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Preface

Edwin A. Abbott (1838-1926)

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, 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 in 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 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 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 your

Spaceland poets has said --



     'One touch of Nature makes all worlds akin'."



[Note:  The Author desires me to add, that the misconception of some

of his critics on this matter has induced him to insert in his

dialogue with the Sphere, certain remarks which have a bearing

on the point in question, and which he had previously omitted

as being tedious and unnecessary.]



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 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."













CONTENTS:







PART I:  THIS WORLD



Section



   1.  Of the Nature of Flatland

   2.  Of the Climate and Houses in Flatland

   3.  Concerning the Inhabitants of Flatland

   4.  Concerning the Women

   5.  Of our Methods of Recognizing one another

   6.  Of Recognition by Sight

   7.  Concerning Irregular Figures

   8.  Of the Ancient Practice of Painting

   9.  Of the Universal Colour Bill

  10.  Of the Suppression of the Chromatic Sedition

  11.  Concerning our Priests

  12.  Of the Doctrine of our Priests



PART II:  OTHER WORLDS



  13.  How I had a Vision of Lineland

  14.  How I vainly tried to explain the nature of Flatland

  15.  Concerning a Stranger from Spaceland

  16.  How the Stranger vainly endeavoured to reveal to me

         in words the mysteries of Spaceland

  17.  How the Sphere, having in vain tried words,

         resorted to deeds

  18.  How I came to Spaceland, and what I saw there

  19.  How, though the Sphere shewed me other mysteries

         of Spaceland, I still desired more; and what came of it

  20.  How the Sphere encouraged me in a Vision

  21.  How I tried to teach the Theory of Three Dimensions

         to my Grandson, and with what success

  22.  How I then tried to diffuse the Theory

         of Three Dimensions by other means, and of the result

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This World Wide Web document is a personal research project motivated by the following claim: "Truth is the object of Knowledge of whatever kind; and when we inquire what is meant by Truth, I suppose it is right to answer that Truth means facts and their relations, which stand towards each other pretty much as subjects and predicates in logic. All that exists, as contemplated by the human mind, forms one large system or complex fact, and this of course resolves itself into an indefinite number of particular facts, which, as being portions of a whole, have countless relations of every kind, one towards another." (The Idea of a University, John Henry Newman, 1801-1890)


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