In 1979, mathÂeÂmatiÂcian Kurt Gödel, artist M.C. EschÂer, and comÂposÂer J.S. Bach walked into a book title, and you may well know the rest. DouÂglas R. HofÂsÂtadter won a Pulitzer Prize for Gödel, EschÂer, Bach: an EterÂnal GoldÂen Braid, his first book, thenceÂforth (and henceÂforth) known as GEB. The extraÂorÂdiÂnary work is not a treaÂtise on mathÂeÂmatÂics, art, or music, but an essay on cogÂniÂtion through an exploÂration of all three — and of forÂmal sysÂtems, recurÂsion, self-refÂerÂence, artiÂfiÂcial intelÂliÂgence, etc. Its pubÂlishÂer setÂtled on the pithy descripÂtion, “a metaphorÂiÂcal fugue on minds and machines in the spirÂit of Lewis CarÂroll.”
GEB attemptÂed to reveal the mind at work; the minds of extraÂorÂdiÂnary indiÂvidÂuÂals, for sure, but also all human minds, which behave in simÂiÂlarÂly unfathÂomable ways. One might also describe the book as operÂatÂing in the spirÂit — and the pracÂtice — of HerÂman Hesse’s Glass Bead Game, a novÂel Hesse wrote in response to the data-driÂven machiÂnaÂtions of fasÂcism and their threat to an intelÂlecÂtuÂal traÂdiÂtion he held parÂticÂuÂlarÂly dear. An alterÂnate title (and key phrase in the book) MagÂisÂter Ludi, puns on both “game” and “school,” and alludes to the imporÂtance of play and free assoÂciÂaÂtion in the life of the mind.
Hesse’s esoÂteric game, writes his biogÂraÂphÂer Ralph FreedÂman, conÂsists of “conÂtemÂplaÂtion, the secrets of the ChiÂnese I Ching and WestÂern mathÂeÂmatÂics and music” and seems simÂiÂlar enough to HofÂsÂtadter’s approach and that of the instrucÂtors of MIT’s open course, Gödel, EschÂer, Bach: A MenÂtal Space Odyssey. Offered through the High School StudÂies ProÂgram as a non-credÂit enrichÂment course, it promisÂes “an intelÂlecÂtuÂal vacaÂtion” through “Zen BudÂdhism, LogÂic, MetaÂmathÂeÂmatÂics, ComÂputÂer SciÂence, ArtiÂfiÂcial IntelÂliÂgence, RecurÂsion, ComÂplex SysÂtems, ConÂsciousÂness, Music and Art.”
StuÂdents will not study directÂly the work of Gödel, EschÂer, and Bach but rather “find their spirÂits aboard our menÂtal ship,” the course descripÂtion notes, through conÂtemÂplaÂtions of canons, fugues, strange loops, and tanÂgled hierÂarÂchies. How do meanÂing and form arise in sysÂtems like math and music? What is the relaÂtionÂship of figÂure to ground in art? “Can recurÂsion explain creÂativÂiÂty,” as one of the course notes asks. HofÂsÂtadter himÂself has purÂsued the quesÂtion beyond the entrenchÂment of AI research in big data and brute force machine learnÂing. For all his dauntÂing eruÂdiÂtion and chalÂlengÂing synÂtheÂses, we must rememÂber that he is playÂing a highÂly intelÂlecÂtuÂal game, one that repliÂcates his own expeÂriÂence of thinkÂing.
HofÂsÂtadter sugÂgests that before we can underÂstand intelÂliÂgence, we must first underÂstand creÂativÂiÂty. It may reveal its secrets in comÂparÂaÂtive analyÂses of the highÂest forms of intelÂlecÂtuÂal play, where we see the clever forÂmal rules that govÂern the mind’s operÂaÂtions; the blind alleys that explain its failÂures and limÂiÂtaÂtions; and the posÂsiÂbilÂiÂty of ever actuÂalÂly reproÂducÂing workÂings in a machine. Watch the lecÂtures above, grab a copy of Hofstadter’s book, and find course notes, readÂings, and othÂer resources for the fasÂciÂnatÂing course Gödel, EschÂer, Bach: A MenÂtal Space Odyssey archived here. The course will be added to our list, 1,700 Free Online CoursÂes from Top UniÂverÂsiÂties.
RelatÂed ConÂtent:
How a Bach Canon Works. BrilÂliant.
Josh Jones is a writer and musiÂcian based in Durham, NC. FolÂlow him at @jdmagness