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 Wake—a 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.)

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 Phys.org, 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