According to Polish physicists, classic world literature consists of fractals and/or fractals of fractals
In January 2016 the Guardian reported that fractal patterns had been discovered by physicists in Poland studying the sentence structure of hundreds of novels and other literary works. A team of researchers at the Institute of Nuclear Physics in Krakow, Poland—where my father worked as a physicist in the 1980s— described the complex “‘fractal’ patterning of sentences in literature” as resembling “ideal” mathematical forms seen in nature. Fractals, according to the Guardian, are mathematical objects “in which each fragment, when expanded, has a structure resembling the whole.” Fractals in nature are found in the structure of snowflakes and galaxies. The Polish researchers made their discovery by counting the sentence lengths of more than one hundred well-known novels written in English, French, Italian, Russian, Spanish, German and Polish, by Balzac, Hobbes, Joyce, Woolf, Cortázar, Dos Passos, Eco, Beckett, Mann, Brontë, James, Dumas, Dostoyevsky, Tolstoy, García Márquez, Austen, Defoe and Gombrowicz, among other authors, as well as the Bible and two dozen plays by Shakespeare.
On their website, the Polish researchers explain that their work with fractals evolved from standard areas of research on standard topics in nuclear and high-energy physics in the 1990s to interdisciplinary topics in natural and social complex systems, including research on financial markets, natural language and fractal music.
I called up my father with this interesting news from his old institute. He said he couldn’t understand why anyone there would want to spend their time counting sentences in great books rather than reading
them. When he worked at the Institute of Atomic Physics in Krakow, he built an MRI unit, likely the first in Eastern Europe (Magnetic Resonance Imaging uses magnetic fields and radio waves to scan tissue for medical diagnosis). Years later he tried and failed to develop an MRI technique that used fractal recognition to diagnose cancerous tumours.
According to the Guardian, some of the works analyzed “were more mathematically complex than others, with stream-ofconsciousness narratives the most complex, comparable to multifractals, or fractals of fractals.” The most fractally complex work was Finnegans Wake, James Joyce’s monumental novel, which neither my father nor I have read in English or Polish. Other fractally complex novels include A Heartbreaking Work of Staggering Genius by Dave Eggers, The Waves by Virginia Woolf (the only woman on the list), the USA Trilogy by John Dos Passos, 2666 by Roberto Bolaño, the second part of Ulysses by James Joyce and Hopscotch by Julio Cortázar—the novel that inspired my father to be a writer when he read it in Latin American literature class in high school; a few months after that he read the lectures of the physicist Richard Feynman and became convinced to take up physics rather than literature.
One of the least fractally complex of the novels analyzed at the institute is In Search of Lost Time by Marcel Proust, which my father read after high school and before he joined the institute, while he was doing his military service. He got the Proust from the military library, which he describes as a sad and empty place. As far as he could tell, volumes 2 through 7 had never been borrowed or even opened, nor had the works of Dylan Thomas. He said that he had plenty of time to read the Proust because shortly after he was conscripted, martial law was declared in Poland in reaction to the growing popularity of the Solidarity movement, and for months soldiers were forbidden to leave the base. The other source of literature at the base was the military newspaper, he said, hundreds of copies of which were delivered to the barracks, then were immediately cut into strips and used as toilet paper.
I realized while reading the article in the Guardian that I owned exactly one book on the list of 113 titles whose sentences had been counted for the study: the Polish classic Ferdydurke, by the great Polish writer Witold Gombrowicz, which I had not read either in English or Polish. I pulled it off the shelf, opened it at random and read:
What’s more, let us consider whether your work, this unique, outstanding, and elaborate work is merely a particle of some thirty thousand other works, equally unique, which make their appearance year in, year out and on the principle of “each year be sure to add, whether bad or good, a new oeuvre to your brood”? Oh, horrid parts! Is this why we construct a whole, so that a particle of a part of the reader will absorb a part of a particle of the work, only partly at that?
On the phone with my father I tried to explain what I thought the physicists in Poland were up to. They seemed to be saying that sentence lengths recur in patterns, and those patterns recur at the same ratio for sentences that are shorter or longer. My father said that was hard to believe. Entropy theory, he said, tells us that sentence length is dictated by the information contained in the sentence, so to me the study implies that these writers are always repeating themselves. He sounded disappointed. Later, after our conversation, I wanted to explain that writers are always repeating themselves, telling the same story, the story of how we see the world, or how we want to see the world, or how we want to be seen to see the world. Only the details change.
When we moved to Canada in 1989, my father got a job as a physicist in Ottawa, at the National Research Council, the institution best known for supplying the CBC with the long dash following a period of silence indicating exactly 1:00 p.m. or 12:00 p.m. or 10:00 a.m. My father, who was then thirty-three years old, supervised MRI experiments alone on night shift. One night when he went out for a smoke he looked up and saw ribbons of green light streaming and swirling across the night sky. He was certain that he was seeing a UFO. Years later he realized that it was more likely he had seen the north ern lights, a phenomenon that rarely occurs in Poland, especially in southern Poland around Krakow.
I continued with the Gombrowicz and found, a few pages later:
One of the least fractally complex of the novels analyzed is In Search of Lost Time by Marcel Proust, which my father read in the army
Whatever you put down on paper dictates what comes next, because the work is not born of you—you want to write one thing, yet something entirely different comes out. Parts tend to wholeness, every part surreptitiously makes its way toward the whole, strives for roundness, and seeks fulfilment, it implores the rest to be created in its own image and likeness.
Michał Kozłowski is the publisher of Geist. He lives in Vancouver. Read more of his work at geist.com.
The Mandelbrot set, a particular set of complex numbers with a highly convoluted fractal boundary when plotted. It was discovered by Benoit Mandelbrot in 1978. Image 12 in this sequence is a detail of image 1 magnified 10 billion times. At that scale, image 1 has a diameter of 4 million kilometres.