Flatland [32]
I. An eye in my inside! An eye in my stomach! Your Lordship jests.
Stranger. I am in no jesting humour. I tell you that I come from Space, or, since you will not understand what Space means, from the Land of Three Dimensions whence I but lately looked down upon your Plane which you call Space forsooth. From that position of advantage I discerned all that you speak of as solid (by which you mean "enclosed on four sides"), your houses, your churches, your very chests and safes, yes even your insides and stomachs, all lying open and exposed to my view.
I. Such assertions are easily made, my Lord.
Stranger. But not easily proved, you mean. But I mean to prove mine.
When I descended here, I saw your four Sons, the Pentagons, each in his apartment, and your two Grandsons the Hexagons; I saw your youngest Hexagon remain a while with you and then retire to his room, leaving you and your Wife alone. I saw your Isosceles servants, three in number, in the kitchen at supper, and the little Page in the scullery. Then I came here, and how do you think I came?
I. Through the roof, I suppose.
Stranger. Not so. Your roof, as you know very well, has been recently repaired, and has no aperture by which even a Woman could penetrate. I tell you I come from Space. Are you not convinced by what I have told you of your children and household?
I. Your Lordship must be aware that such facts touching the belongings of his humble servant might be easily ascertained by any one in the neighbourhood possessing your Lordship's ample means of obtaining information.
Stranger. (To Himself.) What must I do? Stay; one more argument suggests itself to me. When you see a Straight Line—your wife, for example—how many Dimensions do you attribute to her?
I. Your Lordship would treat me as if I were one of the vulgar who, being ignorant of Mathematics, suppose that a Woman is really a Straight Line, and only of One Dimension. No, no, my Lord; we Squares are better advised, and are as well aware as your Lordship that a Woman, though popularly called a Straight Line, is, really and scientifically, a very thin Parallelogram, possessing Two Dimensions, like the rest of us, viz., length and breadth (or thickness).
Stranger. But the very fact that a Line is visible implies that it possesses yet another Dimension.
I. My Lord, I have just acknowledged that a Woman is broad as well as long. We see her length, we infer her breadth; which, though very slight, is capable of measurement.
Stranger. You do not understand me. I mean that when you see a Woman, you ought—besides inferring her breadth—to see her length, and to see what we call her height; although that last Dimension is infinitesimal in your country. If a Line were mere length without "height", it would cease to occupy Space and would become invisible. Surely you must recognize this?
I. I must indeed confess that I do not in the least understand your Lordship. When we in Flatland see a Line, we see length and brightness. If the brightness disappears, the Line is extinguished, and, as you say, ceases to occupy Space. But am I to suppose that your Lordship gives to brightness the title of a Dimension, and that what we call "bright" you call "high"?
Stranger. No, indeed. By "height" I mean a Dimension like your length: only, with you, "height" is not so easily perceptible, being extremely small.
I. My Lord, your assertion is easily put to the test. You say I have a Third Dimension, which you call "height". Now, Dimension implies direction and measurement. Do but measure my "height", or merely indicate to me the direction in which my "height" extends, and I will become your convert. Otherwise, your Lordship's own understanding must hold me excused.
Stranger. (To Himself.) I can do neither. How shall I convince him? Surely a plain statement of facts followed by ocular demonstration ought to suffice. —Now,