kulic01

7/28/2019 kulic01

http://slidepdf.com/reader/full/kulic01 1/10 Received: 15 Jul 2000 © Copyright 2001

Accepted: 01 Nov 2000 – 1 – http://www.complexity.org.au /vol08/kulic01/

http://www.complexity.org.au/

Volume 08

The complexity of architectural

form: some basic questions

V. Kulic

Faculty of Architecture, University of Belgrade

Belgrade, Yugoslavia

Email: [email protected]

Abstract

This paper explores some basic notions relevant for an investigation of the complexity of

architectural form and of a way it changes through time. The hypothesis is that architectural forms

within the same formal tradition tend towards more complex configurations with the passage of

time. Relations between the elements of architectural form at early stages in the development of a

stylistic tradition are simple; they get more complex with applications of methods such as

superimposition and deformation of elements and by more abundant use of curving forms. Two

stylistic traditions are used as examples: Classical (from the Renaissance to the Baroque) and

Modern, although there are others as well.

1. Introduction

The historical unfolding of art seems to be one of the most complex processes imaginable.

Crucially dependent on cultural, technical, societal and political circumstances, not to mention

the ever present subjective factor, this process is quite unpredictable, but at the same time far

from chaotic. That there is a certain regularity in it is testified by the very history of art, which,

as a discipline, is traditionally based upon the notions of style and movement, notions which

represent the most widely recognised ways of systematisation in historical considerations of

art and which introduce an element of order into it.

Architecture seems to be especially convenient for such systematisation, probably because

of its already inherent rationality. From Hegel to Sigfried Giedeon to Colin Rowe and others,

there have been more than a few attempts to surpass purely stylistic classifications and to try

to find more comprehensive ones. One such attempt, which initially inspired this work, was

made by the Croatian architect, Nikola Polak, who claimed that architecture in Europe since

the Renaissance has passed through three stylistic cycles, each consisting of three identical

stages of degradation of three initial paradigms (Polak 1990). Although too strict and too

“Hegelian”, Polak’s classification contains certain elements which can be recognized as

7/28/2019 kulic01

http://slidepdf.com/reader/full/kulic01 2/10

Complexity International Volume 08

kulic01 – 2 – © Copyright 2001

accurate, because its cross-historical approach brings together the simplicity and rigour of the

Renaissance, Classicist and early Modernist architecture on the one side, and the formal

elaboration, drama and liberty of expression of the Baroque, Art Nouveau and Deconstruction

on the other. This insight is almost trivial and can be also applied to other periods in the

history of art and architecture, but as far as I know, no one else has included the most recent

developments, such as Deconstruction, in such considerations.

So, here we have an interesting situation: it seems that one of the keys to dealing with the

complexities of the history of architecture seems to be the complexity of architectural form

and the way it changes with the passing of time. In this text I shall try to examine some basic

theoretical issues of the complexity of form in architecture. Besides that, I shall try to replace

Polak’s tripartite ideal schemes with an investigation of methods through which the

complexity increases, regardless of the specific styles.

2. Complexity and Architectural Form

Our intuitive understanding tells us that some architectural forms are more complex than

others. The fact that Michelangelo’s motif on Porta Pia is more complex than, for example,

some arched passage by Alberti is beyond discussion. But what exactly does that mean? Is itmore complex because it takes more words to describe? Perhaps, but in that case the

complexity would depend on the eloquence and knowledge of the one who is describing it. Or

is it because it is more difficult to build? A large-span suspended bridge is definitely more

difficult to build than a stone gate, although it does not look more complex. So, what is the

criterion for the comparison of the complexity in this case?

For the purpose of this problem I find very useful a very broad definition of complexity

which was given by Bruce Edmonds from the Centre for Policy Modelling in Manchester,

because it is sufficiently comprehensive and suits divergent aspects of architecture. Edmonds

(1998) says that complexity is

“...the difficulty associated with a model’s form given almost complete information about the data

it formulates.”

This definition deals with one notion which is deeply embedded in the nature of

architecture. Architecture was perhaps the first human activity to develop the concepts of

model or design, due to the need to articulate large structures conceived by one man, but

realised with the help of many others. This requires the final result to be more or less

completely defined before any construction is begun, and then to be somehow presented to

those who are actually to do the work. The design (as a drawn model) represents a description

“in advance” and the most widely used ““language” for this description is geometry. The

centuries-long bond between architecture and geometry shows the crucial inter-dependence of

the two disciplines and it is hardly surprising that it was architecture (in a very broad sense of

the word) that gave an impetus for the emergence of geometry in Egypt some 5,000 years ago.

Edmonds’s definition has three important consequences:

1. What we measure is the complexity of the model, rather than the complexity of the actual

physical system (i.e. we do not have to be interested in every little crack in the wall to

discuss the complexity of a building).

2. The complexity depends on the type of difficulty we choose as relevant (i.e. we have to

choose, for example, whether something is difficult to draw or difficult to build or difficult

to perceive, etc.).

7/28/2019 kulic01




3. The complexity of different models can be compared only if they are made within the same

modelling language. For example, the same task, like drawing an ellipse, cannot be

compared if we have a computer with some CAD program and if we have to use only

standard drawing tools, in which case it is only an approximation of the shape. Or, from the

stylistic point of view, it hardly makes any sense to compare two works which belong to

different traditions, because their formal languages differ.

So, what are the model and the language if we want to consider the complexity of the

architectural form? The design is surely one relevant model, but I would say that our

perception can also be seen as a model-maker – the image we have of a building is actually

the ultimate model, the aim of the whole artistic engagement. Moreover, there are various

types of design, and I would like here to make a distinction between the conceptual and

execution design, because they have quite different aims. The conceptual design, if oriented

towards form-making, is closely related to the desired perception of the form, while the

drawings made for the building site have to describe the form in terms of building technology.

These two are not the same, although they naturally have similarities.

Conceptualisation and perception of the form are closely connected, because the former is

aimed at the latter. Both the designer and the one who perceives the work do not think in

terms of precise measures and geometrical relations, but rather operate with pre-established

elements and relations between them. This is sometimes the cause of a gap between theconceptual and actual (structural) complexity, between how something is perceived and how it

is made. For example, very fashionable “distorted” forms are intended to be seen exactly that

way – as regular bodies deformed by some outer force – but are not actually made that way;

they are created as positive statements of construction, following very complex designs which

are supposed to convince us of something else. These two types of complexity – “conceptual”

and “constructional” – besides being incomparable because of different languages, in such

cases have totally different structures. However, this ‘distortion’ has recently turned into a

completely new quality, to which I will return later.

The relevant languages vary even more. The linguistic approach in the interpretation of

architecture is very common and it deals with sets of (pre) established formal elements which,when combined, create a piece of architecture. The often-heard phrase “formal language”

stems from this approach and implies the existence of a multitude of such languages, from

those broadly used and known as styles, to some very personal ones.

What complicates this question is the fact that, apart from these “natural languages”, just

like computer science, architecture also has its own “lower languages”, its “machine codes”

and they depend on drawing/building techniques. Conceptual design can easily be a not-very-

precise free-hand drawing, since it only lays out a general idea of the form and operates with

pre-established formal elements. The design according to which something has to be built

must describe the form in terms of a precise geometry and need not be necessarily connected

to aesthetic considerations. Moreover, this geometrical definition must correspond with the

building technique which is in use. The following example illustrates this quite clearly:

Utzon’s Opera House in Sydney was conceptualised like a sculpture and its curves are a

natural outcome of an “organic” design method. However, when the construction was

supposed to take place, one of the basic problems was how to geometrically define these

curves so that the prefabricated elements of the building’s outer shell could be actually

produced. The complexity of this task was such that it took four years before Utzon finally

found a simple enough solution using segments of the same spherical surface (Frampton

1995). On the other hand, we can always remember Gaudi, whose buildings are full of curves

of all sorts, although he never employed mathematicians to count them. He simply applied

7/28/2019 kulic01




some inventive building methods such as hanging ropes on their ends to get parabolas which,

when turned upside down, outlined his beautiful arches.

3. Paradigmatic group

The history of architecture recognises several large traditions which contain a number of

styles each, or can be divided into smaller stylistic groups. Perhaps the best known among

these traditions is so-called Classical architecture, which is indeed a long succession of styles:Ancient Greek, Roman, Renaissance, Mannerist, Baroque, Classicism, etc. There are also

others, such as the Byzantine, with its numerous local schools, the Gothic, with its several

chronological phases, the Modern, with its numerous threads of development, etc.

What unifies each of these traditions, sometimes bridging centuries and continents, is what

was already mentioned as the “formal language”, a minimum of common formal features

whose persistence determines the longevity of the tradition. Trying to avoid sometimes tricky

linguistic references and paraphrasing Thomas Kuhn’s term, scientific paradigm, we may call

these common features a formal paradigm, or in more mathematical terms, paradigmatic

group, because it contains a set of architectural elements which stand at the architect’s

disposal and a number of operations or allowed compositional rules for combining the basicelements.

Sometimes, the paradigmatic group emerges slowly and gradually and sometimes we can

almost pinpoint the date of its birth, as in the case of the Gothic. Sometimes it is defined very

openly, as in the Renaissance and later, when almost every major theoretician of architecture

of the time had an obsession to prescribe a standardised set of architectural elements. On the

other hand, the paradigm may emerge as a negation, a reaction against the existing practice,

and only later it transforms itself into a positive statement, as was the case with Modern

architecture. In any case, once formed, the paradigm governs and marks the whole

architectural tradition until the moment when it finally gets worn out and abandoned.

To illustrate the above-said, let us examine the following two examples:

The paradigmatic group of the Classical tradition from the Renaissance to Baroque and

Classicism was largely adopted from Antiquity, more specifically from Roman architecture,

which itself was inherited and adapted from the Greeks. It was based on two structural

systems: post-and-lintel and arch (vault) and within them all the elements – columns, arches,

openings, walls – got certain defined articulation. This means – in very rough terms – that if

we want to build an outer wall, it has to rest on a base and has to be finished by a cornice; if

we want to make an opening in it, then this opening must have at least a modest relief profile

around it, if not a whole aedicule, or even something more elaborate. But the best example of

how strictly this paradigmatic set is defined are the columns: they will have to belong to one

of the famous five orders which prescribe their shape and proportions, as well as a number of other elements related to them. The fact that virtually every major theoretician of architecture

of the time presented his own version of the five orders clearly illustrates the strong need to

standardise ideal elements of architecture and, more profoundly, an idea that such a thing as

“ideal architecture” exists (Fig. 1).

There are basically two ways for combining the elements or, to use mathematical term, two

geometrical transformations. One of them is bilateral symmetry, reflecting the symmetry of

the human body. The other is linear translation, resulting in regular sequences of elements,

such as colonnades and arcades. Both of them were inherent to almost all architecture from

very ancient times until recently, but their mutual combinations and juxtapositions, as we shall

see, were never developed to the degree they reached in the period we are discussing here.

7/28/2019 kulic01




Figure 1. The five orders according to Vignola

The situation with the Modern architecture was essentially different. Its “language” is not

so clearly defined, and some more descriptive terms must be used because of two reasons:

firstly, it follows numerous lines of development; secondly, it rests upon a variety of structural

systems, technologies and materials, and finally, it was defined largely as a negation.

However, if we abandon the need to create a totally comprehensive theory, some very useful

lines of development can be found to exemplify the point of this paper.

To put it very simply, the formal features of Modern architecture stem greatly from the 19th

century’s realisation of the difference between structure and decoration which was a result of

the invention of new building techniques. Once this difference was observed, it firstly inspired

a search for new systems of decoration and then a complete rejection of any decorationwhatsoever. Another important source is the so-called “destruction of the box”, an invention

of Frank Lloyd Wright (Brooks 1979), who made the first steps towards dismantling

traditional quadrilateral rooms into compositions of abstract planes. It took only one step from

these negative definitions to a positive expression of the new style. By the beginning of the

30’s it was clear that what tended to be modern, had to have an appearance of abstract

geometrical bodies, preferably of a rectangular or cylindrical shape, or a combination of such

bodies. The most famous and also a very rigorous definition of the style were Le Corbusier’s

“Five points of modern architecture”, which united structural, functional and formal aspects

into a very influential expression (Le Corbusier 1924) (Fig. 2). However, from the formal

point of view, perhaps the best formulation of what would become a new paradigm was given

by Henry-Russell Hitchcock and Philip Johnson in 1932. Their definition of the “Internationalstyle” included several principles, but the most important are architecture as volume and

avoiding of decorative application. All elements are thus reduced to abstract geometrical

entities – points, lines, surfaces, volumes – and there should be nothing that disturbs their

abstractness. The treatment of openings in the walls is also quite indicative. Firstly, they are

arranged in an abstract order, such as long strips, something that does not remind of the

traditional openings, and secondly, they are by no means allowed to disturb the surface of the

wall – the windows and the wall are supposed to create a continuous “skin” of the house

which keeps an impression of the clear volume.

7/28/2019 kulic01




Figure 2. Le Corbusier, Villa Stein in Garches,

one of the manifestos of the “new architecture”

In composition, geometrical translation of elements gained a stronger emphasis, thanks to

the use of the skeletal structural system, and thus it spread in two orthogonal directions. The

domination of symmetry was replaced by a deliberate use of asymmetry and a search for new

ways of creating visual balance. However, the symmetry of individual elements was notquestioned, but nor was it emphasised. Superimposition of points, lines and surfaces appeared

in the arrangement of plans, while interpenetrating volumes dominated from the outside.

Compared with the later phases, the initial phase of the development of the paradigm is

dominated by rather simple arrangements of elements. They stand by each other

independently, subordinated to a hierarchical order, but fully keeping their own integrity –

they do not mix with each other and there is nothing that disturbs their shape. Compositional

principles are used in their simplest form. If the symmetry is in question, then we have two

basic elements placed at an equal distance from the axis; if it is a sequence of elements, then

they are all identical, and the rhythm between them is uniform. The use of simple linear or

circular trajectories exceeds by far the use of more complex curves. Finally, if we examinecombinations of independent systems, such as the Modernist superimposition of grids of

columns on one side, and straight or curving partition walls on the other, we shall see that

these systems never collide – they function independently, but in harmony and almost without

exception share the same geometrical system.

4. Methods for increasing complexity

4.1 Superimposition

It seems that the first step from initial simple configurations is made by the method of superimposition, be it a superimposition of element upon element, or operation upon

operation. For example, if we consider Classical architecture after the Renaissance, then the

credit for a major breakthrough achieved in this field goes to two men who worked around the

middle of the 16th

century. Michelangelo (1475-1564) was the first one to combine different

elements, such as columns and walls, or elements of the same family but of different sizes,

into compositions never seen before. His Porta Pia displays a rather bizarre combination of the

flat arch within a larger arch within a broken pediment within an even larger pediment, all of

this being decorated by volutes, garlands, tablets, etc. The nature of this combination is such

that each of these elements loses its independence, taking part in the composite whole of a

very sculptural character. One of Michelangelo’s inventions was also an interplay of the so-

7/28/2019 kulic01




called giant order (columns or pilasters ascending through two or more storeys) and orders of

smaller scales (one storey high). Although not very reasonable from the structural point of

view, this combination was very influential for its interesting visual effect of the structure

within a structure.

Figure 3. Andrea Palladio’s San Giorgio Maggiore.

Superimposition of two classical porticos.

If Michelangelo combined elements, we can say that Andrea Palladio (1508-1580)

investigated combinations of the two basic operations. Throughout his oeuvre we find him

applying bilateral symmetry and sequences of elements onto each other, exhausting possible

combinations with almost mathematical precision. For example, on the porch of his Palazzo

Chiericati, which is basically a colonnade, i.e. a sequence, he reduced the ending spacings

between the columns, thus giving the colonnade a clear beginning and ending and, what is

more important, an obviously symmetrical character (we could say that he applied bilateral

symmetry onto linear translation). On his Basilica in Vicenza he did the opposite: he made a

sequence multiplying a composition of a symmetrical character, the so-called Venetian

window (applying linear translation onto bilateral symmetry), while in a whole series of

country villas he made symmetrical arrangements of already symmetrical compositions

(applying symmetry onto symmetry) or again symmetrical colonnades (applying symmetry on

translation) (Fig. 3).

Superimposition is also one of the main design methods of Postmodernism, but due to the

movement’s many divergent lines of development, it cannot be so easily summarised. We

recognise it in historicist collages where the classical elements are applied onto the otherwise

pure, modernist forms; we recognise it in Robert Venturi’s application of an asymmetrical

composition on a volume of a very emphasised symmetry; we also recognise it in Michael

Graves’ superimposition of different scales on his Portlandia Building, where a variety of

fenestration methods (mostly of Modernist origin) creates a “drawing” of an enormous

stylised classical column on the building’s flat facade. However, there is one specific branchof architectural Post-modernism which is of a particular interest in this discussion, because it

deliberately formalises a typically Modernist “language” – that of Le Corbusier’s early villas,

a language the elements of which are clearly outlined in his “Five points”. “The Whites” or

“The New York Five”, although not an organised group, took Le Corbusier’s purist works as

their formal point of departure and transformed it in much the same way as Mannerists

transformed the classical language. A layering of structural elements, already inherent in Le

Corbusier’s approach, is further emphasised by rotating their geometrical systems, with the

blended elements losing their integrity and being no longer independent. In some cases we

cannot say whether what we see is a column or a wall; a frame or a wall, with an opening in it,

etc., and the whole begins to look like a sculpture rather than a house.

7/28/2019 kulic01




4.2 Deformations

Deformations of elements include a number of operations, such as “cutting”, “breaking”,

“twisting”, “bending”, etc., but in any of these cases, they presuppose the observer’s

recognition of the element’s original, regular shape and imply that it was changed by some

outer force. Since this is usually not the way these “deformed” elements are actually made,

these “rhetoric” deformations are the greatest causes of the difference between the

conceptual/perceptual and physical/constructional complexity of the form.

Figure 4. A Baroque pediment, cut and curved.

Let us take a look at some examples:

If Michelangelo, as we have seen, blended different elements together, then the Baroque

architects again dismantled this union, but without restoring the initial integrity of the

elements (of course, this does not mean that superimposition as a compositional method was

abandoned – on the contrary). In this way we get, for example, cut pediments whose parts are

completely omitted or set into different planes, or columns and pilasters showing only their

capitals, the rest being swallowed by the wall (Fig. 4).

Deformations are an omnipresent motif in Deconstructivist architecture. From Bernard

Tchumi’s omitted columns in his folies in Park La Vilette in Paris, to Frank O. Gehry’s piled

up cubes and twisted volumes, to Peter Eisenman’s rotated axes and Coop Himmelblau’s

houses looking like they have been shaken by an earthquake, we meet all sorts of

deformations of the initial languages, be it Russian Constructivism, Suprematism, early

Modernism or something else. However, there is a thin line between deformation and an

actual introduction of a new element or a compositional rule. Recent developments, such as

the latest works by Gehry or Eisenman, show that what could be previously seen asdeformations of recognisable forms turns into a completely new geometry (Fig. 5). The

integration of CAD and CAM technologies, which coincides with such projects, seems to add

to this shift in complexity, because the emerging new tools make these projects incomparable

to those built using traditional building methods.

7/28/2019 kulic01




Figure 5. Frank O. Gehry, “Ginger and Fred” Building, Prague

4.3 Curves

Curving lines are man’s most natural way of graphic expression, but as soon as geometry

started dominating architecture, they lost pace with straight lines, simply for being more

complicated to define precisely. The only curve that remained ever-present in almost all

architectures was the circle, surely due to the rather simple way of its construction. Until only

very recently, the use of other curves – ellipses, parabolas, sinusoids, not to mention those

drawn with free hand – meant a complication in the construction and consequently an increase

in the form’s complexity.

The use of various curves is a commonplace when speaking of Baroque architecture. In this

period, ellipses and combinations of them start governing the plans, creating a multitude of

convex and concave spaces. Ellipses also become trajectories for the colonnades, arcades and

walls, the grandest example being Bernini’s colonnade in front of St. Peter’s in Rome. Finally,

ellipses and other curves start affecting the standard geometry of individual elements, like

pediments and openings, either by twisting them to fit the curving walls, or turning them into

a wild play of the concave and the convex. This culminated in Rococo architecture, especially

in Germany, where straight line became an exception rather than a rule.

Modern architecture used curves modestly, with a small number of examples, such as late

Le Corbusier’s works, or Brazilian Modernism. Since the late 1970’s curves started appearing

much more often and have been especially associated with the Deconstructivist movement.

Although curves are not so widely used by all Deconstructivist architects, let alone by most of

the contemporary practitioners, there has never been such a variety of curving geometries in

use before. They range from rather regular ones – ellipses, parabolas, sinusoids, etc., to those

more complex and more subtly defined. However, if we consider the geometrical defining of

curving forms, we will discover a rise of arbitrariness verging on organicism. Sometimes it is

connected with a wish to create an impression of deformation, and sometimes they are a result

of investigations of the possibilities offered by the computer, as in the case of the designs of

Greg Lynn.

7/28/2019 kulic01



8. Conclusion

We have seen how the two analysed sequences of architectural styles follow a similar line of

development, tending towards more complex forms. We have also seen how they share

similar strategies for the enhancement of the formal language, despite their very different

appearances. It could be said that these strategies mark a shift in aesthetic ideals: while the

basics of an “architectural “language”” are being established, architecture is characterised by a

rather direct correspondence between form on the one side, and its function and structure on

the other. Once the “language” is more or less complete, further experiments with it shift the

focus to the formal side, away from the ontological and towards predominantly aesthetic

concerns.

This process should not be mystified, because it is a result of the natural evolution of the

designer’s capabilities to treat the form, from simple to more complex configurations. When

all the possibilities are investigated, the designer has a freedom to choose and what usually

appears after the phase of very saturated form is a reaction against it – a return to formal

simplicity, like Neo-classical architecture, or today’s neo-modern inclinations. However, it is

exactly this freedom to choose that suffocates the paradigm – the feeling that there is nothing

more to discover within the confines of the style makes it inevitable that adventurous spirits

will step outside.

The aim of this investigation is not to “surpass” history, to predict its future development

(nor do I have an illusion that such a thing is possible), but to increase our consciousness of

the processes that have shaped it so far. The current situation in architecture shows a

coexistence of very different formal approaches, from the minimalist to those oriented toward

elaborate form-making, as if the processes which previously took decades and even centuries

to unfold were compressed into a permanent present. In such a situation, where all the

traditional notions of architecture are being melted and blended into each other, it is even

more important to be aware of one’s position.

References

Brooks H. A. (1979), Frank Lloyd Wright and the deconstruction of the box, Journal of the

Society of Architectural Historians, XXXVIII, 1.

Edmonds B. (1998), What is complexity? - The philosophy of complexity per se with

application to some examples in evolution, in The Evolution of Complexity, (eds) F.

Heylighen & D. Aerts (eds).

Frampton K. (1995), Studies in tectonic culture, The MIT Press, Cambridge, London.

Hitchcock H. R., Johnson P. (1932), The international style: Architecture since 1922,Museum of Modern Art, New York.

Le Corbusier (1924), Vers une architecture, Paris.

Polak N (1990), O heterotopiji izmjestene sobe, De re Aedificatoria No. 1, Arhitektonski

fakultet, Beograd.

kulic01

Documents

Transcript of kulic01