Scientists Discover That James Joyce’s Finnegans Wake Has an Amazingly Mathematical “Multifractal” Structure

Fractal Finnegan's Wake

It has long been thought that the so-called “Gold­en Ratio” described in Euclid’s Ele­ments has “impli­ca­tions for numer­ous nat­ur­al phe­nom­e­na… from the leaf and seed arrange­ments of plants” and “from the arts to the stock mar­ket.” So writes astro­physi­cist Mario Liv­io, head of the sci­ence divi­sion for the insti­tute that over­sees the Hub­ble Tele­scope. And yet, though this math­e­mat­i­cal pro­por­tion has been found in paint­ings by Leonar­do da Vin­ci to Sal­vador Dali—two exam­ples that are only “the tip of the ice­berg in terms of the appear­ances of the Gold­en Ratio in the arts”—Livio con­cludes that it does not describe “some sort of uni­ver­sal stan­dard for ‘beau­ty.’” Most art of “last­ing val­ue,” he argues, departs “from any for­mal canon for aes­thet­ics.” We can con­sid­er Liv­io a Gold­en Ratio skep­tic.

Far on the oth­er end of a spec­trum of belief in math­e­mat­i­cal art lies Le Cor­busier, Swiss archi­tect and painter in whose mod­ernist design some see an almost total­i­tar­i­an mania for order. Using the Gold­en Ratio, Cor­busier designed a sys­tem of aes­thet­ic pro­por­tions called Mod­u­lor, its ambi­tion, writes William Wiles at Icon, “to rec­on­cile maths, the human form, archi­tec­ture and beau­ty into a sin­gle sys­tem.”

Praised by Ein­stein and adopt­ed by a few of Corbusier’s con­tem­po­raries, Mod­u­lor failed to catch on in part because “Cor­busier want­ed to patent the sys­tem and earn roy­al­ties from build­ings using it.” In place of Leonardo’s Vit­ru­vian Man, Cor­busier pro­posed “Mod­u­lor Man” (below) the “mas­cot of [his] sys­tem for reorder­ing the uni­verse.”


Per­haps now, we need an artist to ren­der a “Frac­tal Man”—or Frac­tal Gen­der Non-Spe­cif­ic Person—to rep­re­sent the lat­est enthu­si­as­tic find­ings of math in the arts. This time, sci­en­tists have quan­ti­fied beau­ty in lan­guage, a medi­um some­times char­ac­ter­ized as so impre­cise, opaque, and unsci­en­tif­ic that the Roy­al Soci­ety was found­ed with the mot­to “take no one’s word for it” and Lud­wig Wittgen­stein deflat­ed phi­los­o­phy with his con­clu­sion in the Trac­ta­tus, “Where­of one can­not speak, there­of one must be silent.” (Speak­ing, in this sense, meant using lan­guage in a high­ly math­e­mat­i­cal way.) Words—many sci­en­tists and philoso­phers have long believed—lie, and lead us away from the cold, hard truths of pure math­e­mat­ics.

And yet, reports The Guardian, sci­en­tists at the Insti­tute of Nuclear Physics in Poland have found that James Joyce’s Finnegans Wakea nov­el we might think of as per­haps the most self-con­scious­ly ref­er­en­tial exam­i­na­tion of lan­guage writ­ten in any tongue—is “almost indis­tin­guish­able in its struc­ture from a pure­ly math­e­mat­i­cal mul­ti­frac­tal.” Try­ing to explain this find­ing in as plain Eng­lish as pos­si­ble, Julia Johanne Tolo at Elec­tric Lit­er­a­ture writes:

To deter­mine whether the books had frac­tal struc­tures, the aca­d­e­mics looked at the vari­a­tion of sen­tence lengths, find­ing that each sen­tence, or frag­ment, had a struc­ture that resem­bled the whole of the book.

And it isn’t only Joyce. Through a sta­tis­ti­cal analy­sis of 113 works of lit­er­a­ture, the researchers found that many texts writ­ten by the likes of Dick­ens, Shake­speare, Thomas Mann, Umber­to Eco, and Samuel Beck­ett had mul­ti­frac­tal struc­tures. The most math­e­mat­i­cal­ly com­plex works were stream-of-con­scious­ness nar­ra­tives, hence the ulti­mate com­plex­i­ty of Finnegans Wake, which Pro­fes­sor Stanisław Drożdż, co-author of the paper pub­lished at Infor­ma­tion Sci­ences, describes as “the absolute record in terms of mul­ti­frac­tal­i­ty.” (The graph at the top shows the results of the nov­el­’s analy­sis, which pro­duced a shape iden­ti­cal to pure math­e­mat­i­cal mul­ti­frac­tals.)

Fractal Novels Graph

This study pro­duced some incon­sis­ten­cies, how­ev­er. In the graph above, you can see how many of the titles sur­veyed ranked in terms of their “mul­ti­frac­tal­i­ty.” A close sec­ond to Joyce’s clas­sic work, sur­pris­ing­ly, is Dave Egger’s post-mod­ern mem­oir A Heart­break­ing Work of Stag­ger­ing Genius, and much, much fur­ther down the scale, Mar­cel Proust’s Remem­brance of Things Past. Proust’s mas­ter­work, writes, shows “lit­tle cor­re­la­tion to mul­ti­frac­tal­i­ty” as do cer­tain oth­er books like Ayn Rand’s Atlas Shrugged. The mea­sure may tell us lit­tle about lit­er­ary qual­i­ty, though Pro­fes­sor Drożdż sug­gests that “it may some­day help in a more objec­tive assign­ment of books to one genre or anoth­er.” Irish nov­el­ist Eimear McBride finds this “upshot” dis­ap­point­ing. “Sure­ly there are more inter­est­ing ques­tions about the how and why of writ­ers’ brains arriv­ing at these com­plex, but seem­ing­ly instinc­tive, frac­tals?” she told The Guardian.

Of the find­ing that stream-of-con­scious­ness works seem to be the most frac­tal, McBride says, “By its nature, such writ­ing is con­cerned not only with the usu­al load-bear­ing aspects of language—content, mean­ing, aes­thet­ics, etc—but engages with lan­guage as the object in itself, using the re-form­ing of its rules to give the read­er a more pris­mat­ic under­stand­ing…. Giv­en the long-estab­lished con­nec­tion between beau­ty and sym­me­try, find­ing works of lit­er­a­ture frac­tal­ly quan­tifi­able seems per­fect­ly rea­son­able.” Maybe so, or per­haps the Pol­ish sci­en­tists have fall­en vic­tim to a more sophis­ti­cat­ed vari­ety of the psy­cho­log­i­cal sharpshooter’s fal­la­cy that affects “Bible Code” enthu­si­asts? I imag­ine we’ll see some frac­tal skep­tics emerge soon enough. But the idea that the worlds-with­in-worlds feel­ing one gets when read­ing cer­tain books—the sense that they con­tain uni­vers­es in miniature—may be math­e­mat­i­cal­ly ver­i­fi­able sends a lit­tle chill up my spine.

via The Guardian

Relat­ed Con­tent:

Hear All of Finnegans Wake Read Aloud: A 35 Hour Read­ing

See What Hap­pens When You Run Finnegans Wake Through a Spell Check­er

James Joyce Reads From Ulysses and Finnegans Wake In His Only Two Record­ings (1924/1929)

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness

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Comments (10)
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  • Michael Leddy says:

    Well, here’s a frac­tal skep­tic. It’s pos­si­ble to find all kinds of pat­terns in a lit­er­ary text that mean, per­haps, noth­ing. Jonathan Culler’s dis­cus­sion of the pat­terns found by Roman Jakob­son in (I think) Baude­laire’s poet­ry is rel­e­vant here.

    But also: stream of con­scious­ness is a way of rep­re­sent­ing a char­ac­ter’s thought process­es. (Dis­tin­guished, too, from inte­ri­or mono­logue.) It’s hard to call Finnegans Wake a stream-of-con­scious­ness nov­el. Ulysses has many pas­sages of stream of con­scious­ness but much else besides. Proust’s In Search of Lost Time is not an exam­ple of s‑o-c writ­ing.

  • John Selmer Dix says:

    You had me at Dave Eggers.

  • d block says:

    Proust’s nov­el was one of the nov­els they said did not have a frac­tal nature to it. So I don’t think the post meant to describe it as one.

  • Rob Kuhn says:

    That’s inter­est­ing … but … The plain-Eng­lish (non­frac­tal?) expla­na­tion of the mea­sur­ing process seems a lit­tle vague to me — though I could cer­tain­ly just not be “get­ting it.” (I did­n’t click through any of the links.) A sen­tence is the only type of frag­ment mea­sured, is that what it says? I’m hav­ing trou­ble under­stand­ing how all sen­tences in their vari­ety (“each sen­tence”) can then resem­ble the whole book … unless they are start­ing to count let­ters per word?? In any case, while this degree-of-frac­tal­ness could reflect somw writ­ing-style deci­sions, it seems to me it is prob­a­bly more like­ly to be ran­dom in most cas­es; is that a prin­ci­pal fea­ture of frac­tals? Mul­ti­frac­tals? I won­der: Have they got stats on the num­ber of lit-frac­tals per genre — macro (non-fic­tion/­fic­tion) and micro (novel/comic book, etc.)? And do those stats resem­ble a frac­tal? (Final­ly, is a parabo­la a type of frac­tal?) [Real­ly final­ly, how does this com­ment score/graph?]

  • Sebd says:

    Maybe we can call it auto­mat­ic writ­ing, as in sur­re­al­ism and psy­canal­i­sis

  • Michael Leddy says:

    d block wrote: “Proust’s nov­el was one of the nov­els they said did not have a frac­tal nature to it. So I don’t think the post meant to describe it as one.”

    No, the post did­n’t. But the page describes it as s‑o-c: “At the same time, a lot of works usu­al­ly regard­ed as stream of con­scious­ness turned out to show lit­tle cor­re­la­tion to mul­ti­frac­tal­i­ty, as it was hard­ly notice­able in books such as Atlas Shrugged by Ayn Rand and A la recherche du temps per­du by Mar­cel Proust.”

  • Cap­ti­vat­ed by this the­sis and the fol­low-up Qs and push-backs, here and also at the orig­i­nal guardian pub­li­ca­tion site. Curi­ous to know where Buster Keaton’s Sher­lock Jr. would fall on the graph (see “Pass­ing through the Equal Sign” in book edit­ed by Andrew Hor­ton), or on its ana­log for works of film.

    …Not to men­tion Film, Keaton’s off­beat exper­i­ment w/ Beck­ett.

  • Brian says:

    Some­one needs to real­ly dumb this arti­cle down for me–I’m real­ly strug­gling to get this. What exact­ly is frac­tal about these pieces of writ­ing? The only thing I got from the arti­cle was “sen­tence length.” Are they say­ing the fluc­tu­a­tions in sen­tence length are what make up this frac­tal shape?

  • TimJ says:

    My head hurts now, should­n’t have read this post twice. String The­o­ry is way eas­i­er to under­stand. I’ll try again tomor­row.

  • Phil says:

    Some Bach pieces show frac­tal traits in ways that are much more inter­est­ing than sen­tence length- for exam­ple, fugues where the melody pre­dicts what keys the piece will mod­u­late through.

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