“Pardon me, my Lord,” replied I; “but to my eye the appearance is as of an Irregular Figure whose inside is laid open to the view; in other words, methinks I see no Solid, but a Plane such as we infer in Flatland; only of an Irregularity which betokens some monstrous criminal, so that the very sight of it is painful to my eyes.”

“True,” said the Sphere, “it appears to you a Plane, because you are not accustomed to light and shade and perspective; just as in Flatland a Hexagon would appear a Straight Line to one who has not the Art of Sight Recognition. But in reality it is a Solid, as you shall learn by the sense of Feeling.”

He then introduced me to the Cube, and I found that this marvellous being was indeed no Plane, but a Solid; and that he was endowed with six plane sides and eight terminal points called solid angles; and I remembered the saying of the Sphere that just such a creature as this would be formed by a Square moving, in Space, parallel to himself: and I rejoiced to think that so insignificant a creature as I could in some sense be called the progenitor of so illustrious an offspring.

But still I could not fully understand the meaning of what my teacher had told me concerning “light” and “shade” and “perspective”; and I did not hesitate to put my difficulties before him.

Were I to give the Sphere’s explanation of these matters, succinct and clear though it was, it would be tedious to an inhabitant of Space, who knows these things already. Suffice it, that by his lucid statements, and by changing the position of objects and lights, and by allowing me to feel the several objects and even his own sacred person, he at last made all things clear to me, so that I could now readily distinguish between a Circle and a Sphere, a Plane Figure and a Solid.