Mathematics can serve as "extra science" for the arts
COUR TESY OF JOSEPH MEHLING '69
On Jan. 24, chair of the de part ment of math e mat ics and com puter sci ence pro fes sorDan Rock morede liv ered a lec ture about the re la tion ship be tween the dis ci plines of art and math e mat ics. The goal of this lec ture, en ti tled “How Math e mat ics Can Pro vide an Extra Sense for the Arts,” was to con vince his lis ten ers that math e mat ics and art are “very close cousins,” ac cord ing to Rock more.
Rock more opened his lec ture with his tor i cal ex am ples of how math e mat ics have been a muse for the arts.
“Greek ar chi tec ture was built on some no tion of whole num bers, which turned into no tions of ratio and pro por tion," Rock more said. "The Greeks also as pired to ward sym me try, which is a very math e mat i cal con cept."
He also cited the ex am ple of the Dutch artist M.C. Es cher, who is well known for his tes sel lations of the Eu clid ean and hy per bolic planes.
Rock more con tin ued to pro pose the ideas that events in so ci ety in flu ence both art and math e mat ics and that the fa mous move ments in both of these fields in flu enced each other.
“A lot of fa mous art move ments were … of fi cially in spired by math e mat ics, if you look at their man i festos," Rock more said. "Even those that don’t ex plic itly state it seem to have been in spired by math e mat ics.”
Pablo Pi casso, a pi o neer of the Cu bist move ment, spent much of his time in the com pany of math e mati cians who were well versed in geom e try. Rock more also pointed out that the rise of ab stract ex pres sion ism oc curred around the time that math e mat ics was be com ing a more ab stract dis ci pline.
Rock more used this back ground in for ma tion to segue into a dis cus sion about his work with vi sual sty lom e try, which is typ i cally de fined as the de vel op ment of math e mat i cal tools for the mea sure ment and com par isons of in di vid ual styles in the vi sual arts.
He first ex per i mented with vi sual sty lom e try in 2001, when he tested whether a com puter could an a lyze the lin ear con tent of the draw ings of Pieter Bruegel and de ter mine whether they were real or fake. He used eight gen uine Bruegel draw ings and five sketched by Bruegel’s con tem po raries.
Rock more an a lyzed dig i tal im ages pixel-by-pixel and cre ated sta tis ti cal sum maries of each work to cap ture the artist’s math e mat i cal “sig na ture,” which should be con sis tent from work to work. Ac cord ing to Rock more, each artist has a unique, idio syn cratic draw ing or paint ing style, per haps char ac ter ized by a cer tain style of shad ing or brush stroke thick ness. Rockmore’s soft ware then mapped the math e mat i cal sig na tures of the 13 draw ings. Eight works clus tered to gether on the map – the same draw ings that had been ver i fied by ex perts as authen tic Bruegels.
This is only one ex am ple of the ex tra or di nary work that has been done in the field of vi sual sty lom e try. Rock more spoke about Richard Tay lor, a pro fes sor at the Uni ver sity of Ore gon who dis cov ered a pat tern in Pol lock’s drip-and-poured paint ings. After care ful analy sis of the works, Tay lor found frac tals, which are nat u rally oc cur ring geo met ric pat terns that repeat over and over again at var i ous lev els of mag ni fi ca tion. Tay lor claims that these frac tals are the key to au then ti cat ing Pol lock’s works.
In fact, the Pol lock-Kras ner foun da tion com mis sioned Tay lor to an a lyze a trove of 32 works of art — sup pos edly painted by Pol lock right be fore his death — that were found in a storage unit in 2005. With Tay lor’s help, the foun da tion de ter mined that the al leged Pol locks were not au then tic.
Rock more closed his talk by en cour ag ing his lis ten ers to pur sue their in ter ests in var i ous fields and to look for the con nec tions be tween seem ingly un re lated dis ci plines.