This short story was intended to highlight the learning curve of the twins as The Doctor teaches them to stretch their abilities. The multidimensional chess played on a board created purely by the power of thought was a pure invention of mine to highlight the fact that the twins were likely to become as powerful as The Doctor by the time he has finished teaching them. Of course, they are only boys, so they abandon the chess to create their own table football game with the power of their minds.
There are some insights into The Doctorís past, too. Some of my own devising, like Susanís descriptions of how they left Gallifrey in the dark of night when she was just a little girl. Some are part of the existing mythology, such as the story of how Susan came to leave The Doctor and make a new life with David.†
Of course, the main objective of this story is to set up a series of stories in which The Doctor takes the boys with him in the TARDIS.