The novel is set in an alternate universe where two planets orbit each other in close proximity, with a common atmosphere. The civilization on one of the planets is shown to be similar to the western civilization around the 16th century (they are on the verge of discovering the concepts of calculus, starting with limits…). The mathematicians, statisticians, astronomers, chemists, and academicians of similar fields — collectively called “Philosophers” — start raising concerns about energy shortages within a few decades, which finally leads to a mass migration using jet-powered balloons to the twin planet (poetically called “Overland”). Some of the details are very nicely done, though most of the novel is not mathematical in nature. There is one mathematical curiosity: the geometry around the planets is conical in nature, with the value of pi set to equal exactly 3 (one of the mathematicians uses a rolling wooden disk to demonstrate to his
brother that its circumference is exactly 3 diameters in length. He muses, “Even when we go to the limits of measurement, the ratio is exactly three. Does that not strike you as astonishing? That and things like the fact that we have twelve fingers make whole areas of calculation absurdly easy. It's almost like an unwarranted gift from nature”). There is a strong hint that the worlds might be “designed” but that angle is left dangling…a shame, for it is a nicely written novel which would have twisted very well if there were to be some denouement about the particular geometry.