_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 of the neighbourhood possessing your Lordship’s ample means of 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 of 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 the 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 the 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 understand 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, Sir; listen to me.