Michał Kozłowski

Ac­cord­ing to Pol­ish physi­cists, clas­sic world lit­er­a­ture con­sists of frac­tals and/or frac­tals of frac­tals

Geist - - Features - MICHAŁ KOZŁOWSKI

Fractal Life

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.

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