; nay,
when even this hard wall that bars me from my freedom, these very
tablets on which I am writing, and all the substantial realities of
Flatland itself, appear no better than the offspring of a diseased
imagination, or the baseless fabric of a dream.



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
imprisonment, 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 implies 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. 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 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-Cubes--we 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.'" (footnote 1)

On this point the defence 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 Nature's 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 defence 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 (see page 86) 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.

In a still more obscure passage he now desires to disavow the Circular
or aristocratic tendencies with which some critics have naturally
credited him. While doing justice to the intellectual power with which
a few Circles have for many generations maintained their supremacy over
immense multitudes of their countrymen, he believes that the facts of
Flatland, speaking for themselves without comment on his part, declare
that Revolutions cannot always be suppressed by slaughter, and that
Nature, in sentencing the Circles to infecundity, has condemned them to
ultimate failure--"and herein," he says, "I see a fulfilment of the
great Law of all worlds, that while the wisdom of Man thinks it is
working one thing, the wisdom of Nature constrains it to work another,
and quite a different and far better thing." For the rest, he begs his
readers not to suppose that every minute detail in the daily life of
Flatland must needs correspond to some other detail in Spaceland; and
yet he hopes that, taken as a whole, his work may prove suggestive as
well as amusing, to those Spacelanders of moderate and modest minds
who--speaking of that which is of the highest importance, but lies
beyond experience--decline to say on the one hand, "This can never be,"
and on the other hand, "It must needs be precisely thus, and we know
all about it."

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