Development of Thinking and Theory in Architecture


An Essay on a presentation made by Suha Ozkan to Diwan al-Mimar on October 21, 2001

Prepared by Mohammad al-Asad and Dalia al-Husseini, 2003

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Support for the publication of this essay has been made possible by a grant from the Prince Claus Fund for Culture and Development. Additional support has been provided by Darat al-Funun - The Khalid Shoman Foundation

In this presentation to Diwan al-Mimar, Suha Ozkan (1) presented his explorations of the development of thinking and theory in architecture that he has carried out over the past thirty years. The exploration was prompted by his appointment as an instructor in architecture at the Middle East Technical University (METU) in Ankara upon completing his master's degree there in urban design in 1969. As he undertook the challenges of teaching, Ozkan felt a strong need to develop a comprehensive understanding of architectural theory that would aid him as a teacher and researcher. He also studied at the Architectural Association where he produced a thesis entitled "General Conceptual Framework for Methodology of Design." He finished his Ph.D. at METU in 1980, which was entitled "A Categoric Structure for Theory of Design."

Ozkan emphasized that he very much was influenced by the overall developments that were taking place at the time when he began teaching. It was just before the jumbo jet was invented; a number of satellites already were in orbit, and important achievements generally were being realized in science and technology. Also, new social values were coming into being. The social consciousness movement was being formed, and it was the period just prior to the 1968 student revolts in Paris, with which Ozkan sympathized. It generally was a period of anticipation and energy. As for his own intellectual background, he was brought up in the spirit of positivism, as opposed to speculation and artistry. Consequently, his academic and intellectual upbringing emphasized the belief that theology and metaphysics are earlier imperfect modes of knowledge, and that positive knowledge is based on natural phenomena and their properties and relations as verified by the empirical sciences. For Ozkan, positivism meant that theory should inform practice. He explained that in architecture, all speculations, writings, and essays are considered theory, and he noted that every architect who wrote seems to have a theory - a situation that does not apply to the natural sciences. He gave physics as an example. Not every physicist has a theory; instead many make contributions to the development of a theory. The same is true of mathematics and other sciences.

Ozkan started his exploration of the theory of architecture with the premise that whatever does not belong to a building, whatever is externalized in the form of literature - to explain the point of view of an architect, philosopher, or theorist, thus informing the practice of architecture - should belong to the realm of theory. Ozkan then began compiling these writings, starting with the earliest available examples, which are the writings of Marcus Pollio Vitruvius from the 1st century BC, up to contemporary theories such as Deconstruction.

Ozkan added that during this period he also started to take courses in the philosophy of science. In 1969, he went to London to study at the Architectural Association. In London, he was fortunate enough to study with Karl Popper (1902 - 94), considered one of the greatest philosophers of science of the 20th century. (2) At the Architectural Association, Ozkan worked on structuring the various literary contributions to architecture. In the scope of the theory of the philosophy of science, Ozkan came to the conclusion that everything in the universe is structured. At one extreme, there is logic as the basis of knowledge. Logic is transcribed and defined in the form of mathematics, which informs physics and chemistry as applied sciences, which in turn inform engineering. In these cases, theories are physically explicable, and have an axiomatic structure. A basic axiom such as 1+1=2 or true/false might be a basis that develops a whole body of science and reaches the most sophisticated engineering levels, where one deals with systems analysis, operations, and research. Solving complex problems in molecular biology - or any other science - would be through the basic values in mathematics and logic. In other words, the abstract basis of this axiomatic structure leads to engineering sciences in an inductive way, with one informing the other.

On the other hand, Ozkan states that there are fields of knowledge, the most extreme of which is theology, where one does not question the validity of a point through logic. One simply believes in it. One can be Muslim, Christian, Hindu, or Buddhist, and when one believes in the existence of God or in an explanation of the existence of God or Gods, one does not question it. This is a deductive mode of logic that also is meant to inform. Theology and beliefs are then transformed into ethics, which provide codes of behavior.

The same applies to the theory of arts. It is a speculative form of knowledge. They are not scientifically and objectively explicable for they fall within the realm of belief and conviction. Ozkan believes that when exploring architecture, on the one hand there is the part pertaining to what makes the building stand, and this is informed by the basic sciences. On the other hand, one faces the psycho-perceptual entity of what is called beauty or relevance, which belongs to the normative aspect of the sciences. Ozkan noted that this is the reason why architecture has been deprived of an objective theory. It never belonged singly to one or the other of these modes of logic. Painting and the plastic arts in general belong to the more speculative form of logic, and architecture also belongs to them in certain values. However, this does not apply to issues relating to the physical existence of architecture.

Ozkan started his research with Vitruvius' ten-book treatise on architecture, De Architectura, from the 1st century BC. Among other things, this work dealt with the issue of professionalism. It informed us concerning the Greco-Roman practice of architecture, which established three pillars for the validity of a building: utility, firmness, and delight. Utility, notes Ozkan, falls in the socio-psychological realm. Firmness belongs to the engineering realm. Delight is the experiential value of a building. The writings of Vitruvius came to light in the 15th century, with the Renaissance. At that time, architecture began to be considered as a profession, and Vitruvius informed the reader about this profession. Prior to the Renaissance, architecture was not a profession. There were no architects, merely "builders". (3)

Ozkan pointed out that one of the pitfalls he faced in his research was dealing with a tradition such as that of Gothic architecture. The reason lies in that while Greco-Roman architecture has very firm values, an interpretation of which Vitruvius has related to us, Gothic architecture had no surviving theoretical evidence to accompany it. No documentary evidence survives (or probably exists) relating to the construction of the buildings of the period, which when observed from the engineering and aesthetic points of view represent tremendous accomplishment. When observing works of architecture leading up to the 15th century, one encounters many marvelous examples, which could not have been produced without basic information being exchanged between people. Here, Ozkan referred to Joseph Rykwert's explanation that the creation of Gothic works of architecture was a secretive endeavor, and that masons kept the logic behind them to themselves. (4) This knowledge was passed on verbally. It is possible that written documentary evidence also was used to pass on such information, but such evidence would have been deliberately destroyed as a way to protect the knowledge that the masons had amassed. Although the Gothic period presents to us architecture of very high quality and sophisticated structural systems, almost no supporting written documentation survives from that period to help us understand the manner in which its contemporaries viewed it.

Ozkan added that in his research he tried to identify common values amongst the readings he was investigating. In his study, he noted that he did not engage himself too much in the building itself, but rather concentrated on how the ideas behind the building were expressed and passed on from generation to the other. In other words, his main concern was the books of architecture that transferred knowledge and that externalized the thinking process behind architecture. He reasoned that if one were to approach the analysis of buildings, one would synchronically push forward his own contemporaneity and his own interpretations of the buildings, and this would not be factually correct. In order to be "scientifically" correct, Ozkan concentrated on the sources of the period that explain the practice of architecture. He noted that what most art historians do is to project the values of their own society onto the past when explaining and interpreting a work of architecture. The results are genuine and very interesting, but it is not clear in whether they explain the phenomena of architecture as it was explained - if it was explained at all - in its own period. In order to avert that, Ozkan based his research completely on contemporary primary written sources.

In order to explain what a theory does, Ozkan devised a set of semantic categories. He explained that the most primitive and basic form of theory is the image. An image is the icon of architecture. The building once constructed is in itself its own theory, representing a solution that informs people, and that survives from one generation to the other. As an example, Ozkan noted that vernacular architecture represents buildings that contain and express their theory and experiential values. Consequently, the viewer would decipher the building and then adapt it to his own particular social needs and uses. Ozkan explained that he therefore did not dwell on this category of buildings. However, he did make an exception with the work of Mies van der Rohe, who left little written evidence of his architectural thinking, but nonetheless made a significant impact on architecture and informed a whole new series of expression through his designs. Such contributions are iconic in nature.

Ozkan continued that other theoretical contributions could be described as pragmatic. Pragmatic contributions provide practical information on how a building should be assembled, what the values should be, and how it would stand. If an abstract level were added to this level of contribution, one would reach a canonic level of contribution. Here, canons of architecture, certain rules of proportion - or what Vitruvius refers to as delight - all would be considered - in the abstract - to inform architectural design in the form of certain principles that have come to form one of the important aspects of architectural theory.

The fourth category Ozkan tackled is analogic, in which architecture is described as something else. As an example, Ozkan relates Leon Battista Alberti's (1404 - 72) ten books on architecture, De re Aedificatoria, in which he equates the harmony of a building with the harmony of music. This harmony cannot be represented graphically or through simple arithmetic, but represents a more complex form of proportionate relationships. In Ozkan's opinion, analogies have benefited architecture throughout history, and gave as an example the Metabolism movement, which believed that living beings and buildings should bear a resemblance to each other.

The fifth category that Ozkan presented is the utopic. It is one that we cannot realize but are free to think and imagine about. Nothing can stop one from thinking and speculating about an unknown future. Ozkan adds that for an architect or a visionary, if desired conditions are not reached, one is free to imagine that they will be realized in a different time or a different place. Ozkan believes that utopic ideas are amongst the strongest driving forces behind architectural transformation and new forms of expression. He points out that Frank Lloyd Wright (1869 - 1959), Le Corbusier (1887 - 1966), and Peter Cook (b. 1936) were utopist thinkers whose writings had a profound influence on the public.

The sixth category is the descriptive. Here, the situation is described. Ozkan adds that this constitutes the most scientific part of architectural theory, and had reached overwhelming and tedious levels in the 1970s. Ozkan observed that it was very popular for everyone to carry out research on the relevance of one thing to another thing, and this was viewed as being very "scientific." The whole body of information on architecture, especially that developed and conveyed in schools of architecture, was based on these descriptive approaches because there was a strong logic behind it, and it formed a scientific backbone that would inform architectural theory. But all it did was describe what has happened and is happening.

If one takes the process a step further, one reaches an isomorphic or abstract category. Once the elements are described, symbols, and values are assigned to them, which are then manipulated as abstract entities. Ozkan believes that this led to computer-aided design. In fact, many of Ozkan's generation believed that the time would come when computers will be capable of designing anything. Of course, this did not turn out to be the case. Computers are and will remain subservient to architectural designers, merely tools that replace drafting boards, which is what they should be.

In carrying out his readings of primary sources, Ozkan found a point of emergence in the development of architectural theory to be Antonio Filarete di Averlino's (c. 1400 - 69) Trattato d'Architettura (Treatise on Architecture). Filarete can be viewed as a philosopher, but also as an entertainer who entertained his patron Francesco Sforza, the Duke of Milan, with stories about his ideas. In a way, Filarete was sugarcoating his philosophical ideas. Filarete urged Sforza to build a city called Sforzinda. Sforzinda supposedly had a port that allowed it to converse and interact with the sea. It also was a hilltop town with a cathedral located at the top of the hill. Filarete clearly was more or less selling his ideas through a powerful Renaissance-period ruler. He also questions the roots of architecture. Being a Christian, he believed in the story of Adam and Eve, and based much of his ideas on Adam being expelled from paradise and his subsequent fall to earth, completely in the nude, without Eve. Adam then built a basic structure to protect himself and to ensure his survival. Ozkan explained that Filarete speculates his theory of architecture from this point onwards through giving pragmatic rules on the evolution of the first primitive shelter. However, he subsequently moves on to a completely different setup, which is Sforzinda as a utopian setting. Ozkan points out that as a result, we observe in Filarete's work three of the categories he related, the iconic, pragmatic, and utopic.

Ozkan went on to Alberti, a contemporary of Filarete. Alberti was a practicing architect and a theoretician. He makes analogies between architecture and music, as well as with other endeavors of an aesthetic value, while also giving abstract information on the canons of architecture. The Renaissance was the age of humanism in which the human being played a most central role. The human being was considered the perfection of God's creation. It followed that this perfect creation should be the basis for everything we generate. The basic Aristotelian forms of square, circle, or even the more sophisticated types of diagonal relationships were based on the human body, and have been viewed as the appropriate sources for the genesis of information. Ozkan added that this also is evident in Le Corbusier's "modulor," for Le Corbusier wanted to explain everything through the human body and the proportions derived from it.

Ozkan observed that in the 16th century, there was a continuation of the Vitruvian tradition of perpetuating Greco-Roman building traditions in the theoretical form. These traditions were never questioned, only praised.

Later in the 16th century Andrea Palladio (1508 - 80) homogenized the existing architectural discourse. To Ozkan, this constitutes the first modern movement. Palladio stripped most of the unessential aspects of a building and presented the components of the building as easily repeatable forms. Also, through his Quattro Libri dell'Architettura (Four Books on Architecture), he formalized how each and every aspect of architecture must be, can be, or should be addressed. Almost contemporary to Palladio is Philibert de l'Orme (c. 1500 - 1570), who can be viewed as his French equivalent. Ozkan presented two engravings from de l'Orme's Le premier Tome de l'Architecture (figure 1). The engravings both can be referred to as caricatures. The first engraving shows a "bad" architect. He is blind and with no hands. The architecture behinds him is Romanesque and is presented as brutal in character. The sky is cloudy, the animals are dead, and the environment is very discouraging, all of which he relates to the Lombards. In contrast, the second engraving relates the "good" architect from Florence, which represents the sophistication of the Renaissance. The good architect is surrounded by people conversing with him; even the weather is pleasant; the trees are blossoming, and the architecture is well proportioned. Ozkan noted that although he referred to the engravings as caricatures, they are much more serious than that. They show how seriously the architectural profession was taken. He added that some influential people - like The Aga Khan, Georges Pompidou, and François Mitterand - expect architects to have the power to change the world. Through the Aga Khan Award for Architecture, the Aga Khan has put in a system that aims at influencing clients, decision-makers, and politicians to give more power to architecture. Ozkan emphasized that these engravings are in a way an assertion of the claim being made regularly that architects should have the power to define much of the environment in which we live.

The same period saw the appearance of works on architecture in England, which were greatly influenced by the Italian Renaissance, but also expressed a number of highly original concepts. John Shute (d. 1563), for instance, wrote the first book on architecture in English, The First and Chief Groundes of Architecture. This work was also the first in the history of architecture to pair semantic categories with architectural form. Consequently, Shute saw the Tuscan order as crude and the Doric order as even cruder (figure 2). Men in the figures symbolized these orders. In contrast, his drawings of Ionic (figure 3) and Corinthian orders, which are represented by women, are intended to express elegance, proportion, and sophistication. Shute then makes the assertion that the Composite order more or less represents perfection (figure 4). It is noted that Shute defines elegance as female beauty and brutalism as male crudity, a definition that is very widespread, if not almost universal.

Ozkan added that as we reach the 16th century, it is noticed that the Renaissance had reached its maturity, and somewhat more abstract thinking came into being. Ozkan gave Sebastiano Serlio (1475 - 1554) as an example. The perception of a building according to Serlio can be put into perspective and diminishing proportions due to the eye-level of the person. Serlio then projected that the way a building is seen depends on vision and eye-level (figure 5). This approach, explained Ozkan, puts buildings into stage format, and projects them as an experiential entity.

Ozkan went on to explain that the 17th century witnessed an increase in abstraction in the representation of theoretical material. With the maturity of the Renaissance, works of architecture represented high levels of accomplishment. In the Islamic world, this is around the same time at which the Taj Mahal, Suleymaniye, and Selimiye were built, and which expressed equal levels of architectural accomplishment. However, we lack significant written information on these great monuments. Ozkan mentions that a number of Turkish treatises on architecture do exist, but they primarily tackled the physicality of a building for "accounting" purposes (i.e. to calculate costs of materials and labor), but did not approach the theoretical aspects of it. Consequently, Islamic resources are very much lacking when it comes to architecture. (5)

As a representative of the 17th century, Ozkan gave an example of the French Claude Perrault (1613 - 88). Perrault associated entablatures and profiles of buildings with human beings, again giving them an aesthetic quality or elegance, as he sees it (figure 6). In this way, an entablature or frieze carried out in a certain profile would have direct perceptual associations with the human figure as profile.

Ozkan moved on to the 18th century, the age of enlightenment. It was a time when most of the ideas that inform today's architectural theory, such as the Functionalism of Carlo Lodoli (1690 - 1761), were first pronounced. His statement that things should perform a function that is more than just utility is a basic tenet of the modern movement, which finds its roots in this period. According to Ozkan, the sketches of Giovanni Battista Piranesi (1720 - 78) redefined existing perceptions along a utopic line (figure 7). Many canons and abstraction were produced, especially in the Italian intellectual discourse on architecture, and writings coming out of Italy and England informed the descriptive nature of it. It was a period characterized by inquisitiveness, and by investigating the whys and wherefores behind processes. Also, for the first time, there was an attempt at bridging architecture, via aesthetics, with the other fields of philosophy. Ozkan noted that before that the isomorphic aspect of architecture was almost completely absent, and no attempt had been made to define it as part of architectural theory.

A most important contribution to architecture thinking was made by Marc Antoine Laugier (1719 - 69) through his writings that includedEssai sur l'Architecture (Essays on Architecture). Laugier was a priest who also was highly interested in architecture. Ozkan feels that Laugier must have been an architect in some form since he is so well informed about building and construction techniques. Laugier detested the opulence of architectural decoration and rejected all that does not belong to architecture itself. Instead he called for a return to what he referred to as "the primitive hut" (figure 8). Ozkan pointed out that when referring to Filarete earlier in the presentation, he noted that Filarete also viewed the basis of architecture as four columns and a pitched roof on top of it, which to him exemplified beauty in its essence. Ozkan explained that Laugier started from this point, but his goal was to particularly attack existing architectural conceptions, which were bourgeois, opulent, and unnecessarily decorative in nature. Laugier's work was widely read and was translated into a number of languages.

Ozkan explained that the 19th century expresses the advent of the architectural thinking that is with us today. He gave as examples the descriptive works of John Ruskin (1819 - 1900), Georg Wilhelm Hegel (1770 - 1831), and Gottfried Semper (1803 - 79), all of which tackle the different aspects of aesthetics. Also important in this regard is the work of Emmanuel Kant (1724 - 1804), who discussed the notions of ‘wild beauty' and developed a theory of beauty and its perception, and raised the question of whether beauty is in the essence of the object or in the object itself. Ozkan explained that it is through these thinkers that the theory of aesthetics informed architecture, directly and indirectly. In this context Ozkan pointed out that in the writings of Eugene Viollet-le-Duc (1814 - 79) and Theodor Lipps (1851 - 1914), the interest was directly in architecture, while others were more interested in exploring the realm of aesthetics in architecture.

According to Ozkan, numerous abstractions were made to define issues on the same terms as the Renaissance, and considerable efforts were made to refer to the essence of beauty and how to define, decipher, and present it. For example, drawings and analyses of proportion were carried out to inform architects, explain the past, and also build for the future with an underlying abstract notion. This approach carried special importance in Soviet Russia, where most of the academic work carried out was of this nature. It was called "scientific" because measurements and proportions were taken and then explained. However, Ozkan points out that nobody really can very well explain why a certain line was chosen over another, but theorists nonetheless were more interested in explaining what is harmonious and beautiful. Saint Peter's Cathedral, the Suleymaniye, and other monuments all were deciphered and researched in the nineteenth century in the hope of explaining or formulating geometric relationships of the hidden reality of aesthetic truth. This approach came to govern architectural theory in the 19th century.

Ozkan then touched upon the issues of catalog design and computer-aided design. He gave as an example the Neo-classical catalogs of Jean Nicolas Louis Durand (1760 - 1834), which took the form of plans, elevations, and roof forms (figure 9). Durand's approach represented a main school of thought in France during the 19th century, and the idea was directly imported into the United States of America. For years in the United States, and until the advent of the Modern movement, every school had to have a Beaux-Arts teacher who would teach Durand's catalog of forms. The idea was to enable architects to derive their designs and carry them out in Neo-classical forms.

Ozkan stated that the 20th century was an era during which enormous impetus on architectural thinking had evolved. Mies van der Rohe (1886 - 1969) and Walter Gropius (1883 - 69) presented iconic images. Mies did not do much writing, but Gropius, on the other hand, explained his own model set of values composed of dos and don'ts. Le Corbusier essentially presented his ideas in the same manner as Gropius: the roof should be a terrace, the building should be elevated from the ground, ... etc. Ozkan went on to add that early in the century, contributions were made in almost every aspect of architecture, whether on the iconic or pragmatic levels. Consequently, canons and building techniques were put forward. One example is found in the writings of Julien Guadet (1834 - 1908), who was a professor at the French Academy of the Beaux-Arts. Guadet put down a set of design rules that relied on beaux-arts principles such as symmetry and axiality. Also, Ezra Ehrenkrantz developed in the 1960s modular building systems that addressed certain servicing elements of the building, but left its appearance to be determined by the architect. In addition, Le Corbusier made analogies with other areas of technology and produced his own utopia for new urban life.

On the other hand, authors such as Nikolaus Pevsner (1902 - 83), Sigfried Giedion (1888 - 1968), and Bruno Zevi (1918 - 2000) developed a more descriptive handling of architecture. This also is a time when analogies with music arose again under what was called the "theosophy of architecture." Some theories, he explained, aimed at showing how musical scores correspond to buildings, and thus turning them into melodies. For example, in his proportioning of facades and plans architect Claude Bragdon (1866 - 1946) employed ratios expressive of musical intervals (figure 10).

Ozkan explained that a substantial re-formulation came from Giedion who for the first time took and abstract concept "space" as an entity to explain the works of architecture. In a related manner, Zevi analyzed various aspects of a building such as Saint Peter's Cathedral in Rome. He examined its structure, circulation, building mass, and levels, and accordingly made exhaustive diagrams of the cathedral (figure 11). This served to draw the space, redefine it in plan form, and use it as an abstract entity to define architecture itself. This approach to architectural theory was very much favored by members of Ozkan's generation. According to this approach, people started thinking of space apart from many other things, and space almost became a faith in conceptualization of architecture. Any exercise from any level could be abstracted and brought to the level of space. Ozkan noted that this would have been the source of an axiomatic theory of architecture, if it were to be known from its beginning as a concept. Ozkan said that architecture, like physics, chemistry, or mathematics, probably would have evolved around the concept of space if it could have been defined with certain explicable forms that would allow us to make some associations, abstractions, and constructions.

Increasingly, during the last three to four decades abstract entities were brought into the realm of architecture in order to explain the internal relationships of design complexities. This is expressed in the work of the architect - mathematician Christopher Alexander (b. 1936, see below), the systems scientist M. Asimow, Thomas Markus, and Lionel March. For example, Lionel March, in his The Architecture of Form, (Cambridge: Cambridge University Press, 1976) defined architectural relationships in binary diagrams forms (figure 12) in order to process them in newly emerging computer techniques. Ozkan noted that most of those responsible for such interpretations were of the generation that studied the Fortran computer programming language, and therefore knew computers when they were at the primitive level, and were defining buildings in abstract language. Ozkan noted that substantial research was conducted in this line in University of Cambridge.

Ozkan also showed structural relationship diagrams representing different plans reducing them into abstract mathematical matrix formulae in order to manipulate them, as developed by Philip Steadman and Lionel March in their Geometry of Environment: An Introduction to Spatial Organization in Design (Cambridge, MA: MIT Press, 1974) (figure 13). He noted that when an architectural complexity is reduced to this level of abstraction, the meaning was inevitably lost and therefore these theoretical approaches remained under the privileged realm of "Design Research" and did not have much impact on the mainstream of the theory.

Ozkan went on to explain that during the period following the 1970s, interest arose in the participation of people in the process of architectural creation and the democratization of the environment. Canons and abstract geometric patterns always were thought of as providing guidance, and as analogies with nature. Also, utopias were used to project into the future and produce freer environments. Certain utopic descriptions and descriptive utopias went hand in hand. There were those who explained what happened to architecture post-facto, and attempted to define what architecture is, and how it is. With Christopher Alexander's Notes on the Synthesis of Form, (Cambridge, MA: Harvard University Press, 1964), which aimed at understanding the design process and how design problems are solved, new approaches arose. However, Ozkan added that Alexander himself later on, in anger, declared that he did not want to be associated with what was called then "Design Methods" and that was partly initiated by his own books. Ozkan believes that Alexander made a substantial contribution to the analyses of architectural form due to his background as a mathematician. He was successful in defining architectural and urban entities in a very eloquent, non-simplistic, and sophisticated manner.

Ozkan moved on to mentioning that he had attempted to organize architectural developments from the beginning of the century to recent years in the form of movements, and to illustrate how these movements started and evolved.

In the iconic scale, Reductionism took shape in the designs of Mies van der Rohe, which then became Regionalism informing itself from local tradition and environment. In the 1950s, Bureaucratic and High-Tech building traditions arose. Expressionism started before World War II, while Mannerism and Postmodernism came after it. Postmodernism informed itself from more sublime and sophisticated forms, and became Classicism. Deconstruction was preceded by a short period of Fascist architecture that overpowered the Modern movement in the earlier decades of the 20th century. Vernacularism made an entry as a savior of the environment. (6)

On the pragmatic level, Alternative Technology movements arose, developing structures that could be easily constructed. This was followed by the Developmental approach, and then Democratization, which gave people the right to build their own environment as they would form it. Ad hoc-ism then came into being, which solves problems with the means and ways that are readily available to owners, users, and designers of buildings. Other approaches include Eclecticism and Do-it-yourself approaches, the latter of which turned into Self-help, and in more sophisticated forms became Participationism.

The canonic form had a flow of Neo-Classicism, which was very pragmatic, and therefore also can be located at the upper end of the canonic level. It basically tells one "how it should be done." Geometric minimalism also took shape, followed by Neo-Vernacularism, which again informs itself from existing traditions, and also can be considered a pragmatic movement. Modularism finds itself on the abstract side of canonic thinking, with order and typology being the main discourse in the 1970s and 1980s, when building typologies were compared and used to generate new forms.

At the analogic level, Theosophy, explained earlier with musical scores, is followed by the Organic movement of Frank Lloyd Wright. Symbolism makes use of symbolic analogies, while Abstract Regionalism looked back to old repetitive forms, but with an abstraction of ideas. And those were followed by Metabolic and Biomorphic traditions.

Utopic form manifested itself earlier this century in Futurism. The proponents of this movement, which became quite popular in the 1960s, are still alive but have since stopped building the mega-structures of that day. Consequently, its proponents, such as Fumihiko Maki (b. 1928), brought a new direction to their work. Technophilia was generated by Norman Foster (b. 1935) and others who had a very high regard for technology.

In descriptive terms, Aestheticism was the academic interpretation of the beauty of the building. While Functionalism was more of an ideological stand: form follows function. Vernacular Research was important in circumventing the mistakes of the past. Relativism provided the comparative basis for that research. Semiotics, as developed by Charles Jencks and others, saw meanings become forms of architecture. Then Critical Regionalism made its appearance through Kenneth Frampton (b. 1930) to add a critical element to the repetition of the regional, elevating the level of thinking to a higher level, with a tremendous effect. Architectural Psychology, or the Psycho-Environmental aspects of architecture, also arose with many schools of architecture specializing in this field. Psychology and architecture became closely associated with each other since many people thought that satisfaction and perception are based on psychological input. Ozkan noted that much meaningless research was carried out on such issues. A caricature of such research would be to put one chair in a room and find it spacious. Two chairs would be fine. Twenty chairs would make the room crowded, and fifty chairs would make it unbearable. The movement basically went to the level of experimental psychology, putting statistics together, and asking people about their likes and dislikes. It was basically a perception of ideas.

In the isomorphic stage Design Methods, Geometry, and Computer-Aided Design movements came into being, making this stage the most sophisticated aspect of architectural discourse.

Ozkan ended by noting that quite a few valuable books have emerged about the subject of architectural theory. One of them is a compendium of writings by Hanno-Walter Kruft entitled History of Architectural Theory: From Vitruvius to the Present (Princeton: Princeton Architectural Press, 1994), which was published after Kruft's death. It basically is a history of architectural thinking, not theory of architecture, which is a distinction that Ozkan finds imperative. Ozkan added that he has become very cautious in his use of the words ‘theory' and ‘architecture', which nonetheless are used together in a very casual manner, thus referring to any writing about architecture theoretical, and any speculation about it a theory. It seems that everyone has a theory of their own, a matter which in Ozkan's opinion is the problem with architectural teaching and research today.

Questions and Answers

Ozkan was asked concerning the category in which he would place his presentation. He answered that it would be descriptive. He then was asked why he did not develop the presentation beyond the descriptive category. Ozkan noted that the work he has presented has not been published, and he still is involved in a process of exploration. He added that this presentation is based on a manuscript he prepared in 1990, and that he has not been able to update it since then because of his other work commitments. He also mentioned that he had developed the categories from examining the literature on operations research, which looks at an organization's operations and uses analytical approaches, including mathematical or computer models, to identify better ways of carrying out those operations. Ozkan specifically examined the work of Russell Ackoff and Ludwig von Bertalanffy. He used their writings as a basis for model making, and explained that a model is built to explain an entity. It would necessarily emphasize certain things, and ignore others, which would be the fault of the researcher. But if the emphasis were placed on the relevant issues, then one would be, more or less, communicating correctly.

Ozkan added that before he decides whether to incorporate a certain reading in his writing, he asks whether the reading informs architectural theory or not. For instance, when he reads Peter Eisenman's (b. 1932) work, he does not know where to place it, as it is very speculative. He sees it as being very interesting and informative, but it is not clear as to what it achieves, and that is why he decided to place it in the iconic category as part of the Deconstruction movement, which also includes the work of Zaha Hadid (b. 1950) and Frank Gehry (b. 1929). However, he added that he could not keep on doing this, as he would then be talking about buildings, not expressions regarding them.

Ozkan admitted that his heart always has been in academia, and if he goes back to teaching, he would like this work to be the basis of a textbook. He would then start from the beginning, and arrange and rearrange the categories with his students in the manner of a jigsaw puzzle, placing books, articles, and ideas within it, and even adding more categories.

Ozkan was asked how he would answer students who often inquire why they should care at all about architectural theory. Here, Ozkan mentioned that this is a very valid question. As a teacher, one equips one's students to perform and function in society. That performance is defined to a great extent by building rules and codes, in addition to a certain expertise in problem solving. However, if the students were to bring depth to such skills, and wanted to go beyond them, they would need to be taught architectural theory. Otherwise, they would be "doing their own thing." He admitted that "everyone has a right to commit his own [architectural] crime," but there are many mistakes that can be avoided if students are exposed to the whole spectrum of architectural thinking, and if they are made aware of what, how, and when a given architectural development took place.

Ozkan was asked why he mentions the utopic as a separate category, as it talks about content rather than the way people inform each other, and that it can be informed through iconic, analogic, or other categories. Ozkan answered that for years he had thought about this matter, and the reason why he developed the utopic category as an independent category placed between the canonic and the descriptive is that most utopias have a descriptive content of projects of the future. Many utopic projects are neither explicable nor acceptable today, so one has to make a jump in time, and wait for a change in technology or other variables to make it realizable. Ozkan added that there are numerous works that belong to more than one category. He gave the example of Le Corbusier, who produced writings of utopic, canonic, analogic nature. He was prolific in that sense, and every one of his contributions is important.

Another question inquired whether it is correct to assume that architecture precedes writing, and whether there are any visionary writings that preceded the design process. Ozkan answered that there are many such writings by authors ranging from Filarete to Peter Cook, who started the idea of Archigram. He noted that Cook never built anything substantial, but managed to change the discourse on architecture, and it was from that discourse that Renzo Piano (b. 1937) and Richard Rogers (b. 1933) designed a building such as the Pompidou Center in Paris (1972 - 1976), which is considered a pioneering example of High-tech architecture.

Another question inquired as to what Ozkan thought one should do when teaching the architectural traditions of the Islamic world. There are great works of architecture, but very limited writings of relevance to architecture have survived. These include writings on beauty by Ibn al-Haytham (AlHazen; c. 965 - 1039), and technical design and construction manuals by al-Buzjani (940 - 998) and al-Kashi (d. 1429). Here, Ozkan stated that he usually apologizes to his students because there is such a small number of surviving manuals on architecture from the Islamic world. Moreover, it is very difficult to determine the level of effectiveness of such manuals. In contrast, even in the case of Gothic manuals, of which very few survive, it is known that they were influential with masons, and that they were passed on from mason to mason. Gothic manuals, explained Ozkan, seem to have been effective in that they informed the practice. In this context, Ozkan brought up the example of Sinan (d. 1588), the great Ottoman architect, who served as chief royal architect during the 16th century under the Ottoman Sultans Suleyman and Selim II. There are about 1000 buildings attributed to Sinan that are found in different parts of the Ottoman Empire. Here, one realizes that he could not have designed all of them. Therefore, design and construction manuals must have existed to allow the various master masons, masons, and various craftsmen who worked under his supervision to build this large number of buildings in different parts of the Ottoman world. Ozkan therefore is confident that design and construction manuals must have existed in the Islamic world, and that these would have explained issues such as aesthetics and systems of proportion. The question that remains however is "where are they?" He added that we would have to wait for historians to uncover more information that would better inform us about this matter. (7)

Another questioner suggested that since so few written sources on architecture have survived in the Islamic world, we might have no alternative but to project our thinking on this heritage, and maybe start from there to develop some clues that would help us understand its architectural traditions. Ozkan answered that he absolutely agrees with this approach. In fact, he mentioned that one exercise he would like to carry out in this context is to imagine what if, in the 16th century, Sinan got the brief for the design of the Church of Saint Peter from Pope Pius IV, while Michelangelo got the brief for the Suleymaniye from Sultan Suleyman. It would be very interesting to see how each of these two architects would react. It would be an exercise in history, he explained, since one would have to understand the conditions of the project. It also would be an exercise in creativity, which, in order to be valid, has to take on synchronic lines of thinking. He added that it is true that he did not want to project his own values on works of architecture, but he is finding out that by developing his system of categorization, he in fact already has done that. He expects that if he were to tell Alberti he was an ‘analgoic theorist,' Alberti would be very unhappy about it!

Another question commented on the absence of writings on architecture in the contemporary Islamic world. The questioner mentioned that the two most prolific writers from the Islamic world are Hassan Fathy and Rifat Chadirji. However, it is interesting to note that Chadirji the architect and Chadirji the author have not overlapped, since Chadirji stopped practicing architecture in 1979, and since then has turned his attention fully to writing. The questioner inquired if Ozkan has come across any other contemporary architects from the Islamic world who made any valuable contributions as writers. Ozkan responded that if one was to refer to the "Eastern," instead of Islamic world, we have Charles Correa's The New Landscape (London: Butterworth Architecture, 1989), which effectively defines new ideas on urbanism. (8)

The questioner went on to ask if we might conclude that since the contemporary Muslim world has not been able to support its architectural production with the written word, might we consider this as a sign of a weakness in its architectural production? After all, many of the great architects of the Western tradition, ranging from Palladio to Le Corbusier, are known for their writings as well as for their designs. Ozkan responded by using Turkey as an example. He stated that Turkey has over thirty thousand architects, of whom ten to twenty are rather famous. It seems that every year one of them decides that a book should be published about their work. And what a number of them do is call him to ask if he would write about their work. However, they themselves do not do any writing. He mentioned a personal experience involving Sedad Hakki Eldem (1908 - 1988), who can be viewed as one of Turkey's most prominent modern architects (9). When Ozkan and a number of his colleagues started a project of putting together a monograph about Eldem, they found one piece of writing by him. In this article, Eldem more or less expressed the opinions that the state should govern everything, and that all buildings should be built of stone. It was very difficult to present this architect through this lone piece of writing. Instead what Ozkan and his colleagues did was to meet with Eldem on a regular basis to ask him about various issues, such as his work, his life, his views, ... etc. However, Eldem, who was a very polite man, got very nervous about this process of interviewing and eventually stated: "Sir, I thought you were going to write a book, not interrogate me!" In the end, Ozkan and his colleagues did manage to put together ideas that represented Eldem's thinking. However, as he now reflects on the project, he believes that they had to deal with Eldem more or less as psychoanalysts, who worked on drawing thoughts out of him. In other words, Eldem ended up offering something that is intuitive, but did not go much more beyond that into the realm of effectively articulating his thoughts.

Ozkan continued by bringing a somewhat similar example, that of the British architect James Sterling (1926 - 92), under whom he studied. He mentioned that Sterling often took his students to see his buildings, and when he was asked "why did you do that?" he would get angry and respond "what's wrong with it?". Basically, that was his "theory." This is the answer one would get from an architect as prominent as James Sterling. Ozkan added that it is such attitudes that made him decide not to go into the design realm itself, which he nonetheless very much likes, enjoys, and appreciates, but to explore a different line of discourse, which is the externalization of the ideas.

Another questioner inquired why the Aga Khan Award does not acknowledge writing as a category that would receive an award, and maybe even compel those who compete for the award to write something. Here, Ozkan answered that the Award does encourage that, and pointed out that they did produce the Mimar series of books, which consumed much of his time and energy, and to which the book on Eldem belongs. The series of books also featured Hassan Fathy, Charles Correa, and Raj Rewal. (10) It was thought that the Award should "create our own heroes," in that he and his colleagues at the Award believed there were many talented architects in the Islamic world whose ideas and work needed to be presented to the world. However, Ozkan added that writings of this nature should not always come from the Award. As he sees it, the Aga Khan Award has dominated the architectural scene in the Islamic world. Consequently, it is imperative that other cultural institutions in the Islamic world play a more active and effective role in promoting its architecture.

The last question commented on the fact that the Chairman's Award has only been given to architects who also have written: Hassan Fathy and Rifat Chadirji. Ozkan replied that the statement is both true and not true. It is not true because the upcoming Chairman's Award (for the eighth cycle, which took place in 2001) will acknowledge the architectural contributions of Geoffrey Bawa, who has no writings whatsoever. Here, it should be emphasized that in contrast to the other prizes of a given cycle of the Award, the Chairman's award is not awarded for buildings, but to acknowledge the work and thinking of a specific architect. For instance, Hassan Fathy talked about architecture for the poor, and ignited a whole spectrum of voluntary activity, prompting many people to work in helping other people, thus making Fathy very influential and effective from that point of view. As for Chadirji, he effectively raised the issue of contextualism. In other words, they received the Chairman's Award in recognition of their ideas rather than their architecture. For this cycle, Ozkan stated that the Chairman's award is being given to a person who has no writings, only works of architecture.

A follow-up question was whether the Chairman's Award could be given to someone who is not an architect, a politician, for instance, or maybe a mayor of a certain city. Ozkan answered that while such people have not been considered for the Chairman's Award, they have been acknowledged among the recipients of the Aga Khan Award. After all, in order to come up with good architecture, the architect should have certain input from the client in the form of architects' briefs and the like. For instance in the field of conservation the Association de Sauvegarde de la Medina de Tunis has received more than one Aga Khan Award. This association is a leader in the field of conservation in the Arab world. Also worth noting is the Riyadh Development Authority, which received the Aga Khan Awards a number of times. Mohammad al-Shaikh, who served as the president of the authority, was a most effective client. He has strong ideas and a clear vision on a variety of issues relating to the built environment, ranging from landscaping to roads. In this context, Ozkan also gave the example of Jaime Lerner, the former mayor of Curitiba in Brazil, who was able to transform this city into a model developing-world urban center. Although he is not involved in serving Muslim communities, he presents the type of leadership that the Aga Khan Award looks for in determining the Award winners.

Notes

(1) Suha Ozkan was born in Ankara, Turkey, in 1945. He studied architecture at the Middle East Technical University (METU) in Ankara, and theory of design at the Architectural Association in London.

Ozkan has undertaken extensive research on the theory and history of architecture, design, vernacular form, and emergency housing, and has published numerous articles and monographs. At METU, he taught architectural design and design theory for fifteen years, and became associate dean of the faculty of architecture in 1978; he was appointed vice-president of the university in 1979. He taught and lectured extensively in North America, Europe, Central-, South-, and Southeast Asia, and throughout the Middle East. He has served as a jury member for many architectural competitions, and as an external examiner for diploma and doctoral assessments at the schools of architecture of the universities of Paris, Lausanne, Zurich, York and Trondheim. He was instrumental in the establishment of the XXI Architectural Culture Centre in Ankara and publication of the centre's journal entitled XXI. During May 2000, he served as a member of the jury for the architectural competition for the Martin Luther King, Jr., National Memorial in Washington, D.C. Ozkan is cochair of the Sustainable Architecture task force of the Hassan Fathy Institute and the United Nations Centre for Human Settlements (Habitat) in support of the Habitat Agenda.

With the Aga Khan Award for Architecture in Geneva, Ozkan served as the deputy secretary general from 1983 to 1990, and has been the secretary general since 1991. On behalf of the Aga Khan Trust for Culture, Ozkan has organized two important international architectural competitions, for the Revitalization of Samarkand, Uzbekistan (1991), and the New Museum of Islamic Arts in Doha, Qatar (1997). He also served as an advisor for the architectural competition for the new campus of the American University of Cairo, Egypt, during 1999.

In 2002, Ozkan was elected as a Council Member (Region II) of the International Union of Architects (UIA), and is the President of the Scientific Committee for the International Union of Architects (UIA)'s XXII Congress to be held in Istanbul during 2005. He is also a member of the UIA International Competitions Committee.

(2) According to John Cottingham, Karl Popper suggested that "the problem of induction was irrelevant to scientific knowledge. How scientists arrived at their theories was a matter of psychology not logic. What was important was the testing of a scientific theory once proposed. And here Popper argued that strictly logical, deductive reasoning is applicable: scientific theories cannot logically be guaranteed to be true, but they are capable of being proven false." See John Cottingham, "Popper, Sir Karl Raimond," in Dictionary of Modern Culture, edited by Justin Wintle (London: Routledge and Kegan Paul, 1981), p. 316. For additional information on Popper, see Stephen Thornton, "Karl Popper," in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta (Winter 2002 Edition), forthcoming. (http://plato.stanford.edu/archives/win2002/entries/popper/)

(3) For information on the architects mentioned in this essay, see Adolf K. Placzek, ed., Macmillan Encyclopedia of Architecture (New York: The Free Press, 1982); and V. M. Lampugnani, ed., The Thames and Hudson Encyclopedia of 20th-Century Architecture, 2d ed. (London: Thames and Hudson, 1986).

(4) Joseph Rykwert, "On the Oral Transmission of Architectural Theory," in Les Traites d'Architecture de La Renaissance, edited by J. Guillaume (Paris: Picard, 1988), pp. 31 - 48. Rykwert states that "... masons like all other craftsmen, were always bound into a guild, that the transmission of ideas went on inside it and that was a secret society whose proceedings were therefore inevitably unrecorded.... In later years, ..., the invention of printing weakened the hold of the secret oath on craftsmen, as well as the fascination of the secret."

(5) For an example of an architectural treatise from the Islamic world, see Ca'fer Effendi, "Risale-I Mi'mariyye": An Early Seventeenth-Century Ottoman Treatise on Architecture, facsimile, with translation and notes by Howard Crane (Leiden: E. J. Brill, 1987). Also see Gulru Necipoglu,The Topkapi Scroll - Geometry and Ornament in Islamic Architecture(Santa Monica, CA: The Getty Center for the History of Art and the Humanities, 1995).

(6) For additional information on a number of the twentieth-century architectural movements featured in this essay, see Charles Jencks,Modern Movements in Architecture, 2d ed. (Hammondsworth: Penguin Books, 1985); and Lampugnani, Thames and Hudson Encyclopaedia.

(7) Concerning the issue of design and construction manuals in the Islamic world, see Necipoglu, The Topkapi Scroll.

(8) The book also is available online on the ArchNet site athttp://archnet.org/library/documents/one-document.tcl?document_id=3540.

(9) See, S. Bozdogan, S. Ozkan, and E. Yenal, Sedad Eldem (Singaphore: Concept Media, 1987). An online version of the monograph is available at http://archnet.org/library/documents/one-document.tcl?document_id=3020.

(10) These books are available online on the ArchNet site. They can be accessed at http://archnet.org/library/documents/documents.tcl?publication_type=Book. For additional information on the Aga Khan Award for Architecture, see their web site at http://www.akdn.org/agency/aktc_akaa.html#2001.

Additional Selected Readings

Ackoff, Russell L. Scientific Method, Optimizing Applied Research Decisions. New York: John Wiley and Sons, 1962.

Asimow, M. Introduction to Design. Englewood Cliffs, N.J.: Prentice Hall, 1962.

Bertalanffy, Ludwig von. General System Theory: Foundations, Development, Applications. Rev. ed. New York: George Braziller, 1976.

Bragdon, Claude. The Beautiful Necessity, Seven Essays on Theosophy and Architecture. New York: Alfred A. Knopf, 1910.

Cook, Peter. Archigram. New York: Praeger, 1973.

Durand, Jean Nicolas Louis. Précis des Leçons d'Architecture. Paris : Ecole Polytechnique, 1802.

Frampton, Kenneth. Modern Architecture, A Critical History. Rev. ed. London: Thames and Hudson, 1985.

Giedion, Sigfried. Space, Time and Architecture. London: Oxford University Press, 1941.

Gropius, Walter. Scope of Total Architecture. New York: Macmillan, 1970 (1943-1955).

Guadet, Julien. Elements et Theorie de l'Architecture. 3d ed. Paris: Librairie de la Construction Moderne, 1909.

Le Corbusier. The Modulor 1 & 2. Translated by Peter de Francia and Anna Bostock. Cambridge, MA: Harvard University Press, 1980.

__________. Towards a New Architecture. Translated by Frederick Etchells. London: Architectural Press, 1927.

Markus, Thomas. ed. Building Performance. New York: John Wiley and Sons, 1974.

Pevsner, Nikolaus. Pioneers of Modern Design. Harmondsworth: Penguin Books, 1936.

Ruskin, John. The Seven Lamps of Architecture. New York: The Noonday Press, 1977 (1849).

Viollet-le Duc, Eugene Emmanuel. Habitations of Man in All Ages. Translated by B. Bucknall. Ann Arbor, Michigan: Gryphon Books, 1971 (1875).

Wright, Frank Lloyd. An Organic Architecture. Cambridge, MA: MIT Press, 1939.

__________. On Architecture, Selected Writings, 1894-1940. New York: Grosset and Dunlop, 1941.

Zevi, Bruno. Architecture as Space. New York: Horizon Press, 1957.

List of Illustrations*

Figure 1: De l'Orme's engravings of the "bad" and the "good" architect, from his Le Premier Tome de l'Architecture, 1567.

Figure 2: Shute's illustration of the Doric order, from his First and Chief Groundes of Architecture, 1563.

Figure 3: Shute's illustration of the Ionic order, from his First and Chief Groundes of Architecture, 1563.

Figure 4: Shute's illustration of the Composite order, from his First and Chief Groundes of Architecture, 1563.

Figure 5: Serlio's illustration of vision and eye-level in perspective, from his De Geometrie et De Perspective; Il Primo Libro d'Architettura, 1545.

Figure 6: Perrault's association of entablatures with a human profile.

Figure 7: Piranesi's sketch of an imaginary prison interior, from the series of etchings called Carceri (Prisons), 1744.

Figure 8: Laugier's "primitive hut," from his Essai sur l'Architecture, 1755.

Figure 9: Durand's catalog of plans, elevations, and roof forms, from his Précis des Leçons d'architecture, 1802.

Figure 10: Bragdon's ratios expressive of musical intervals, redrawn from his The Beautiful Necessity, Seven Essays on Theosophy and Architecture, 1910.

Figure 11: Zevi's diagrams of St. Peter's cathedral, redrawn from his Architecture as Space, 1957.

Figure 12: March's definition of architectural relationship in binary diagrams, redrawn from his Architecture of Form, 1976.

Figure 13: March and Steadman's mathematical formulae of plans, redrawn from their Geometry of Environment, 1974.

* All redrawn images are by Suha Ozkan.

Figure 1: De l'Orme's engravings of the "bad" and the "good" architect, from his Le Premier Tome de l'Architecture, 1567.

Figure 1: De l'Orme's engravings of the "bad" and the "good" architect, from his Le Premier Tome de l'Architecture, 1567.

Figure 2: Shute's illustration of the Doric order, from his First and Chief Groundes of Architecture, 1563.

Figure 2: Shute's illustration of the Doric order, from his First and Chief Groundes of Architecture, 1563.

Figure 3: Shute's illustration of the Ionic order, from his First and Chief Groundes of Architecture, 1563.

Figure 3: Shute's illustration of the Ionic order, from his First and Chief Groundes of Architecture, 1563.

Figure 4: Shute's illustration of the Composite order, from his First and Chief Groundes of Architecture, 1563.

Figure 4: Shute's illustration of the Composite order, from his First and Chief Groundes of Architecture, 1563.

Figure 5: Serlio's illustration of vision and eye-level in perspective, from his De Geometrie et De Perspective; Il Primo Libro d'Architettura, 1545.

Figure 5: Serlio's illustration of vision and eye-level in perspective, from his De Geometrie et De Perspective; Il Primo Libro d'Architettura, 1545.

Figure 6: Perrault's association of entablatures with a human profile.

Figure 6: Perrault's association of entablatures with a human profile.

Figure 7: Piranesi's sketch of an imaginary prison interior, from the series of etchings called Carceri  (Prisons), 1744.

Figure 7: Piranesi's sketch of an imaginary prison interior, from the series of etchings called Carceri 
(Prisons), 1744.

Figure 8: Laugier's "primitive hut," from his Essai sur l'Architecture, 1755.

Figure 8: Laugier's "primitive hut," from his Essai sur l'Architecture, 1755.

Figure 9: Durand's catalog of plans, elevations, and roof forms, from his Précis des Leçons d'architecture, 1802.

Figure 9: Durand's catalog of plans, elevations, and roof forms, from his Précis des Leçons
d'architecture
, 1802.

Figure 10: Bragdon's ratios expressive of musical intervals, redrawn from his The Beautiful Necessity, Seven Essays on Theosophy and Architecture, 1910

Figure 10: Bragdon's ratios expressive of musical intervals, redrawn from his The Beautiful Necessity, Seven Essays on Theosophy and Architecture, 1910

Figure 11: Zevi's diagrams of St. Peter's cathedral, redrawn from his Architecture as Space, 1957.

Figure 11: Zevi's diagrams of St. Peter's cathedral, redrawn from his Architecture as Space, 1957.

Figure 12: March's definition of architectural relationship in binary diagrams, redrawn from his Architecture of Form, 1976.

Figure 12: March's definition of architectural relationship in binary diagrams, redrawn from his Architecture of Form, 1976.

Figure 13: March and Steadman's mathematical formulae of plans, redrawn from their Geometry of Environment, 1974.

Figure 13: March and Steadman's mathematical formulae of plans, redrawn from their Geometry of Environment, 1974.