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

: OTHER WORLDS

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

writing.
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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

meaning.



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.





***





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

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."