A Square wakes up from his dream and decides to start his mission of enlightenment with his Wife. At that moment, however, he hears a proclamation from the Council declaring the arrest, imprisonment, or execution of anyone who attempts to enlighten others of revelations from another World.
It has been evident throughout the whole book that the Circles maintain their social power by cracking down on anyone who poses a threat to their authority, here silencing anyone who might contradict their “natural laws.”
Threatened by the Council’s proclamation, A Square decides to keep his own revelation secret and to demonstrate what he has learned instead. He forgoes his plan to begin with his Wife and considers starting with his hexagonal Grandson. His Grandson had already shown his cognitive potential by meditating on 3 to the third power, and is young enough to not understand the Proclamation. On the other hand, A Square’s pentagonal sons are already too loyal to the Circles to take A Square’s words seriously without handing him over to the Circles.
The fact that A Square cannot even teach his own sons the Gospel of Three Dimensions because they have been brainwashed by the doctrines of the Circles demonstrates another aspect of how the social hierarchy is maintained and truly how engrained it is in the mind of a society. The Grandson, on the other hand, is still young enough to not have been indoctrinated.
First, A Square relieves his Wife’s questions about the other night’s encounter with the Sphere. Then he immediately seeks out his Grandson, since he feels that all his experiences and the knowledge he has learned are slowly fading away. A Square sits down with his Grandson and resumes the previous day’s lesson of a point creating a line and a line creating a square, when he hears the proclamation being announced outside again.
A Square’s determination to spread the idea of the third dimension is truly praiseworthy. However, the very abstract nature of the third dimensional concept makes it hard for him to retain that knowledge, suggesting that some higher mysteries are simply difficult to understand with human faculties, like the mysteries of God.
A Square’s Grandson hears the Proclamation and begins to cry at his grandfather’s request to repeat what he had been thinking the other day concerning three-to-the-third. The Grandson does not take A Square’s words seriously, assumes A Square is joking, and runs out of the room.
A Square fails to convert his Grandson because, unfortunately, the little hexagon is already very much aware of the Circles’ power and their intolerance for outspoken Flatlanders.