Flatland : A Romance of many Dimensions.

 With illustrations by the author, A SQUARE. London : Seeley and Co. 1885.

Speaking in parables has been a favourite method with many teachers. It has the advantage of the pleasant surprise that follows a little preliminary deception, and the mind of the learner is stimulated into activity when he finds that what he thought was a pleasant story is only the vehicle for a serious moral. But there are people who can read through allegories without seeing that there is any moral at all. When "Sartor Resartus" was coming out in Fraser, a nobleman wrote to the editor to ask when that stupid story about the tailor would be finished. Such readers have eyes, but they see not. They follow the grammar and the outer sense, but the inner sense is hidden from their eyes.

It is possible that the writer of "Flatland" may have readers who will go right through his book, and think it nothing but a droll idea, for he has not troubled himself to make his purpose too obtrusive, having apparently no ambition that every reader should understand him at once, and content to be appreciated by the esoteric circle. He might have taken for his motto Hamlet's thoughtful remark on his first intercourse with the world beyond the grave, " There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy ; " for the object is to show how unscientific it is to assume that our world is the only world, that the limits of our knowledge are the limits of all knowledge, and that the conditions under which we live are the only existing and the only possible conditions. Instead of indicting a solemn and formal treatise to stall, illustrate, and enforce this doctrine he indulges himself in a quaint conceit, and gets into the mind of his reader, not by way of the reason, but by way of the imagination. The author of this book is supposed to be a native of Flatland; that is, of a land in which there are only two dimensions, length and breadth, and where nothing more is known or dreamt of. To keep up this fancy, the writer goes into a number of minute details as to the superficial shape of the various social classes, and of the method by which triangles, squares, polygons, circles, &c, recognise each other, and carry on all the business of life. Minute descriptions, almost worthy of Defoe, are mixed up with sarcastic allusions to our own customs not unworthy of Swift, though free from the vicious malice of the celebrated Dean.

After completing his description of the country of Flatland, the author has a vision which gives him what we all so dearly love—a delicious indulgence in the sense of superiority. He is taken into a country of only one dimension, namely, the straight line, but where after overcoming his own first difficulty of understanding how there can be such a country, he tries to make the king of it understand the possibility of there being two dimensions, and of course fails. " Outside his world of line, all was a blank to him ; nay not even a blank, for blank implies space —say rather all was non-existent." To the visitor's elaborate explanation, and even attempt at illustration to prove that there are two-dimensions, the monarch of Lineland replies, " If you had a particle of sense you would listen to reason. You ask me to believe that there is another line besides that which my senses indicate, and another motion besides that of which I am daily conscious. I, in return, ask you to describe in words, or indicate by motion, that other line of which you speak. Instead of moving you merely exercise some magic art of vanishing and returning to sight, and instead of any lucid description of your new world, you simply tell me the numbers and sizes of 40 of my retinue ; facts known to any child in any capital. Can anything be more irrational or audacious ? Acknowledge your folly or depart from my dominions." In angry protest at this ignorant perversity he wakes from his dream.

His next experience is not in vision, but by actual fact, and instead of lamenting the inexpansiveness of the minds of others, he has to submit to be scolded, and ridiculed, and taught in his turn. By way of preliminary teaching, his grandson, a sharp young mathematician, after being taught that geometry has only two dimensions, the one by a point moving to make a line, and, the other by a line moving to make a superficial figure, asks with the inconvenient precocity of childhood why a square should not move and make something else. The parental reply was, " Go to bed. If you would talk less nonsense you would remember more sense." Then, muttering to himself " The boy is a fool," he became conscious of a presence which contradicted him, and which had the appearance of a circle, but which reported itself to be many circles in one, or in other words a sphere. The stranger vainly endeavours to make him understand the existence of the third dimension, but at last, angry with his stupidity, carries him off into space, lifts him to look down on the superficies of his own house, and see it, as he had never before seen it, from above ; and carries him over the metropolis of Flatland, where he sees the General Assembly passing a resolution to punish all persons pretending to have received revelations from another world. He is then introduced to the understanding of solids, and in the first exuberance of his joy at tracing the upward path of a point to a line, of a line to a superficies, and of a superficies to a solid, he asks his teacher to go forward with his education, and instruct him in the mysteries of four dimensions, and teach him about thought, and where it will be possible to see the inside of all solid things just as he had now been shown the inside of superficies. His spherical teacher upheld, "There is no such land ; the very idea of it is utterly inconceivable." He asks, "Is it or is it not the fact, that ere now your country-men also have witnessed the descent of beings of a higher order than their own, entering closed rooms even as your Lordship entered mine, without the opening of doors or windows, and appearing and vanishing at will? " To this the Sphere replies, "They have vanished certainly, if they ever appeared. But most people say that these visions arose from the thought—you will not understand me—from the brain ; from the perturbic angularity of the seer." Encouraged by this explanation the denizen from Flatland presses his argument, but only angers his teacher, and is driven back home. There, however, he receives a visit from the Sphere, who, to complete his education, takes him in vision to Pointland, or the Country of No Dimensions, where the monarch, who is merely a point, is perpetually occupied in contemplating himself, and enjoying the self-sufficiency of his sense of completeness. This is the soliloquy of the Point, speaking of himself in the third person with royal dignity:—" It fills all space, and what it fills it is. "What it thinks that it utters, and what it utters that it hears ; and it itself is thinker, utterer, hearer, thought, word, auditor. It is the one, and yet the all in all. Ah ! the happiness of being ! " 

Recovering from this vision, and anxious to teach what he has learned, he tries to explain to his grandson that his notion of a square, moving and becoming something else is a correct one ; but the clever youth, who has become acquainted with the national decree against new knowledge of this kind, altogether disowns ever having had such an idea, and ridicules it. The unhappy being, big with knowledge which he is longing to impart, tries to write it out under an imaginative disguise. Of course he is haled before the authorities, makes his manly avowal of what he knows, and is consigned to perpetual imprisonment "With this martyrdom as the reward for his missionary work—a fate so unlike, so very unlike ! anything ever known in our own world—the allegory closes.

 The Sydney Morning Herald 27 February 1886,