Preface to the Revised Second Edition, 1884

6 min

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.

If my poor Flatland friend still had the mental strength he enjoyed when he began writing these Memoirs, I would not need to speak for him in this preface. He has three wishes. First, he wants to thank his readers and critics in Spaceland. Their appreciation has made a second edition of his work necessary sooner than expected. Second, he wants to apologize for certain errors and misprints, though he is not entirely responsible for them. Third, he wants to clear up one or two misunderstandings. But he is not the Square he once was. Years of imprisonment have combined with the even heavier burden of widespread disbelief and mockery, and the natural decline of old age. Together, these have erased many thoughts and ideas from his mind. He has also forgotten much of the terminology he learned during his short stay in Spaceland. He has therefore asked me to answer two specific objections on his behalf. One is intellectual, and the other is moral.

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.

The first objection is this: when a Flatlander sees a Line, it must look THICK as well as LONG. Otherwise, without some thickness, the Line would not be visible. So, the argument goes, he ought to admit that his countrymen are not only long and broad. They must also be THICK or HIGH, though doubtless only very slightly. This objection seems reasonable, and Spacelanders find it almost impossible to resist. So I confess that when I first heard the objection, I did not know how to answer. But my poor old friend's answer seems to me to address the objection completely.

"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.

"I admit," he said when I mentioned this objection to him, "I admit your critic's facts are true. But I reject his conclusions. We really do have a Third Dimension in Flatland called 'height', though we do not recognize it. Just as truly, you have a Fourth Dimension in Spaceland that you do not recognize. Your Fourth Dimension has no name yet, but I will call it 'extra-height'. But we can no more perceive our 'height' than you can perceive your 'extra-height'. Even I have been in Spaceland and had the privilege of understanding the meaning of 'height' for twenty-four hours. Yet even I cannot understand 'height' now, or grasp it through sight or any process of reasoning. I can grasp it only through 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.

"The reason is obvious. Dimension implies direction, direction implies measurement, and measurement implies more and less. Now, all our lines are EQUALLY and INFINITESIMALLY thick (or high, whichever you prefer). So nothing in our lines leads us to imagine that Dimension. One overly hasty Spaceland critic has suggested using a 'delicate micrometer'. But no such instrument would help us at all. We would not know WHAT TO MEASURE, NOR IN WHAT DIRECTION. When we see a Line, we see something long and BRIGHT. BRIGHTNESS, like length, is necessary for a Line to exist. If the brightness disappears, the Line goes out. So I tell all my Flatland friends about the unrecognized Dimension that is somehow visible in a Line. They say, 'Ah, you mean BRIGHTNESS'. When I reply, 'No, I mean a real Dimension', they immediately answer, 'Then measure it, or tell us in what direction it extends'. Their answer silences me, because I can do neither. Only yesterday, the Chief Circle came to inspect the State Prison and paid me his seventh annual visit. The Chief Circle is our High Priest. For the seventh time, he asked me, 'Was I any better?' I tried to prove 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—

"Does this still seem strange to you? Then imagine yourself in a similar position. Suppose a person from the Fourth Dimension lowered himself to visit you and said, 'Whenever you open your eyes, you see a Plane (which has Two Dimensions). You INFER a Solid (which has Three). But you also see a Fourth Dimension, though you do not recognize it. This Fourth Dimension is not colour or brightness or anything like that. It is a true Dimension, although I cannot show you its direction, nor can you possibly measure it.' What would you say to such a visitor? Wouldn't you have him locked up? Well, that is my fate. For us Flatlanders, locking up a Square for preaching the Third Dimension is just as natural. It is no different from you Spacelanders locking up a Cube for preaching the Fourth. Alas, how much blind, persecuting humanity resembles one family across all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes, we are all prone to the same errors. We are all equally Slaves to the prejudices of our own Dimensions, as one of your Spaceland poets has said:"

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

'One touch of nature makes all worlds feel like family'."

[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.]

[Note: The Author asks me to add that some of his critics have misunderstood this matter. Because of their misunderstanding, he has added some relevant remarks to his dialogue with the Sphere. He had previously left out these remarks because he thought they were 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.

On this point, the Square’s defence seems to me impossible to challenge. I wish his answer to the second (or moral) objection were equally clear and convincing. Critics have accused him of hating women. The accusation has been pressed fiercely by those whom Nature has made the somewhat larger half of the Spaceland race. I would like to answer the accusation, as far as I honestly can. But the Square is unfamiliar with Spaceland’s language of morality. I would therefore do him an injustice by copying his defence against this charge word for word. Instead, I will interpret and summarize his answer. I gather that during his seven years in prison, he has changed his personal views. These changes concern both Women and the Isosceles or Lower Classes. Personally, he now leans toward the Sphere’s opinion that Straight Lines are superior to Circles in many important respects. But as a Historian, he has adopted the views generally held by Flatland Historians, perhaps too closely. He has been told that even Spaceland Historians generally share these views. Until very recently, their histories have seldom treated the fates of Women and the masses of mankind as worth mentioning. They have never treated those fates as deserving 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."

In an even less clear passage, he now denies the Circular or aristocratic leanings some critics have naturally attributed to him. He acknowledges the intellectual power of the few Circles who have ruled vast numbers of their countrymen for many generations. Yet he believes the facts of Flatland speak for themselves, without his commentary. They show that Revolutions cannot always be crushed by slaughter. They also show that Nature, by condemning the Circles to infertility, has doomed them to eventual failure. "And in this," he says, "I see the great Law of all worlds fulfilled. While human wisdom thinks it is achieving one thing, Nature's wisdom forces it to achieve another. The result is quite different and far better." He also asks his readers not to assume that every tiny detail of daily life in Flatland must match a detail in Spaceland. Still, he hopes his work as a whole may offer food for thought as well as amusement. He hopes it will do so for those Spacelanders whose minds are measured and modest. When discussing matters of the greatest importance that lie beyond experience, these readers refuse to take either extreme. They will neither say, "This can never be," nor insist, "It must be exactly like this, and we know all about it."