The Literary World (March 21, 1885), p. 93.
This brilliant jeu d'esprit, published anonymously in England but attributed by the Spectator to the eminent Shakespearian scholar and educator, Rev. Edwin A. Abbott of London, has deservedly attracted much attention across the water. The mathematically-inclined will particularly enjoy its attempt to work out, as consistently as possible, the picture of a world having only the two dimensions of length and breadth. For such is Flatland, as the author, an enlightened and traveled Square, calls his native land, to make its nature clear to us. It is like ``a vast sheet of paper on which straight Lines [the women], Triangles, Squares, Pentagons, Hexagons, and other figures move freely about, on or in the surface, but without the power of rising above or sinking below it.'' With vast ingenuity and occasional shy satirical
allusions to life in our Space-Land, `A Square' describes the climate, the houses, the women, the methods of recognition by feeling and sight, the ancient practice of painting, the universal color belt, and the final suppression of the chromatic sedition. The Priests of Flatland are Circles; they have almost complete control of all affairs, and their doctrine is summed up in a single maxim, ``Attend to your Configuration.'' They teach men to honor their grandsons most of all, and that women should be left without education.
The author has a vision of Lineland where there is only one dimension; he endeavors to convince a native that there is another world, of two dimensions, but the labor is in vain, as the King of Lineland's senses and consciousness are alike incapable of grasping the second dimension. This is but a dream however. Hard upon the dream comes the invasion of Mr. Square's house by a stranger from Spaceland, a Sphere, who after long and unsuccessful efforts to beat the notion of thickness into Mr. Square's head, at last carries him off bodily to Spaceland to convince him by actual experience. Returning home, after another vision, this time of Pointland, Square undertakes to teach the existence of Spaceland, the Gospel of Three Dimensions. But he is soon arrested for heresy, by order of the grand Council, and condemned to perpetual imprisonment. Yet worse than prison is his present inability again to grasp, himself, ``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.''
With so much wit and grace of style is this clever satire on the limits of our knowledge wrought out that we shall not be surprised to see it take a permanent place in literature. Our friends, the Spiritists, will be sure to hail it as a strong argument in behalf of their much talked-of fourth dimension. But we should be inclined to say that this was not the author's intention; his aim is more general to satirize the infallibility too common in Spaceland, which confounds the thinkable and the possible universes. The trouble with the alleged fourth dimension of Spiritism would seem to that it annihilates the third dimension, instead of adding to it.