Ithaca takes the form of a catechism somewhat like the religious ones that the author had to memorize as a child. But rather than using theology to explain the ways of God, these questions and answers examine human life in its state of nature, and many of them mimic scientific discourse. Joyce once called his strange creation "a mathematical catechism," and he establishes that tone in the first paragraph by using geometry to describe the "parallel courses" which Stephen and Bloom take to Bloom's house, including a "diametrical" passage through a plaza.

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 defines the paths that the two men follow on their way to Bloom's house as "parallel courses"—an arrestingly abstract way of referring to the perfectly ordinary phenomenon of two people walking this way and that, but always at about the same distance from one another. Readers may wonder why they are being required to look down from a high elevation, as it were, to see paired lines being traced on Dublin's pavements. They may or may not care for the wrenching narrative experience, but they should appreciate an evocative side effect of the word "parallel": it manages to suggest that Stephen and Bloom are following different trajectories in life but, for a brief time at least, coming into close conjunction with one another. Starting with its first three words, Ithaca conjoins Olympian detachment with empathic involvement.

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'." Conversely, as angle A increases the ratio d:d' falls further away from 1:1 until it is minimized at an angle of 180 degrees. At that point chord d = D x 2 while arc d' = D x ~3.14, meaning that the diameter of a circle is less than 2/3 as long as the semicircle it defines. This represents a significant reduction of energy expenditure for two walkers who started their journey "at normal walking pace" but have since proceed "at reduced pace," and then "at reduced pace with interruptions." Every step counts.

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. In British usage a circus is an open circular plaza where streets converge. But of course this terminology comes from the Latin word for circle, circus. And although English idiom often refers to two things as far apart from one another as possible being "diametrically opposed," in this case that word refers to the straight line that passes through the center of the circus.

Readers who find such hyper-precise language tedious may initially be put off by Ithaca. But they will find its questions and answers more playful, adventurous, and liberating than those of the Maynooth catechism, and also more descriptive of the ordinary problems of human existence.

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