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.
Works Cited
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.
This interesting paper raises some important questions about a number of aesthetic/rhetorical issues, knowledge and awareness of which may enrich the activity of reading, but I do think a few things need to be fleshed out and made explicit.
We are presented with rhetorical structures which we are told Joyce deploys in Dubliners. We are presented with the names of a number of scientists who pioneered object relations, and we are presented with the names of a number of artistic people whose works applied these interesting theoretical and mathematical elements in their works. The following observations may help.
Descartes is credited with creating the standard x/y lattice, the graph which for example shows how many books you have read between 2000 and 2022, information about which there is really no interpretive disagreement. x = years. Y= number of books. Easy.
Comte was a positivist who asserted that the world could be easier to understand if we used logical, deductive rules to determine what is true and what is not. (George Boole’s notation). Positivism was inter alia an effort to combat irrational belief but was also found to be somewhat limited where for example, to the person’s eye, the sun does appear to be rising and setting when in fact it neither rises nor sets. The sun does not orbit us. It just looks that way and here is the heart of our conundrum. The language we use (rising and setting) is vestigial, unsuited to the ‘New Science’ that was being theorised to improve our understanding of the role of perception, what is happening when we look at something (or someone). (A lot of fundamental Greek theory was rediscovered in English from about the time of Francis Bacon onwards, circa the 16th Century, the study of which took several centuries before anything resembling a reliable account of perception emerged. It’s a work in progress but certain aspects are settled).
So, besides being stuck with vestigial language and cliched collocations (groups of words which appear together) which pre-figure the way we see or interpret the world, (like for example the fact that English doesn’t have masculine feminine or neuter nouns), we have another problem or two.
Descartes’ graph was good for tracking your book reading over time but not very good for tracking your mental health or the way you experience time or food or other people, and so some modification or improvement was deemed necessary. Physicists chipped in and Walter Heisenberg, mentioned in the piece, evolved the axiom that “you cannot detach the observer from the thing observed”, to mean that when examining certain data, the role of the observer (z) played a critical role in how a person experiences or interprets data. If as a citizen of the South Pole, you’ve only ever seen flightless penguins, then you will naturally assume that a. birds can’t fly. b. all birds are black and white and c. they all walk funny, observations which while correct from your vantage point do not allow you to arrive at satisfactory general principles as such observations are not good for Miami or Dalkey.
The implications of Heisenberg’s maxim are enormous as it suggests that our environment and culture pre-determine how we perceive the world (which may explain why there have been so many conflicts). So, artists, keen to communicate the complicated nature of perception began to experiment as we see with people like Magritte who, unlike say Rembrandt, departs from classical art which sought to depict objects as they actually are. Likewise, people like Picasso deviate from classical iconography by depicting subjects not as they are but as they are experienced by the viewer, giving his mistress Dora Marr sometimes one, sometimes three eyes. Picasso’s blue period also suggests that during particular phases of our lives, the objects we see are ‘coloured’ by our temperment, how they do not exist as things in themselves (a Hegelian concept to mean that objects exist independent of our perception of them). So, people like Picasso and Duchamps applied these concepts which were pioneered by physicists and aestheticians.
As readers of Ulysses, you will have recognised that characters which remain undeveloped in Dubliners seem more developed in Ulysses, reflecting perhaps the writer’s limited capacity to find depth in them, or, more likely, a young Joyce first wanted to present a traditional picture of a European society before he began experimenting with literary form, as he did in Ulysses and Finnegans Wake (which privileges sound over spelling, and word association over linear concerns).
In terms of psychoanalysis, the implications are also enormous as these findings suggest that people are pre-disposed to interpreting reality in a particular way, how perception is often culturally, linguistically, domestically determined by race, gender, and so on. That people may be possessed of certain predispositions suggests that such psychological complexes must be brought to awareness if we are to master them and not be pushed around by them, never easy. Ulysses I believe is an implicit account of the process of individuation, where a rather bookish brave young man finds himself evolving as he elects to find what kind of person he wishes to become. Religion and nationality and family are the preliminary obstacles he must encounter as he goes forth to forge in the smithy of his soul, the un-created conscience (superego) of his race, thereby acting as an exemplary presence for others confronted with the challenges of individual and group identity. It couldn’t be more topical. Thanks.
p.s. Where Shakespeare says “there is nothing good nor bad but thinking makes it so”, he is supplying us with a diagnosis for logic, critiquing its limitations.
Martin, this is not only interesting but also fun to read. Thanks for posting. ~Don