Still the last day of 1999, A Square is sitting with his Wife and recalling an earlier incident with his Grandson. A Square had been teaching him that 3 to the second power can be represented by the construction of a large square with sides 3 units long with 9 smaller ones, when his Grandson asked if 3 to the third power has any geometrical meaning. Although A Square replied that it did not, his Grandson insisted that it must, in the same way that 3 to the second power is a square. Annoyed by his Grandson’s nonsense, A Square sent him to bed.
In the way that Abbott relies on analogy to satirize British society, A Square relies on analogy to teach his Grandson the meaning of exponents with geometry. Yet he reacts to his Grandson’s extrapolating with annoyance (an emotion), much in the same way that the Monarch of Lineland did to him. Thus, Abbott challenges the idea that reason trumps emotion, or that emotion is solely the realm of women.
A Square exclaims out loud that his Grandson is a fool, and immediately he feels a presence in the room. When A Square further states that 33 is meaningless, a voice replies, “The boy is not a fool; and 3 to the third power has an obvious geometrical meaning.” A Square and his Wife suddenly see a figure before their eyes. A Square’s Wife asks to feel the Stranger, and believes him to be a perfect Circle. The Stranger then asks for A Square’s Wife to allow him and A Square to have a word alone, and she leaves the room.
A Square is no different from the Monarch of Lineland regarding new knowledge. He dismisses his Grandson’s enlightened insight, offering an additional example of how potentially dangerous ignorance can be. Thus, the Stranger appears in response to A Square’s display of self-contentment and willful ignorance.