To Err is Human

Orsolya Gaspar

Interior space of the Rotunda di San Tomé. The neat overall tectonic order grows out of happenstance stereotomy.
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Interior space of the Rotunda di San Tomé. The neat overall tectonic order grows out of happenstance stereotomy.

Introduction

Upon enter­ing on a bright sum­mer day, it takes a cou­ple of sec­onds to get used to the dim light­ing of the Roton­da di San Tomé and absorb the straight­for­ward tec­ton­ic order of this 12th-cen­tu­ry mar­vel of Lom­bard Romanesque archi­tec­ture.[1] The cen­tral dom­i­cal space is defined by the pyra­mi­dal stack­ing of an ambu­la­to­ry and a gallery. The build­ing is enclosed by mas­sive, stone walls, with eight columns arranged con­cen­tri­cal­ly on each lev­el in the inte­ri­or. Upon clos­er inspec­tion, it becomes appar­ent that this neat over­all tec­ton­ic order grows out of total dis­or­der: Each col­umn is dif­fer­ent, some cap­i­tals are invert­ed col­umn bases from ear­li­er build­ing phas­es, the stereoto­my of the arch­es is dis­tinct in each bay, the lay­ers of the stone mason­ry both in the dome and the wall are uneven [ 1 ].

Fast-for­ward­ing eight hun­dred years, anoth­er dome of com­pa­ra­ble dimen­sions was erect­ed in Jena, Ger­many, for a tem­po­rary plan­e­tar­i­um. It was the world’s first geo­des­ic dome, and a pio­neer­ing thin con­crete shell (the grid was sprayed with con­crete).[2] The steel grid was designed with a pre­ci­sion of 1/20 mm, which is beyond even the cur­rent state of the art in met­al-work­ing capa­bil­i­ties. Only thir­ty years lat­er, a late descen­dant of the Jena plan­e­tar­i­um dome —a clever, yet unas­sum­ing, thin con­crete shell fac­to­ry roof­ing in Hun­gary —got extend­ed.[3] The project marked one of the ear­ly uses of com­put­ers in design. The exten­sion mim­ic­ked the orig­i­nal geom­e­try, but it was based on a more intri­cate mechan­i­cal mod­el, not man­age­able by hand cal­cu­la­tions. The com­plex­i­ty of those cal­cu­la­tions stems from the slight mod­i­fi­ca­tion of the orig­i­nal geom­e­try. Ever so sub­tle, that it is hard­ly notice­able; more­over, it bare­ly affects construction.

The builders of all three exam­ples erred in their treat­ment of pre­ci­sion, as in, align­ment: San Tomé is less pre­cise in its details than one would antic­i­pate, while the two shells aim at more pre­ci­sion than what is phys­i­cal­ly fea­si­ble or what is notice­able. Such errors result in incon­sis­ten­cy between design, con­struc­tion, and per­cep­tion. How­ev­er, once we con­sid­er pre­ci­sion in the meta­phys­i­cal sense, as in match­ing the intent, they all seem to be just pre­cise enough. The paper iden­ti­fies this con­flict between pre­ci­sion in the meta­phys­i­cal (idea) and the phys­i­cal (mate­ri­al­iza­tion) sense as one way to cre­ate poet­ics in con­struc­tion. Pre­ci­sion, in its meta­phys­i­cal sense strong­ly influ­ences the nar­ra­tive of the build­ing, which in turn impacts affect. 

This paper is not about the van­i­ty of pre­ci­sion. It is also not a swan­song for the ancient uni­ty of mate­r­i­al, build­ing, and con­struc­tion in the age of cod­i­fied design and com­put­ers. Rather, it is about the (cor­rect) scale and zooma­bil­i­ty of tec­ton­ics in a dig­i­tal era.[4]. I will use Frampton’s def­i­n­i­tion as a start­ing point, which states that tec­ton­ics is struc­tur­al and mate­r­i­al pro­bity but also a poet­ics of con­struc­tion”.[5] Such a def­i­n­i­tion is well-posi­tioned to con­sid­er when and which tools and mea­sures are appro­pri­ate in design and con­struc­tion, so that they enable rather than con­trol the process, and hence, ulti­mate­ly, serve both pro­bity and poetics. 

This paper is, fur­ther­more, about being fal­li­ble as a builder (that is, being incon­sis­tent as design­er and/or con­struc­tor). If being fal­li­ble, or to err, is essen­tial­ly human, is that desir­able, nec­es­sary, or per­mit­ted with­in the realm of archi­tec­ture today? It is beyond the scope of this paper to lament whether the future of archi­tec­ture, includ­ing pro­gram and tec­ton­ics, is to be defined by humans or machines. How­ev­er, I attempt to show that archi­tec­ture becomes poet­ic pre­cise­ly because of the minor incon­sis­ten­cies, errors, that cre­ate a rift between what it is meant to be and how it mate­ri­al­izes, i.e., between the act of con­stru­ing and the act of con­struct­ing.[6]

The select­ed exam­ples are fraud­u­lent in many ways: they all rep­re­sent the same, spe­cial archi­tec­tur­al form (dom­i­cal space), were not con­ceived by an archi­tect, and are all con­ve­nient­ly dat­ed. How­ev­er, they share two fea­tures that make them well-posi­tioned to illus­trate the argu­ments of this text: They all treat struc­tur­al and mate­r­i­al pro­bity as com­mon­place, which makes them high­ly tec­ton­ic, and they are all extreme­ly func­tion­al or pro­gram­mat­ic.[7] Their sim­i­lar­i­ty to each oth­er and their good match with many qual­i­ties appre­ci­at­ed in tec­ton­ic archi­tec­ture make them excel­lent guinea pigs to test the hypothe­ses of the paper: First, that pre­ci­sion is a design para­me­ter that is depen­dent not only on the tools and mate­ri­als but also on intent. While this might seem obvi­ous, it is eas­i­ly over­looked when our cur­rent tools allow prac­ti­cal­ly infi­nite pre­ci­sion. Sec­ond, that sub­tle incon­sis­ten­cies between idea and mate­ri­al­iza­tion can be virtues, and more impor­tant­ly, they might be the fea­tures that cre­ate affect, or poet­ics. Con­sis­ten­cy between design and con­struc­tion (i.e., focus­ing on pro­bity) was right­ful­ly pur­sued when archi­tec­ture was, by default, cre­at­ed by humans, who are incon­sis­tent by nature. In an era, how­ev­er, when machines, being pre­sum­ably con­sis­tent by nature, are becom­ing increas­ing­ly involved in the gen­er­a­tion of archi­tec­ture (includ­ing design and con­struc­tion), to pre­serve poet­ics, maybe it is the desired lev­el of con­sis­ten­cy that deserves a clos­er look. 

Dramatis Personae

As the three build­ings used as case stud­ies through­out this paper are not wide­ly known, a short intro­duc­tion seems adequate.

The Roton­da di San Tomé, also known as San Tom­ma­so, is locat­ed near the town of Almen­no San Bar­tolomeo, out­side Berg­amo, Italy. It was built in the 12th cen­tu­ry, like­ly replac­ing an ear­li­er struc­ture and reusing some of its build­ing mate­ri­als. It is a well-pre­served edi­fice of Lom­bard Romanesque archi­tec­ture, char­ac­ter­ized by its dis­tinc­tive fea­tures, includ­ing a sparse­ly dec­o­rat­ed exte­ri­or (lack­ing sculp­tures) and a series of blind arch­es crown­ing the walls, divid­ed by pilaster strips. The cir­cu­lar build­ing with a 16‑m diam­e­ter (exte­ri­or) was con­struct­ed using local stones, with­out mor­tar, and fea­tured 1.15 m‑thick walls filled with rub­ble. The few open­ings are strate­gi­cal­ly placed, ele­vat­ing light­ing into the tran­scen­dent. While its ori­gins are debat­ed, it is assumed that it was part of a female monastery from the 13th cen­tu­ry; as such, it served both the local com­mu­ni­ty and the con­vent. This dual pur­pose is evi­dent in the dis­tinct nar­ra­tives and dif­fer­ent crafts­man­ship of the ambu­la­to­ry and gallery detail­ing. The lat­ter, which served the nuns, is more refined and nuanced. The cen­tral space is capped by a stone mason­ry dome with an ocu­lus on top and four open­ings (two in the shape of a Greek cross and two cir­cu­lar) arranged even­ly around the base. The struc­ture repeat­ed­ly sus­tained severe dam­age over the cen­turies, due to light­ning, and it has been restored mul­ti­ple times. 

First Planetarium of Jena, exterior. The geodesic grid is recognizable under the thin layer of concrete.
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First Planetarium of Jena, exterior. The geodesic grid is recognizable under the thin layer of concrete.

The so-called first Plan­e­tar­i­um of Jena, built in 1922, was a tem­po­rary mock­up struc­ture erect­ed on the top of a build­ing in the Zeiss Fac­to­ry [ 2 ]. Zeiss, a man­u­fac­tur­er of opti­cal devices, devel­oped a new plan­e­tar­i­um device and need­ed a smooth, spher­i­cal sur­face to test it. The dome was designed by Walther Bauers­feld, the lead engi­neer of the plan­e­tar­i­um device. Due to the tem­po­rary nature and lim­it­ed load-bear­ing capac­i­ty of the roof, he opt­ed for a light­weight solu­tion. The orig­i­nal design of the 16 m‑diameter dome envi­sioned a light steel grid dressed in can­vas. How­ev­er, can­vas was not avail­able at the time, and Bauers­feld, advised by the con­crete-con­trac­tor Dywidag com­pa­ny, decid­ed to spray the grid with 3 cm of con­crete. Hence, this dome became the unlike­ly ear­ly pro­to­type of the pio­neer­ing Zeiss-Dywidag rein­forced con­crete shell con­struc­tion sys­tem. While the rein­force­ment in an ordi­nary rein­forced con­crete struc­ture is also assem­bled before the con­crete is poured, it is usu­al­ly done over form­work. Bauersfeld’s grid was self-bear­ing. It was a tri­an­gu­lat­ed grid, cre­at­ed as the sub­di­vi­sion of a spher­i­cal icosa­he­dron, made of approx­i­mate­ly 4,000 pieces of 60 cm long steel bars. As such, it was a geo­des­ic grid, built more than 20 years before Buck­min­ster Fuller coined the term geo­des­ic dome’. Bauers­feld lacked the means (in terms of the­o­ry and com­pu­ta­tion­al pow­er) to cal­cu­late such a com­plex struc­ture as a space truss; instead, he devised an inge­nious rule for tri­an­gu­la­tion that allowed him to esti­mate the strength of the struc­ture as a con­tin­u­ous sur­face. It also allowed him to use rel­a­tive­ly few dif­fer­ent bars, all with­in 20% dif­fer­ence in length. Intrigu­ing­ly, he set­tled for a rea­son­able” approx­i­ma­tion of what he aimed for (equal-area tri­an­gu­la­tion of the sphere), and yet he pre­scribed the length of each bar with 1/20 mm pre­ci­sion (that is less then 0,01%).

KÖFÉM Factory, second phase, shell roofing. The design accentuates the uninterrupted horizontal joint between wall and roof, despite the segmented shell roofing.
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KÖFÉM Factory, second phase, shell roofing. The design accentuates the uninterrupted horizontal joint between wall and roof, despite the segmented shell roofing.

The roof­ing of KÖFÉM Fac­to­ry is a cast-in-place thin con­crete shell, designed by Lajos Kol­lár, a struc­tur­al engi­neer and inter­na­tion­al­ly estab­lished schol­ar of shell struc­tures. The build­ing is an emi­nent exam­ple of mid-twen­ti­eth-cen­tu­ry indus­tri­al mod­ernism in East­ern Europe, where shell struc­tures enjoyed a late hey­day (com­pared to West­ern Europe). As labor was cheap, their mate­r­i­al effi­cien­cy made them an eco­nom­ic choice, a prime argu­ment in the cen­tral­ized, social­ist build­ing indus­try. It was built in 1967 as an exten­sion of an alu­minum pro­cess­ing plant in Székesfe­hérvár, Hun­gary. The roof­ing con­sists of a series of sad­dle shells (30 m x 11 m span, with a thick­ness of 6 cm). The first phase (com­plet­ed ten years pri­or, and visu­al­ly iden­ti­cal to the sec­ond phase) spear­head­ed a renewed inter­est in cast-in-place con­crete shells in Hun­gary after WWII. It was much cel­e­brat­ed for its econ­o­my and sim­ple, but ele­gant shape.[8] While sad­dle sur­faces are both prac­ti­cal (it is easy to inte­grate cleresto­ry win­dows) and struc­tural­ly ben­e­fi­cial, their joint with the enclos­ing walls cre­ates a design chal­lenge (the edge of a sad­dle is curved by default). The orig­i­nal KÖFÉM design addressed this issue by adding a conoid seg­ment to the short­er edge of the sad­dle, enabling a con­tin­u­ous, hor­i­zon­tal joint with the wall [ 3 ]. Kollár’s main con­tri­bu­tion in the sec­ond phase was that he sub­sti­tut­ed the three shell seg­ments (two conoids on the side and a sad­dle in the mid­dle) with a sin­gle, con­tin­u­ous sur­face, i.e., he form-found’ a shell with two curved and two straight edges. He achieved a geo­met­ri­cal­ly more hon­est solu­tion, but it required a dif­fer­ent, more com­plex mechan­i­cal mod­el, hence, more com­plex cal­cu­la­tions.[9]

Observ­ing chrono­log­i­cal­ly, there is a move from assem­bly towards con­tin­u­um, from rugged to smooth. The two lat­er struc­tures also chal­lenge the Sem­per­ian cat­e­gories of stereotom­ic and tec­ton­ic (i.e., frame-like), even­tu­al­ly dis­solv­ing into a hybrid form. It is hence tempt­ing to sim­pli­fy the emerg­ing sto­ry on pre­ci­sion into a trend from less­er to greater. This sim­pli­fi­ca­tion would miss the point, as it only con­sid­ers pre­ci­sion as a phys­i­cal phe­nom­e­non. Meta­phys­i­cal­ly, pre­ci­sion emerges (or should emerge) as a bal­ance between mate­ri­als, tools, and process­es. In short, it is intrin­si­cal­ly linked to the con­text. In this sense, all three build­ings are extreme­ly pre­cise, and it should strange­ly be most evi­dent for San Tomé, which is the ruggedest of them all: Just imag­ine what it would take today to erect a build­ing of com­pa­ra­ble dimen­sions as dry (!) con­struc­tion (no mor­tar, no binder).

Meta­phys­i­cal­ly, as I argued, pre­ci­sion is also linked to intent, which cre­ates a non-tan­gi­ble lay­er of tec­ton­ics. As I will show, the sub­tle pri­ma­cy of idea over mate­ri­al­iza­tion is appar­ent in all three cas­es. All builders erred, ever so slight­ly, on the side of the idea, and this trans­lates into tan­gi­ble incon­sis­ten­cies in pre­ci­sion in the phys­i­cal sense.

Dome, Rotunda di San Tomé, showing the clerestory openings
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Dome, Rotunda di San Tomé, showing the clerestory openings

Narratives and Perceptions 

While the Rotun­da has a cen­tral lay­out, it has an ori­en­ta­tion: the altar, the focal point in the Chris­t­ian litur­gy, is placed in an apse towards the north-east­ern side. This dis­po­si­tion slight­ly devi­ates from the tra­di­tion­al east-west ori­en­ta­tion of Chris­t­ian church­es, for a good rea­son: It has been shown that the axis aligns with that of the ris­ing sun on July 3rd, which cel­e­brates the trans­la­tion of Saint Thomas, to whom the Rotun­da is ded­i­cat­ed.[10] Light­ing plays a cru­cial role in the sym­bol­ism of the Roman litur­gi­cal space. Accord­ing­ly, the per­pen­dic­u­lar axes cre­at­ed by the cleresto­ry open­ings on the drum fol­low the same ori­en­ta­tion, allow­ing the ris­ing sun around the sum­mer sol­stice to project the Greek cross into the Rotun­da. Dur­ing the win­ter sol­stice, the cross appears with the set­ting sun. This care­ful over­all com­po­si­tion, with the nuanced ori­en­ta­tion and shap­ing of the cleresto­ry win­dows, is in stark con­trast (or, incon­sis­tent) with the hap­pen­stance’ stereoto­my of the build­ing, which Kings­ley describes as “(…) formed of rather rough­ly dressed blocks show­ing great vari­a­tion in size.”[11] [ 4 ] . While such rough­ness is most like­ly relat­ed to the incor­po­ra­tion of reused mate­r­i­al, and as such, obeys or embraces an exter­nal con­straint, there is also an intent. There is an appar­ent pref­er­ence for align­ment with the ethe­re­al by incor­po­rat­ing cos­mogo­ni­cal sym­bol­ism, as opposed to align­ment in the banal sense, as in obey­ing the hor­i­zon­tal when lay­ing cours­es. In terms of pre­ci­sion, as in align­ment, the Rotun­da is not nec­es­sar­i­ly a sto­ry of what was pos­si­ble, but about delib­er­ate choice, which results in incon­sis­tent tectonics.

Incon­sis­ten­cy is also encod­ed into the tec­ton­ic nar­ra­tive more explic­it­ly: as briefly men­tioned dur­ing the intro­duc­tion of the build­ings, there are marked dif­fer­ences in crafts­man­ship, mate­r­i­al, and, though less rel­e­vant to the present dis­cus­sion, in orna­ment, between the two sto­ries of the inte­ri­or spaces. His­to­ri­ans link those dif­fer­ences to the use of the space.[12] They argue that the ground floor is fin­ished in a much crud­er man­ner than the gallery, as per the client’s pref­er­ence. The ground floor was intend­ed for the pop­u­lus, while the gallery served the com­mu­ni­ty of the con­vent. Accord­ing­ly, their con­struc­tion is cred­it­ed to two dif­fer­ent groups of masons, with those work­ing on the gallery iden­ti­fied as hav­ing more advanced skills. The use of pil­fered mate­r­i­al is most appar­ent on the ground floor: the columns are reused from (like­ly) an ear­li­er build­ing phase. As they did not meet the height require­ment for their new place­ment, they have been accom­mo­dat­ed by var­i­ous mea­sures. This vari­ety is linked to the dif­fer­ent dimen­sions of the pil­fered bases (many of them for­mer cap­i­tals). The cap­i­tals across the eight columns have vary­ing heights and dif­fer in shape and orna­ment. In con­trast, the columns in the gallery appear to be cus­tom-made for the Rotun­da. Their for­mal lan­guage is con­sis­tent, with all cap­i­tals based on the Corinthi­an style – albeit their orna­ment is also unique. Hav­ing unique orna­men­ta­tion for each cap­i­tal was not uncom­mon in Chris­t­ian reli­gious archi­tec­ture, as the sculpt­ed ele­ments were lit­er­al­ly meant to tell sto­ries, in this case that of Tobit from the Old Testament. 

These dif­fer­ences in the tec­ton­ics of the two ambu­la­to­ry spaces can also be under­stood as dif­fer­ences in pre­ci­sion (as in join­ing, rich­ness of detail, or smooth­ness). Based on what we know, this also appears to be a delib­er­ate act. The emerg­ing over­all tec­ton­ics is not a mere con­se­quence of the use of reclaimed mate­r­i­al or a cer­tain lev­el of crafts­man­ship. It is guid­ed by a pro­gram­mat­ic intent; hence, the nar­ra­tive is care­ful­ly construed. 

In case of San Tomé, even with­out the his­tor­i­cal details and my inter­pre­ta­tion, much of its tec­ton­ics is relat­able, read­able’, the act of con­stru­ing can be phys­i­cal­ly expe­ri­enced. This also holds, though to a less­er extent, for ele­ments that are intan­gi­ble, such as the mes­sage of the light­ing. How­ev­er, con­stru­ing can remain unseen for the most part, as is the case for the two oth­er domes dis­cussed below. Just like with a text, the read­abil­i­ty’ of archi­tec­ture is not, and has nev­er been[13] absolute; it depends both on the cre­ator and the read­er (user).

Construing and Constructing 

Fras­cari refers to tec­ton­ics as both con­struct­ing and con­stru­ing.[14] Con­struct­ing encom­pass­es a whole range of activ­i­ties from con­cep­tu­al­iza­tion to mate­ri­al­iza­tion, from mate­r­i­al engi­neer­ing to the join­ing of steel bars that even­tu­al­ly lead to a con­struct. Much of the the­o­ry of con­stru­ing, implic­it­ly or explic­it­ly, is relat­ed to the idea(l) of a think­ing hand, an intu­itive (and human) under­stand­ing of the innate prop­er­ties of mate­r­i­al and the process of con­struc­tion.[15] Per the premise of this paper, I sug­gest that an intu­itive under­stand­ing of both tan­gi­ble (as mate­r­i­al) and intan­gi­ble (as geom­e­try and struc­tur­al behav­ior) aspects of the act of build­ing can man­i­fest as con­stru­ing. An intu­itive under­stand­ing (exper­tise) is devel­oped over time through ded­i­ca­tion. A pref­er­ence for using that intu­itive knowl­edge is the pay­off for such a cog­ni­tive­ly cost­ly process. It cre­ates a sub­jec­tive (or biased) focus dur­ing the process.[16] I argue that this focus inad­ver­tent­ly cre­ates minor incon­sis­ten­cies in tec­ton­ics, which can affect (and pos­si­bly ben­e­fit) its per­cep­tion, and often man­i­fests itself in rela­tion to precision.

Original Zeiss planetarium projecting device
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Original Zeiss planetarium projecting device

Subdivision scheme, geodesic gridshell of the first Planetarium of Jena.
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Subdivision scheme, geodesic gridshell of the first Planetarium of Jena.

Bauers­feld, who designed the geo­des­ic grid­shell encased in con­crete for the Zeiss Plan­e­tar­i­um, was a mechan­i­cal engi­neer by train­ing and worked in the opti­cal indus­try. He devel­oped the con­cept for the mod­ern plan­e­tar­i­um pro­ject­ing device [ 5 ], for which the dome was to serve as a test­ing ground. When prompt­ed to design a match­ing, dom­i­cal pro­ject­ing sur­face, he turned to the same Pla­ton­ic sol­id, the icosa­he­dron, which served as a base for the design of the plan­e­tar­i­um device. Because the struc­ture had to be light­weight, he con­sid­ered a grid­shell. The require­ment for smooth­ness neces­si­tat­ed the sub­di­vi­sion of the icosahedron’s faces. He devel­oped a spe­cif­ic sub­di­vi­sion scheme, based on the spher­i­cal pro­jec­tion of the icosa­he­dron, which result­ed in an almost equal-area tri­an­gu­la­tion[17] of the sphere [ 6 ].[18] Bauersfeld’s expressed moti­va­tion in pur­su­ing an equal-area tri­an­gu­la­tion was to ensure a good fit between what he intend­ed to build and the struc­tur­al mod­el he want­ed to use. He aimed to approx­i­mate the dense assem­bly of the bars as a con­tin­u­ous shell sur­face, and the cho­sen tes­sel­la­tion pro­vid­ed a rea­son­ably uni­form dis­tri­b­u­tion of bars. 

By opt­ing for a grid­shell, Bauers­feld chose a struc­tur­al solu­tion that was mate­ri­al­ly and eco­nom­i­cal­ly fea­si­ble, like any engi­neer would. There is no clear ratio­nale for con­nect­ing the geom­e­try of the grid­shell to that of the pro­ject­ing device, though. As the final sur­face was meant to be plastered/concreted over, its tan­gi­ble impact was much lim­it­ed. Such geo­met­ri­cal finesse was a sub­jec­tive pref­er­ence, a poet­ic com­po­nent of con­stru­ing, and yet, not com­plete­ly l’art pour l’art. Con­struc­tion and per­cep­tion also ben­e­fit­ed from Bauersfeld’s deep, intu­itive under­stand­ing of the geo­des­ic geom­e­try (i.e., a geom­e­try based on a spher­i­cal poly­he­dron). There is an intri­cate bal­ance of how a geo­des­ic geom­e­try is per­ceived (how smooth a tes­sel­la­tion looks) and how com­pli­cat­ed its assem­bly is (how many dif­fer­ent bars are need­ed), and Bauersfeld’s solu­tion pro­vid­ed an excel­lent trade-off.[19]

There is an inter­est­ing fluc­tu­a­tion of ide­al­ism and prag­ma­tism in Bauersfeld’s work that affects both con­stru­ing and con­struct­ing. Dur­ing the design phase, when he aimed at the equal-area tes­sel­la­tion he was an ide­al­ist, when he set­tled for the approx­i­mat­ing algo­rithm, which also allowed him to stan­dard­ize much of the bar-lengths, he was a prag­mat­ic. And yet again, in the phase of con­struc­tion, once the bars need­ed to be dimen­sioned, he pre­scribed their lengths with­in 1/20 mm pre­ci­sion, neglect­ing the real­i­ties of steel con­struc­tion. There is an anec­dote, how­ev­er, shared by a long-time col­lab­o­ra­tor of Bauersfeld’s, Franz Dischinger, on a sub­se­quent project, where a bar that was off by only 1 mm (on a 60 cm length) caused such defor­ma­tions in the grid that con­struc­tion had to be stopped and the faulty bar replaced.[20] Pre­scrib­ing pre­ci­sion an order of a mag­ni­tude high­er than the per­mis­si­ble range of error makes sense. Rather than see­ing a fluc­tu­a­tion, the process can there­for also be inter­pret­ed as guid­ed by intent[21]. Being loose where pos­si­ble and strict where nec­es­sary. More­over, the recur­sive for­mu­la he used for the tri­an­gu­la­tion of the sphere, instead of being a gen­er­a­tor of impre­ci­sion (even if very small), can be under­stood as a simul­ta­ne­ous act of con­stru­ing and con­struc­tion[22]: It works as if some­one were draw­ing or act­ing out the sub­di­vi­sion. It can be under­stood as a meta­phys­i­cal link between tools and processes. 

Bauersfeld’s bril­liance was in his abil­i­ty to over­come the lim­i­ta­tions of his tools (i.e., pen and paper) dur­ing the com­plex opti­miza­tion task he under­took. His approach was the­o­ry-dri­ven. Lajos Kol­lár, the design­er of the KÖFÉM exten­sion, on the oth­er hand, lever­aged the then-emerg­ing tech­nol­o­gy of com­put­ers to tack­le a prob­lem that was pre­vi­ous­ly suc­cess­ful­ly approx­i­mat­ed by hand cal­cu­la­tions. His approach was dri­ven by tech­nol­o­gy, but, like the­o­ry did for Bauers­feld, tech­nol­o­gy served Kollár’s vision.

Kol­lár was at the same time a prac­tic­ing struc­tur­al engi­neer with exten­sive expe­ri­ence and a respect­ed schol­ar and aca­d­e­m­ic. He felt that engi­neer­ing edu­ca­tion lacked strate­gies to devel­op design think­ing, and he emerged as an advo­cate for a holis­tic approach to design, some­thing he active­ly pur­sued in his prac­tice. In the case of the KÖFÉM fac­to­ry, the poet­ic he sought was an hon­est match between geom­e­try, struc­tur­al behav­ior, and per­ceived forms.

Enablers and Controllers 

The three exam­ples —San Tomé, the Plan­e­tar­i­um, and the KÖFÉM roof­ing —sug­gest a trend from less to greater con­trol dur­ing the design phase, and con­se­quent­ly, less auton­o­my for the builders. Indeed, such a trend exists. The engi­neer­ing rev­o­lu­tion in the eigh­teenth cen­tu­ry altered our expec­ta­tions of design: we require more cer­tain­ty, which is gen­er­al­ly a good thing, as it leads to safer con­struc­tion. We are, nev­er­the­less, oblig­ed to ques­tion the desired lev­el of con­trol case by case, so that it enables high pre­ci­sion, in the meta­phys­i­cal sense, achiev­ing the desired trade-off between mate­ri­als, tools, and processes.

Shells are extreme­ly thin struc­tures. They can be thin, because (thanks to their curved shape) they pri­mar­i­ly car­ry their loads through com­pres­sion and ten­sion which is more effec­tive than through bend­ing. Their thin­ness makes them high­ly impact­ful as tec­ton­ic objects, but it also makes them high­ly sus­cep­ti­ble to mis­takes, includ­ing those dur­ing design and con­struc­tion. There­fore, while the the­o­ry of shells devel­oped rapid­ly in the first half of the twen­ti­eth cen­tu­ry, mod­el build­ing and test­ing, often on a full-scale basis, remained an inte­gral part of shell design. The col­lapse of the mock­up built to demon­strate the fea­si­bil­i­ty of the orig­i­nal design for the KÖFÉM fac­to­ry roof­ing (first phase) almost sank the project. Even­tu­al­ly, the design could pro­ceed, as the inves­ti­ga­tion iden­ti­fied that con­struc­tion defi­cien­cies caused the col­lapse. Such dra­mat­ic events, as the col­lapse of the mock­up, were rare. Instead, the mod­el exper­i­ments helped design­ers and con­trac­tors eval­u­ate their pre­dic­tions based on the­o­ry alone and refine their struc­tur­al mod­els accord­ing­ly. Kol­lár had exten­sive expe­ri­ence with phys­i­cal mod­els, which gave him an intu­itive, expe­ri­en­tial under­stand­ing of the behav­ior of shells and an appre­ci­a­tion for the more com­plex, com­pu­ta­tion­al­ly inten­sive struc­tur­al mod­els for shells. 

Shell surface of the KÖFÉM Factory roofing
7

Shell surface of the KÖFÉM Factory roofing

The so-called mem­brane mod­el, which com­plete­ly dis­re­gards bend­ing moments in the shell, is ele­gant and straight­for­ward, but its applic­a­bil­i­ty is strict­ly con­strained. While it suits cer­tain process­es well (such as form-find­ing), in oth­er sit­u­a­tions, it becomes a con­trol­ling rather than an enabling tool. Such lim­it­ing con­trol affects tec­ton­ics. As described in the intro­duc­tion to the build­ings, the first phase of the KÖFÉM Fac­to­ry roof­ing appears to be a con­tin­u­ous shell from wall to wall, but in fact, it con­sists of three shell seg­ments. More­over, tech­ni­cal­ly only one of them, the sad­dle in the mid­dle, acts as a shell; the conoids are can­tilevered from the walls, and their behav­ior is clos­er to a plate. The first phase design, from an engi­neer­ing point of view, was inge­nious: the saddle’s shape (side-length ratios) was cho­sen so as not to exert any thrust on the conoids [ 7 ]. The design cre­ative­ly relied on the sim­pler mem­brane mod­el to min­i­mize cal­cu­la­tions (which were done by hand), but a dis­so­nance remains between per­cep­tion and behav­ior. Kol­lár resolved that dis­so­nance by defin­ing a sin­gle, con­tin­u­ous sur­face that act­ed as a shell, albeit one that’s behav­ior is more com­plex[23] than what the mem­brane mod­el can describe. The then-emerg­ing com­put­ers enabled him to apply the more com­plex mod­el accord­ing­ly, and, from a con­cep­tu­al point of view, to pur­sue a more holis­tic aim.

The con­sis­ten­cy Kol­lár achieved in the sec­ond phase of the KÖFÉM Fac­to­ry is excit­ing from the per­spec­tive of this paper, as it is almost post-human, which would make him the oppo­site of fal­li­ble. How­ev­er, it is essen­tial to note that his design builds upon an exist­ing one. He did not change the mate­r­i­al or the con­struc­tion tech­nol­o­gy. The two geome­tries are indis­tin­guish­able to the untrained eye (most eyes are untrained). He changed an excel­lent design main­ly to make the unseen, right. Not unlike Bauersfeld’s dimen­sion­ing, his process seems too pre­cise, in the phys­i­cal sense.

Epilogue

As exem­pli­fied above, high pre­ci­sion in the phys­i­cal sense can be both a virtue and a vice, and it can be inter­pret­ed vast­ly dif­fer­ent­ly depend­ing on the mate­ri­als, tools, and process­es involved. Today, amidst rapid tech­no­log­i­cal devel­op­ment, it is tempt­ing to opt for high­er pre­ci­sion, because the con­struct is made infi­nite­ly zoomable dur­ing the design phase. The then-emerg­ing tec­ton­ics is only con­strued, though, it is vir­tu­al. To allow for con­struc­tion to shape tec­ton­ics in the phys­i­cal realm, it is vital to treat pre­ci­sion in the meta­phys­i­cal sense, which depends on the con­text and not on scale.

The dis­cussed case stud­ies rep­re­sent dif­fer­ent regions on the broad spec­trum of archi­tec­ture, span­ning from the pri­mor­dial hut to struc­tur­al art. In the phys­i­cal sense, their pre­ci­sion is in vast­ly dif­fer­ent dimen­sions, meta­phys­i­cal­ly how­ev­er, all three are just pre­cise enough. They are all high­ly pro­gram­mat­ic; they show hon­est­ly what they are made of and how they stand up, and, while for dif­fer­ent rea­sons, each of them is poet­ic. I argue that they are poet­ic because they err in their treat­ment of pre­ci­sion, in the phys­i­cal sense. They treat it incon­sis­tent­ly. Such incon­sis­ten­cy is present in each case either with­in the design con­cept or it cre­ates a rift between the idea and its realization. 

These exam­ples are shaped by these sub­tle incon­sis­ten­cies, because their cre­ator was fal­li­ble. The tan­gi­ble pre­ci­sion of each project is not only sub­ject to what was pos­si­ble, but to what the design­er intend­ed. Those intents are high­ly sub­jec­tive, informed by a ded­i­ca­tion (to the divine), or years of train­ing in the­o­ry or prac­tice. To fall for one’s inter­est or intu­ition, to be biased, to err in this sense, is in fact, no longer only a human trait. Just as archi­tec­ture is no longer prac­ticed by humans with­out sig­nif­i­cant assis­tance from tech­nol­o­gy. It is there­fore vital to be mind­ful of the role incon­sis­ten­cies played in cre­at­ing the var­i­ous com­po­nents of tec­ton­ics in the past. It might guide us in shap­ing archi­tec­ture to our lik­ing in the future, either con­sis­tent­ly or incon­sis­tent­ly, but intentionally.

  1. 1

    Kings­ley, 1915.

  2. 2

    Gáspár, 2022.

  3. 3

    Designed with archi­tect Ipoly Farkas, and engi­neer Lajos Sem­sey. Kol­lár, 1969.

  4. 4

    Gar­cia, 2014.

  5. 5

    Framp­ton, 1990.

  6. 6

    This is relat­ed to con­cepts vir­tu­al and actu­al form as in Fras­cari, 1984. p 501

  7. 7

    Zumthor, 2006.

  8. 8

    Mán­do­ki, Gáspár, 2017. The econ­o­my stemmed from the con­struc­tion tech­nol­o­gy, which ben­e­fit­ted from a reusable form­work and the inte­gra­tion of the scaf­fold­ing sys­tem with the future-to-be over­head crane of the plant.

  9. 9

    There was a slight kink between the sad­dle and the conoid (they were only G0 con­tin­u­ous). The orig­i­nal design relied on the so-called mem­brane the­o­ry of shells for the sad­dle sur­face (which has lim­it­ed applic­a­bil­i­ty but allows cal­cu­lat­ing the stress­es in the shell as if it was a bend­ing-free sur­face), and the conoid was con­sid­ered as a can­tilever (sup­port­ed by the wall). The sad­dle was a sec­ond order sur­face (a qua­drat­ic sur­face). Kollar’s design was a fourth order sur­face, and he relied on the bend­ing the­o­ry of shells, which accounts for pos­si­ble moments in the shell.

  10. 10

    Paris et al, 2024.

  11. 11

    Kings­ley, 1915, p. 41.

  12. 12
  13. 13

    The intri­cate geo­met­ri­cal pro­por­tions shap­ing Goth­ic struc­tures (which are close­ly relat­ed to San Tomé, both tem­po­ral­ly and tech­no­log­i­cal­ly) extend from the build­ing scale down to orna­ments, pro­vid­ing a well-known example.

  14. 14

    Fras­cari, 1984. p 506.

  15. 15

    Pal­las­maa, 2009

  16. 16

    Yann LeCun, a lead­ing expert of AI and deep learn­ing sug­gests that the need to focus on select­ed pref­er­ences is inher­ent­ly human, and stems from the cog­ni­tive lim­its of the human brain. LeCun, 2019.

  17. 17

    Assum­ing pin joints, a sin­gle lay­er grid­shell can only be rigid if tri­an­gu­lat­ed. When con­sid­er­ing an equiv­a­lent con­tin­u­ous sur­face, the pin-joint assump­tion in the grid aligns well with the sim­pli­fied, mem­brane mod­el of con­ti­nous shells –bend­ing moments can be neglect­ed in both.

  18. 18

    Gáspár, 2022. The recur­sive algo­rithm he devised can­not achieve equal area tes­sel­la­tion the­o­ret­i­cal­ly, but it was easy to cal­cu­late, and the result­ing tes­sel­la­tion only devi­at­ed by 1% from the the­o­ret­i­cal optimum.

  19. 19

    So good that it out­per­forms most geo­des­ic geome­tries devel­oped by schol­ars and prac­ti­tion­ers (includ­ing Buck­min­ster Fuller) over the rest of the twen­ti­eth cen­tu­ry. Bauers­feld was aware of the ben­e­fits of his design: by inci­dent, I refer to the fact that start­ing with an icosa­he­dron was not self-evi­dent, but rather intuitive.

  20. 20

    Dischinger, 1929. Giv­en the con­scious and assertive pub­li­ca­tion cam­paign around the Zeiss-Dywidag sys­tem (May, 2015), this anec­dote might or might not be true, espe­cial­ly, as two sim­i­lar sto­ries are told by Bauers­feld him­self (Bauers­feld, 1942 and 1957), where the casus bel­li is iden­ti­fied as (a) a (since then proved) tem­po­rary sta­bil­i­ty prob­lem of the incom­plete grid­shell and (b) the tim­ing of the pour­ing of con­crete (either of them would be less flat­ter­ing for the new busi­ness ven­ture than show­ing off its almost insane precision).

  21. 21

    As appeal­ing as it sounds, it is unlikely(=unproven) that Bauers­feld was con­scious­ly aware of the room of error for the bar-length. At best, it can be assigned to the uncer­tain ter­ri­to­ry of intuition.

  22. 22

    It is still an open ques­tion if it is the­o­ret­i­cal­ly pos­si­ble to tes­se­late the sphere sim­i­lar­ly, i.e., with rea­son­ably reg­u­lar’ equal area triangles

  23. 23

    Kollár’s ver­sion was mod­elled and cal­cu­lat­ed based on the so-called bend­ing the­o­ry of shells, which indeed accounts for the pres­ence of bend­ing moments.

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https://www.lombardiabeniculturali.it/architetture/schede/BG020-00689/ last accessed 07.07.2025