In 1872 Richard Dedekind establishes that no such thing as a continuum exists in mathematics. Modernism's generic concept is discontinuity. Between the numbers 1 and 5 you can increase the population infinitely by adding fractions. There is no "smooth change."
Ludwig Boltzmann calls continuity a statistician's illusion since atoms behave unpredictably. By 1900 Albert Einstein praises Boltzmann's work. George Seurat paints "Sunday Afternoon on the Island of la Grande Jatte" using thousands of colored dots that form "a harmonious whole that radiates an extraordinary calm."
1891: Seurat dies, Matisse enters art school, Edison patents kinetograph movie camera (the eye interprets 16 still photos per second as movement). Seurat understood that nature is discontinuous and that Impressionism was "the first discontinuous painting since the Renaissance."
Each new episode of Joyce's "Ulysses" invokes a new hour, a new place, often new protagonists and a new narrative voice. Dickens wanted his words to blur into one continuous whole.
Whitman, Rimbaud and Laforgue create "poems without meter." "Ambiguity is more than a style, irony more than an attitude. It is the epistemological principle of modernism." Emotions are passed from poet to reader without predictability, logic or coherence.
1889, the discovery of the neuron and that there is no continuity inside the brain itself. Instead there is a host of atomlike cells. Alfred Jarry is writing shocking words and nearby Marie Curie is refining the first milligram of radium. Mallarme, Henri Poincare, Gabriel Faure, Claude Debussy and Erik Satie are also around the neighborhood.
1905, Albert Einstein's famous equation was implying a funnel between mass and energy, its governing constant being the velocity of light. 1938, nuclear fission would show "how mass could be deliberately converted to energy in microgram quantities. 1945, Hiroshima. 1906-7, Picasso paints "Les Demoiselles d'Avignon." One figure is perceived to be the first of all figures in Western art to have been painted from all sides at once. Breaking of the painting and the world into discrete parts or atoms and opens the way to recombining those parts in new and startling ways
New York Times Book Review. June 29, 1997.