Episode 17 (usually known by the Homeric name Ithaca) takes the form of a catechism, the kind of Q & A dialogue by which Catholic schoolchildren are indoctrinated in the faith. (Joyce had to memorize two of them before his 10th birthday.) But rather than using theology to explain the ways of God, this catechism uses science to explain the ways of the material world. Scientific inquiry is certainly not evoked by all of its hyper-rationalistic questions and answers, but the first pair sets a distinctive tone by using geometry to describe the "parallel courses" which Stephen and Bloom "follow" to Bloom's house.
The schema that Joyce gave to Stuart Gilbert lists "Cathechism (impersonal)" as the technique of Ithaca, and "Science" as its art. We see this pairing in action in the first Q & A, which describe the route that the two men follow on their way from the cabman's shelter to Bloom's house, the varying paces at which they follow it, and their physical connection or separation at various points along the route, as two "parallel courses"—a strangely abstract way of describing the perfectly ordinary phenomenon of two people walking this way and that, but always at about the same distance from one another.
Similarly, at the end of the paragraph, the perfectly ordinary experience of cutting across the interior of a circular path to shave off distance is laid out schematically as a geometry problem: "they crossed both the circus before George's church diametrically, the chord in any circle being less than the arc which it subtends." A mathematician would say, as the physicist on the Rutgers website to the right does, that "As A becomes smaller, the chord length d becomes a better approximation to the arc length d', that is, d ~ d'." And, conversely, as angle A increases, the ratio of d to d' becomes progressively smaller, so the greatest reduction in length will be achieved when the angle is maximized at 180 degrees. At this angle, arc d' will equal D x 3.14159, while chord d will equal D x 2, a significant savings of energy for two tired walkers.
These walkers are indeed maximizing their energy savings, because they cross the "circus" in front of St. George's church—the Latin word means simply circle, and in British usage it refers to an open circular plaza where streets converge—"diametrically," i.e. by hewing to the straight line that will take them through the very center.
Readers who find such uses of language arcane, tedious, or irrelevant to the conduct of life may initially be put off by Ithaca. But they will quickly find its questions and answers to be far more playful, adventurous, and liberating than those of The Maynooth Catechism. And, for some modern readers at least, the subjects covered in the chapter will seem more relevant to the problems of life than learning exactly how many angels can dance on the head of a pin.