The Spectator (November 29, 1884), pp. 1583--1584.

Flatland : a Romance of Many Dimensions.
A Square. London: Seeley and Co.

Strange are the tales of travelers, decisive the effect of experience upon previous speculations, and marvelously appropriate the morals brought home from outlandish quarters. Such are the reflections suggested by the attractive little book now before us. It tells of a region more unfamiliar than that of giants or pygmies, of anthropophagi, or men whose heads do grow beneath their shoulders. It throws a light on the question of the nature of space, which will be eagerly welcomed by seekers after a Fourth Dimension; and it proves that the institutions and failings of the race which inhabits the strangest countries bear a curiously perverted resemblance to those of our own.

Mathematicians have long speculated on the nature of space, and some have even questioned its universality. While rejoicing in the fact that their hands were free to move upwards as well as sideways, they have speculated on the possibility of worlds whose inhabitants should to be limited in their movements to the three prosaic directions of forwards, sideways, and upwards. They have lamented over the absence of the invaluable sense which would enable a man to get out of a closed cage without passing through the top, the sides, or the bottom, and to read all the contents of a shut book without touching its cover. They have hoped in a future state to enjoy an extended felicity in Space of Four Dimensions. They have dreaded the worse than flat-fish fate of being eternally confined to a limbo of two. These comfortable doctrines have long been a speculation and a pious opinion to the few, and a stumbling-block and foolishness to the uninitiated. They will receive a fresh impulse from the works of the adventurous traveler whose melancholy history is now before us. It is true that he cannot tell of a world of Four Dimensions. What he describes is almost as wonderful and more intelligible. He depicts life in which there is no possibility of sideways motion, a world where a man meeting another in the street cannot pass him except by jumping over his head, a world which would look to us only a large-sized map, and men who would appear moving anatomical diagrams. Such is his native world, but to that world he has not been confined. He tells of his mysterious and painful initiation into the larger world of Three Dimensions. He tells us, too, of his vision of the world whose universe was confined to a line, and of his contempt for the beings whose range appeared to him as limited as those of his own countrymen appear to us. He tells of the still more limited being, itself its own universe, whose conceptions were limited to the point which itself occupied. These unique experiences he dedicates to the inhabitants of space in general, in the laudable hope of ``thereby contributing to the enlargement of the imagination and the possible development of that most rare and excellent gift of modesty among the superior races of solid humanity.''

For a full description of these new worlds, their optics and physics, their ethics and politics, we must refer to the treatise of our author. Flatland is inhabited by a race whose shape is that of geometrical figures. The women are straight lines, the men vary from triangles in the lower orders to circles in the highest. Regularity of figure is the fundamental fact upon which the whole social life of Flatland rests, and is enforced upon the race by legislation as stern as that of Pharaoh. The other social problems, including the position of women, the shape of houses, the education of children, and the suppression of useless speculation, are dealt with in an equally drastic spirit. We will give an example, which will at the same time show the liberal spirit of the author.: ---

``About three hundred years ago, it was decreed by the Chief Circle that, since women are deficient in Reason but abundant in Emotion, they ought no longer to be treated as rational, nor receive any mental education. The consequence was that they were no longer taught to read, nor even to master Arithmetic enough to enable them to count the angles of their husband or children; and hence they sensibly declined during each generation in intellectual power. And this system of female non-education or quietism still prevails. My fear is that, with the best intentions, this policy has been carried so far as to react injuriously on the Male Sex. For the consequence is that, as things now are, we Males have to lead a kind of bi-lingual, and I may almost say bi-mental existence. With the Women, we speak of `love,' `duty,' `right,' `wrong,' `pity,' `hope,' and other irrational and emotional conceptions, which have no existence, and the fiction of which has no object expect to control feminine exuberances; but among ourselves, and in our books, we have an entirely different vocabulary and I may almost say, idiom. `Love' then becomes `the anticipation of benefits;' `duty' becomes `necessity' or `fitness;' and other words are correspondingly transmuted. Moreover, among Women, we use language implying the utmost deference for their Sex; and they fully believe that the Chief Circle Himself is not more devoutly adored by us than they are; but behind their backs they are both regarded and spoken of --- by all except the very young --- as being little better than `mindless organisms.' Our Theology also in the Women's chambers is entirely different from our Theology elsewhere. Now my humble fear is that this double training, in language as well as in thought, imposes somewhat too heavy a burden upon the young, especially when, at the age of three years old, they are taken from the maternal care and taught to unlearn the old language --- except for the purpose of repeating it in the presence of their Mothers and Nurses --- and to learn the vocabulary and idiom of science. Already methinks I discern a weakness in the grasp of mathematical truth at the present time as compared with the more robust intellect of our ancestors three hundred years ago. I say nothing of the possible danger if a Woman should ever surreptitiously learn to read and convey to her Sex the result of her perusal of a single popular volume; nor of the possibility that the indiscretion of disobedience of some infant Male might reveal to a Mother the secrets of the logical dialect. On the simple ground of the enfeebling oft eh Male intellect, I rest this humble appeal to the highest Authorities to reconsider the regulations of Female Education.''

But the chief interest will lie in the initiation of our author into the mystery of the Third Dimension. In the matter-of-fact account of the unintelligible entrance into Flatland, of the terrible Sphere from whom no secrets were hid, there is a weird suggestiveness of the possibilities that beset us, and of a catastrophe that might at any moment, for anything we know to the contrary, befall ourselves. The Sphere enters the room, where all doors are shut, on a disinterested mission of enlightenment, and the climax of the interview, as narrated by the Square, is as follows:---

``It was in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping from my contact; not edging to the right nor to the left, but moving somehow out of the world and vanishing to nothing. Soon there was a blank. But I still heard the Intruder's voice.

Sphere. Why will you refuse to listen to reason? I had hoped to find in you --- as being a man of sense and an accomplished mathematician --- a fit apostle for the Gospel of the Three Dimensions, which I am allowed to preach once only in a thousand years: but now I know not how to convince you. Stay, I have it. Deeds, and not words, shall proclaim the truth. Listen, my friend. I have told you I can see from my position in Space the inside of all things that you consider closed. For example, I see in yonder cupboard near which you are standing several of what you call boxes (but like everything else in Flatland, they have no tops or bottoms) full of money; I see also two tablets of accounts. I am about to descend into that cupboard, and to bring you one of those tablets. I saw you lock the cupboard half an hour ago, and I know you have the key in your possession. But I descend from Space; the doors, you see, remain unmoved. Now I am in the cupboard, and am taking the tablet. Now I have it. Now I ascend with it. I rushed to the closet and dashed the door open. One of the tablets was gone. With a mocking laugh, the Stranger appeared in the other corner of the room, and at the same time the tablet appeared upon the floor. I took it up. There could be no doubt --- it was the missing tablet. I groaned with horror, doubting whether I was not out of my sense, but the Stranger continued:--- `Surely you must now see that my explanation, and no other, suits the phenomena. What you call Solid things are really superficial; what you call Space is really nothing but a great Plane. I am in Space, and look down upon the insides of things of which you only see the outsides. You could leave this Plane yourself if you could but summon up the necessary volition. A slight upward or downward motion would enable you to see all that I can see. The higher I mount, and the further I go from your Plane, the more I can see, though of course I see it on a smaller scale. For example, I am ascending; now I can see your neighbour the Hexagon and his family in their several apartments; now I see only just departing; and on the other side a Circle in his study, sitting at his books. Now I shall come back to you. And, as a crowning proof, what do you say to my giving you a touch, just the least touch, in our stomach? It will not seriously injure you, and the slight pain you may suffer cannot be compared with the mental benefit you will receive.' Before I could utter a word of remonstrance, I felt a shooting pain in my inside, and a demonical laugh seemed to issue from within me. A moment afterwards the sharp agony had ceased, leaving nothing but a dull ache behind, and the Stranger began to reappear, saying, as he gradually increased in size, `There, I have not hurt you much, have I? If you are not convinced now, I don't know what will convince you. What say you?' ''

Conviction, as might be expected, is only produced by hurling the unfortunate Square out of his plane; but for his feelings in the new world to which he is so unceremoniously introduced, and for the unfortunate results of his subsequent futile attempts to explain his experiences to his fellow-countrymen, we have no room.

The book has obviously been a source of much pleasure to the writer, and may be safely recommended to any mathematician fond of paradox. It is very pleasantly got-up in paper, print, and cover. Much of it will also be read with amusement, as satire, by those who do not appreciate its scientific bearing, or as pure nonsense by those who are not searching for satire. The chief fault we have to find is a want of proportion by which one or two rather heavy dissertations, such as that upon sight recognition, occupy an unnecessary and alarming amount of space. The assumption of the author is worked out with wonderful consistency, and his mathematics are thoroughly sound, though they are disfigured by two or three slips in the use of technical terms.