Parallel courses

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The schema that Joyce gave to Stuart Gilbert lists "Cathechism (impersonal)" as the technique of Ithaca, and "Science" as its art. The art of geometry is applied to the route that the two men follow on their way from the cabman's shelter to Bloom's house. Their paths are called "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 cited here 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' falls further away from 1/1. When the angle is maximized at 180 degrees, chord d = D x 2, while arc d' = D x ~3.14, for a ratio of less than 2/3––a significant reduction for two tired walkers. Stephen and Bloom save energy in this way by crossing the "circus" in front of St. George's church "diametrically." Joyce has chosen both words carefully. The Latin word circus means simply circle. (In British usage it refers to an open circular plaza where streets converge.) The diameter traced by the two men's feet is the straight line through the center of this circle.

Readers who find such hyper-precise language arcane, tedious, or irrelevant to the conduct of life may initially be put off by Ithaca. But they will find its questions and answers 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 how many angels can dance on the head of a pin.