Knowl­edge Apparatus

Mark John­son, philoso­pher and the­o­rist in the field of embod­ied cog­ni­tion, employs the fig­ure of the line recur­rent­ly as the main com­po­nent of visu­al schema­ta. For embod­ied cog­ni­tion, the the­o­ry which demon­strates how our phys­i­cal expe­ri­ence of the world pro­found­ly influ­ences abstract thought, schema­ta are struc­tures which are extract­ed from bod­i­ly expe­ri­ences and trans­lat­ed as cog­ni­tive instru­ments which our brain employs to con­vey mean­ing. The recur­ring schema­ta of ​“path”—the phys­i­cal expe­ri­ence of mov­ing from one place to another—is thus rep­re­sent­ed by a sim­ple line and trans­lates in cog­ni­tion in the idea of con­nec­tion, the way two enti­ties relate one anoth­er1.

The line which con­nects dots and thus estab­lish­es imme­di­ate social rela­tions between data, con­cepts, geo­gra­phies appears as the visu­al metaphor of the net­work (the cen­tral fig­ure in con­tem­po­rary infor­ma­tion-based soci­ety). The mul­ti­ple lines defin­ing a net­work mate­ri­alise human abil­i­ty to relate sub­jects and con­struct knowl­edge out of iso­lat­ed objects, while ​“mov­ing” from one con­cept to another. 

The work of Cata­lan poly­math Ramon Llull (1232–1315), con­sid­ered among the ances­tors of for­mal sys­tems of log­ic and even of com­pu­ta­tion and arti­fi­cial intel­li­gence, con­sti­tutes a prece­dent in the visu­al con­struc­tion of rela­tion­ships through mul­ti­ple lines shap­ing a network.

Llull’s Ars gen­er­alis ulti­ma (“The Ulti­mate Gen­er­al Art”) or Ars Magna includ­ed paper-based mech­a­nisms aim­ing to cre­ate new knowl­edge from the con­nec­tion and com­bi­na­tion of dif­fer­ent con­cepts. In the first illus­tra­tion of the Ars, nine points equidis­tant on a cir­cum­fer­ence are all con­nect­ed through sim­i­lar lines. This sys­tem allows all the words writ­ten beside a rim to asso­ciate mutu­al­ly. As metaphors of mul­ti­ple paths, the lines mate­ri­alise here the active role of the var­i­ous terms and the way they inter­act in a dynam­ic sys­tem of relationship.

Llull ini­tial­ly con­ceived the Ars Magna as a device des­tined to the con­ver­sion of Mus­lims through the log­ics of Chris­t­ian faith. How­ev­er, the work pro­gres­sive­ly revealed an intrin­sic capac­i­ty of act­ing as a ​“log­i­cal machine:” an appa­ra­tus able to pro­duce knowl­edge in dif­fer­ent fields through mul­ti­ple com­bi­na­tions of notions. Through the sym­bol­ic poten­tial of the line, Llull con­struct­ed the very first demon­stra­tion that a device can imi­tate human thought.

Based on Llull’s pre­vi­ous dis­cov­er­ies, Jesuit­ic poly­math Athana­sius Kircher devel­oped var­i­ous com­bi­na­to­ry sys­tems capa­ble of gen­er­at­ing all pos­si­ble com­bi­na­tions from a finite col­lec­tion of ele­ments. Such tech­niques applied to the com­po­si­tion of aleatoric music, the descrip­tion of alchemic tables of trans­for­ma­tion, the con­struc­tion of a lan­guage. When the lines inter­twine, they draw fig­ures whose strik­ing visu­al qual­i­ties reveal Kircher’s aes­thet­ic preoccupations.

When, in 1666, Got­tfried Leib­niz wrote his youth­ful work Dis­ser­ta­tio de arte com­bi­na­to­ria, he was inspired by Ramon Llull’s Ars Magna. Despite late­ly con­sid­er­ing his text as imma­ture, the Ars com­bi­na­to­ria con­sti­tut­ed the philosopher’s access­way to the world of log­ic. In this work, all con­cepts derive from com­bi­na­tions of a small num­ber of sim­ple notions. A series of lines con­nect­ing basic con­cepts is again the fig­ure which defines the intel­lec­tu­al oper­a­tions. How­ev­er, the lines are no longer just pure con­nec­tors; here, they get suf­fi­cient­ly thick­ened to include the kind of rela­tion­ship they are sup­posed to sym­bol­ise (con­traria, pos­si­bilis, sum­ma). The lines do not lie on the same plane as in Llull’s fig­ures, but they are super­posed to con­struct an actu­al tis­sue of relationships. 

All these his­tor­i­cal fig­ures rep­re­sent ear­ly attempts to exte­ri­orise human thought and log­ic through sim­ple devices based on the abil­i­ty of the line to act as a con­nec­tor. Or, as Mark John­son implied, to trans­late fig­u­ra­tive­ly the act of walk­ing from one place to anoth­er into the con­cep­tu­al oper­a­tion of relat­ing notions to con­jure up con­cepts. The visu­al appear­ance and intrin­sic log­ic of those ear­ly devices resur­faced in the sym­bol­ic rep­re­sen­ta­tion of the net­work, a fig­ure made of inter­con­nect­ing lines, which became wide­spread with the ampli­fi­ca­tion of com­mu­ni­ca­tion infra­struc­tures. In the net­work, more points are con­nect­ed by more lines, inter­sect­ing and trans­mit­ting infor­ma­tion on dif­fer­ent scales. The basic schema­ta of the path turned into the uni­ver­sal metaphor of how a mul­ti­plic­i­ty of things com­mu­ni­cate and even­tu­al­ly pro­duce a world-wide brain. 

Such a cog­ni­tive anal­o­gy would become lit­er­al through the mod­el of the ​“arti­fi­cial neur­al net­work”, the typ­i­cal rep­re­sen­ta­tion of com­put­ing sys­tems inspired by the bio­log­i­cal neur­al net­works in the human brain. ANNs visu­al­i­sa­tions are an attempt to sim­u­late the archi­tec­ture of the human brain to improve the per­for­mances of con­ven­tion­al algo­rithms. The points in the net­work rep­re­sent arti­fi­cial neu­rons and the lines (here, called edges), act like the synaps­es in a bio­log­i­cal brain, capa­ble of trans­mit­ting sig­nals to oth­er neurons. 

For the lines in the net­work to lit­er­al­ly con­fig­ure phys­i­cal paths and the points to appear as real des­ti­na­tions, we have to look at a fur­ther mate­ri­al­i­sa­tion of the notion of the net­work, in which the metaphor becomes space, and space an archi­tec­tur­al project. In 1963, the archi­tects Can­dilis, Josic, Woods and Schied­helm won the inter­na­tion­al com­pe­ti­tion for the new cam­pus of the philo­log­i­cal insti­tute in Berlin. Their design had the pur­pose of trans­form­ing the cam­pus in a deeply inter­con­nect­ed ​“city” endowed with inter­nal streets, squares, court­yards and mul­ti­ple walk­ways. The net­work would appear as a guid­ing scheme in the project pre­sen­ta­tion, as it would trans­late in a spa­tial grid with­out any hier­ar­chi­cal dis­tinc­tion between class­rooms, depart­ments and facil­i­ties. Behind the pro­pos­al was a rad­i­cal rethink­ing of the edu­ca­tion­al sys­tem: the fig­ure of the network—the ide­al of hor­i­zon­tal com­mu­ni­ca­tion among stu­dents and teachers—becoming actu­al space. In this project, the think­ing-devices based on com­bi­na­to­ry log­ic which exte­ri­orise the brain process­es would become a full envi­ron­ment where mul­ti­ple paths allow peo­ple to walk across an urban land­scape of infor­ma­tion and pro­duce new knowledge.