The Language of Architecture 26 Principles Every Architect Should Know by Andrea Simitch, Val Warke

The CaixaForum gallery in drapery, window as opening
Madrid by Herzog & de or marking, and building as
Meuron (completed 2007) entity or material. A familiar
incorporates the brick body building is rendered unfamiliar,
of a former power station, promoting previously
estranging its fundamental unthinkable perceptions of
character: its stone foun- architecture. The adjacent
dation is removed; its brick Vertical Garden by Patrick
envelope suspended above a Blanc (2007) further
sunken entry court; and a defamiliarizes concepts of
ponderous, oxidized steel mass and material, with
volume erupts as an alien “wall” as “ground,” sugges-
mansard. The manipulation ting a dislocation of the
of the older structure nearby botanical gardens.
contests our understandings
of brick as structure or 17 Defamiliarization

Walter De Maria’s The New columns seem to “grow” from Poetics almost perverse, collision of vehicular and
York Earth Room (1977), the dirt, lighting fixtures The defamiliarized form, shaken loose from domestic cultures. For those observers, the
curated by the Dia Foundation, seem as sunlight penetrating its rote denotation, is free to develop new defamiliarization of the cladding of an
consists of a second-floor a canopy of foliage, walls as levels of connotation. With this “thickening” everyday, mass-marketed wagon—an object
Manhattan loft filled with fragments of a ruin. The of architecture’s language, observers become that would normally be visually consumed in
140 tons (127 metric tons) of persistent whiteness, almost aware of architecture’s capacity for poetic a moment—initiated a thoughtful contempla-
dirt. Discovering the loamy- a platitude in modern implication: Even the most prosaic forms tion that would forever alter their percep-
scented space in Soho not apartment lofts, exaggerates begin to resonate with unforetold significa- tions of such wagons and, possibly, of
only underscores the rarity of the unnatural contrast, tions and possibilities. These poetic artificial veneers and even industrialized
earth in this part of the suggesting a reciprocal consequences may influence our societal, domesticity.
city—of country relocated artificiality between the environmental, ethical, emotional, and
into city—but it suggests a vacancy of the loft and the esthetic prejudices and understandings. Exposure to the unfamiliar aspects of the
reevaluation of the elements soil permanently tilled for familiar, the habitual, and the commonplace
comprising the space: growth that never happens. Extension of Awareness not only discloses the lost and hidden
When the vinyl wood-grained body paneling meanings behind the forms in our world, but
fell from a colleague’s 1970s station wagon, frequent encounters with the unfamiliar
she felt it was necessary to somehow cover extend our abilities to “read” the world
the exposed splotches of black glue and through forms.
rusted screw heads. Combining inexpensive-
ness, efficiency, and an architect’s sensibility, 148 149
she replaced the plastic wood with thinly
molded sheets of plastic bricks. The
unremarkable wagon became a very
remarkable object. While few people were
willing to park next to it, many were willing to
comment on what the wagon revealed of the
suburban esthetic it engaged: “wood” siding
on automobiles represents a very peculiar,

THE LANGUAGE OF ARCHITECTURE Architecture’s capacity for transformation
can sponsor alternative programs, inhabi-
tations, appearances, and performances.

18 150 151

transformation

Transformations occur at multiple scales, from the smallest particle to an entire building,
and at any interval, from a one-time event to a cyclical transformation.

While the material of architecture might be predomi-
nantly static—concrete, steel, stone, glass, wood—the
experience of architecture can be a highly dynamic
one. Architecture has the capacity to transform from
minute to minute, day to day, year to year.

Ernst Giselbrecht in 2005–07 allowing for both personalized
created the “Dynamic orientations and environ-
Façade” for the Kiefer mental responsiveness.
Technic Showroom in Bad The origamilike surface
Gleichenberg, Austria. Here continually transforms the
an independent surface of experience of the building
perforated light metal bifold and the landscape from
panels can be positioned in within and from without.
an infinite variety of ways,

THE LANGUAGE OF ARCHITECTURE By inserting a series of full- Hangar 16 in Madrid, Spain,
height steel doors into the creates multiple spatial
vast, seemingly limitless readings that also facilitate a
space of the former range of programmatic scales—
slaughterhouse structure, from intimate art openings to
Iñaqui Carnicero’s 2012 full-blown rock concerts.

These transformations can be literal, implied, movement of the Sun), programmatic (a Temporal (Animation)
or often both. In other words, a panel can train compartment transforms from living Architecture registers the passage of time.
slide from one position to another, or as light room by day to bedroom by night with the Embedded within its transformations are the
moves across its surface, it can transform lowering of the bunks), or spatial (a volume traces of human rituals and environmental
from reflective solid to transparent. But in all enlarges as its occupancy increases). stimuli. The sliding, rotating, opening, and
cases, this transformative capacity can Transformations occur at multiple scales, closing of surfaces have the ability to
sponsor alternative programs, inhabitations, from the smallest particle to an entire transform spatial scales and relationships,
appearances, and performances—in other building, and at any interval, from a one- determine conditions of public and private,
words, architecture really is never very static time event to a cyclical transformation. and transform functions and operations.
at all.
For example, it is very common in modern Topological
Literal theaters for the audience/performance Architectural space, form, and surface can
A kinetic architecture not only registers and relationship to be physically altered by also transform through the deformation of
adapts to the effects of external stimuli but it rotating stages, lifts, and movable loge underlying structural patterns, based on
also provokes behaviors as a function of its seating; while projection technologies can mathematical models that subsequently
transformation. External stimuli can be perceptually alter the sense of enclosure, inform the qualitative aspects of such
environmental (shutters adapting to the weather, and time. patterns. As an alternative to literal

Eileen Gray’s expanding furnishings transform to 18 Transformation
wardrobes in Tempe à serve multiple spatial and
Pailla—the house she functional programs. The
designed for herself in entry hall’s extendable
Castelar, France, from wardrobe expands to
1932–34, are but one example accommodate its changing
of an interior conceived as contents, but in doing so,
an enormous piece of transforms the entry hall’s
furniture—where both spatial sequence.
surfaces and freestanding

movement, these seamless physical Implied In 2013, Skylar Tibbits of the absorbing material equips 152 153
transformations produce a fluidity of form Architecture transforms in nonkinetic ways Self Assembly Lab at MIT, the resulting composite
where walls become floors become ceilings as well, where the implication of transforma- along with Stratasys and material with a built-in
as they respond to programmatic stimuli. tion can reside in programmatic, formal, or Autodesk Inc., have functionality when exposed
perceptual interpretations. developed a process whereby to water, one that, when
Smart Materials a composite material can multiplied and introduced
Programmable materials—synthetic materials Programmatic expand and deform according over a larger territory,
that can be “stitched” into everyday materials Buildings that undergo programmatic to preprogrammed constraints. anticipates the transfor-
and that self-activate when exposed to heat, transformation appropriate elements that The binding together of a mation of form as it responds
water, and electricity—transform the surfaces were once designed for another specific malleable material with a to external stimuli.
and forms into which they are embedded purpose. For example, light projected polymer-based, water-
through processes such as contracting, through the stained glass windows of a
swelling, and thinning. Often these church-turned-nightclub transforms the
activations occur at the nanoscopic scale— meaning of those windows from religious
the scale at which particles, hence material, texts to disco balls. While nothing has
undergo change. physically changed, it is the context of the
experience that transforms one’s perception
of the work.

In their 2009 design for the produce a continuous vertical one, where the
Astana National Library in spiraling path, a three- patterns of its surfaces map
Kazakhstan, BIG (Bjarke dimensional Möbius strip, the thermal requirements of
Ingels Group) combines a that begins as a horizontal its changing orientations.
series of geometries to space but that shifts to a

THE LANGUAGE OF ARCHITECTURE The ground floor of Norman space used by Filipina
Foster’s HSBC building in domestics. Plugged into an
Hong Kong (1978–85) is a existing infrastructure of
permeable space that, during pedestrian, vehicular, and
working hours, operates as subterranean networks, it is
institutional entry to the a continuously transforming
banking halls and offices public space with the ability
towering above, yet on to be appropriated by an
Sundays is transformed into a evolving urban culture.
marketplace and gathering

Theme and Variation
Recognizable repetition that constructs a
recognizable and cohesive overall “pattern”
permits uniqueness and difference to exist
within it without destroying the cohesiveness
of the whole.

Role of Perception and Memory Donald Judd’s 1980–84 to enclosed on only the two its individual frames and
Things once experienced in a specific way collection of sixty-four 2.5 x short sides. Any single strewn across the landscape.
appear to undergo change when perceived 2.5 x 5 m (2.8 x 2.8 x 6 yd) volume does not literally The comprehensive
from a context that has been altered. concrete boxes distributed in transform, but when understanding is of a form
Architecture has the ability to anticipate, fifteen clusters across the experienced as a collection, and of a space that is
and even produce, this altered context. Chinati Foundation’s valley in the implication is that each undergoing transformation—
On the other hand, memories of previously Marfa, Texas, are each container and each cluster is and as a result transforming
experienced architectures rarely remain constructed in one of several a formal variation of the the perception of the
intact when revisited, as meanings are often states of enclosure, from other, as if an animated landscape in which they have
drawn from and transformed by experiences enclosed on all sides save one filmstrip were dissected into been located.
collected over time.

Bernard Tschumi‘s Parc de la 11.8 x 11.8 yd]), its material
Villette in Paris, France (steel), and its color (red),
(1982–98) presents a grid of each pavilion is a unique
thirty-five pavilions super- spatial exploration of the
imposed onto an open field to cubic volume, developing its
create an urban park. While specificity in relation to the
each pavilion is related to the spontaneous programs that
other in its basic dimension they were intended to sponsor.
(10.8 x 10.8 x 10.8 m [11.8 x

Through the carefully ceiling of the interior is
calibrated orientation of the perceptually dematerialized,
exterior glass surfaces of transforming the space into
Philip Johnson’s 1949 Glass an exterior arbor supported
House in New Canaan, by trunks of steel and bark.
Connecticut, the solid plaster

154 155

THE LANGUAGE OF ARCHITECTURE Infrastructure introduces a systemic
order, an identifiable armature to which
other components can be subsequently
attached.

19 156 157

infrastructure

Infrastructural systems are intermediary devices between the requirements of the program
for which they have been designed and the context in which they are located.

Like the human body, buildings, cities and landscapes
have intertwined layers of independent networks, or
infrastructural systems, that work together to create
a total system. A network not only serves a specific
function, but that function, in turn, establishes the
parameters of the network—its scale, its dimension,

THE LANGUAGE OF ARCHITECTURE The infrastructural network highways produce an
of Japan’s highway system independent, constructed
follows an entirely landscape. The Hakozaki
independent spatial logic Interchange of the Tokyo
than the cities over which it Metropolitan Expressway is a
passes. Motivated by automo- dense structural web of
tive access to dense urban enormous scale, transforming
conditions with severe spatial the exterior spaces of the city
constraints, these layers of into a cathedrallike interior.

its functionality, and its visibility. And like an Physical Weiss/Manfredi’s 2007 uninterrupted circulation
orchestra, where each instrument contributes Infrastructure introduces a systemic order, an Seattle Art Museum: Olympic through the complex site,
to the overall symphony, each network is also identifiable armature to which other things can Sculpture Park blurs the spanning existing highway
independent, serving a specific purpose and subsequently attach. At a larger scale, boundaries between museum and rail infrastructures while
behaving in a specific way, yet together they infrastructure often becomes the connective and city, building and providing site drainage and
operate to create the larger work. tissue that links fragments of existing landscape. Conceived as a remediation systems. Within
programs, creating a larger and more visible continuous landscape linking the building, the topography
Infrastructural systems can be physical or network. A series of parks can establish an the city’s sidewalks above to is reiterated at a smaller
ephemeral. As a physical network, they are urban infrastructural network, with individual the waterfront esplanade scale, as a sequence that cuts
intermediary devices between the require- neighborhoods organizing themselves, both below, the museum’s concept through and connects its
ments of the program for which they have culturally and physically, around a specific park motivates all architectural galleries. Finally, its exterior
been designed and the context in which they along the network. Alternatively, a system of and environmental decisions. surfaces provide outdoor
are located. A network of highways operates repeating structural pylons that supports an At the urban scale, its amphitheaters and exhibition
as an interface between the speed and overhead viaduct might become an organizing undulating topography both areas, expanding the
turning radii of the automobile and the city device that serves as points of reference for houses the museum’s museum’s cultural program
or topography through which it passes. the neighborhoods nestled below. principal galleries and service into the city.
Alternatively, one may have an ephemeral spaces and creates
network that is not physically constructed. Systemic Armatures
For example, the Freedom Trail is a Like the grand structures of the Roman
collection of buildings and sites where aqueducts, basic infrastructural amenities
important events throughout Boston’s history such as transportation, water, plumbing,
have occurred. It is an historic armature that electricity, and so on can operate as
crosses time and space, marked by a simple architectural armatures that spatially
red line inscribed on the sidewalks of Boston. organize the complexes they serve. When
visible, they become orienting devices that
provide an underlying structure to the
context within which they exist.

An abandoned rail line that buildings into primary faces, 19 Infrastructure
once served to bring meat always demanding alternate
into lower Manhattan is forms of orientation and
transformed into an urban access. The continuity of this
park, lifting pedestrians into new linear park overlays an
a part of the city they were uninterrupted spatial
never intended to utilize. experience onto what is
This now occupiable typically the interrupted
infrastructure reframes the series of urban blocks and
urban experience as it streets below.
develops a secondary route
that engages the city in Diller Scofidio + Renfro
unanticipated ways, Architects and James Corner
transforming the previously Field Operations with Piet
inaccessible backs of Oudolf (Phases I, II , and III:
2009–15)

Introducing a formal circu- a spine of commercial activity
lation network into the to areas that would otherwise
informal hillside neighbor- be too dangerous to venture
hoods of Medellín, Colombia’s within, much less service.
Metrocable links the crowded Here, infrastructure operates
and marginalized, often both as cultural lens and as
dangerous, communities to connective and programmatic
the city’s primary subway armature, transforming
routes. Floating gondolas the context through which
that scan the densely it passes.
populated landscape not
only bring an audience to Proyecto Urbano Integral
communities that are (Integral Urban Project),
typically very insular, but the The Metrocable San Javier,
cable car stations introduce completed in 2008

158 159

Exquisitely thin armatures introduce a series of At Álvaro Siza Vieira’s 1977 the separate residential
inscribe pedestrian structural ribbons that Quinta da Malagueira clusters is attached. The
movement over and through tip-toes three dimensionally housing community in Évora, structures that support the
the Icelandic landscape—lift- across a newly constructed Portugal, a system of raised raised channels overhead
ing skyward what appear to highway and from which concrete aqueducts not only mediate between individual
be mysterious traces of pedestrians can experience provides the infrastructure houses and shops and the
Viking passages. Studio an expanded and directed necessary for water and adjoining public spaces while
Granda’s 2003 Footbridges visual field. electric distribution but also creating shaded loggias along
over Hringbraut & Njardagata an armature to which each of which the residents circulate.

THE LANGUAGE OF ARCHITECTURE One of the ten themed it not only creates an isolated Here storm drainage pipes In his meticulous urban with the historic city, same diameter, which then
gardens at Parc de la Villette and unique ecosystem of become elevated thresholds renovations for Guimarães, underscoring the bay serve a series of functions:
in Paris, France, Alexandre bamboo forests and falling beneath which one moves, Portugal (begun 1987), rhythms and motifs of the as fountain ornament, as
Chemetoff’s Bamboo Garden waters, but also exposes the assembled into a network of Fernando Távora uses paving, city’s more public buildings. boundaries for the pedestrian
(1987) is sunken below the layers of infrastructure that bridges and walkways an occasional fountain, and Here, in Largo de João realm, and even as parking
rest of the park. In so doing, normally remained concealed. hovering above. various infrastructural Franco, the round windows of bollards.
elements to initiate what is, the building at the end are
in effect, an analytic dialogue translated into spheres of the

Scales of Engagement
Bus stops, street furniture, fountains, street
lighting, and the like, are infrastructural
elements whose details, textures, and
dimensions introduce a scale of engagement
that mediates the human body with its larger
environment.

Evanescent In the Netherlands, Thor ter
Making visible what is typically invisible or Kulve converts the prosaic
appropriating existing infrastructural urban infrastructures of
elements in surprising ways are devices that streetlights and fire hydrants,
can raise ecological consciousness, often parking poles, and garbage
introducing an unexpected dimension to an receptacles into whimsical
otherwise necessary, yet prosaic, function. and unexpected programs.
In other words, while infrastructural projects Temporary installations
might be motivated by functional necessities, attach themselves directly
they can also provide shelter, recreational, to existing structures,
environmental, and cultural amenities. interpreting their intrinsic
and passive functions into
Cultural playful urban interventions.
Processional routes can be important A fire hydrant is transformed
infrastructural systems that reside in the into sprinkler, a metal
memories or behaviors of the cultures in signpost into swing, a
which they occur. Sometimes unmarked, it is garbage can into barbeque,
through their occupation that they momen- and a streetlight into
tarily isolate a particular route within an glowing place marker.
otherwise unremarkable context. Pasadena,
California’s annual Rose Parade celebrates

Constructed from the
material in which they are
located, rocky cairns, like
these in Iceland, are an
example of way-finding
devices that mark routes
through often inhospitable
landscapes. From each one,
the next is perceived,
bringing measure to an
otherwise infinite horizon.

19 Infrastructure

the first day of the new year with flower- Frederick Law Olmstead and aquatic. Additionally, the 160 161
covered floats, horses, and bands as it Calvert Vaux’s 1858–73 New spatial experience, and often
follows a 5.5-mile (9 km) route defined York Central Park created a the separation of one system
primarily by the hundreds of thousands of series of independent from the other, is achieved
spectators that line its sidewalks. circulatory networks that through sectional and
was given material and topographic manipulation,
Circulatory dimensional specificity carefully calibrated to choreo-
Circulation networks that are embedded according to the particular graph views or minimize
within or overlaid upon existing urban program for which each was conflicting programs and
landscapes are rendered “visible” by the designed—be it vehicular, experiences.
bridges, shelters, or pathways that mark their pedestrian, equestrian, or
trajectories. A bus route, for example, is
populated at specific intervals throughout the
day and night, marked by a series of shelters
that line its path and that serve to trace a
route that would otherwise be invisible.

Anticipatory
An infrastructural network can be open-
ended—explicitly designed as an incomplete
system that provides the framework for
transformation over time. Because the
precise requirements for future usage can
never be known, with changes in population,
changes in technology, and changes in
society and taste, the network that antici-
pates change will inevitably be the one that
remains functional for the longest time.

THE LANGUAGE OF ARCHITECTURE The five main arteries that the riders pass, purchase post offices, and small retail.
constitute the backbone of tickets, and access the buses. Dimensionally and formally
the Bus Rapid Transit system They provide not only shelter suggestive of the buses to
in Curitiba, Brazil, are and functional requirements which they allow access, the
identified through their of accessibility and ticketing, kiosks mark a route that
raised cylindrical steel and but have the added would otherwise be invisible.
glass bus stops through which functionality of news kiosks,

Cedric Price’s 1960–61 Fun
Palace is an example of a
structural infrastructure—
in this case a steel grid of
occupiable columns (contain-
ing stairs, plumbing, electrical)
and beams—one that antici-
pates programmatic elements
that could be subsequently
attached or suspended. These
“plug-in” elements comprised
floors, walls, and ceilings, as
well as theaters, restaurants,
and workshops; and, as with a
theatrical production, the
elements were to be easily
mounted and demounted to
produce a continuously
transforming environment.

In New York City, a series of 19 Infrastructure
urban infrastructural
initiatives aims to construct
the missing links of a
continuous 32-mile (51 km)
Waterfront Greenway Park
that encircles Manhattan
Island. SHoP Architects’ East
River Waterfront Esplanade
(2007–11) is defined by an
armature of plug-in programs
that include bicycle and pedes-
trian paths, recreational, event,
and community spaces with
seating areas, all serving to
define this urban infrastructure.

Alejandro Aravena’s 2001 with each unit subsequently 162 163
low-cost housing project, and progressively modified
Quinta Monroy in Iquique, by its inhabitants. An
Chile, introduces an infrastructural field is
aggregation of standard introduced that facilitates
concrete units that are individual transformation
intentionally incomplete, and yet resists total chaos.

THE LANGUAGE OF ARCHITECTURE A datum is the point of reference
that collects dissimilar or random
elements into a unified whole.

20 164 165

datum

Common data are surfaces, spaces, geometric organizations, visual phenomena, and very
large masses.

A datum can be thought of as a singular and hierarchi-
cally identifiable object, space, or organization. It is the
common denominator, the point of reference, by which
dissimilar or random elements can be measured, located,
or given dimension or scale. A datum can be composed
of similar elements that, together, form a primary and

Le Corbusier’s 1932–33 City contains the communal
of Refuge—or Salvation Army spaces of entry, reception,
Building—aggregates the and library. Here, the
repetitive dormitory spaces dormitory building operates
into a hierarchically dominant as a datum that provides a
linear building in front of common background surface
which are collected a series of for the objects arranged
smaller unique buildings that along its base.

In their 2004–07 public
housing scheme in Madrid’s
new peripheral district of
Carabanchel, Design
Dosmasuno Arquitectos
cantilevered steel-framed
“object rooms” to extend the
interior spaces that reside in
the concrete “wall” of the
primary apartment block that
supports them. These
additions reflect the variety
of apartment types and sizes
producing an ever changing
shadowed texture onto the
surface datum from which
they are attached.

Adler and Sullivan’s 1886–89 zones (a base, middle, and recognizable figure that has the ability to relationship between two or more elements
Auditorium Building in top). This façade interface subsequently organize its surrounding “field.” establishes a visual datum along which other
Chicago, Illinois, is a thus operates as a datum that This datum figure can take on many forms: unrelated elements might be gathered. A
multifunctional building of simultaneously registers a surface, space, grid, axis, horizon line, mass, horizon line or plane provides a singular
theaters, offices, and hotel two scales: one of its interior and so on. visual reference that locates elements that
rooms. Instead of expressing organization that then are either below or above it. A mass is a
each floor as a separate gives way to the scale of its A continuous street wall, for example, can be recognizable volume from which spaces are
entity, its façade collects urban context. the organizing surface that connects a series excavated or objects are extruded.
multiple floors into discrete of individual buildings. A courtyard can be
the organizing space that relates the irregular Surface
rooms that surround it. An identifiable grid A surface can be a principal organizing
of streets produces an organizational device as it provides visual continuity. Like a
structure that collects an infinite variety of canvas, a vertical surface can provide the
individual buildings and programs. An axial backdrop for a series of independent objects

(continued on page 169)

John Hejduk’s Protagonist Wall

In John Hejduk’s Wall Houses, his multiple John Hejduk: Wall House 2 (Bye House),
meditations over the tensions between the Ridgefield, Connecticut, USA, 1973
two-dimensional surface upon which art-
ists and architects work (draw) and the Model by the NAi Collection
three- or four-dimensional world that is
depicted upon that surface is fundamen-
tally important. In fact, one might say it is
the whole point. As such, it represents an
invitation for us to ponder basic questions
about representation and larger philosoph-
ical questions about our place in the world.

In all of the Wall Houses the place of this
tension is most clearly enacted by the wall,
a datum that paradoxically both joins and
separates the independent elements in the
house’s composition. Typically, the free-
standing—and functionally purpose-
less—wall divides the support elements
of the house (a ramp or passageway and
services such as stairs and bathrooms)
from the living elements (living, dining,
and sleeping spaces). One approaches the
house and enters through a threshold in
the wall that would typically mark the tran-
sition from exterior to interior, only to find
oneself on the exterior once again.

This experience is repeated as one passes
through the wall and from exterior to exte-
rior whenever one passes from one room to
another. In this way, the wall is both the
primary, mysterious protagonist of the
house and also that element that structures
a profound engagement in space and time;
or as Hejduk himself stated, “The wall is a
neutral condition … It is a moment of pas-
sage. The wall heightens that sense of
passage, and by the same token, its thin-
ness heightens the sense of it being just a
momentary condition … what I call the
moment of the ‘present.’ ” (Hejduk, page 67)

Hejduk was an architect who built very
little but drew very much. The drawings of
the Wall Houses, particularly the frontal
drawings of the major living elements of
the Bye House, embody some of his most
important preoccupations with representa-
tion. This is the transformation of the three
dimensional into the two dimensional and
the moment that stands between them: the
blank surface of a piece of paper. And it is
made possible by Hejduk’s use of oblique
axonometric projection where plan and
section are simultaneously present without
the distortions of conventional axonomet-
ric projection.

Drawings such as these tend to “flatten”
the illusory space of the drawing and
emphasize the surface of the page. And in
the case of the Wall Houses, this becomes
true for the wall that is drawn upon it as
well. In this way, the “present moment” to
which Hejduk refers is also the threshold
between the architect and an idea that
he or she might project into the future.
The datum, in this case, is the paper itself,
the site—for Hejduk—of the mystery of
architecture.

—Jim Williamson (Cornell University)

John Hejduk: Wall House 2 (Bye House),
Ridgefield, Connecticut, USA, 1973
Drawing by John Hejduk, Collection
Museum of Modern Art, New York

At Bernard Tschumi’s 1991–97 the technologically addition of this new roof not 20 Datum
Le Fresnoy Art Center in sophisticated new structure. only collects the existing and
Tourcoing, France, a new roof And while the old buildings randomly organized buildings
blankets the existing 1920s house the spaces traditionally into a cohesive whole, but it
structures, collecting them associated with an art and produces a discovered space
beneath one continuous education center—exhibition of walkways and suspended
surface, producing a liminal spaces, a library, a cinema, a seating areas: an extension of
space between the roofs of restaurant, and apartments the urban landscape beyond.
the old and the underbelly of for faculty and students—the

José María Sánchez García’s again objectified, while also that might otherwise not have any spatial 168 169
2011 project in Mérida, Spain, producing a continuous relationship to one another. It can also serve
mediates between the pattern of volumes on the as an interface that simultaneously separates
archeological ruin of the other side that allows it to yet collects opposite conditions on either
Temple of Diana and the stich itself into the dense side of it. A horizontal surface, as in a large
existing encroaching urban urban fabric surrounding roof, for example, can act as an umbrella,
fabric, producing a perimeter the temple. Here, the datum one that collects smaller elements beneath it.
wall on one side that makes a has two faces, operating Likewise, it can be a common base on which
continuous backdrop for the as a mediator between two a variety of structures might stand.
temple and a cleared space in distinct conditions.
which the temple is once Space
Spaces are recognizable references that
exist in both buildings and cities. Spaces
with recognizable shapes—such as squares,
rectangles, or ovals—act as orienting devices
to which one often returns. These become
especially recognizable references if they
exist in contrast to a series of smaller spaces,
as with a significantly larger space or
exterior courtyard surrounded by smaller
rooms or, within the density of an urban
fabric, as in a public square or a larger
avenue flanked by a continuous surface of
similarly scaled buildings.

This is true even of curved armatures. The
Grand Canal in Venice, for example, is not
only an armature collecting the palaces that
line its edges, but it is also a datum that
provides spatial orientation within the city’s
dense urban fabric.

João Álvaro Rocha’s 1991–98 laboratories of varying sizes,
National Veterinary the employee cafeteria, and
Investigation Laboratory in the oval animal corral at its
the parish of Vairão in Vila do end. This space of circulation
Conde, Portugal, is an steps down the sloping
example of a datum that terrain as it provides the
physically constructs the skeletal armature for the
circulation zone as a wall that various building blocks that
links the head administrative are plugged into it from
block, the blocks of either side.

THE LANGUAGE OF ARCHITECTURE Axis and Grid
An axis is a line that connects two or more
things (this line might be folded or bent). It
determines the relationship between a series
of spaces or things. This line can be a visual
and/or physical one, such as a line of sight or
a procession along which one walks (as in a
series of rooms enfilade). A grid, on the
other hand, provides a reference field, a
continuous framework of repeated and
recognizable dimensions by which multiple
objects can be measured.

Horizon
The horizon is the line that literally separates
earth and sky and, as in a perspective drawing,
it is the line of human sight. In architectural
space, the horizon line is a constant visual
datum that locates and relates elements that
are both below and above it. It is also the datum
shared by both infinite space and foregrounded
elements. Spatial depth is shaped by the
continuous dialogue and fluctuation between
this background and foreground.

Mass Aurelio Galfetti and Flora sports facilities along its way. various programs at multiple
A dense volume can serve as a powerful Ruchat’s 1967–70 public pool Nestled beneath the walkway scales but also provides a
physical datum—it can be a constructed in Bellinzona. Switzerland, is are the entry stalls, changing continuous line through
object or a metaphoric ground. It is the an elevated open-air rooms and facilities through which the sky, the horizon,
mass from which occupiable space can circulation path that begins in which the pedestrians access and the landscape can be
be extracted or objects can be extruded. the city and extends to the the variety of pools below. measured.
river, a linear datum that The concrete path not only
collects a series of pools and physically connects the

In Frank Lloyd Wright’s 1908 20 Datum
Frederick C. Robie House in
Chicago, Illinois, the unbroken Georges-Henri Pingusson’s
rhythm of continuous 1953–62 Memorial to the
fenestration reestablishes the Martyrs of the Deportation
horizon line of what was once in Paris, France, is located
an open prairie—a space on the southeastern tip of
captured between the planes Île de la Cité. The sequence
of the cantilevered roof and into the memorial is
continuous terraces and initiated by symmetrical
parapets. The domestic rituals staircases inscribed into the
of living and dining play out horizontal ground plane of
against this horizontal datum the island, bringing the
interrupted only by the visitor down into the space
vertical chimney mass. of the river below. Its
interior spaces are
Paolo David’s 2004 Arts subsequently excavated into
Center—Casa Das Mudas in the mass of the island,
Vale dos Amores, Madiera, terminating with an
Portugal, is conceived not as infinitely projected hall of
an object but as an extension illuminated glass beads.
of its surrounding landscape.
This topographic datum 170 171
produces a surrogate ground
from which the occupiable
spaces appear to be excavated.

THE LANGUAGE OF ARCHITECTURE In architecture, the concepts of order
that are evident in a design can affect
our understandings of a design’s
intended uses, of its potential alternate
use patterns, of its sociocultural
milieu, and of its designer’s attitudes
and priorities.

21 172 173

order

A reason that the orders of architecture have occupied much of architectural is that they
inevitably brought order to programs that were becoming increasingly complex.

Whether because of an innate need or an intel-lectual
desire, much of mankind’s inventiveness—artistic and
scientific—has involved a search for order, and for new
systems of order when older systems seem insufficient.
We look for order in nature and, if we suspect that it
is not there, we find ways to formulate the disorder, to

THE LANGUAGE OF ARCHITECTURE An undulating landscape of nonhierarchical space without Moshe Safdie’s Habitat ’67, multiple levels are combined
2,711 concrete blocks of orientation or reference, a (constructed 1964–67) in with the urban prototype of
varying heights memorializes city of the dead that is Montreal, Canada, arranges communal dwelling, building
the approximately 6 million subsequently appropriated 354 externally similar, density, and collective
Jews who were killed during and brought back to life only prefabricated concrete units amenities. Up to eight
the Holocaust. The seemingly by an engaged public. Peter stacked in three pyramids to concrete boxes are linked in a
infinite pattern of blocks Eisenman: Berlin, Germany, produce a dense urban variety of combinations to
creates an intentionally completed 2004. structure. The suburban provide a range of dwelling
prototypical characteristics sizes, each with multiple
of individual identity, views and exterior terraces.
exterior gardens, and

program randomness, to find complex layers of engagement—such as probable entries The iconic form of the single twelve iconic single-family
of order in chaos. and possible destinations—and, at times, family house has been houses has been repeatedly
even a sense of program. An observer’s abstracted, repeated, and stacked, with each “house”
In architecture, the concepts of order that recognition and identification of such aggregated to form focusing on a remote
are evident in a design can affect our components (the first stage of a discursive Vitrahaus—a showroom for landscape. The intersecting
understandings of a design’s intended uses, engagement) can occur at the level of the domestic furniture designed volumes introduce an interior
of its potential alternate use patterns, of its system, of the unit, or of the increment. by Herzog & de Meuron in spatial complexity that cuts
sociocultural milieu, and of its designer’s 2006–09 in Weil am Rhein, diagonally up and across the
attitudes and priorities. This is as true for the To this end, similar elements are most often Germany. A suburban field of domestic shells.
design of a doorknob as of a city. placed together in a row, in a stack, or in a
mat. The degree of similarity (as with two
Repetition versus one bedroom apartments) or the
A basic design tenet has always been that irregularity of secondary attributes (terraces
“like elements should be treated alike, and appearing off living versus dining rooms)
different elements should be treated may suggest an overlaid system, a counter-
differently.” This is especially helpful in large point rhythm.
complexes when there is a field comprising
many similar units (such as housing) against The apparently endless repetition of objects
which one can identify a number of unique is undoubtedly dramatic in certain circum-
objects (community facilities). stances, rousing the sense of awe that can be
inspired by magnitude. However, when the
Also, whereas some projects might be designer is required to accommodate a large
designed to suggest to observers something number of similar elements for inhabitation—
mysterious or ineffable, it is much more
common that a work communicates a sense (continued on page 177)

Louis Kahn, Rome,
and the Greek Cross

The dictionary defines order as “A condi- Louis I. Kahn (with Anne Tyng): Trenton Jewish Community
tion of logical or comprehensible arrange- Center Bath House and Day Camp, Ewing, New Jersey, 1954–59,
ment among the separate elements of a sketch plan and photograph
group.” For Louis Kahn, especially after his
experience in 1950 as a Fellow at the Ameri-
can Academy in Rome, the discovery of this
logic became the main challenge in the
design process.

Kahn discovered, in some of the ancient
buildings of the city, a deep connection
between the geometry that forms the space
and the program for which it was designed.
For example, the circle that generates the
plan of the Pantheon is a perfect response
to the structure’s goal: defining a space for
a multitude of divinities without prefer-
ence for any individual god.

Frank Brown, a former history professor at
the American Academy in Rome, taught
Kahn that “the first Roman architects were
the priestly leaders who prayed, made sac-
rifices, and asked the gods for signs. For
these rituals of worship they framed the
appropriate spaces.” The idea that event
generates space will be present for the
remainder of Kahn’s career, despite his
defense of the “the room” as a generic
space where various programs can occur:
“Architecture comes from the making of a
room,” he said, and “[i]t is the creating of
spaces that evoke a feeling of appropriate
use.” (Kahn, page 68)

The architecture of Andrea Palladio offered
Kahn a great source of inspiration, particu-
larly in the ways in which a geometrical
pattern can be used to define a specific order
and hierarchy among spaces. Similarly, Pal-
ladian villas would constitute excellent
examples of the richness and variations that
can be achieved between parts and a whole.
Louis Kahn used the drafting table as a labo-
ratory for discovering the patterns that

define the perfect relationships between Louis I. Kahn: Adler House, 1954–55
spaces. His design process generally began project sketches
by defining a generic space—a room—with
its own structural and functional identity, a
unit he would repeat until fulfilling the pro-
gram requirements. In his own words, “The
plan is a society of rooms … where it is good
to learn, good to work, good to live.” (Kahn,
page 254) The process ends with the discov-
ery of an overall geometry that perfectly
adapts and transforms a collection of indi-
vidual spaces into a whole.

After 1950, Kahn returned to Philadelphia
and began using a specific form—the Greek
cross, with its four equal arms—as a mecha-
nism to provide order, constantly reusing
it regardless of program or scale. We rec-
ognize this form as an obsession in designs
such as the Trenton Baths, the Washington
University Library competition, the Mill-
creek Apartments, and the Adler, Fleisher,
and Goldenberg houses.

In some cases, Kahn implements this geom-
etry as a constraint that would remain
through the final version—in the Trenton
Baths, for instance—whereas, in other
cases, such as the Adler House, the Greek
cross that appears in the early sketches
disappears once the final program is
installed into the plan and the house begins
to address its context. Kahn consistently
used the historically symbolic geometry of
the Greek cross as the primary mechanism
for initiating a comprehensive arrange-
ment of the distinct elements of a plan’s
organization.

— Iñaqui Carnicero (Cornell University;
Polytechnic University of Madrid)

often the case with housing, offices, or
schools—the challenge is to avoid tedious
repetition, ideally without resorting to
arbitrary distinctions.

Especially with housing, it is often believed The four distinct programs of program are iterations of the 21 Order
that the ability of people to identify their the Wolfsburg Cultural same form, increasing in scale
own units is an important aspect of promot- Center, designed by Alvar from the smallest which holds
ing a sense of individuality within a context Aalto in 1958–62 in Wolfsburg, 26 persons, to the largest
of community. The challenge is to develop Germany, are organized which holds 238, all fanning
distinction within a repetitive system, often around an exterior central out as the principal marquis
accomplished by composing variable overall court. The five lecture halls for the building’s entry from
masses, arranging the units into several that comprise the adult the town square below.
typologies (such as courtyards, slabs, and education component of the
towers), or, often with less success, using
changes in materials or colors to artificially whole—circulatory, services, units, and heights or volumes based on degrees of
indicate uniqueness. Of course, when every possibly even structural and mechanical. public or private usage.
unit is treated distinctly, the opposite of It is often common to identify the various
particularity occurs; the complex is perceived hierarchies that emerge within these systems, The organization of similar elements that
as a uniform, mottled texture. with, for example, entry circulation, vertical vary only slightly (by volume or height, for
circulation, and horizontal circulation each example) can be accommodated through
In projects founded on texture, especially given a distinct form. This can even extend clustering or by serial sequencing, whereby
those involving pattern fields, the manipula- to the level of the city, with hierarchies of both their similarities and their differences
tion of the pattern—three dimensionally, vehicular traffic or public transit being are identifiable.
morphologically, through distortion or articulated in terms of highways, boulevards,
transformation—is the primary tool in streets, and alleys, or hierarchies of building
developing a sense of variation and order.

A typical strategy in organizing highly
repetitive elements is to emphasize the
individual systems that comprise the

MVRDV’s 2001–12 Mirador in 176 177
Madrid, Spain, takes the
typical urban block composed
of a series of individual apart-
ment typologies surrounding
a collective courtyard space,
and conceptually hinges it
90 degrees to create a single
vertical neighborhood of
connected, yet still distinct,
apartment complexes with
the former “courtyard”
becoming a window that
frames the city beyond.

THE LANGUAGE OF ARCHITECTURE While the plan of Jørn modestly dimensioned space
Utzon’s Bagsværd Church above the congregation and
outside Copenhagen, builds to an enormous wave
Denmark (completed 1976), of concrete reaching toward
is extremely straightforward, the sky above the altar,
the interior section is defined capturing the Nordic light
by an undulating concrete and drawing it deep into the
roof plane that begins with a primary space of the church.

Aggregation fragment. The various programmatic Hierarchy
The designer is presented with different elements might be given their own materials Hierarchy can provide an ordering system in
challenges when attempting to represent or even their own stylistic languages. which elements or groups of elements, while
order when given a series of individual recognized as being related to an overall
elements with little or no repetition. Decisions Alternatively, the designer might wish to whole, are not necessarily of equal signifi-
must be made regarding how the identity of suppress difference, to cloak everything cance. It is this inequality that signals the
the elements might be constituted and how within the same skin, possibly within a relative significance of the part to the whole.
conspicuous these identities might be. The singular mass, so that only internal divisions
designer must consider the varying scales determine the differences. Hierarchies are revealed in every aspect of
that must be accommodated, even when architecture’s constitution. One can identify
those scales run counter to the relative Similarly, a reason that the orders of architec- levels of importance in the composition of
importance of the elements. Finally, perhaps ture—Tuscan, Doric, Ionic, Corinthian, and plans, in the development of sections, in the
of the greatest consequence, is the problem Composite, among the most familiar—had disposition of elevations, and in the produc-
of how the disparate elements might be occupied much of architectural theory from the tion of distinctive objects or figural voids.
associated. In situations involving the Renaissance until the twentieth century is that
aggregation of such elements, the connective they inevitably brought order to programs that While a program might suggest hierarchies,
tissue—circulation, structure, services, were becoming increasingly complex. There the designer’s determination of program-
surfaces—might, paradoxically, be the most were prescriptions regarding the appropriate matic hierarchy can have great significance.
important aspect of the design. hierarchies of orders and even suitable When designing a city hall, for example, an
functional uses for the orders when used in a architect communicates much about a
The designer may choose to merge a design. Each order proposed its own propor- government when determining whether the
collection of distinct elements into the tioning system. It was possible to understand meeting hall or the mayor’s office predomi-
intrinsic differences of a city, dispersing a the interior of a building by reading the orders nates in the building’s organization.
building throughout an urban fabric or used on its exteriors. A street, district, or entire
simulating the production of a new city city could be unified by subscribing to a Hierarchy can also be sociocultural. For
consistent theory of the orders. example, the mihrab, denoting the direction

for prayer in a mosque, may be one of its Louis Kahn’s Dominican
smallest spaces, but it is also one of its most Sisters’ Convent designed in
hierarchically important components, a focal 1965–68 organizes the cells
point of the mosque. Or the only fragment into a perimeter wall,
of a village to have survived an earthquake creating a large “container”
may develop a special place in the new city. within which is arranged the
communal programs of the
When the components of a work are nested convent, with the exterior 21 Order
within each other—when the overall archi- spaces between these primary
tecture frames other architectures, like a figures and the enclosing
set of matryoshka dolls—the sense of order cell wall forming a series of
resembles the mise en abyme effect: the private “cloisters.” The corner
process of penetrating buildings within connections allow for a
buildings reveals the relationships between continuous sequence through
the pieces. This is, for example, frequently the interior of the complex.
the case in buildings like theaters and
concert halls, where one moves through The forum of Pompeii is the around large open spaces.
numerous distinct buildinglike spaces— primary urban “courtyard” Beyond are the residential
entryway, lobby, stairways, loges, hall, and around which the city’s public blocks, with interior court-
then (vicariously) the space of the stage buildings are gathered, yards that both organize
with all of its autonomous architectures— and the first of a series of and bring light to rooms
each proposing its own identity. courtyards begetting that surround them while
courtyards. This organizing choreographing the sequence
While rare, the absence of hierarchy may device of a primary space that moves from the public
be intentional in designs where complete lined by subsidiary spaces is street to the atrium and
equality or anonymity is desirable. And while a frequent motif in ancient finally to the inner sanctum
a sense of order may be one of the basic Roman towns. From the of the peristyllium (garden
human compulsions, human involvement forum one moves to the courtyard).
can always be counted on to introduce an basilicas and markets with
element of vital disorder to even the most interior spaces also organized
rigorously ordered architectural designs.

The two distinct semispheres which are located the 178 179
of Oscar Niemeyer’s 1957–64 complex’s more public spaces,
National Congress of Brazil in their forms demonstrate their
Brasilia both house and programmatic and cultural
represent the two principal significance. Additionally, the
government bodies, the complex’s siting on the capital
Senate and the Chamber of city’s main visual and organi-
Deputies. Juxtaposed against zational axis announces its
the low rectangular plinth in significance at the urban scale.

THE LANGUAGE OF ARCHITECTURE A grid is the stage on which something
might happen. It exists in anticipation
of an event.

22 180 181

grid

Without the ideal aspect of the grid, the distinctiveness of the incidental would
go unnoticed.

If there is perhaps one central phenomenon to all of
architecture, from the smallest shed to the largest city
and even, at times, to entire states and provinces, it is
the grid. Given the expansiveness of the environment
in which we live, laying out a grid provides an acces-
sible field of operations for the designer. It provides a

A gridded “forest” of 856 cathedral being methodically
columns fills the interior of inserted into the midst of the
the Mosque-Cathedral of column field. Despite their
Córdoba (first built 784–786, uniform layout, the columns—
extended 833–852, 961–976, reused from various Roman
987; current church inserted, and early Christian construc-
with modification, in the tions—retain their individuali-
sixteenth century). The ties, each telling of a different
various building campaigns past. Their rhythm and regu-
are evident in the thickened larity is alternately disorient-
walls and piers in this plan by ing or serene, facilitating
James Cavanah Murphy, meditation and reverie.
published in 1816, with the

THE LANGUAGE OF ARCHITECTURE means of marking locations within a poten-
tially boundless field. From the earliest
days of human settlement, the grid has
represented humankind’s attempt to organize
nature, to propose an order, even where
a sense of order seems ungraspable.

Grids are always implicitly infinite, and so Since the sixteenth century, but also a refined sense of
they end only by collision with a natural or the rooms of traditional proportion. In his own home
constructed entity, with a predetermined Japanese homes were often in Seijo (1953), for example,
boundary—such as a property line or a zoning composed of an array of Kenzo Tange combines a grid
envelope—or by the intentional decision of tatami mats, usually made of of tatami mats and sliding
the designer. Still, while grids can suggest rice straw and in a 2 : 1 fusama screens with a very
infinity, they also foreshadow their own ends. proportion, with its length slender wooden skeletal
The regular pattern of a grid means that close to the dimension of a structure and an open plan
each section forecasts every other section, prone human body. These to achieve a modern version
thereby already implying in their centers mats bring not only a sense of of the Japanese house.
their eventual and probable boundaries. gridded order to a dwelling

A grid can be two dimensional—flat on the
ground or on the surface of a building—or
three dimensional, as in a structural grid.
Grids often represent an ideal condition
that can be replicated throughout a building
or a site. It can be a condition derived from
the proportions of the human body (as
with the tatami mats of traditional Japanese
residential construction), from an optimal
dimension for spanning a space, from
harmonic proportions derived from natural
phenomena, or from the apparently efficient
accommodation of a programmatic require-
ment (as with classroom sizes, parking bays,
and hotel rooms).

(continued on page 185)

Mies van der Rohe
and the Grid as Site

The grid is the beginning and end of Mies’s perspective-negating fluctuations of vision

architecture—the site of architecture’s produced in Crown Hall, where the glass is

emplacement and its eventual effects. frosted to a line just above the horizon, thus

Mies’s grid operates on two different planes. forbidding access to the stabilizing vanish-

The first plane is the plane of Idea. The grid ing point; or the whirl of space in the plaza

on the plane of Idea is a template compris- in front of Seagram’s vibrating surface, as

ing instructions for organizing forms, well as surface qualities like reflectivity,

materials, and functions to which it stands refractivity, dullness, and blankness; or the

in a transcendental relation. This grid is 6-foot (1.83 m) deep roof of the New

deeply imbricated in the history and disci- National Gallery, floating on trabeated

pline of architecture, which provides whispers, disturbing the certainty of stabil-

specific precedents (Schinkel, Behrens, and ity of the earth itself. This second plane

Wright among them) and guarantees rigor brings together heterogeneous elements

and relationship. Consider, for example, the and makes them function together, creating

urban connections organized by Mies’s plan unprecedented and continually shifting

of IIT, where the grid—originary diagram relations without unifying or fixing them.

of the polis itself—represents the ideal The vocation of this plane is not to produce

urban condition of Chicago’s South Side. Or a whole but to constantly search for the new.

the metrically controlled surface of glass Its nature is virtual and abstract. Ludwig Mies van der Rohe: S. R. Crown Hall
interior (with the architect), IIT, Chicago, 1956
and metal panels at the Seagram Building,

which confronts metropolitan chaos with Thus the grid as site comprises both gen-

the sheer materiality of abstraction. erative concepts and relational, sensual

events. The grid announces and insists on

Mies’s grid operates simultaneously on a architectural autonomy and authority, and

second plane, which is a virtual site where yet is infinitely productive of difference

architectural experiences and events cir- and otherness. The grid is pure relation-

culate, combine, and recombine. It is the ship, perhaps the degree zero of architec-

plane of Event. This plane hovers just above tural thought.

or just below the actual elements of archi-

tecture, more like a field of potential —K. Michael Hays (Harvard University)

charged by invisible forces than a thing or

even a geometry. The grid on this plane is

not an inaugural ground or the source of an

idea. Indeed, the grid on this plane is but a

shimmering phantasm, the constant flux of

immanent material and spatial images.

Here percepts and affects are organized

into material architectural experiences.

Examples of such experiences include the

Ludwig Mies van der Rohe: Seagram Building, New York, 1958

The founding of the New presented by William Penn—
World required the founding the grid became the device
of a multitude of new settle- of choice. But such neutrality
ments that attempted to is never ensured, if even
represent the colonies’—and desirable: the occasional park
later, country’s— aspirations or nearness to water even-
for legislating and formalizing tually alters the value of one
an egalitarian society by property over another, so
means of property divisions. that the development of the
In Philadelphia, seen in this grid inevitably becomes
detail of Thomas Holme’s distorted by economic and
1705 map of Pennsylvania— environmental pressures.

THE LANGUAGE OF ARCHITECTURE Each grid type carries its own spatial and hierarchical implications when used to influence the organization of structure or partitions.

The four-square grid provides The nine-square grid, on Once the grid reaches a
equal status to each of its the other hand, brings an certain density, the relative
quadrants and suggests a inherent dominance to the equality of the bays is ensured
centrifugal movement pattern. space located in its center. and the grid begins to imply
Medieval chapter houses were Such grids were strongly infinite extension, although
often versions of this grid type, preferred in church design, peripheral bays might assume
with a large, supporting column most evident in those of the some prominence, as in the
located in the center, branching equal-armed Greek cross case of market buildings.
into an ornate ceiling. plans in which the central
element would be topped
with a dome.

Irregular grid patterns, Irregular grid patterns can Of course, not every building
however, can relocate these also create a mixture of major utilizes an obvious grid.
hierarchies, suggesting, and minor zones as in a The absence of a grid makes
for example, diagonal “tartan” grid, suggesting the columns or partitions
developments. directional movements as dominant elements of the
well as possible service and composition. This situation
stair precincts. This is an can emphasize the presence
organization common among of a casually defined space,
villa designs from Palladio like a clearing in a crowd.
onward through Wright
and Le Corbusier.

The surfaces of Charles But it is also a function of the grid, funda- 22 Grid
and Ray Eames’s own house mentally neutral and indefinite, that the
(Case Study House #8) in intentional disruption of its regularity—
Los Angeles, (completed through the introduction of a rotated grid,
1949) consist of a regular sudden shifts in bay sizes, or the insertion of
steel grid approximately figures that resist conformity—can bring note
7.5 x 8 ft. (2.3 x 2.4 m) to unique or special elements. In the later
tall, with additional sub- grid paintings of Piet Mondrian, for example,
components between the the variable grid itself becomes the subject
floors. This grid not only of the work. Without the neutral, ideal
summarizes the architects’ aspect of the grid, the distinctiveness of the
aspirations for industrial incidental would go unnoticed.
prefabrication but also
generates both structural Reference
elements as well as interior Just as a Cartesian coordinate system
partitions, collects a variety provides an essential tool for understanding
of infilled elements, and the characteristics of various points, lines,
lends the overall structure and figures, grids permit occupants of an
a unified system while architecture to fully understand the locations
visually organizing the of elements within a space, from columns
trees on the site. and walls to constructed and inserted
furnishings.

The Carré d’Art in Nîmes, Another important trait of the grid is its
France (1987–93), by Norman usefulness as a measuring device. As
Foster + Partners, provides discussed in chapter 11: Space, grids can
one edge of a large plaza provide an indication of height and width,
containing the Maison Carrée, and a useful indication of spatial depth.
a Roman temple from the After walking through one bay of a grid, we
first century BCE. Foster’s develop a sense of cadence and an anticipa-
building is itself a temple of tion of our further movements through a
expanding and contracting space. In this sense, grids can be understood
grids, with a huge but slender as demarcating linear measurements,
five-columned portico that volumetric measures, and increments of time.
contrasts with the regularity
and density of the columns of The grid has long been used (1525), Albrecht Dürer 184 185
the Maison Carrée, beneath as a device for the transfer demonstrates the use of a
which a smaller, six-columned of one image to another or gridded wire frame and an
volume corresponds more from an actual figure to a obelisk (in order to fix the
directly to the size and front drawn representation. In location of the eye) in
portico of the monument. his Draftsman Drawing a transferring a figure to
From the interior, the columnar Recumbent Woman from his a similarly gridded piece
grid of the Carré d’Art provides Four Books on Measurement of paper.
both a measure and a locator
for the temple outside.

THE LANGUAGE OF ARCHITECTURE Tartan plaids are composed establishing a complex multiple rhythms of For the final version of his structured the façade of the distinct component of the
of specified combinations arrangement of varying color superimposed grids. On the courthouse addition to the existing town hall. While this town government while
of colored threads woven fields. In architecture, the right is a tartan grid derived Gothenburg (Sweden) Town reductive approach was maintaining a staid symmetry
together in perpendicular “tartan grid” is a term used from the “MacGregor of Hall, completed in 1937, Erik considered scandalous at the for the original structure and,
warp and weft patterns of to describe a similarly Cardney” tartan shown on Gunnar Asplund constructed time, it has proven very at the same time, providing a
varying dimensions, variegated grid comprising the left. a version of the underlying successful in asserting its consistent surface for one
organizational grid that presence as a functionally edge of a major public square.

The proportions of the belief that the human body is In one sense, a grid is the ultimate abstrac- Additionally, a grid can be generated from a
human body have been a shaped in the image of God, tion, most evident in its ability to legislate distortion of an orthogonal grid, warping a
frequent template for the which would suggest that an order without being fully present; in pattern so as to imply a directional inflection,
disposition of grids, even proportions derived from the another sense, it is one of architecture’s most an adjustment to an irregular site boundary,
when not at human scale, as body would transfer upon a substantive mechanisms of comprehension. the accommodation of an irregular insertion
in this sketch for a church building a divine and In the end, a grid is the stage on which (such as a theater volume), or even an
design by Francesco di therefore beautiful harmony something might happen. Grids exist in attempt to develop an exaggerated depth or
Giorgio Martini (c. 1492). and coherence. anticipation of an “event” that is then shallowness by means of false perspective.
This often follows from the quantified and identified by its occupation
within the gridded system. Proportions
The selection of a grid’s increment is perhaps
Rhythm the clearest way in which to develop a
While structural grids are the most common, proportioning system that can permeate a
grids can be composed of circulation paths, building’s design, unifying its parts with its
service elements (like plumbing or lighting whole. A grid might be based on specific
systems), systems of furnishing (such as dimensions (such as those of a standard
library shelves or auditorium seating), or human body, of a regularized work space, or
even daylighting elements (including of the predominant grid in a neighboring
skylights or windows). structure), or on proportional relationships
that are independent of scale (as with
Often, a grid may consist of more than one proportions derived from string lengths in
increment, as in the case of tartan grids, with the production of musical chords).
their counterpoint of major and minor bays.
Such complex grids can also be understood Regulating lines have been an important
as an overlap of grids, with a consequent aspect of architectural aesthetics since
compounding of rhythms, hierarchies, and ancient times. Such lines are based on the
programmatic attributes. characteristics of similar triangles—those
sharing identical angles, regardless of the

In his Vers une architecture of Chaux-de-Fonds, Switzerland
1928, Le Corbusier dedicates (1916). The repetition of
a chapter to the importance angle A (and its complemen-
of regulating lines, which he tary angle) across the
considers to be “an inevitable elevations provides the villa
element of architecture” and with an intrinsically harmonic
a “basis of construction and a proportioning system
satisfaction.” He illustrates whereby the proportion of
this chapter with numerous the elevation’s central block
buildings of historical is present throughout the
importance, among which he various subdivisions and
locates several of his own, fenestration elements.
such as the Villa Schwob in La

22 Grid

An “active” grid becomes the figures, service elements, lengths of their sides. Such triangles will 186 187
subject and object of Peter circulation systems, always share proportional relationships
Eisenman’s House II (1969) enclosure, glazing, and among their sides, so that the use of
in Hardwick, Vermont. The gradients of density. The regulating lines in architectural design lends
building is the consequence result is a house that uses a consistent proportion to the entirety of the
of a series of three-dimen- one of architecture’s most structure. For this reason, regulating lines
sional manipulations of a fundamental and abstract are considered an effective technique for
basic nine-square grid— components, the grid, as an guaranteeing harmonic proportions
dislocations, solidifications, all-encompassing generative throughout a building, from elevations to
evacuations, transpositions— device, eliminating nearly all sections to plans, with regulating lines
that leave traces that the artifacts of traditional often providing the basis for variations and
engender elements such as domestic architecture. subdivisions within the fundamental grids.
physical structure, spatial From the Renaissance onward, there was a
distinct relationship between the use of such
lines and the construction of linear perspec-
tives, where similar rectangles would be used
to imply the recession of a figure in depth.

Le Corbusier was one of modernism’s most
vociferous advocates of regulating lines—
more often than not based on the golden
section ratio—seeing in them “[t]he
obligation to order. The regulating line is
a guarantee against arbitrariness. It brings
satisfaction to the mind.” (Le Corbusier,
page 132) Despite this, very few of his
contemporaries had enthusiasm for what was
inevitably considered to be a remnant of the
architecture they were trying to leave behind.

THE LANGUAGE OF ARCHITECTURE A knowledge of geometry not only
provides the architect with the ability
to represent and communicate basic
ideas, but it is also an essential aspect
of understanding the genuine and
illusionistic aspects of architectural
space, for calculating the actual surface
areas and volumes being described, and
for describing the potential fabrication
of forms to others.

23 188 189

geometry

There is a certain aspect of descriptive geometry that prefigures the visual impact of certain
forms: geometry can present not only what something physically is, but projective geometry
can also prefigure what can be seen from specific viewpoints, and how complex figures can be
broken down into buildable components.

As alchemists sought inscrutable objectives that included
philosophical and spiritual insights, material transmuta-
tions, astrological projections, and even immortality, they
forged a path that led them to discoveries in sciences
such as chemistry and medicine. Similarly, architects

THE LANGUAGE OF ARCHITECTURE The golden section rectangle Senatore in Rome (completed Vincenzo Scamozzi’s merged with hexagons,
has been used throughout in the seventeenth century), Palmanova (designed 1593) squares embedded in
much of architecture’s history revealing golden ratios was considered to be the ideal trapezoids—combined
as a proportioning tool. Here, between the base and upper fortified outpost city of the optimized strategies of
it is superimposed on stories as well as within the Venetian Republic. Its defense with Renaissance
Michelangelo’s restructured overall dimensions of the original ramparts form a theories of ideal proportion
façade for the Palazzo del surface. nine-pointed star with its and universal harmony. As
three entry boulevards with most intended utopias,
culminating in a hexagonal Palmanova’s idealization has
central piazza. Its proven uncongenial to
geometries—nonagons everyday inhabitation.

Le Corbusier’s Modulor 2 use of these proportions with diverse utopian aspirations, including artists for over 2500 years. Golden ratios
proportioning system begins throughout a building would the idealization and optimization of various and their rectangles have a capacity for
with the height of a 6-foot assure a harmony of the parts spiritual, cultural, aesthetic, material, health, continuous regeneration and subdivision,
(1.83 m) person—the ideal and a sense of human scale and environmental goals, have found their and can be found throughout nature, from
English detective hero, as well as to foster the paths most frequently plotted through nautilus shells to the length of our finger
according to Le Corbusier— development of potential geometry. bones, and it forms the basis for many
with an uplifted arm at 7 feet, standards for building investigations into five-fold symmetry
5 inches (2.26 m), subjecting materials and fixtures. It is For thousands of years, most architecture has (important in pattern theories). Perhaps
the increments to subdivision here imprinted on his Unité been composed of cubes, cylinders, spheres, because of its ubiquitousness, artists and
by means of a Fibonacci d’habitation in Marseille, cones, and pyramids. Perhaps more than the architects have long considered the golden
series. His belief was that the France, of 1947-52. development of new materials, new represen- rectangle to be one of the most visually
tational techniques eventually accompanied pleasing geometric figures.
In Jan Blažej Santini’s cally appear in every aspect by new skills in fabrication have caused
exuberant Church of St John of the building complex, architectural form to develop more elaborate The golden ratio is closely approximated by
of Nepomuk at Zelená hora in often combined with the geometries. Guilds of medieval stonemasons the more finite Fibonacci series—1, 1, 2, 3, 5,
Žd’ár nad Sázavou (Czech figure of a tongue, relating sharpened their skills as cathedrals reached 8, 13, and so on—which approaches the
Republic, 1721), the numbers to the legend of St. John’s higher. In the Renaissance, linear perspective golden ratio of 1:⌽ (1.6) as it progresses.
five and three—which figure martyrdom upon his reputed expanded techniques for the study of The Fibonacci series forms the basis for
prominently in the saint’s refusal to break the silence descriptive geometry. Later, in the baroque, Le Corbusier’s Modulor proportion system
hagiography as well as of the confessional. geometries merged and warped as stereo- as well as numerous theories of plant and
Christian theology—symboli- tomic techniques were perfected and animal growth.
craftsmen developed skills in turning wood
and ivory on lathes in fabricating exception- Religious and governmental architecture
ally complex objects. has frequently employed geometries for
their symbolic significance, with equilateral
Numbers triangles, squares, pentagons, hexagons,
Perhaps the most pervasive and persistent and so on being used in plan, elevation,
geometries are those based on the golden and volumetrically in order to emphasize
ratio. Known since the time of Pythagoras, the liturgical or historical importance of
this ratio has fascinated mathematicians and certain numbers.

(continued on page 192)

Geometry of Pure Motion: Buckminster Fuller’s
Search for a Coordinate System Employed by Nature

Richard Buckminster Fuller, a self-proclaimed Buckminster Fuller: Geodesic dome Donald Ingber: Geodesic form
design scientist, is perhaps best known for (U.S. Pavilion, Montreal, Canada, 1964-67) in the tensed cytoskeleton of
his lightweight geodesic domes and his drawing a human cell, 2011
structural concept of tensegrity. While his
applied geometries in a variety of forms— described as a network of discrete com- concept of synergy as it forms a bridge
from tents to domes—served highly
functional purposes for clients including pression components held in continuous between the purity of mathematics and
the U.S. military, and also garnered numer-
ous patents, Fuller’s dedication to solving tension. Each member is dependent upon geometry with the instability and complex-
the world’s problems through functional
geometries was driven by a much larger the next in a network of forces that undu- ity of nature. Given the systemic properties
obsession with the fleeting relationships
between nature and mathematics. Fuller’s lates in an on/off fashion, much like of these lightweight skeletal assemblies,
obsession was rooted in an omnirational
understanding of the universe, where the process of weaving. Fuller observed such structures are capable of changing in
form emerges from a continuous chain of
connected events. He understood the limi- the efficiency and economy displayed by response to their environments. The result
tations of the Cartesian system as it
emphasizes fixed coordinates as opposed the sculptural work of the artist, Kenneth is a variegated tensegrity system where
to coordinated variations of geometry and
matter. Fuller was interested in a design Snelson, thus leading to Fuller’s term internal rule systems share reciprocal rela-
space that embraces all the known mathe-
matics from Euclidean to non-Euclidean. “tensegrity,” a combination of the terms tionships with external and environmental
Therefore, he abhorred disciplinary
“silos” as they fundamentally undermined “tension” and “integrity.” forces. This differentiated behavior oper-
his concept of synergy, that is “…the behav-
ior of whole systems unpredicted by ates at the level of the individual com-
the behavior of their parts taken sepa-
rately.” Fuller’s applied projects such Perhaps limited by technology and a mod- ponents and at the level of the global
the Dymaxion House (a conflation of
dynamic + maximum + ion) explored dynam- ernist bias toward the reproduction of system. Imagine these structures growing,
ics in form through the application of his
synergetic principles combined with a single parts, Fuller was not able to realize contracting, and expanding in response to
search for structures that he considered
minimal through a reduction of overall his theories of variation between parts and the presence of people, light, or tempera-
weight but were ultimately limited in their
ability to change dynamically in response whole systems in his functional geometries. ture. Fuller pioneered a systemic design
to environmental conditions. Interestingly,
Fuller’s concept of tensegrity, which he Recent advances in digital and fabrication process, where flows of energy connect
understood as a system of energy where
space is not static, has subsequently been technologies allow for the exploration of form with communication, geometry, and
adopted by the pioneering cell biologist,
Donald Ingber, as a model for understand- interconnected parts and material behav- matter. Digital technologies and computa-
ing how cells are structured at the nano-
meter scale. Tensegrity may be simply ior, where forces external to three- tional thinking have afforded a material

dimensional tensegrity structures may translation of Fuller’s “geometry of think-

influence and alter the continuity of the ing” that will finally fully realize his

tensional forces and the discontinuity of functional geometries, as informed by the

the compressive forces. Ingber’s link dynamics and complexity of an expanded

between the mechanics of the cell cytoskel- context.

eton with the dynamics of tensegrity is,

perhaps, the closest translation of Fuller’s —Jenny Sabin (Cornell University)

In his treatise of 1567, corner and a convexity—
Le Premier tome de beneath a small chamber in
l’Architecture, the French the Château d’Anet. Careful
Renaissance architect reading of the drawing
Philibert de L’Orme reveals the actual dimensions
illustrates his method of and angles a mason would
stereotomically representing need in order to accurately
the squinch—a vaulted cut the seven pieces of ashlar.
transition between an inside

THE LANGUAGE OF ARCHITECTURE Descriptive Geometry
Every architect can benefit from an under-
standing of the fundamentals of descriptive
geometry (also called “applied” or “construc-
tive” geometry). Not only is the ability to
represent three-dimensional forms two
dimensionally a necessity for representing
and communicating basic ideas, but it is also
an essential aspect of understanding both the
genuine and illusionistic aspects of architec-
tural space, for calculating the actual surface
areas and volumes being described, and
for describing the potential fabrication of
forms to others.

With descriptive geometry, one can present
not only what something physically is, but
projective geometry can also prefigure what
can be seen from specific viewpoints, and
how complex figures can be broken down
into buildable components.

Modern descriptive geometry also assists Amid concerns regarding the wooden model (c. 1961) that
the designer in being able to identify and structural and constructional each of the shells could be a
quantify linear curves in space, as well as the possibilities of the shells in segment of the same sphere,
measures of warped surfaces and irregular the original design for the meaning that curvatures
volumes. But while many computer graphic Sydney Opera House (inaugu- would be identical,
programs can simulate much of the construc- rated 1973)—especially based facilitating structural
tive aspects of descriptive geometry, allowing on the technologies of calculations and
programs full control over the formation 1960—architect Jørn Utzon prefabrication.
of such figures means that the designer demonstrated with this
becomes merely a consumer of predeter-
mined forms and techniques. For example,
rather than understanding a sphere as a
singular geometric figure, certain programs

23 Geometry

UNStudio’s Burnham Pavilion then distorts the roof plane
in Chicago’s Millennium Park of this grid using various
(2009) begins with a plat- parametrics in recognition of
form organized on Daniel specific vistas within the park
Burnham’s famous Chicago and toward the city.
grid as its initial figure and

require it to be understood as a polyhedron central to constructive solid geometry (CSG) etries can approximate highly irregular and 192 193
that approaches an infinite number of sides, a techniques of modeling solids. even organic figures. Nonhierarchical meshes
hosohedron composed of lunes, or a circle can be subjected to specific metrics—by
rotating about one of its diameters. The Also, the use of parametrics in design has means of Voronoi diagrams or Delaunay
version of the sphere to which one subscribes become a significant tool in the designer’s triangulations—in order to achieve more
directly affects the transformations to which repertoire, influencing every scale and aspect regulated surfaces and masses. These
the sphere can be subjected. of design, especially in academic settings. techniques are especially important in the
Parametrics, at its most fundamental, development of responsive surfaces.
Complexities involves the use of a set of parameters or
The combination of forms through Boolean limits—such as networks of circulation, In these instances, the geometric complexi-
operations—merging positive forms (solids), patterns of congregation, or measures of ties often prohibit nondigital methods of
positive and negative (subtractive) forms daylight—as a means for exploring a range three-dimensional modeling.
or more complex combinations resulting in of geometries through multiplication,
the systematic addition or subtraction of distortion, transformation, or all three. The challenge is for parametrics, useful for
overlapped forms—is one aspect of design developing tantalizing formal abstractions,
that has become vastly facilitated by digital Various meshes can also be introduced, to transcend predictable outputs based on
representation. Such Boolean operations are whereby an aggregation of surface geom- predetermined inputs. A continuous reevalua-

THE LANGUAGE OF ARCHITECTURE It is often assumed that there Line Array project (2010) from columns to beams and
is a singular relationship proposes the use of from tensile to compressive.
between the geometry of protocell-based materials in These materials are composed
a structure and the mater- the construction of an of cells capable of gathering
ials of its construction. asymmetrical, highly variable or dispersing at the nanoscale
San Francisco–based structure with irregular spans, in response to requirements
IwamotoScott Architecture’s loads, and that even change at the macroscale.

In this project by James tion of the initial and evolving parameters organization through constant adaptation.
Pelletier, a simple repertoire is critical to its instrumentality. And for Many architects argue for an architectural
of forms—teardrops, wedges, meshed surfaces, which tend to solidify their version of this biological epistasis in which
and tubes—is distorted, “responses” to the designer’s input during variation occurs well beyond the onset of a
multiplied, rescaled, and the design process, to become actively building’s design, even throughout the life of
treated alternately as solids responsive during the life of a construction. the building. The configurations of spaces
and voids, and then used as might change as the users age, with changes
the geometric primitives Variability in family dynamics, with altered economic
for the simultaneous Genuinely responsive surfaces and objects— situations, or with seasonal and long-term
development of both a those that morphologically alter throughout climatic changes.
complex architecture and the life of a structure—are beginning to
the manipulation of its site. appear as new materials and techniques are Similarly, concepts of self-organization—
Such modeling would be being developed, often through convergent whereby a system finds its own optimized
impossible using exclusively technologies and disciplinary hybridization. structure, often with very little predictabil-
analog tools. (Critics: Andrew ity—seem to more fully duplicate natural
Batay-Csorba, Thom Mayne, One of the issues facing architecture is the human settlement patterns. Self-organization
and Val Warke; Cornell extent to which variation and variability enter may prove quite valuable at developing
University) the process, and for how long they persist large-scale organizations.
within the work. In biology, a homogeneous
system, determined by genetics, is often Networks
transformed into a heterogeneous system Today, there can be a direct, instantaneous
by its immediate contexts, deforming a connection between design, two-dimensional
predetermined and undifferentiated digital modeling, rendering, and three-

23 Geometry

The sinuous geometries of BIM management company dimensional modeling, so the designer has of being shared among architects, project
Trahan Architects’ Louisiana Case, making it possible to immediate access to a vast array of consultants, fabricators, and contractors,
Sports Hall of Fame Museum carve a path directly from representations and viewpoints for exploring whereby changes made to one element
in Natchitoches, LA, USA design to fabrication. The the qualities of a design. instantly affect changes in related areas.
(2011), would have been interior is shaped by over
virtually impossible to con- 1,000 individually cast stone It is becoming increasingly necessary for the Graphic programs have fostered an
struct a decade ago. The close panels supported by an equally designer to utilize and combine numerous ability to generate forms that are imaginable
digital collaboration, begin- individualized steel framework software systems during each phase of the only through digital processes. As these
ning with the architects’ with thirty connection types, design process, especially as the information programs become more available for
three-dimensional documents, all digitally programmed involved in producing the representation of adaptations and modifications through
included steel consultants through a combination of ten a design can also be used to investigate scripting, designers begin to require a keen
David Kufferman and Method software packages. multiple facets of that design. Digital models knowledge and skepticism of available data
Design, and fabrication and can be used to evaluate a work’s environmen- sources, with input needing careful ranking
tal relationships (such as solar orientation, and traceable algorithms so that portions
heat loss or gain, and various comfort of the process can be edited or redirected 194 195
criteria), material usages (including types and upon evaluation of the output. Such
amounts), contextual aspects (shadows cast, evaluation will require the development of
view corridors, public accessibility), and even effective skills and tools. While the digital
legal compliance (zoning or other codes). realm will provide real-time data as a design
evolves, the designer will still need to
Additionally, building information modeling select and prioritize the data, humanize its
(BIM) has become a contemporary version of conclusions, and assess esthetic qualities.
stereotomy, with digital representations—even
during the earliest stages of a design—capable

THE LANGUAGE OF ARCHITECTURE Aspects of fabrication—the equipment,
tools, and methods that form and
assemble a structure’s materials—are
essential in defining the character of
a finished work.

24 196 197

fabrication

Techniques of fabrication often expand the characteristics of an existing technology that
might have originally been intended or limited to a particular, even nonarchitectural applica-
tion, making material and structural discoveries that were previously untapped.

Construction methodologies—how a material, a detail,
or a building is made—are an important aspect of the
design process. Where a knowledge and appreciation
for a specific construction method is privileged
and subsequently embedded within the conceptual
development of a work, the specifics of those methods

The architecture of Ciudad concepts into houses and
Abierta in Ritoque, Chile, a academic structures. Here
school that was founded in the construction process
the 1970s, is a built emphatically does not come
expression of a participatory from a set of architectural
process that engages an drawings. Instead, it is the
unstable landscape of sand result of a continuous and
dunes and wetlands. ongoing process—an
Architectural concepts are architectural laboratory for
initiated through poetic the testing of ideas,
collective events and materials, and rituals in a
happenings, with faculty and continuously evolving
students developing these environment.

THE LANGUAGE OF ARCHITECTURE

In Laxe, Spain, in 2010, earth serving as formwork
Studio Ensamble constructed into which the concrete was
the Truffle—a mass of space poured. As the concrete
that emerged from its hardened and the earth was
environment. A hole was dug scraped away, the hay was
and subsequently filled with slowly consumed by a cow,
bales of hay, with the existing revealing the space within.