With this object in view let us contemplate a certain story which bears on our problem.
It is said that once in a certain region of Ireland there took place a curious contest. For in Kilkenny there were two cats so alike in size, vigour, determination, and prowess, that, fighting, they so clawed, scratched, bit, and finally devoured each other, that nothing was left of either of them save the tail.
Now, on reflecting on this story, it becomes obvious that it originated when looking-glasses were first imported into Ireland from Italy. For when an Irishman sees for the first time anything new, he always describes it in an unexpected and yet genial and interesting manner. Moreover, we all know what contentious fellows they are, and how all their thoughts run on fighting. And I think if we put this problem to ourselves, how by bringing in fighting to describe a looking-glass, we shall see that the story of the Kilkenny cats is the only possible solution. For consider evidently how it arose. Depositing his favourite shillaly in a corner, the massively-built Irishman, to whom the possession was a novelty, saw reflected in his looking-glass the image of his favourite cat. With a scrutinizing eye he compared the two. Point for point they were like. “Begorra if I know which of the two would win!” he ejaculates. The combat becomes real to him, and the story of the Kilkenny cats is made.
Now, to our more sober mind, it is obvious that two cats—two real material things—could not mutually annihilate each other to such an extent. But it is perfectly possible to make a model of the Kilkenny cats—to see them fight, and to mark the issue.
And I propose to symbolize or represent the Kilkenny cat by a twist. Take a pencil, and round it twist a strip of paper—a flat spill will do. Now, having fastened the ends on to the pencil by two pins, so that it will not untwist, hold the paper thus twisted on the pencil at right angles to the surface of a looking-glass: and in the looking-glass you will see its image. In Diagram I., M represents the mirror, and on the left hand is shown the twist, on the right hand the image twist. Now take another pencil and another piece of paper, and make a model of what you see in the glass. You will be able to twist this second piece of paper in a spiral round this second pencil so that it is an exact copy of what you see in the glass. Now put the two pencils together end to end, as they would be if the first pencil were to approach the glass until it touched it, meeting its image: you have the real copy of the image instead of the image itself. Now pin together the two ends of the pieces of paper, which are near together, and you have your two Kilkenny cats ready for the fray. To make them fight (remember that the twists—not the paper itself, but the paper twisted—represent the cat), hold firmly and pull the other ends (the tail ends, so to speak), so as to let each twist exercise its nature on the other.