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, Sir; listen to me. You are living on a Plane. What you style Flatland is the vast level surface of what I may call a fluid, on, or in, the top of which you and your countrymen move about, without rising above it or falling below it. I am not a plane Figure, but a Solid. You call me a Circle; but in reality I am not a Circle, but an infinite number of Circles, of size varying from a Point to a Circle of thirteen inches in diameter, one placed on the top of the other. When I cut through your plane as I am now doing, I make in your plane a section which you, very rightly, call a Circle. For even a Sphere--which is my proper name in my own country--if he manifest himself at all to an inhabitant of Flatland--must needs manifest himself as a Circle. Do you not remember--for I, who see all things, discerned last night the phantasmal vision of Lineland written upon your brain--do you not remember, I say, how, when you entered the realm of Lineland, you were compelled to manifest yourself to the King, not as a Square, but as a Line, because that Linear Realm had not Dimensions enough to represent the whole of you, but only a slice or section of you? In precisely the same way, your country of Two Dimensions is not spacious enough to represent me, a being of Three, but can only exhibit a slice or section of me, which is what you call a Circle. The diminished brightness of your eye indicates incredulity. But now prepare to receive proof positive of the truth of my assertions. You cannot indeed see more than one of my sections, or Circles, at a time; for you have no power to raise your eye out of the plane of Flatland; but you can at least see that, as I rise in Space, so my sections become smaller. See now, I will rise; and the effect upon your eye will be that my Circle will become smaller and smaller till it dwindles to a point and finally vanishes. [Illustration 8] [ASCII approximation follows]