The Jesuits taught Joyce that Euclid’s influence extended beyond angles, legs, and cosines. According to Wertmeimmer’s Gestalt, Euclidean geometry creates a search for consistency (Miller 248). Rene Descartes, also Jesuit educated, balked against Aristotelian logic and set geometry on a course toward the concrete application of simple principles. Descartes’ influence may have been the reason why, as a schoolboy, Joyce detested Geometry. Descartes criticized his instructors for making the most straightforward matters “complex and mysterious.” He quantified geometry by assigning coordinates. The word “geometry” in Greek is, after all, the “measure of the Earth” (Rice 17-21). Geometry’s complexity, mystery, and abstraction would later lure Joyce back, but not to Cartesian geometry that had become a strictly practical matter.
Joyce found Plato’s ideas about Geometry more appealing. The Greek said, “… the knowledge at which geometry aims is knowledge of the eternal, and not of aught perishing and transient” (412). Gaston Bachelard observed Cartesianism geometry’s “reality” came at the expense of other possibilities. He was speaking of the physical view of the electron. When that view proved flawed, it damaged the reputation of Euclidean Geometry, but, more importantly, it buckled society’s belief that science could solve every problem (Rice 73). In 1905, Joyce was about to set the principles of his Jesuit Geometry on the course Plato described.
Rice describes one element of Joyce’s approach as a Euclidean “compulsion to arrange his materials” (25). Dubliners resulted from that focus on assembling and ordering. The collection applied the principles of geometric order in three ways: in overall design, weaving gnomon-like mysterious conclusions to the stories, and using syllogistic logic in resolving the plots.
Imagine a design that conjoins the points (or angles) of triangles together. That was James Joyce’s first conception. Childhood, Youth, and Maturity were identical in dimensions and congruent in purpose. At their juncture, a third shape, shorter in scope but congruent to all three in purpose, covers the point of the graph (you may access the graph below). This umbrella-shaped union was initially the story “Grace.” This was to be the final story of the collection even before it had been written or even named [Ellmann 208]. It would join the first story to the last and collect elements of paralysis, gnomon, and simony from the contributing stories along the way. The categories are consistent, each representing a stage of life, and members of those categories are visually identifiable, children distinguishable from adolescents, adolescents from mature adults. In July of 1905, with the completion of “Ivy Day in the Committee Room,” a new design was necessary.
In creating this original schema, Joyce’s Euclidean thinking relied on visible connections. This was the only acceptable form for scientific proofs under Comte’s Positivism until Einstein overturned the reliance on the visible in science and Picasso did the same subsequently in art. [Note: More detail on Positivism and James Joyce’s Modernism can be found at https://jamesjoycereadingcircle.com/2021/11/07/james-joyces-modernism-the-rise-of-uncertainty-in-a-portrait-of-the-artist-as-a-young-man/ .] Einstein’s thinking was as reliably minimalist as Joyce’s design for Dubliners. Like Einstein, James Joyce shunned redundancy. Meanwhile, in the graphic arts, Picasso, Braque and Gris succeeded in breaking down “realistic” images into minimalist geometric shapes. According to Kahnweiler, these three were the only artists of the day creating true subjective art (Miller 166).
Delays in the publication of Dubliners were so protracted that scientific Modernism had moved the horizon of possibilities not only for Joyce but also for Einstein and Picasso. In 1905 as Einstein experienced the miracle year that ultimately tumbled the certainty of the visible universe, Joyce created his story “Grace” as the conclusion and capstone for Dubliners. In June of 1907, Pablo Picasso attended a show of primitive art at the Musée Ethnologie du Trocadéro. There he was inspired to use geometric shapes to depict the effect of movement across time in Les Demoiselles d’Avignon (Miller 92).
Dubliners did not appear in print until 1914. By that time, Joyce had written new stories, created a new capstone story in “The Dead.” He switched from the earlier Euclidean design to a non-Euclidean ( less “visible” or self-evident) schema. The non-Euclidean order reached beyond the predictable and physical classification of stories sorted by the protagonist’s age. The city became a character. The new category leaped from physical development into the character’s role in Dublin’s community. It was impossible by looking at a citizen to know if she were active in religious, cultural, or political affairs. This invisible feature was to become the connection among the new set of stories. Although participation in these sectors of public life was not detectable on sight, the classification was factual nonetheless.
Before the first manuscript appeared on publisher Grant Richards’ desk, the collection had grown to twelve stories in four sections. As Joyce added stories, he assembled the fourth group to represent public life (Scholes and Litz ix). Some Dublin adults participated in the arts and politics, including Irish Nationalism. Even children participated in religious life. An observer might not know by sight if a Dubliner engaged with the city’s artistic, political, or political communities. Visual evidence sometimes failed to disclose reality, just as early-stage black lung might be undetected by observation before the invention of the x-ray. Like Einstein’s intuitive insistence that Newton’s Laws were incomplete and Picasso’s insisted that images change instantaneously in spacetime, Joyce’s design employed motifs Euclid and Positivism would shun.
Invisible facts, ignored by Positivism, were gradually gaining acceptance and made useful through the science of the new century. In addition to x-rays, developments including wireless signals, the telegraph, Max Planck’s quantum theory (which Einstein used in 1905 to explain the photoelectric effect) all made it impossible to ignore the reality of the invisible world. Picasso experimented with moving art (photography and moving pictures) and changing perspectives. He used non-Euclidean geometry in designing his finished products.
Incorporating the invisible public life of Dublin into his collection, Joyce created a new non-Euclidean design. Including the invisible became necessary because “Joyce was to devote a patient lifetime to illuminating his subject (Dublin) from within” (Kenner 265). The invisible qualities would become gnomons, unseen but undeniable elements of the structure. The gnomon, the quincunx, and the syllogism are all discussed in Book 4 of the Euclid. Later Joyce would continue to experiment with spacetime and invisible actuals. For now, he concentrated on three Euclidean abstractions in Dubliners. The concept of the gnomon is introduced in the collection’s opening story, “The Sisters.” Gnomons are present in every story where the reader faces an unresolved conflict after the protagonist’s epiphany. The reader is left to complete the story from conclusions that are invisible in the plotline. The quincunx is also a particular type of gnomon. It appears in “Grace” as an ironic cross that confines the reluctant and unenlightened Kernan in a church pew. Any number of syllogisms are also implicit in the fifteen stories. Rice details one example from “Eveline,” which might guide the reader to the gnomon’s solution left by the unexplained decision to remain in Dublin.
A. Eveline sees relationships between men and women as abusive;
B. Frank offers a relationship;
C. Frank is “not altogether frank.” (Rice 24-25).
After about 1880, the scientific, mathematical, and artistic tides began to turn against Positivism and the certainty that science could solve every problem (with the help of unfailing Euclidean Geometry). The Catechism, which relied on the writings of Euclideans Aristotle and Aquinas, also suffered in consequence. In a domino effect, Positivism teetered with the discovery of invisible entities with visible effects (like radiation), the Euclid wobbled under the weight of a perhaps intentionally vague Book 5 dealing with what was to become the non-Euclidean mysteries.
Despite having advanced science and the graphic arts into a new era, neither Einstein nor Picasso moved far beyond their great initial leaps. Einstein was never fully reconciled with The Copenhagen Group’s Quantum Theory. When Heisenberg theorized unvisualizable quantum particles, Einstein resisted the theory until Feynman produced a convincing graphic depiction (Miller 255). Picasso never turned away from representative art and toward the truly abstract.
Critics classify Einstein, Picasso, and Joyce as conservatively tied to the disciplines that nurtured them. Howard Gardner classifies geniuses as either masters or makers (Miller 255). In creating Dubliners using these techniques, Joyce showed himself among those whose collection designs enhanced the art. In this, he proved himself a master of the craft. With Finnegans Wake, he would reveal himself also to be a maker of a new class of long fiction by Gardner’s definition. Finnegans Wake will remain outside the scope of this series of essays, but we will see an increasing interest by Joyce in spacetime and something akin to Relativity as early as Ulysses.
Ellmann, Richard. James Joyce, Oxford University Press, Oxford, 1983, pp. 207-210.
Joyce, James. Dubliners. Enhanced Media, 2016, Retrieved November 8- November 22, 2021.
Joyce, James. James Joyce’s Dubliners: An Illustrated Edition with Annotations, edited by John Wyse Jackson and Bernard McGinley, St. Martin’s Griffin, 1995.
Joyce, James. James Joyce’s Dubliners: Text and Criticism, edited by Robert Scholes and A. Walton Litz, Penguin Books, 1996, ix-xxviii.
Kenner, Hugh. “‘Ezra Pound and the Light of France,'” Gnomon. McDowell, Obolensky, New York, 1958, pp. 263-279.
Miller, Arthur I. Einstein, Picasso: Space, Time and the Beauty That Causes Havoc. BasicBooks, 2002.
Rice, Thomas Jackson. Joyce, Chaos, and Complexity. University of Illinois Press, 1997.