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Realizing Architecture’s Disruptive Potential

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Volume 38 Article 7
1-1-2016
Realizing Architecture’s Disruptive Potential
Shajay Bhooshan
Zaha Hadid Architects
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42
Realizing Architecture’s Disruptive Potential
Shajay Bhooshan
Zaha Hadid Architects, Computation and Design Group
Digital technologie s—computers and
computer-controlled machines—
have pervaded all aspects of life, de-
livering sustained and accelerated
rates of societal and economic evo-
lution. Yet, in architecture, such an
embrace of digital technologies and
attendant intellectual disposition is
not widely accepted.1 Whilst increas-
ing numbers of progressive rms and
research institutions are forging rap-
idly forward in such a technological
upgrade, the larger populace of archi-
tects and the architecture produced
thereof is decidedly averse to it. is
unfortunate and hopefully temporar y
resistance notwithstanding, digital
technologies will in controvertibly be
one of the key drivers of Innovation
of our discipline and consequently
the built environment in the twenty-
rst century.
Artificial Intelligence and
Intelligence Augmentation
Closer inspection of the previous
examples of machines bettering hu-
mans at innately human tasks, reveals
some nuances. Post the cataclysmic
event in 1997, the quality of human
chess players worldwide improved
dramatically by incorporating soft-
ware in their training.2 Additionally
and interestingly, human-machine
combinations routinely outperform
supercomputers and superhumans.
is can also be observed in the more
recent development of Go players,
robotic musicians accompanying hu-
man musicians,3 in rescue operations
post-natural disasters,4 etc. Comput-
ers and robots are, contrary to popu-
lar belief, making humans better.
Rapidly better. is lends credence to
the underrated but seminal hypoth-
esis of human-machine symbiosis by
Licklider:5 in the long-term future
it seems entirely plausible that an
articial intelligence will dominate
and, more pragmatically, in the near
future there is an exhilaratingly-rich
period of symbiotic progress to be
worked and capitalized on. In other
words, we are in the Intelligence Aug-
mentation phase of human evolution.
Architecture should not, and cannot,
aord to be marginal to this. is
article will, outline the two critical
endeavors to exploit this innovation
potential—a framework of architec-
tural knowledge and collaborative
design practice. e article will also
illustrate the same with exemplar
projects from Zaha Hadid Architects.
In 1985, the world’s best human chess player of the time, Garry Kasparov,
simultaneously played against 32 computers. He comprehensively beat all
of them. In 1996, he narrowly beat the world’s most advanced chess-playing
computer. In 1997 he was comprehensively beaten by the same machine. In
2016, a computer repeated the feat in the more dicult and ancient game of
Go. In 2012, as a tting tribute to Articial Intelligence pioneer, Alan Turing,
the London Symphony Orchestra played music that was composed entirely
by a machine, Iamus. e composition was widely applauded for its expres-
siveness and suciently intrigued human musicians.
Architectural Knowledge
What could be the nature of an ar-
chitectural knowledge that provides
the foundations for architectural pro-
duction in the digital age? Inspecting
the concerns of such a knowledge
base, one would discern two major
divisions:6 one aspect concerning
itself with the Technologies of De-
sign and Construction and the other
with the Conception of Design. e
former concerns itself with opera-
tional knowledge of computers and
machines, material behaviors, struc-
tural systems, use of specic software,
programming, etc. e latter includes
knowledge related to spatial organi-
zation, styles of design, socio-cultural
implications, and theoretical schools
of thought. Witt poetically traces
back such divisions, at least back to
the famously contrary positions of
the two protagonists of the Italian
renaissance—Filippo Brunelleschi
and Leon Batista Alberti. He sug-
gests, implicitly inclined towards
Brunelleschi that the current digital
age could learn substantially from
nineteenth-century efforts in sys-
temic generation of architectural
knowledge of the rst kind—abstrac-
tion of mathematical knowledge into
drawing instruments for specific
types of complex geometry, manu-
als of construction for their physical
realization. Schumacher, inclined
towards Alberti’s eorts, argues for
a similar eort in incorporation of
computational tools and scientic
methods in the conception of design
as well—specically in the study of
human perception of spatial features
and the subsequent production of
architectural meaning.7 In others
words, a computational understand-
ing of semiosis that can then be used
to generate spatial constructs that
enhance such a process. is in turn
helps humans to navigate the spac-
es harmoniously, complement and
augment human activity within the
space. us a fundamental necessity
for sustained innovation is the devel-
opment of a computational basis for
both aspects of architectural knowl-
edge—Technological and Concep-
tual—and further, their unication
into a framework. ere have been
several, episodic and p artial attempts
at such frameworks: mathematician-
turned-architectural-scientist Lionel
March set up an architectural science
research laboratory in Cambridge
in the 1970s8 and produced several
influential publications including
Architecture of Form.9 His colleague
Christopher Alexander made several
seminal and influential contribu-
tions with his writings, especially his
dissertation—Notes on Synthesis of
Form.10 Nicholas Negroponte set-up
the Architecture Machine Group at
MIT, also in 1970s. e necessity now
is for unhindered, devoted pursuit
and expansion of the same. is is
imperative for architecture to be able
to deliver similar accelerated rates
of evolution as some of the other
aspects of human evolution previ-
ously mentioned.
Collaborative and
Co-Authored Design
e nature of relationship between
architects, engineers, and c ontractor-
builders in post-Renaissance hi story,
43
has uidly oscillated between being
unied to being distinct and domain
specialised11 ese role changes be-
tween architects and engineers are
fascinating. Initially the two profes-
sions were indistinguishable on the
basis of skill, but more by building
task—civil buildings by architects,
bridges by engineers for example.
By the twentieth century, the roles
had emerged to account for division
of labour on the same building proj-
ect—architect Sauvestre inecting
engineer Gustave Eiel’s tower, or
architect Utzon’s Sydney opera house
being physically realized by engineer
Ove Arup. In the present time, the
increased use of digital means in
the design of the spatial, geometric
aspects along with the structural
and construction aspects of building,
presents an opportunity for increased
collaboration and co-authorship of
design—i.e., a relationship situated
between the domain-general, am-
biguous distinction of the eighteenth
century and the domain-specialized,
hard distinctions of the twentieth
century. e use of computers pro-
vides a unifying platform between
various disciplines, especially in the
early generative stages of design. us,
the computational medium allows
for the (equal) participation of not
only the traditional stakeholders of
design process—architects, engi-
neers, and builders, but also other
sciences that operate using the me-
dium—mathematicians, biologists,
sociologists, etc. e nineteenth-cen-
tury architect Antonio Gaudi could
draw inspiration from the biological
ideas and drawings of Ernst Haeckel,
or develop an artistic repertoire in-
uenced by the formal appearance of
new mathematics of the time.12 Con-
temporary computational desig ners,
on the other hand, can use the very
biological models that generate our
physiology to produce geometry of
architecture.13 ey could, in equal
part utilize the code of complex
mathematics to generate structural
systems as in the Beijing water-cube
stadium.14 However, legally and in
the nal execution of the projects,
hard distinctions are productive and
necessary. us, digital technologies
can allow for uid transition from a
co-authoring early stages to a col-
laborative, specialized later stages
of design and execution.
Exemplar Project:
The Gallery for Mathematics
and Computing
e Analytical Engine weaves alge-
braic patterns, just as the Jacquard
loom weaves owers and leaves.
—Ada King Lovelace
The design atelier of Zaha Hadid,
founded in 1979, was an early pio-
neer in and adopter of both these key
necessities of innovation—systemic
knowledge generation and collab ora-
tive design. e Computation and
Design research (CoDe) group of
the company was an eort initiated
in 2007, in line with the preceding
pioneering eorts of the company.
e explicit aim for the research and
development eorts of the group was
to harness the opportunities latent in
the inter-disciplinary collaboration
of computationally literate archi-
tects, engineers, and emerging digital
manufacturing methods. e atelier
has now grown into a large rm with
several seminal built projects in this
new paradigm of Parametricist ar-
chitecture. It would only be tting
to describe one of the latest projects
to embrace the ethos—the design for
the Mathematics and Computation
Gallery at the Science Museum in
London, to be complet ed by Novem-
ber 2016. We, the CoDe team, started
work on the gallery, by a wonderful
coincidence, in the bicentennial year
of birth of Ada Lovelace, a pioneering
woman in the history of computers
and of poetic science”—a resonant
desire for a synergetic union of man
and machine, articulated more than
two centuries ago. e project is a
testament to the aforementioned
critical aspects of innovation, col-
laborative design processes, and the
uid exchange of means, methods,
and models across disciplines.
Conception of Design
Central to any gallery is the curatorial
vision and the objects themselves.
e architecture augments this vi-
sion, spatially supplements the nar-
rative, and amplies the assimilation
of the information presented. It is
therefore natural to make the objects
and the narrative into the motivating
driver for the spatial organization of
the gallery. Additionally, if the objects
changes, the spatial organization has
to accommodate. e approach to
this was a data-driven one. e rst
step was to tabulate the data—the
data of the 100-odd objects, their
80-odd showcases, and their relation
to their principal storyline as also
the remaining 25 storylines, their
position within the six categories, di-
mensional information, sensitivity to
light, requirements of preservation,
etc. Next, was to format the data to
44
enable consumption by a data-pro-
cessing algorithm. A bespoke algo-
rithm then processed the information
and laid out the objects to negotiate
the often disparate requirements—
curatorial vision, object dimensions,
ease of navigation, available space,
access and circulation requirements,
construction costs, etc. is enabled
the spatial layout of the gallery to
be changed easily, were the objects,
stories, or any another aspect of the
curatorial vision to change. This
is often the case to accommodate
several vagaries and multitude of
stake-holders involved in the com-
missioning, design, execution, and
maintenance of a permanent exhi-
bition. Additionally, such a process
enables easy measurement of critical
performance criteria of the proposed
layouts. Apart from the functional
metrics such as structural and ma-
terial feasibility, we were principally
concerned with the user-experience
of the space. e visual eld of an
average visitor across several possible
access routes were routinely stud-
ied and the spatial layouts adjusted
accordingly. Primary user naviga-
tion and storyline distribution is
naturally emphasized using spatial
and easy-to-register aspects such
as curvature, uid, and interrupted
visual field, etc. This obviates the
need for way-nding signage. is is
further accentuated by resonance in
several other ancillary features such
as the lighting and oor tile layout,
color scheme, and height distribu-
tion of the showcases. All the major
features of the space thus become
inter-correlated and cohesive with
the human navigation and occupa-
tion of the spaces.
Technology of design and construction
Two specic features—the central
fabric structures and the bespoke
seating design—of the gallery are
worth mentioning in the context
of historic knowledge of design and
construction. These also highlight
the need for innovative design to
follow a research program,15 as op-
posed to ad-hoc solutions to design
tasks. Imre Lakatos, a philosopher
of mathematics and science, used
the word – research program—both
in pragmatic terms of cultivating
experience and also the philosophical
45
Display Case Forms
Study of 3D Surface Variations
sense of maintaining a set of core-
beliefs (about design in this case).
Fabric Structures
e geometry and mat erialization of
these central organizing features of
the gallery are a result of both prac-
tical transfer of knowledge across
disciplines and also lineage fabric
structures that the oce has under-
taken in the past. e geometry of
these constructs—so called minimal
surfaces—were intensively studied by
pioneering architect-engineer Frei
Otto. He studied them physically as
soap-lms that form against a given
wire boundary. These geometries
have also been studied mathemati-
cally. 16 eir computational genera-
tion—a so called form-nding pro-
cess—usually employs one of two
popular methods—the force density
method17 and the dynamic rela xation
method.18ese seminal methods
have been made more accessible
to architects and engineers alike
by research institutions like Block
Research Group19 and University of
Bath,20 their architectural material-
ization as stretched cable and fabric
forms has been studied by several
architectural and engineering rms,
including ours. Prominent prior ex-
amples include the seminal Munich
Stadium by Frei Otto, and the tem-
porary Serpentine Pavilion (London),
the Magazine restaurant (London),
and the interactive Parametric Space
installation (Copenhagen) by Zaha
Hadid Architects. Thus, the latest
46
manifestation of such structures in
the Mathematics Gallery is a result
of a long history of prior experience
and historically assimilated and
transferred research.
Wire-Cut Concrete Benches
e gallery has several moments of
pause” including fourteen bench-
es—designed as cast, ultra-high
performance concrete benches. e
shape and physical production of
these furniture also owes its develop-
ment to a long lineage of research in
the mathematics, engineering and
materialization of a certain class of
surfaces called ruled surfaces. Math-
ematically these surfaces have been
known for centuries but its in depth
study gained traction after the inven-
tion of calculus and is widely credited
to French mathematician Gaspard
Monge.21 As mentioned in the intro-
duction, such in-depth mathemati-
cal knowledge was abstracted and
captured as drawing machines and
construction manuals during the
nineteenth century.22 ese inven-
tions, in turn, made them widely ac-
cessible and their materialization in
stone and timber signicantly more
feasible. ese were very prominent
and widely used in the nineteenth-
century masonry and timber struc-
tures23—perhaps most famously by
the Spanish architect Antonio Gaudi,
in his church for the Sagrada Familia,
Barcelona. e gallery benches in-
herit this mathematical, physical,
and material history and employ it
in a contemporary setting including
a collaboration with state-of-the-art
robotic company specializing in hot-
wire cutting of foam24 to produce the
molds for the cast concrete.
Wire-Cut Benches.
ese central, organizing structures of the gal-
lery for Mathematics and Computing at the
Science Musuem, London are a result of several
years of collaborative projects, research, and
prototyping by ZHA and its collaborators and
consultants. e design unies historic methods
of form-nding with contemporary design and
manufacturing technologies. (Specialist contrac-
tor: Base Structures).
47
Collaborative Design
As mentioned previously, the com-
putational methods employed to
generate the shapes and spaces of
the gallery, especially in early stages
of design, were a result of a uid ex-
change of means, methods, and mod-
els across disciplines. For instance,
the simulation of the airow around
the key guring object of the Hadley
Page airplane has a lineage in the
physics of uids dynamics going back
to Gabriel Navier and Claude Stokes
in the 1840s. ey were made further
accessible and amenable for use in
early, interactive stages of design by
sustained research in computational
fluid dynamics by the likes of Jos
Stam,25 Ro n Fed kiw, 26 and others from
the computer animation and graph-
ics industry. us we were able to
utilize the actual models and code as
opposed to merely drawing inspira-
tion from the formal appearance of
uid-ows. Similar inuences on the
central fabric structures have already
been mentioned. Su ch interdisciplin-
ary osmosis in the early stages has
now transmuted into more clearly
dened roles—architects, engineers,
and contractors—in the later stages
of the project. Industry standard
building information modeling and
similar digital technologies are en-
abling a well-coordinated execution
of the project.
Bench Geometry, Science Museum,London.
e benches are algorithmically generated—
negotiating ruled-surface geometric constraints
with motion limitations of an industrial robot,
and manufacturing constraints of ultra-high-
performance concrete. e design learns from
projective geometry and stone-cutting tech-
niques pioneered in the nineteenth century by
the likes of Antonio Gaudi. e formwork for
the benches will be robotically fabricated and
subsequently cast upon with high performance
concrete. is project is a collaboration between
ZHA(CODE), ODICO Robotic Formworks and
HiCon concrete specialists.
48
Conclusion
Parametricist or generative design
has the potential to overcome the
mass-produced, homogenous, and
disorienting sterility of twentieth-
century architecture. It has the po-
tential to re-associate with historic
practice, and amplify assimilated
knowledge. It has the potential to
heighten the inference potential of
spaces—of enabling meaning ful oc-
cupation and navigation of spaces by
humans. To fulll this potential for
rapid evolution of our discipline and
upgrade of our built environment, it is
imperative that designers and other
stakeholders of architecture, invest
in it—invest in digital technologies
not just digital means of producing
known tropes, invest in making de-
sign processes amenable for the use
of computers, invest in making mate-
rialization of architecture amenable
to the use of robots. Digitization of
architecture and intelligence augm en-
tation of designers is a necessary and
imperative path to a superior design
intelligence.
Vol u .
A contemporary dining pavilion that fuses com-
putational design, lightweight engineering, and
precision fabrication, Volu’s design embeds the
tectonics of its manufacture within the form
itself. All the timber elements are produced
from at-sheet material with innovative use of
kerf-cuts to bend them into loops. (Specialist
fabrication and engineering: OneToOne with
Ackermann GmBh)
49
Notes
1. P. Schumacher, “Parametricism 2.0: Gearing
Up to Impact the Global Built Environment,
Architectural Design, 86(2), 8–17.
2. Author unknown, “Comparison of Top
Chess Players throughout History,” Wikipe-
dia, https://en.wikipedia.org/wiki/Compari-
son_of_top_chess_players_throughout_history,
accessed April 4, 2016.
3. G. Weinberg, “Robotic Musicianship-
Musical Interactions Between Humans and
Machines,” INTECH Open Access.
4. S. Sankar, “People and Computers
Need Each Other,CNN, http://edition.cnn.
com/2013/02/03/opinion/sankar-human-
computer-cooperation/, accessed April 4, 2016.
5. J.C.R. Licklider, Man-Computer Symbiosis,
Human Factors in Electronics, IRE Transac-
tions, 4–11.
6. A.J. Witt, A Machine Epistemology in Ar-
chitecture: Encapsulated Knowledge and the
Instrumentation of Design,” Candide. Journal
for Architectural Knowledge, 3(03), 37–88. See
also P. Schumacher, e Autopoiesis of Archi-
tecture: A New Framework for Architecture,
John Wiley & Sons.
7. P. Schumacher, “Advancing Social Function-
ality Via Agent-Based Parametric Semiology,
Architectural Design, 86(2), 108–113.
8. S. Keller, “Fenland Tech: Architectural
Science in Postwar Cambridge,Grey Room,
(23), 40–65.
9. L. March, e Architecture of Form, Cam-
bridge Urban and Architectural Studies, Cam-
bridge University Press.
10. C. Alexander, Notes on the Synthesis of Form,
Harvard University Press.
11. A. Saint, Architect and Engineer: A Study in
Sibling Rivalry, Yale University Press.
12. M.G. Lorenzi and M. Francaviglia, Art and
Mathematics in Antoni Gaudí’s Architecture:
‘La Sagrada Familía,’” APLIMAT Journal of Ap-
plied Mathematics, 3(1), 125–145.
13. Andy Lomas, in ACM SIGGRAPH 2005
Electronic Art and Animation Catalog, ACM,
104–105. See also N. Oxman, “Templating
Design for Biology and Biology for Design,”
Architectural Design, 85(5), 100–107.
14. P. Ball, “Science in Culture: Beijing Bubbles,”
Nature, 448(7151), 256.
15. I. Lakatos, e Methodology of Scientic
Research Programmes.
16. K.A. Brakke, “Minimal Surfaces, Corners,
and Wires,” e Journal of Geometric Analysis,
2(1), 11–36.
17. H.J. Schek, “e Force Density Method for
Form Finding and Computation of General
Networks,Computer Methods in Applied Me-
chanics and Engineering, 3(1), 115–134.
18. A.S. Day, “An Introduction to Dynamic
Relaxation,” e Engineer, 219, 218–221.
19. S. Adriaenssens, et al., Shell Structures for
Architecture: Form Finding and Optimization,
Routledge.
20. C.J.K. Williams, “Dening and Designing
Curved Flexible Tensile Surface Structures,”
e Mathematics of Surfaces, 143–177. See also
A. Bak, P. Shepherd, P, and P. Richens, “Intui-
tive Interactive Form Finding of Optimized
Fabric-Cast Concrete,Second International
Conference on Flexible Formwork (ICFF2012).
21. S. Lawrence, “Developable Surfaces: eir
History and Application,” Nexus Netw ork Jour-
nal, 13(3), 701–714.
22. A.J. Witt, A Machine Epistemology in Ar-
chitecture: Encapsulated Knowledge and the
Instrumentation of Design,” Candide. Journal
for Architectural Knowledge, 3(03), 37–88.
23. Robin Evans, e Projective Cast: Archi-
tecture and Its ree Geometries, MIT Press.
24. W. McGee, J. Feringa, and A. Søndergaard,
“Processes for an Architecture of Volume,” Rob|
Arch 2012. Springer, 62–71.
25. J. Stam, “Real-Time Fluid Dynamics for
Games,Proceedings of the Game Developer
Conference, 25.
26. O. Deusen, et al., “e Element s of Nature:
Interactive and Realistic Techniques,” ACM
SIGGRAPH 2004 Course Notes, ACM, 32.
Prototype 3D Printed Chair.
is research prototype was a result of collabo-
ration between ZHA(CODE), and Stratasys Inc.
It incorporates contemporary developments in
designer-friendly technologies inherited from the
computer animation industry, material-saving
algorithms (topology optimization) developed
by Altair Technologies and other researchers,
with innovations in 3D printing to materialize
the same.
Chapter
This chapter describes the influence of topology and of topological thinking on the work of the great architect Zaha Hadid.
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Developable surfaces form a very small subset of all possible surfaces and were for centuries studied only in passing, but the discovery of differential calculus in the seventeenth century meant that their properties could be studied in greater depth. Here we show that the generating principles of developable surfaces were also at the core of their study by Monge. In a historical context, from the beginning of the study of developable surfaces, to the contributions Monge made to the field, it can be seen that the nature of developable surfaces is closely related to the spatial intuition and treatment of space as defined by Monge through his descriptive geometry, which played a major role in developing an international language of geometrical communication for architecture and engineering. The use of developable surfaces in the architecture of Frank Gehry is mentioned, in particular in relation to his fascination with ‘movement’ and its role in architectural design.
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Andrew Saint is general editor of the Survey of London. His book is a study of relations between engineering and architecture since their modern emergence in Europe and the United States. Relations between the two professions are complex and varied. Sometimes the Renaissance fantasy obtains: an architect designs a masterpiece, then hands the vision to an engineer to figure out how to make it. Sometimes engineers are part of the design process, working closely with architects from the beginning. At other times, engineers do the work we might expect architects to do yet produce buildings that continue to delight. Inventors of architectonic forms may belong to neither profession. Posterity remembers Eiffel as an engineer, though more accurately he was a contractor-fabricator. There is more to this book than descriptive history. Saint chronicles the rising tide of cant about the architect as an artist (who makes things beautiful), while the engineer is a technician (who makes things work). Any way you look at it, this dichotomy fails. Engineering is a highly inventive practice, and as "intuitive," "irrational," and "aesthetic" as anything in architecture. Engineering forms are never calculated. There are calculations aplenty, but the form is not arrived at by calculation, as if it were a mathematical result. Moreover, aesthetic accomplishment cannot be limited to a design; it requires a work, and one that is well made. When an architect, Le Corbusier for example, is indifferent to mechanics, his buildings begin to look shabby almost immediately. Inventive engineering has an aesthetic moment; memorable architecture has a structural moment. Engineers must visualize and make aesthetic choices, and only architects who appreciate the work of engineering can take the invention of form to the limits of new technologies. Barry Allen is the author of Truth in Philosophy, Knowledge and Civilization, and Artifice and Design: Art and Technology in Human Experience. He teaches philosophy at McMaster University and is associate editor of Common Knowledge for philosophy and politics.
Article
This updated course on simulating natural phenomena will cover the latest research and production techniques for simulating most of the elements of nature. The presenters will provide movie production, interactive simulation, and research perspectives on the difficult task of photorealistic modeling, rendering, and animation of natural phenomena. The course offers a nice balance of the latest interactive graphics hardware-based simulation techniques and the latest physics-based simulation techniques. Interactive implementations and approximations of complex physics-based simulations will be presented, as well as procedural approximations and combined hybrid techniques. Interactive demonstrations and discussions of implementation details impart a working knowledge of these techniques that can't be acquired by reading papers on the topics.
Article
A new method for network analysis, the “force density method”, is presented. This concept is based upon the force-length ratios or force densities which are defined for each branch of the net structure. It is shown that the force densities are very suitable parameters for the description of the equilibrium state of any general network: the associated node coordinates of the structure are obtained by solving one single system of linear equations. A Gaussian transformation of the topological branch-node matrix yields the equation matrix.A method based on force densities renders a simple linear “analytical form finding” possible. If the free choice of the force densities is restricted by further conditions, the linear method is extended to a nonlinear one. A damped least squares approach is then introduced. In this version the method may be applied to the detailed computation of networks.Moreover, an interesting cross-connection between geometrical minimum way nets and prestressed unloaded structures is derived using the force densities.
Book
Winner of the 1997 Alice Davis Hitchcock MedallionAnyone reviewing thehistory of architectural theory, Robin Evans observes, would have to conclude thatarchitects do not produce geometry, but rather consume it. In this long-awaitedbook, completed shortly before its author's death, Evans recasts the idea of therelationship between geometry and architecture, drawing on mathematics, engineering, art history, and aesthetics to uncover processes in the imagining and realizing ofarchitectural form. He shows that geometry does not always play a stolid and dormantrole but, in fact, may be an active agent in the links between thinking andimagination, imagination and drawing, drawing and building. He suggests a theory ofarchitecture that is based on the many transactions between architecture andgeometry as evidenced in individual buildings, largely in Europe, from the fifteenthto the twentieth century.From the Henry VII chapel at Westminster Abbey to LeCorbusier's Ronchamp, from Raphael's S. Eligio and the work of Piero della Francescaand Philibert Delorme to Guarino Guarini and the painters of cubism, Evans exploresthe geometries involved, asking whether they are in fact the stable underpinnings ofthe creative, intuitive, or rhetorical aspects of architecture. In particular heconcentrates on the history of architectural projection, the geometry of vision thathas become an internalized and pervasive pictorial method of construction and that, until now, has played only a small part in the development of architecturaltheory.Evans describes the ambivalent role that pictures play in architecture andurges resistance to the idea that pictures provide all that architects need, suggesting that there is much more within the scope of the architect's vision of aproject than what can be drawn. He defines the different fields of projectivetransmission that concern architecture, and investigates the ambiguities ofprojection and the interaction of imagination with projection and itsmetaphors.