The little Hexagon meditated on this a while and then said to me; “But you have been teaching me to raise numbers to the third power: I suppose 3 3 must mean something in geometry; what does it mean?”

“Nothing at all,” replied I, “not at least in geometry; for geometry has only Two Dimensions.” And then I began to show the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by 3; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which may be represented by 3 2 .

Upon this, my grandson, again returning to his former suggestion, took me up rather suddenly and exclaimed, “Well, then, if a Point by moving three inches, makes a Line of three inches represented by 3; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by 3 2 ; it must be that a Square of three inches every way, moving somehow parallel to itself (but I don’t see how) must make something else (but I don’t see what) of three inches every way⁠—and this must be represented by 3 3 .”

“Go to bed,” said I, a little ruffled by this interruption: “if you would talk less nonsense, you would remember more sense.”