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Surname or Family name: Hosseinabadi

First name: Sanaz Other name/s:

Abbreviation for degree as given in the University calendar: PhD

School: School of Architecture Faculty: Built Environment

Title: Residual Meaning in Architectural Geometry: Tracing Spiritual and Religious Origins in Contemporary European Architectural Geometry

Abstract 350 words maximum: (PLEASE TYPE)

Architects design for more than the instrumental use of a buildings. Geometry is fundamental in architectural design and geometries carry embodied meanings as demonstrated through the long history of discursive uses of geometry in design. The meanings embedded in some geometric shapes are spiritual but this dimension of architectural form is largely neglected in architectural theory. This thesis argues that firstly, these spiritual meanings, although seldom recognised, are important to architectural theory because they add a meaningful dimension to practice and production in the field; they generate inspiration, awareness, and creativity in design. Secondly it will also show that today’s architects subconsciously use inherited geometric patterns without understanding their spiritual origins.

The hypothesis was tested in two ways: 1) A scholarly analysis was made of a number of case studies of buildings drawn from different eras and regions. The sampled buildings were selected on the basis of the significance of their geometrical composition, representational symbolism of embedded meaning, and historical importance. The analysis clearly traces the transformation, adaptation or representation of a particular geometrical form, or the meaning attached to it, from its historical precedents to today. 2) A scholarly analysis was also made of a selection of written theoretical works that describe the design process of selected architects. The sample of architects was selected on the basis of their differing influence in radical and remarkable productions and how these architects may change the future of design work. The focus was on the awareness of each architect’s representation by studying their personal and professional backgrounds and their writings about their work.

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Residual Meaning in Architectural Geometry: Tracing Spiritual and Religious Origins in Contemporary European Architectural Geometry

Sanaz Hosseinabadi

A THESIS SUBMITTED TO THE FACULTY OF THE BUILT ENVIRONMENT IN FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

University of New South Wales Sydney, Australia

August 2015

ORIGINALITY STATEMENT

‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’

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‘I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only). I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation.'

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‘I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital format.’

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Date ...... ABSTRACT

The conclusion from these analyses was that the path in making meaningful architecture has been achieved through the application of an important architectural tool – geometry. This vital role of geometric forms and their composition has been significant in the past and is still relevant today, but might now have a diversified value or none at all. Architects from the early 20th century have striven to use geometric forms in a different way, in a new way, entirely different to past beliefs. On the other hand a beholder who has a knowledge and awareness of those past meanings, will still respond to such symbolism when experiencing an architectural space. Further research on how this

ii awareness of meaning can affect beholders psychologically in their experience of space will yield a deeper understanding of the ideas covered in this thesis. Placing the selected case studies in relation to these social and psychological evaluations may allow the terms of ‘aesthetics’ and ‘beauty’ to be defined from a more objective position.

iii ACKNOWLEDGMENTS

This thesis has been a challenging yet rewarding experience for a number of reasons. The journey would not have been possible without the generous assistance of many people who have helped mould this thesis and through their work helped me grow.

First and foremost, my most sincere gratitude to my direct supervisor Dr Tom Loveday and for the last 12 months Professor Jon Lang, Their thoughtful criticism, encouragement, wisdom, advice and information throughout my years at the University of New South Wales have guided me in the completion of this thesis. In particular Professor Lang valuable guidance and advice always encouraged me to walk more strongly along this path and helped me brave the uneasy times and continue more confidently.

Acknowledgment and thanks are extended to the members of the Faculty of Built Environment: Special thanks to the directors of postgraduate students, Dr Judith O'Callaghan and Dr Christine Steinmetz, for their great help and support. I also extend my thanks to Suzie Scandurra, Professor Alec Tzannes, Professor Xing Ruan, Kirsty Mate and Andrew Macklin and Dr Russell Rodrigo, for their encouragement, support and considerable insight.

My gratitude to my family and friends cannot be overstated. I am truly blessed to have these individuals on my side throughout the good and bad times. My mother Soheila Eghani, no matter how tough times get, her unconditional and limitless love, patience and support, always make life easier to handle. I cannot express how important she is to me. And my brother Khashayar Hosseinabadi, my sister Sahar and my father Korous, whose love and guidance have fostered my self-confidence.

iv THESIS CONTENTS

Title Page ...... i Abstract ...... ii Acknowledgements ...... iv Table of Contents ...... v List of Illustrations ...... vii

INTRODUCTION ...... 1 Overview ...... 1 Problem and scope of Research ...... 2 Semantics ...... 4 The Philosophical Approach of This Study ...... 4 Thesis Outline ...... 7

CHAPTER ONE: From the Pre-Christian Era to the Christian Era ...... 13 The Divine, the Sacred and the Creation of the Universe ...... 13 Ancient Art and Architecture ...... 18 The Symbolism of Ancient Egyptian Temples ...... 20 The Pyramids and the Symbolism of the Polyhedral ...... 27 Number, Symbolism and Sacred Geometry in Hindu Temples ...... 33 Derivations of the Hindu Temple in Western Geometric Philosophy ………… 40 Conclusion ...... 44

CHAPTER TWO: On Architecture and Medieval Geometry ...... 45 The Beauty of Order, Harmony and Balance ...... 46 The Representation of the Cross as an Architectural Symbol ...... 47 Medieval Architecture ...... 56 Conclusion ...... 63

CHAPTER THREE: Religious Geometry in the European Renaissance ...... 64 Myth, History and Elements in Geometric Structure ...... 64 Belief and De Re Belief ...... 67 Renaissance Architecture ...... 78 Conclusion ...... 81

CHAPTER FOUR: On Geometry and Enlightenment Philosophy ...... 83 Beliefs, Culture and Composition ...... 84 Baroque Architecture and the Beginning of Modernity ...... 86 The Sacred Subject: Geometry as Mirror ...... 88 Enlightenment Architecture ...... 93 Astronomical nova to Keplerian composition ...... 100 Conclusion ...... 105

CHAPTER FIVE: On Modernism and its Sources in Geometry ...... 106 Wars, Revolution and Nihilism ...... 107 Numerological Mysticism, Golden Section and Modern Architecture ...... 110 Production of Forms and Geometric Numbers ...... 123 Conclusion ...... 130

CHAPTER SIX: From Early Russian History to the Age of Avant-gardism ...... 132 Symbol and Universals in Architecture ...... 132 Transformation of Multi-domes, Wooden Churches to Man’s Forgotten Reality ...... 135 The Virtues of Building: Architecture Beyond Building...... 143 Public Architecture and Chaos in the Age of Machines and Fine Arts ...... 153 Conclusion ...... 159

CHAPTER SEVEN: Implications for Design Today ...... 161 The Machine and the Guilt of Meaning ...... 162 Deconstruction of Geometry and Architecture of Rebellion ...... 163 Architecture as Proposition of Becoming ...... 167 Computerisation of Architecture ...... 184 Conclusion ...... 187

CONCLUSION ...... 190 The Contribution of the thesis to knowledge ...... 196 Limitations of the Thesis ...... 197

APPENDICES ...... 198 Appendix A: Bibliography ...... 198 Appendix B: List of publication by Author ...... 212

vii List of Illustrations

Figure 1.1 The cave paintings at Lascaux, Dordogna, France, axial gallery...... 18 Figure 1.2 Temple of Horus at Edfu: main gateway...... 22 Figure 1.3 Temple of Horus: Hypostyle hall or middle hall entrance...... 23 Figure 1.4 Temple of Horus: floor plan...... 24 Figure 1.5 Temple of Horus: Interior view of main entrance...... 26 Figure 1.6 The Great Pyramids of Giza in Egypt...... 29 Figure 1.7 The Great Pyramids of Giza in Egypt: aerial view...... 31 Figure 1.8 Sri Yantra: Early coloured diagram...... 34 Figure 1.9 Borobudur Temple in Central Java ...... 37 Figure 1.10 Borobudur Temple: aerial view...... 38 Figure 1.11 The Enneagram diagram by Gurdjieff...... 40 Figure 1.12 Claude Bragdon: the projections made by a cube in traversing a plane. . 43 Figure 2.13 The Creation. Bible Moralisée, France, 1250...... 48 Figure 2.14 Geometrical analysis of ‘The Creation’, by the author...... 48 Figure 2.15 The Dantean Universe : illustration by M. Cactani, 1855...... 56 Figure 2.16 Byzantine architecture: Hagia Sophia, Istanbul. Ground floor plan ...... 61 Figure 2.17 Hagia Sophia: Byzantine architecture, section through the centre...... 61 Figure 3.18 Vitruvius’ description of ‘Human Proportion’...... 65 Figure 3.19 A dodecahedron from Luca Pacioli’s De Divina Proportione: illustration by Leonardo da Vinci, 1509 ...... 70 Figure 3.20 Leonardo da Vinci: Vitruvian Man—illustration, 1490...... 72 Figure 3.21 Leonardo da Vinci: The Last Supper. Mural painting, late 1490...... 73 Figure 3.22 Albrecht Dürer: studies on the proportions of the female body, 1528. . 77 Figure 3.23 Francesco Di Giorgio: Human body inscribed in a building plan, 1470. 80 Figure 3.24 Leonardo da Vinci: Sketch of the plan of a church, 1490...... 80 Figure 4.25 Apollodorus of Damascus: The Pantheon, Rome, 126 AD...... 83 Figure 4.26 Gianlorenzo Bernini: Ecstasy of Saint Teresa, Italy, 1645–1653...... 87 Figure 4.27 Francesco Borromini: San Carlino Alle Quattro Fontane, section engraving...... 88 Figure 4.28 Borromini: San Carlino alle Quattro Fontane, floor plan, Rome ...... 90 Figure 4.29 Pythagorean mystical symbol Tetraktys, consisting of four rows and ten points ...... 92 Figure 4.30 Borromini: pencil sketch of Minerva Medica in 1643. There are dimensions and grids illustrated on this sketch...... 95 Figure 4.31 Maderno: St Peter, Carlo Maderno, façade constructed in 1506, Rome. 96 Figure 4.32 Borromini: San Carlino alle Quattro Fontane, dome, Rome ...... 97 Figure 4.33 Bernini: St Peter’s dome, Rome...... 98 Figure 4.34 Bramante: St Peter, floor plan, Rome...... 99 Figure 4.35 Kepler: Laws of planetary motion, oval orbits...... 101 Figure 4.36 Johannes Kepler: Mysterium Cosmographicum, diagram of the planetary spheres, 1596...... 102 Figure 4.37 Borromini: San Carlino, façade, Rome...... 104 Figure 5.38 Le Corbusier: en la Acropolis Atenas (Acropolis in Athens), 1911. .... 106 Figure 5.39 Le Corbusier: Notre Dame, Paris …………………………...………110 Figure 5.40 Le Corbusier sketches. Left is the Casa delle Nozze d’Argento, Pompeii, 1911. To the right is the house of Sallustius, Pompeii, Italy...... 111 Figure 5.41 Le Corbusier: Open Hand, Chandigarh...... 115

vii Figure 5.42 Le Corbusier: Study of pine trees (1905–06)...... 116 Figure 5.43 Le Corbusier: The Modulor, 1948...... 119 Figure 5.44 Le Corbusier: Villa Schwob, back elevation, Chaux-de-Fonds. ……....124 Figure 5.45 Le Corbusier: Carpenter Centre, Cambridge, Massachusetts...... 129 Figure 5.46 Le Corbusier: Cow with calf, 1950, View of landscape passing over Colombia from aeroplane, 1951 ...... 130 Figure 6.47 Albrecht Dürer: Melencolia I, engraving, 1514 ...... 134 Figure 6.48 El Lissitzky: Tatlin working on the Monument to the Third Internationa, 1922 ...... 134 Figure 6.49 The wooden Church of Transfiguration in Kizhi, west view, Russia, 1714...... 136 Figure 6.50 Eastern façade of Saint Sophia Cathedral, Kiev in Russia, 1037...... 138 Figure 6.51 Kizhi Pogost, Lake Onega in the Republic of Karelia, Russia,1714. .... 139 Figure 6.52 Saint Basil’s Cathedral, Red Square in Moscow, 1555...... 141 Figure 6.53 Vladmir Tatlin: Model of the Monument to the Third International, 1919...... 146 Figure 6.54 El Lissitzky: Proun Room, 1923...... 152 Figure 6.55 Rem Koolhaas and Elia Zenghelis, Exodus, or ‘The Voluntary Prisoners of Architecture’, London, 1972...... 154 Figure 6.56 Kazimir Malevich painting: Suprematism, No.85, oil on canvas, Krasnodar Museum of Art, Russia, 1916...... 156 Figure 6.57 Kazimir Malevich: Black Square, oil on canvas, State Russian Museum, St. Petersburg, Russia 1915 ...... 157 Figure 6.58 Zaha Hadid: Horizontal Tektonik, acrylic on cartridge, London, England, 1977 ...... 157 Figure 6.59 Zaha Hadid: MAXXI, Rome, Italy, 2010 ...... 158 Figure 7.60 Bernard Tschumi: Parc de la Villetter, Paris, 1982...... 161 Figure 7.61 Zaha Hadid: Grand Buildings, Trafalgar Square London, England, acrylic on canvas, 1985...... 165 Figure 7.62 Benoit Mandelbrot: Four stages in the construction of the Koch snowflake...... 167 Figure 7.63 Peter Eisenman: House 11a, produced during the Cannaregio design seminar in Venice, Italy, 1978...... 168 Figure 7.64 Peter Eisenman’s, House I, Princeton, 1967...... 171 Figure 7.65 Peter Eisenman’s, House II, Hardwick, Vermont, 1970...... 171 Figure 7.66 Andrea Palladio: Villa Rotonda, Vicenza, 1570...... 173 Figure 7.67 Peter Eisenman: Diagrams of transformation of House IV, 1971...... 184 Figure 7.68 Frank Gehry: The Guggenheim Museum, Bilboa, 1997...... 187 Figure C.69 Le Corbusier: Villa Schwob, La Chaux-de-Fonds, Switzerland, 1916. Floor plan...... 193

viii Introduction

Overview

We live in an era dominated by rapid developments in science and technology. Across the world, new settlements are growing and in our cities, buildings reach skywards to accommodate daily human activities, to provide shelter, and collectively form the setting for urban life. While today’s buildings may be glorious in design, to many critics they are soulless.1 If one takes this position, it seems the role of architects in urban development has been compromised; their core duty to provide for human well-being, lost. Comprehension of the built environment has become limited to its physical appearance, with no place for consideration of how the end-user is affected or interprets the design form. As British psychologist, David Halpern attests:

Physical and social planning are unavoidably enmeshed. Environments are typically constructed for social reasons, designs lead to social consequences whether intended or not, and even the humblest construction inevitably acquires a socially ascribed meaning.2

A city’s soul is shaped or strengthened by the layout of its streets and buildings. How we experience the milieu has become a significant focus in architectural theory and practice.3 Although there is diversity in individual demands and experiences, the essence of humankind’s needs is universal. People everywhere seek to find meaning in the world around them. However, not all designs are based on a plan or a promise to create a built environment with some aspect of meaningfulness. Writing in the 1980s, Paolo Portoghesi criticised twentieth century cities and suburbs, making the following observation about contemporary urban development:

The modern city, the suburbs without quality, the urban environment devoid of collective values that has become an asphalt jungle and a dormitory; the loss of local character, of the connection with the place, the terrible homologation that has made the outskirts of the

1 Crooke, D. Intelligent Buildings: Design, Management and Operation, (London: Thomas Telford limited. 2004), p.58. 2 Halpern, D. Mental Health and the Built Environment: More than Bricks and Mortar? (London: Taylor & Francis. 1995), p.2. 3 Evidence for this statement can be found in two key treatises, Juhani Pallasmaa, Architecture and the Senses (London: Academy Group Ltd, 1996) and, Steen Eiler Rasmussen, Experiencing Architecture (New York: John Wiley and Sons, Inc., 1959). 1

cities of the whole world similar to one another, and whose inhabitants have a hard time recognising an identity of their own.4

Almost all modern cities contain some high status buildings, their creators seeking to solidify their identity and create a niche in the design world. They are the so-called ‘celebrity architects’. Their core objective is uniqueness of approach in handling design problems. If there is any degree of consideration for human needs, it is usually based on the individual architect’s self-reflection. It seems to me there is a preoccupation with creative self-expression, which overrides other considerations in their work. This style of architecture, which employs geometry as a leading tool in its designs, aiming to elevate the spirit of the beholder, seems egoistical. In early architectural history, such geometric forms were stable and alive with symbolic meaning. The principles expressed during early fourth millennium BC geometric patterns represented a distinct set of meanings, either representing spiritual meanings, or symbolising a belief or set of beliefs. Today, one can witness how celebrity architects bend, break, fold and unfold geometric forms in an abstract, artistic way, but with less emphasis on past architectural design principles

Problem and scope of Research

The above observations led me to test two hypotheses in this thesis. The first is that spiritual meaning and symbolic function can be understood by, and are currently available for the explicit use of, architects. This hypothesis is supported by an analysis of the development of symbolic meanings in architecture from ancient times until the advent of modernist architectural theories, when symbolic meaning were abandoned. As these symbolic meanings are no longer well understood by the public today, architects have to explain them theoretically to represent such theory effectively in their design. In doing so, they enrich how people experience the works the architect creates.

My second hypothesis is that architects today use geometric patterns without understanding their true meanings or spiritual origins. The nature of spiritual meaning and symbolic function and its connection to cultural, social and theological values forms an important dimension of architectural theory, but it often seems clouded in

4 Paolo Portoghesi, Post Modern: the Architecture of the Postindustrial Society (New York; Rizzoli, 1982), p.7. 2 mystery. Architects who pay careful attention to the meanings associated with specific geometric patterns can thus create a more efficacious and desirable built environment, that resonates sun-consciously with users of the buildings and the milieu they create.

To test these two hypotheses, my thesis investigates the meanings embedded in various geometrical patterns in architecture. This was motivated by a desire to fill a gap in the understanding of the significance of applied geometry in architecture. Specifically, this deficiency has become evident in the practice of twentieth and twenty-first century architecture. The geometric patterns that had meaning in the past seem to be applied by today’s practitioners in an ad hoc way. There is little in architectural theory to guide today’s architects and there is less emphasis on generating meanings to symbolise architectural forms.5 Awareness of the historical significance and meanings attached to these geometrical patterns is either disregarded or completely overlooked in the theoretical development and work of current major architects and emerging architects who follow them. I believe this gap in twentieth and twenty-first century architectural theory needs to be filled if architects are to fully understand and appreciate the implications for their own works.

One could argue that a major problem is that the creative minds behind new building designs neglect the importance of the fundamental, explicit theory and design principles for creating environments that are rich in meaning to the architects themselves, let alone the consumers who actually inhabit or use these buildings. The modern approach to the use of architectural geometry assumes that meaning can be embedded in a form of created abstraction that results from the exchanges that occur within different influential factors (social, theological, cultural, political etc.). Consequently, in order to understand the production of meaning in the practice of architecture, I believe it is first necessary to understand the process through which the development of meaning has been presented and become ascribed to specific geometrical shapes.

In this thesis, I begin by providing a detailed account of some of the varied and specific meanings associated with patterns of built form throughout key historical eras. My objective is to show the connections to related areas of influence (theology, politics, economics, culture, etc.) in order to provide a clear frame of reference for understanding

5 Mark Wigley, Constant’s New Babylon: The Hyper-architecture of Desire (Rotherland: 010 Publisher, 1998), p.16 3 the implied meanings in architectural forms today. Throughout history, the same geometric figures have been used in a range of belief systems to carry similar meanings. Therefore, over many generations, these belief systems have influenced the meanings attached to those geometric figures that today’s architects might apply in their design and in space making. These meanings are embedded in particular geometries and endure; even after the belief system has disappeared or is no longer influential.

Semantics

The question is how do people perceive the milieu that they occupy? This question is asked from an essentially ‘structuralist’ point of view that has become the foundation of most cultural theory, despite the philosophical critique it received in the middle of the twentieth century. One core ‘structuralist’ figure was French anthropologist, Claude Levi Strauss (1908–2009). He based his approach to meaning and human perception of the universe on ‘binarism’, a theory that there are always two diametrically opposed things, or two sides to any argument. In a 1972 lecture, he declared, ‘From the very start, the process of visual perception makes use of binary oppositions’.6 According to this view, there will always be more than one interpretation of the correlation between object and meaning; thus, one particular geometric form may convey more than one singular meaning.

The Philosophical Approach of This Study

Despite its reliance on a ‘structuralist’ analytical approach, my thesis argues that there are some meanings that indeed do adhere to objects, despite their cultural context. In the early chapters of this thesis, I describe how these meanings are identified as ‘spiritual’, and I demonstrate how they are embedded in geometry. In later chapters I also explain the dramatic transformation and reformation of this approach to spirituality and generation of other meanings.

In 1878, German philosopher, Friedrich Nietzsche (1844–1900) sparked contention when he made the following observation about transformation of religion to science:

6 C. Lévi-Strauss, Structuralism and Ecology: Gildersleeve. A lecture delivered March, 1972 (New York: Barnard College, 1972). 4

Art raises its head where religions decline. It takes over a number of feelings and moods produced by religion, clasps them to its heart, and then itself becomes deeper, more soulful, so that it is able to communicate exaltation and enthusiasm which it could not do before ... Growing enlightenment has shaken the dogmas of religion and generated a thorough mistrust of it; therefore feeling, forced out of the religious sphere by enlightenment, throws itself into art in certain instance, into political life, too, indeed even directly into science.7

Consequently, the thesis adheres to a ‘postmodern’ argument and methodology. My argument employs the concept of ‘re-enchantment’ of objects that can be connected to pre-modern notions of anthropomorphic ideas such as ‘animism’, and various forms of 8 archaic and so-called ‘primitive’ beliefs. Following this approach, I will show there is a clear path from animism and archaic beliefs to understanding the various dimensions of visual geometric forms, which are integral to embedded meaning in twentieth century architecture.

The critical review of the work of 1990s architects in my thesis is necessary to consider their approach to applied geometry and highlight their knowledge of the meanings it contains. Understanding animism and various archaic beliefs in relation to architecture is difficult; it is a subject to which a number of philosophers (Roland Barthes, Robert Evans, Alberto Perez Gomez, Mark Wigly, etc.), have devoted many years of thought. Through close historical and theoretical study, I believe it is possible to develop an understanding of such correlations between meaning and form. In order to address this

7 Friedrich Wilhelm Nietzsche and R. J. Hollingdale, Human, All Too Human (Cambridge Texts in the History of Philosophy; Cambridge: Cambridge University Press, 1996), p.150. 8 According to the Oxford dictionary the phrase, enchant means, to cast a spell on. The origin of the word is from the old French enchanter, and from Latin incantāre that in both languages comes from the word canere, and translates to sing. The introduction of this term after the time of enlightenment in England (era of magic and witches) was applied through the theory of Max Weber (1864-1920), German philosopher on understanding of secularization and modernity. He affirmed: ‘Many old gods ascend from their graves; they are disenchanted and hence take the form of impersonal forces ... What is hard for modern man, and especially for the younger generation, is to measure up to workaday experience ... The fate of our times is characterized by rationalization and intellectualization and, above all, by the ‘disenchantment of the world.’ Max Weber, David S. Owen, and Tracy B. Strong, The Vocation Lectures : 'Science as a Vocation'; 'Politics as a Vocation' (Indianapolis: Hackett Pub., 2004), p.150-154. ‘Re-enchantment’ was first used by American cultural historian Morris Bermann (1944- ) in his book 'The Re-enchantment of the World', a discourse about the possibilities of reviving the connection between man and nature (existing prior to the scientific revolution of the sixteenth and seventeenth centuries) in an effort to gain a deeper understanding, and preservation of, modern day society and environment. Art historian Suzie Gablik (1934 - ), in her 1994 book 'The Re-enchantment of Art' expands, on Bermann's theme and outlines her view for a new form of art, rooted in a reawakening between individuals, community, ecology and spirituality. 5 matter effectively, the various case studies conducted in my thesis trace the transformation of applied geometry and meaning in order to demonstrate the importance of the questions posed by theorists and architects.

Understanding how geometry was used to express meaning in past forms of architecture reveals that these archaic meanings are still present in modern design and available to people who understand the relationship between form and meaning. The symbolism in applied geometry has been portrayed in various buildings for different purposes, and these offer new material for future interpretation and understanding of the meanings geometry originally embodied. The key argument on which my hypotheses are based— that of geometry and meaning in architecture—revolves around a gradual transformation of beliefs that shifted from divinity to nihilism, from man to machine, and finally, from reality to abstraction.

Architectural historian, Alberto Perez Gomez (1949–), has explored the shift from divinity to nihilism pertaining to meaning in architecture. He related it to the concept of love (the Greek god Eros) and architecture. Gomez proposed that a shared accountability for humanity should be regarded as the core motivation for architectural creativity, and stated that the unification of built form and love is part of an ‘architect’s wishing to design a beautiful world and architecture’s imperative to provide a better place for society’.9 In his later study into post-eighteenth century architecture, he expressed the belief that ‘Deprived of a legitimate poetic content, architecture was reduced to either a prosaic technological process or mere decoration’.10

In order to validate my overall premise that geometry is a potent visual tool for an architect in shaping a conscious or subconscious reaction to places, I have examined and analysed the factors leading to changes in the use of geometry, the belief systems in architectural design and the aesthetics attached to geometry visual field together with other subjective and physical variables that shaped man’s architectural perception. Among individuals or groups of people, these reactions are also influenced by societal factors such as politics, theology, finance and culture, as well as personal factors such as memory, education and occupation, etc. Such cultural and personal references are

9 Alberto Perez Gomez, Built Upon Love : Architectural Longing after Ethics and Aesthetics (Cambridge: MIT Press, 2006), p.4. 10 Alberto Perez Gomez, Architecture and the Crisis of Modern Science (Cambridge: MIT Press, 1983), p.11. 6 causative, influencing the way in which people view or are affected by particular architectural designs.

In the twenty-first century, continued population expansion and our daily lives and living conditions are increasingly imbued with the intensification of science and technology are important factors for consideration in creating the future built environment. Consequently, architecture strives to keep up with these fast-moving transformations and developments. I believe a good architect must recognise and accommodate these factors into what is an increasingly complex and challenging role.11 The popularity and growth of the digitalisation of modern formal representation, with its various interpretations of geometric configurations that have been developed over the centuries, has in turn affected how architects respond to social change. This is in contrast to the past, when architectural symbolism was extensively influenced by a controlled, obligatory belief system. To write a complete account of architectural symbolism and historical analysis is beyond the scope of this thesis, therefore, to argue my hypotheses effectively, I have focused on selected key architectural and theoretical examples from different eras and regions.

Thesis Outline

The thesis is divided into seven chapters. In the first three chapters, I test the first hypothesis mentioned above—that spiritual meanings formerly embedded in architectural forms can be understood and are available for explicit use by architects today. In these chapters, I illuminate the historical development of meanings associated with architectural forms, to show that an understanding of the meanings traditionally carried by architectural forms, while still embedded in the patterns of building, are no longer well understood. The next four chapters contain my perceptions as to how these meanings can be recaptured. These four chapters are composed to test my second hypothesis—that by paying careful attention to the meanings associated with specific geometric patterns, today’s architects can once again create a more efficacious and desirable built environment. I conclude the thesis by summarising the extent to which I

11 The reference to ‘good architect’ is to a practitioner who tries to fulfil not only functional, utilitarian requirements, but who also considers different aspects of man/users, such as their psychological needs. The position taken here is that the effects of architectural spaces on common people are the core responsibility of its creators. 7 tested the two hypotheses in the previous seven chapters, and briefly present a suggested picture of future lines of research that I believe will enhance pedagogy to deepen our understanding of meanings embedded in architectural form, to improve architecture as we advance further into the twenty-first century, and how best to utilise this understanding for the benefit of all.

Chapter One begins with a discussion of humankind’s first attempts at the creation of meaning in built form. My point is to demonstrate the earliest use of geometry as a dynamic tool in architecture carrying meaning. This point is established through the chronological evaluation of some well-known and lesser-known examples of earlier eras in humankind civilisation, to provide the foundation for testing the first hypothesis of my thesis that these meanings are still embodied in architectural form and are available for utilisation by architects. It is also necessary for me to give a clear definition of geometry for the purposes of describing its importance to the thesis’ hypotheses. Hence, Chapter one works from the early origins, including the study of concurrent ancient Egyptian, Mesopotamian and Indian philosophies. The mystery and precision of early geometry in architecture, with its deep-rooted beliefs, serves to communicate information or readings regarding the human cosmos. Sacred buildings, the major structures during ancient times, are analysed in relation to the use of numerology and geometry to express a particular meaning through their symbolic use. This includes the major concept of representation of the creation of the universe in ancient architecture; in particular, the study of the great Egyptian pyramids of Giza, the Temple of Horus, and the ancient Hindu symbol of Sri Yantra, which sets the pattern predominant in Hindu and Buddhist temples. Thus, I present a point of departure for discussion of the evolution of widely understood meanings communicated by architecture. In addition, I begin to elucidate the first hypothesis by evaluating early examples in the history of architecture and ancient approaches to revealing meaning through built form.

In Chapter Two, I expand upon Chapter One by carrying the discussion of spiritual symbolism into the next eras of architectural history. The purpose of the second chapter is to describe the correlation between architecture and medieval geometry. The relevance of my analysis in its application to the first hypothesis overall, is to present the primary theoretical works that shaped the future practice of sacred architecture.

Based on an examination of the selected examples, I will show that numerological and geometrical figures were a fundamental component of the design and symbolism of medieval architecture. My analysis focuses on the work of early Christian writers who inspired the development of architectural symbolism. In this chapter, by close analysis of texts such as the ‘Divine Comedy’ and the ‘City of God’, in contrast to writings of other European philosophers, I present an explanation of the symbolism of architectural geometries as a basis for the subsequent chapters.

One of the points I make in testing this first hypothesis is that many similarities existed in the interpretation of architectural meaning among ancient civilisations. There was a formal association between ancient Egyptian practices and Greek thinkers in that the study of philosophers such as Pythagoras of Samos (570–495 BC), Plato (427–347 BC) and Euclid of Alexandria (325–265 BC) led the major schools of learning in mysticism, mathematics and geometry, and influenced Roman architects. Medieval architects, who in turn gained knowledge from previous eras, refined their understanding of creating beauty for architectural order, achieving harmony and balance through their use of numerology in the geometries they used. At the same time, the beginnings of theological influence is traced through the writings and practices of medieval man, who represented and elevated the symbolism I discuss in Chapter One to a new level. In particular, the study of the Gnostics and of number philosophy of that era helps us to comprehend the cultural and social changes in the earlier era of civilisation. This understanding is necessary, in terms of the first hypothesis of my study, to show that written theological texts formed the foundation for new compositions of geometric patterns and became core reference material in building design.

My research into the meanings expressed in architectural geometry is continued in Chapter Three by considering the use of religious geometry during the European Renaissance. The meanings expressed in architectural geometry lay the groundwork for a theoretical approach to the works of a number of influential figures and their effects on the voices of power during the early Renaissance period. To demonstrate this point using a more contemporary approach, I give a brief overview of the works of German philosopher, Hegel concerning the relationship between meaning and spirituality, which in turn leads my argument to the works of Vitruvius, The Ten Books of Architecture and the concept of Vitruvian Man (also known as the Canon of Proportion).

By a selective review of architectural examples from the Renaissance era, I demonstrate how the major thinkers of that period were those who, around the fifteenth century, expressed great interest in Greco–Roman symbolism and methodology. In this chapter I employ the theories of Francesco di Giorgio, Luca Pacioli and Leonardo Da Vinci to demonstrate the position of myth in elements of geometric structure in early Renaissance architecture. The importance of the human form in relation to the universe as a whole relates back to the demonstration of the microcosm-macrocosm in order to create meaning in theory and practice, as I discuss in Chapter One.

The evolution of meaning in architectural geometry throughout the ages continues in Chapter Four. In this chapter, I focused on the Baroque era and the development of the Age of Enlightenment when, beginning with the antagonism between theology and the advancement of science, representation and symbolism were taken to a different level. In Chapter Four, I also offer a discursive examination of how geometry in enlightenment philosophy explains the transformation of cultural and architectural movements. The development of architectural design using geometrical composition came about due to profound changes in the belief system of both creative minds and the general population. This review supports my second hypothesis by showing the radical changes in architectural practice and the breaking away from past beliefs and practices—the beginning of modernity.

Chapter Four also covers one of the foremost revolutions in Christian history. I describe how the Protestant Reformation, led by Martin Luther, brought about doubt and loss of trust in the teachings of the Roman Catholic Church. From there, I look at how the work of Galileo and other influential mathematicians and astronomers influenced religious belief in metaphor and allegory. This flourishing of scientific, mathematical and geometrical knowledge, balanced against mythological compositional elements, brought meaning and sacred totality to the design of spatial environments. The production of Baroque architects, such as Bernini and Borromini, helped to demonstrate the development of the use of meaning and sacredness in architectural form. My explanation of geometry in architecture as a ‘mirror’ to show beliefs during the period of Enlightenment leads to the beginning of the next chapter. It is also another step forward in testing the second hypothesis of my thesis by exploring selected case studies and evaluating architectural doctrine and formal composition. Additionally, my findings

10 in this chapter demonstrate further development of the position of meaning in architectural practice.

Chapter Five builds on the findings of the four previous chapters on the genesis and evaluation of the meaning of geometrical forms in architecture. My investigation brings the historic examination forward into the eighteenth and nineteenth centuries. Modernism and its sources in geometry created a point of departure for avant-gardism in art and architecture. The most influential factors at the time were major political and social changes such as war and the industrial revolution, which provoked diverse doctrines such as Nihilism and Anomie. During the progression of ideas associated with modernity, emphasis was placed on the belief that mechanisation was the only way to achieve a better life—socially or individually.12 Thus, in modern architecture the production of forms using geometric numbers gained its power from the authority of the machine.In this chapter, I underpin my arguments through a study of the philosophy of that era, namely the work of Nietzsche in relation to architectural research, and the work of Henry Provensal (1868–1934) and Le Corbusier (1887–1965) in terms of production. The definition of beauty, meaning and symbolism took a different turn, based on the advancements in technology and science. Because of these changes, the universe for modern man became increasingly disconnected; ancient beliefs were now the distant past.

The purpose of the next chapter, Chapter Six, is for me to apply the previous findings to an analysis of the 1990s movements in architecture. To support the second hypothesis of my thesis, I argue there is a lack of awareness of past beliefs and meanings in both the theoretical and built work of the practitioners of the 1990s, who instead strove to achieve autonomous architecture. Ideologies such as postmodernism, constructivism and deconstructivism represent different views of the use of geometry in architectural theory and practice. The lack of concern for embedded symbolism in the geometrical

12 The aftermath of WWI affected the public perception in Europe in that they could see that the only winner of this devastating conflict was ‘the machine’. So the position of anything machine-like, or anything in relation to the machine, was perceived as superior and brought empowerment and stability to social activities. Inevitably, it became the important part of European culture after WWI. The machine presented the world with an image that guaranteed survival in another tragic event. Ideas such as those can be found in the work of Adolf Loos about race and crime, Stravinksy ‘s ‘Rite of Spring’, Sigmund Freud’s reinterpretation of the Oedipal complex model in relation to civilization, and Le Corbusier’s ‘engineer’s aesthetic’. Such influential ideas turned out to be more than a conceptual model of events and, rather, became an attractive baseline for the practitioners of the age.

11 composition of contemporary architects relates back to twentieth century Russian constructivists such as El Lissitzky (1890–1941), Kazimir Malevich (1879–1935) and Vladimir Tatlin (1885–1953). This lack is further demonstrated through an analysis of the works of Rem Koolhaas (1944–), Zaha Hadid (1950–) and Peter Eisenman (1932–).

The highly rational nature of buildings formed under principles of artistic self- expressionism has resulted in the transformation of architecture beyond its physical appearance as a building. As I described in detail in Chapter Five, the total transformation of symbolism and applied geometry reached a new era in the history of architecture. Through their theoretical positions, the influence of Martin Heidegger (1889–1976), Ferdinand de Saussure (1857–1913), Jacques Derrida (1930–2004) and Theodor Adorno (1903–1969), clearly supports my second hypothesis that meaning in current architecture stands in strong contrast to that of the architectural creations in ancient times.

The final chapter leading to the Conclusion is Chapter Seven, in which I test the second hypothesis of my thesis through a review and analysis of selected architectural works. In this chapter, I reflect on twentieth century architectural practice and theory in relation to the second age of machines. Identifying the factors that influenced the changes and radical transformation of deconstructivist theory and built form is my core argument in this chapter. The study of Derridian and Sassurian’s linguistic philosophy in relation to fast growing scientific development formed the main viewpoints for the selected architectural case studies. The main case study I use in this chapter is the practice of contemporary architect, Peter Eisenman, through his designed milieus and writings from 1970 until present day. In the final segment, I explicitly examine the effects of digitalisation on architecture. The use of computers in every stage of the design process, especially in relation to configuration of form, geometry and neglect of meaning, comprise my final argument in this chapter in relation to thesis’ hypotheses.

In the Conclusion of my thesis, I review the extent to which I have tested the two hypotheses in the previous seven chapters, and briefly present a suggested picture of future lines of research that I believe will enhance pedagogy to deepen our understanding of meanings embedded in architectural form, to improve architecture as we advance further into the twenty-first century, and how best to utilise this understanding for the benefit of all. 12

Chapter One. From the Pre-Christian Era to the Christian Era

‘All men by nature desire to know.’13

To support the first hypothesis that the spiritual meanings embedded in built forms are important to architectural theory, this chapter is an examination and review of the architecture of various cultures in the ancient era and the use, in building, of geometry to express beliefs. The intention is not simply to equate the spiritual influence of several ancient cultures on their architecture; rather, it is to perform a chronological evaluation of a number of examples to reveal the very early use of geometry as an active element in building design.

The Divine, the Sacred and the Creation of the Universe

Man’s search for his connection with the universe that surrounds him and of which he is a part is so strong that to this day, Western architecture still relies upon geometry by connecting built form with judgements about quality of life, beliefs and metaphysics.14 To begin an anthropological study of geometry in ancient civilisations, I was faced with a broad selection of different historical structures that could assist me with the study of representations of different beliefs and cultures.15 It is beyond the scope of this thesis to analyse them all, therefore, the few I selected for detailed study in this chapter, form a foundation for the subsequent chapters. This selection was based on the substance of design and geometrical arrangement of each case in relation to significant meaning and belief system underlying it.

13 Aristotle and Werner Jaeger, Metaphysica (Scriptorum Classicorum Bibliotheca Oxoniensis; Oxonii, Typographeo Clarendoniano, 1957), p.21. 14 The use of term ‘Metaphysics’, or any reference to it which occurs in the context of this thesis, is in accordance with study of French scholar René Guénon (1886-1951). ‘Metaphysics is essentially the knowledge of the Universal, or, if preferred, the knowledge of the principles belonging to the universal order, which moreover alone can validly lay claim to the name of principles; but in making this statement, we are not really trying to propose a definition of metaphysics, for such a thing is a sheer impossibility by reason of that very universality which we look upon as the foremost of its characteristics, the one from which all the other are derived. In reality, only something that is limited is capable of definition, whereas by definition metaphysics is on the contrary by its very nature absolutely unlimited, and this plainly does not allow our enclosing it in a more or less narrow formula’. René Guénon. Introduction to the Study of the Hindu doctrines (Luzac & Co, London, 1945), p.70. 15 There is a large body of literature that demonstrates these different cultures and their various beliefs and symbols. Bruce G. Trigger, Understanding Early Civilizations : A Comparative Study (Cambridge: Cambridge University Press, 2003). 13

The sacred buildings of past civilisations such as the Sumerian civilisation, ancient Egypt, classical Greece and the ancient Mayan—and their art, mythology and created regional beliefs, inspired later architects. In addition, the development of all these ancient groups’ knowledge in mathematics, astronomy and geometry, in addition to other contributing factors such as theology, cultural beliefs and mythology, assured that their structures incorporated a variety of compositional elements. These culminated in relatively unified, meaningful and sacred forms of cultural expression.16

In a limited sense, there is a measured and intentional symbolism in the three- dimensional representation of ancient milieus, which indicates the teaching of a tradition. The result of this architectural application reveals that the convention of assigning the term ‘symbol’ to a referent is related directly to the teaching of the foundations of when, and in what form, the symbolic meaning explicitly occurs. These symbols have an ability to evoke a memory of a supramundane model, and in that way, they are infused with the sacred.

The importance of the definition of ‘symbol’ is that it is described as within the theoretical realm, recognisable by the human senses or understandable by the mind.17 Nevertheless, the origin of the term ‘symbol’ is from the Greek symbolon—‘to throw together’, which itself suggests to bond, or to place a referent to an object’s intended meaning or meanings. Now, if the reflection returns to architectural meaning in the traditional sense, symbolism is seen as something beyond ‘commodity, firmness and delight’.18 Symbolism dictates the composition of the design. As Adrian Snodgrass (1938–2009) attests:

Traditional architecture possesses a symbolic content. The built form is a symbol pertaining to supra-physical, principle realities. Symbolism regulates and determines the forms of traditional buildings.19

16 William H. Stiebing, Ancient Astronauts, Cosmic Collisions, and Other Popular Theories About Man's Past (Buffalo: Prometheus Books, 1984), p.17-40. 17 R. Livingstone, The Traditional Theory of Literature (University of Minnesota, Minneapolis, 1962), p.57-59. 18 Marcus Vitruvius Pollio, Ten Books on Architecture (New York: Cambridge university press, 1999) 19 A. Snodgrass, Architecture, Time And Eternity: Studies In The Stellar And Temporal Symbolism Of Traditional Buildings (Pradeep Kumar Goel, Delhi, 1990), p.15. 14

In contrast, the close relationship of symbolism and science in the architectural design of ancient, sacred edifices reveals the dual necessity to design and construct a building with attention to the practical, as well as to the conceptual. Thus, symbolism in those structures was not only spatial but also applied to reflect particular meanings with ritualistic, theological, mythological or even philosophical references. On the other hand, the sacred purpose of these symbols underlies the utilitarian and physical necessities of those structures, in order to accomplish a relationship to the universe beyond their physical grasp—one that only appears to the ‘third eye’.20

The reason for analysing sacred buildings instead of domestic dwellings from the ancient era is due to the lack of evidence available for the latter. The importance of religious and spiritual meanings in ancient beliefs meant that sacred buildings were both well-constructed and preserved. American art and humanities historian, Sarah Iles Johnston (1959–) researched surviving documentation and illustrated in depth the difference between domestic and sacred buildings, and the influential events in their design.21 People in ancient times placed so much importance on their cultural and mythological beliefs that all their efforts and resources were used to construct detailed, solid and long-lasting sacred buildings. These buildings were evidence of and gave permanence to their devotion, their beliefs, and to their search for connection to the universe of which they were a part.

The means by which some of them were known in later times have been preserved, and they indicate that they were intended not merely to resemble, but to be, mountains. The sacred buildings design aimed to bond ‘heaven and earth’ … also a religious concept of many-sided significance. It stood for the whole earth, and within it, therefore, were concentrated the mysterious power of life which bring forth spring and autumn.22

The reflection of divine patterns became an essential part of building design because spiritual leaders oversaw every detail of the construction process. Some evidence of

20 The third eye is the allegory that was first revealed by Buddhist teaching on spiritual awareness. It is also popularly referred to as the ‘inner eye’ that can view the supreme realm that is beyond physical and mental being. 21 Sarah Iles Johnston, Religions of the Ancient World : A Guide (London: Belknap, 2004), p.253-260. 22 Henri Frankfort, Michael Roaf, and Donald M. Matthews, The Art and Architecture of the Ancient Orient (5th edn., Yale University Press Pelican History of Art; New Haven ; London: Yale University Press, 1996), p.7. 15 their orders and instructions remain today.23 The era described and its architectural doctrine is not the image of life after the fall of the Roman Empire, or the so-called ‘Dark Ages’, but goes back thousands of years to ancient Egypt and the Indus Valley civilisation.

Furthermore, this chapter’s investigation into ancient symbolism could not be effectively addressed without a clear understanding of the role of buildings as evidence of ancient cultural beliefs. These beliefs were primarily concerned with the structure of the universe and what was beyond the naked eye. Emphasis in this chapter has been placed on providing a greater insight into the cultural contexts within ancient sacred structures, which were repeated in many forms and shapes by the designers. This chapter contains a number of case studies and an analysis of the meaning of form attached to ancient buildings. The purpose was to allow me to configure a narrative to provide an evidence in support of the first hypothesis of my thesis, that ‘spiritual meanings were formerly embedded in architectural forms’.

St. Bernard of Clairvaux (1090–1153), the French abbot and an influential figure in twelfth century Catholicism, was once asked, ‘What is God?’ His response was, ‘He is within all. He is length, width, height and depth.’24 In this quote, he was referring to ancient Greek geometry, which in his time seemed deeply mysterious and sacred. He was attaching his view of God to Plato’s ideals—the secret inner world of pure forms and laws of geometry, which his audience would not have understood—regarding it as truth taken on faith, something that would have been very useful for convincing a credulous public to have faith. In particular, St. Bernard was rationalising the idea of infinite dimension in all directions, Pythagorean concepts and Euclidean solid geometry.

There is no suggestion that all sacred structures were a representation of universal order and the derivation of the universe; rather these structures project a view that the peoples

23 The original written records/tablets discovered in the Great Pyramids in the third millennium before Christ have been gathered in ‘Memphite Theology of Creation’ and translated by American Egyptologist, John Wilson (1899-1976). This has been published in James B. Pritchard, The Ancient Near East : An Anthology of Texts and Pictures (Princeton, N.J. ; Oxford: Princeton University Press, 2011), 30. There is also further evidence in R.T.R. Clark, Myth and Symbol in Ancient Egypt (University of Minnesota: Grove Press, 1960), p.138-140. 24 Bernard and G. R. Evans, Bernard of Clairvaux : Selected Works (Classics of Western Spirituality; New York: Paulist Press, 1987), p.170. 16 of these ancient civilisations believed in the greater universal order and its principles, and reflected this knowledge and its position in the secular world through architecture.

The intent of this chapter is to display the contribution of interrelated disciplines from archaeology and cosmology to mathematics and geometry in order to synthesise beliefs that are instrumental in redefining our concepts of ancient sacred architecture. Two main influential factors help interpret and justify our understanding of the meanings attached to symbolic geometrical compositions embedded in ancient buildings. These are cultural beliefs and mythological principles that together aided people’s representation of the universe in the form of architecture.

Before further discussion of geometry’s importance to ancient architecture, it is necessary to clarify its definition. Although the word ‘geometry’ has been defined a number of ways throughout history, one concept that unifies them all is the quantifying aspect of geometry, as demonstrated by the origin of the word in the ancient Greek words, geo as earth and metry as in measurement. Moreover, geometry defines the ordering and associations of forms.25

In ancient Egypt, geometry was referred to as a tool for ordering, marking and defining boundaries for farm areas after the yearly flood of the Nile.26 It was a system or set of principles for the law and order of measuring the earth. Plato demonstrated in Phaedrus, that Socrates clearly sources the birth of geometry and arithmetic back to an Egyptian God:

And the name of this demon is Theuth. Now, this one first found number and calculation, geometry and astronomy, and further, draughts and games of dice, and then, indeed, written letters.27

Later, geometry became part of the Egyptians’ structured education, consisting of rhetoric, dialectic, astronomy, arithmetic, grammar, music and geometry—currently referred to as the seven liberal arts. Eventually, this was passed on to Greeks and

25 The use of the term ‘form’ is frequently used in reference to geometrical shapes but originally the word comes from the Latin forma, meaning concept or idea. Therefore, forma only has the ability to describe the shape or the principle of the geometry, but on its own has no body. This can be seen in Plato’s Republic and his demonstration of the allegory of the cave. Plato and Henry Desmond Pritchard Lee, The Republic (2nd edition (revised); Harmondsworth: Penguin, 1974), p.324. 26 Robert Lawlor, Sacred Geometry : Philosophy and Practice (London: Thames and Hudson, 1982), p.6. 27 Plato and C. J. Rowe, Phaedrus (2nd corr; Warminster: Aris & Phillips, 1988), p.274. 17

Romans during the Middle Ages for their fundamental studies on harmony, architectural order and theological growth.28 The ancient Egyptian thinkers applied such findings in order to explain and illustrate a celestial existence for the wondering mind of man. For Egyptian intellectuals, geometry and numbers formalised and configured primary energies in man’s deeply embedded eternal being. As Taylor and Valpy state, ‘All mathematical forms have a primary subsistence in the soul so that prior to the sensible she contains self-motive numbers’.29

The vital position of mathematics and geometry thus cannot be underestimated when reviewing the works of ancient man—to whom the presentation of order and the demonstration of sacred rules was by far the most important responsibility of all.

Ancient Art and Architecture

Figure 1.1 The cave paintings at Lascaux, Dordogna, France, axial gallery.30

For ancient people, the initial purpose of building any structure was to fulfil their spatial needs, not only for protection from the environment, but also to accommodate and reflect their psychological and spiritual beliefs. Evidence for this claim is the work of

28 David L. Wagner, The Seven Liberal Arts in the Middle Ages (Bloomington, Ind: Indiana University Press, 1983), p.86. 29 Thomas Taylor and Abraham Valpy, Theoretic Arithmetic, in Three Books; (London: Walworth publishing, 1816), p.14. 30 Georges Bataille, Prehistoric Painting : Lascaux : Or, the Birth of Art (Great Centuries of Painting; Lausanne: Skira, 1955), p.78. 18

French intellectual, Georges Bataille (1897–1962), specifically his essays on the Lascaux caves. In these, he elucidated a unique view concerning the cave paintings at Lascaux, which he saw as the beginning of humanity (Figure 1.1). He further argued that humankind’s spatial needs have always included a spiritual dimension intimately connected with everyday life.

The apparition of the animal was not, to the man who astonished himself by making it appear, the apparition of a definable object, like the apparition in our day of beef at the butcher that we cut up and weigh. That which appeared had at first a significance that was scarcely accessible, beyond what could have been defined. Precisely this equivocal, indefinable meaning was religious.31

The use of geometric figures as a major tool, in a symbolic and technical sense, helped ancient man to perfect this purpose in his building designs. Some of these buildings still exist today; the remains of ancient constructions, for example in Egypt, India and Mexico display their creators’ endeavours to mirror what they believed to be a ‘cosmic order’ and its harmonic, stable arrangement on their earthly environment. As a result of such strong beliefs the buildings were designed in such precision and perfection for their time that effectively they have survived centuries of natural disaster and eruption, some are still standing to tell their stories.

Traditionally, historians and reviewers of ancient sacred buildings are focused on the utilitarian functions and materiality of the structures. This chapter looks beyond aspects of simple functionality to examine the social and cultural beliefs on which those structures were built and which coincide with the spiritual dimension. A chronological study of the observations of critics and historians in cultural history, such as Heinrich Wölfflin (1864–1945) or his pupil, Ernst Hans Josef Gombrich (1909–2001), provides the basis for this research and more specifically, I rely on their views of ancient architecture. Furthermore, several specific studies are included. The section on Egypt is based on the seminal treatise of French occultist, Schwaller de Lubicz (1887–1961); the section on India is founded on definitive works by American art historian, Stella Kramrisch (1896–1993) and the influential Australian scholar, Adrian Snodgrass’s writings on Buddhist art/architecture and, in particular, stellar symbolism.

31 Georges Bataille, Stuart Kendall, and Michelle Kendall, The Cradle of Humanity : Prehistoric Art and Culture (London: MIT [distributor], 2005), p.135. 19

The Symbolism of Ancient Egyptian Temples

The buildings of ancient man - those that have been defined through proportion, scale, geometry and measurements - can be studied to discover the meaning of the sacred features of a building. These mute elements are the result of canonical rules, and man’s mental processes are seen to come to life through his total awareness of beliefs and values of the period, and consequently his serious dedication is reflected in his building design.

Lubicz in his definitive work, The Temple in Man, demonstrated the profound reference to numerology in the ancient temple civilisation of Egypt. In his work, numbers not only defined the quantitative aspect of building design but attended to the more significant realm of symbolism. Symbolising the order and form of natural word. ‘… The Egyptians called these energetic principles Neters, a word which is conventionally rendered as “gods”’.32 Furthermore, throughout this core research of Lubicz is the concept of applied geometrical forms in Egypt’s temples and their symbolic function in relation to numerology. They are not simply applied as a form of abstraction, but to provoke the consciousness of what the Egyptians call ‘god’. The symbolic function of their building’s geometric design brings a sense of harmony, proportion and order that reflected the Egyptian’ beliefs.

When they drew a geometrical pattern to plan a temple, it was not out of pure interest or creativity, but the application of the unavoidable principles and beliefs that dictated the minds of the architects. Admittedly, the relationship between architecture, religion and astronomy placed applied geometry and its composition in a sacred position that symbolised geometry as a source of power. Using geometry, building designers could create a pattern with a system for achieving order, measurement and proportion. That pattern in most cases in ancient building represented their attempt to echo their understanding of the universe. As this section purely focuses on early architecture in relation to my thesis’ first hypothesis, the intention is not to speculate about the significance or meaning of a chosen example of construction, but to reveal how and why a sacred building was designed the way it was. More specifically, the focus is on the way the design included the use of sacred meaning in geometry. To use an example

32 R. A. Schwaller de Lubicz, The Temple in Man: Sacred Architecture and the Perfect Man (Rochester: Inner Traditions press, 1998), p.10. 20 to clarify this assertion, the Egyptian temples, especially the Temple of Horus, and the ancient Egyptians’ belief systems are the most relevant.

We must be able to transcribe what is in us into our mental and objective consciousness, by establishing a relationship between the life in us and observation of that life in Nature. This we find supremely well expressed by the ancient Egyptians. Their temples devoted to the spiritual conception of man. Although they never sacrificed anything for aesthetics but conformed solely to the reality of the symbol, the pharaonic builders always achieved masterpieces of harmony even in intentional deformities and ugliness—through symbolic and geometrical exactitude. Nothing is sensual for them; and this shocks our Western sense of aesthetics. Everything is solely didactic, of an esoteric nature; it is a teaching for understanding, for pure intellect, a teaching that cannot be described in explicit terms.33

The Temple of Horus at Edfu, one of the late Egyptian temples, built between 237–57 (BCE) and located in the west bank of the River Nile, is an example of precise planning and design (Figure 1.2). The structure and careful selection of location represents the significance of this temple for its people. Their aim was to build such a solid and detailed structure that it would last for centuries, would serve unborn future generations, and inform them of their important findings of universal principles of deity and belief.34

33 Lubicz, p.33. 34 In Egyptian hieroglyphs, Horus is depicted as a falcon-headed man, a Sun God. ‘Textual evidence from the Pyramid Era refers to Horus as lord of the sky or as a god of the east’. George Hart, The Routledge Dictionary of Egyptian Gods and Goddesses (2nd edn.; London: Routledge, 2005), p.74. 21

Figure 1.2 Temple of Horus at Edfu: main gateway.35

The reason for selecting this temple as one of the case studies for this chapter is its clear references to the traditional beliefs and sacred composition of structure belonging to the late era of Egyptian religion, and its multiple insights into the meaning of geometrical layout and features. The system the designer used in this temple preserves the purpose of presenting wholeness through frequent, coinciding criteria. This characteristic manner of design creates a pattern that has meaning and carries multiple layers of a belief system. The foremost part of this whole structure is the main entrance on the southern side, historically accessed only by the pharaoh or god, and the priests of the temple, and prohibited to the public.

The Egyptians regarded their land not only as being at the centre of the world but also as being the whole world. Thus, they called their country ‘that which the sun encircled’. The Egyptian cosmos was conceived primarily as consisting of three realms: the flat mountain-rimmed earth; the sky above the earth; and the atmosphere between them. The aim of that was to describe the both the Egyptian cosmos and a world of divine beings.36

35 Byron E. Shafer and Dieter Arnold, Temples of Ancient Egypt (London: I.B. Tauris, 1998), p.188. 36 Jeremy Naydler, Temple of the Cosmos : The Ancient Egyptian Experience of the Sacred (Rochester, VT: Inner Traditions International, 1996), p.13. 22

Figure 1.3 Temple of Horus: Hypostyle hall or middle hall entrance.37

The temple has two areas, the outer and inner areas as can be seen in Figure 1.3. The inner area (area 1 in Figure 1.4) was built on a raised floor in relation to the progressive height change of the walls and ceiling, thus preserving the inner area within the frame of the outer area’s stonewalls. This variation in the height of walls and lowering of the ceiling symbolised the ancient Egyptian belief of creation, or Tatenen.38

The interior of the temple is divided into three noticeable sections: the motif of the order of the universe, numerologically and hierarchically. The ritual purpose of each section is illustrated on its walls and columns. The lower section is the common area (area 14 in Figure 1.4), which allows the people and their gifts or offerings entry to the interior of the temple. The middle section (area 11 in Figure 1.4), as illustrated on the wall, is where only the kings were allowed to bring their offerings to a deity or deities. All the figures demonstrated on the walls, up to the last section, are facing towards this final area, where believers imagined their god to be.

This third, final and most sacred part of the temple (areas 1 to 10 in Figure 1.4) is designed differently, and in a most complex manner when compared to the other two areas of the temple. The third part or inner sanctum contains the beliefs of a higher

37 Shafer and Arnold, Temples of Ancient Egypt, p.187. 38 Tatenen was the name of an ancient Egyptian God. It means ‘the risen land’ and originated from the primeval mound. There is a myth that it was an upsurge from watery chaos, which might also be the reason for calling Tatenen the God of resources. ‘Tatenen ... from whom have proceeded all things in the shape of food and viands, divine offers, all good things’. Claas Jouco Bleeker and Geo Widengren, Historia Religionum : Handbook for the History of Religions, 2 vols. (Leiden: E. J. Brill, 1969), p.68. 23 realm and man’s responsibility to protect the belief in its sacredness and to keep it secret. Justifiably, it is defined by the elements that allude to earth on the side, to support and reach the cosmos. Overall, these three utterly separated areas symbolically represent the ordering of the world from one extreme (commonplace) to another (place of deities), but more importantly, they illustrate the systematic manner of this ordering.

Figure 1.4 Temple of Horus: floor plan.39

39 Shafer and Arnold, Temples of Ancient Egypt, 193. 24

In addition, the untreated floor still holding Egyptian sand, the remnants of blue paint on the ceiling, and the plant-like decorated columns, clearly indicate a representation of the universe or cosmos, as well as a place for the gods to inhabit. It is also evident that the structure of this temple is designed in a way that is precisely symmetrical and systematically ordered (Figure 1.4). Another crucial aspect to the symbolic structure of this temple is the progressive darkness that occurs while moving towards the north end.

The inner chapel lies in total darkness with no opening in the roof. The darkness of the interior represents night, and is made explicit in different ways, both in decoration and in rituals. The ceiling contains decorative elements identifying it with the night sky. In the ritual texts, the God is said to ‘sleep’ in the closed sanctuary; sleep and death being the anthropological parallels to the cosmological chaos.40

40 Ragnhild Bjerre Finnestad, Image of the World and Symbol of the Creator : On the Cosmological and Iconological Values of the Temple of Edfu (Wiesbaden: O. Harrassowitz, 1985), p.12. 25

Figure 1.5 Temple of Horus: Interior view of main entrance.41

The Temple of Horus at Edfu is based on a rectangular floor plan containing twelve immense columns in each of two halls. The front entrance of this temple is signified by two perfectly symmetrical sides of the huge threshold into the temple, and four upright niches on either side of this entrance (Figure 1.5). Like every other line (vertical or horizontal) placed in the design and construction of the temple, these are faultlessly aligned and parallel to symbolise the Nile River, connecting north to south, or symbolising water (one of the four elements). This symbolic alignment may also mark the path of the sun, rising from the east and setting in the west, or can be interpreted to symbolise the fire element.42

41 Shafer and Arnold, Temples of Ancient Egypt, p.208. 42 People in the ancient era believed that everything in the universe was formed and created based on four elements: Fire, Water, Air, Earth. The significance of this belief has been mentioned in the 26

The design principles and patterns of the Temple of Horus and many other similar ancient Egyptian edifices can be traced forward in time all the way through to the Greco-Roman period of architectural design. In contrast, the meanings and beliefs attached to these geometrical compositions and architectural elements did not continue through to their later applications, and were even given new meanings in their representation. Before reviewing this later approach, and to retain the chronological order of events and gain a clearer comprehension of the origin of symbolic meaning imbedded in geometry, my thesis continues to explore how geometry was applied in the development of the pyramids in ancient Egypt.

The Pyramids and the Symbolism of the Polyhedral

I came here in my true form upon the foundation ground of the Great Seat of Ra- Harakhte. I cause its long dimension to be good, its breadth to be exact, all its measurements to be according to the norm, all its sanctuaries to be in the place where they should be, and its hall resemble the sky.43

Djehuti, a pharaoh of ancient Egypt, affirmed the above on the foundation ground of a new temple when ordering the builder to layout the foundation for the temple dedicated to Atum.44 The theological centre of ancient Egypt was located at the north end of Cairo, as it is known today, and the builders habitually followed the same sacred arrangement and rules in their design. The canon of ancient Egyptian architecture has been kept secret and passed down to generations of builders only through clandestine training and strict theological schools.

Whosoever shall make a copy thereof, and shall know it upon earth, it shall act as a magical protector for him in heaven and in earth, unfailing and regularly and eternally.45

The sacredness of their teachings was reserved only for the ones who could maintain stringent discipline through their scientific and spiritual training.46 The first point of

Babylonian tablets. George Smith and A. H. Sayce, The Chaldean Account of Genesis (London: Searle and Rivington, 1880), p.61. 43 E. A. E. Reymond, The Mythical Origin of the Egyptian Temple (Manchester: Barnes & Noble, 1969), p.309. 44 Atum can be interpreted as ‘the complete one’, the first ancient God of Egypt that was referred to frequently by the Heliopolitan priests in the pyramid texts and religious compositions of that region. 45 F. Silva, Common Wealth: Our Legacy of Places of Power and the Transfiguration of the Human Soul (Charlottesville: Hampton Roads Publishing Company 2010), p.12. 27 exposition of this sacred knowledge to the rest of the world was through the formal teaching of Pythagoras of Samos (570–497 BC), who introduced the teachings of the ancient Greek philosopher, Thales of Miletus (620–543 BC), to ancient Egypt.47 It was under his training and study of Egyptian teaching in the temples of Memphis and Thebes in 548 BC that Pythagoras learned about geometry, numerology, cosmology and mystic sects of the divinity.48 He took this knowledge of mathematics, sacred geometry and cosmology back to the land of his birth and indirectly passed it on to his pupils in the Pythagorean School.49 It may be that this was the starting point of the spread of this knowledge to the surrounding regions, and then worldwide.50

The Great Pyramid of Khufu at Giza (2644 BC) was created based on the shape of an irregular pentahedron.51 The architectural and structural composition of the great pyramid is one of the so-called ‘Seven Wonders’ of the ancient world (Figure 1.6).52 The complex of three large and six small pyramids is aligned on the far southern outskirts of modern Cairo.53 Some historians believe that the great pyramid was created by Pharaoh Cheops to serve as his mausoleum, but other historians believe its purpose was to signify deities or the universe.

46 Tons Brunes, The Secrets of Ancient Geometry--and Its Use (Copenhagen: Rhodos, 1967), p.55. 47 Thales of Miletus was the first mathematician and philosopher who incorporated a geometrical system for measuring distances. He was the first Greek taught by Egyptian priests and was the first mathematician to attempt to measure the height of the great pyramid using geometry. K.M. and K. Moore, Freemasonry, Greek Philosophy, the Prince Hall Fraternity and the Egyptian (African) World Connection (Bloomington: AuthorHouse, 2008), p.130. 48 Iamblichus, Thomas Taylor, and Stobaeus, Iamblichus' Life of Pythagoras, : Or, Pythagoric Life (London: J. M. Watkins, 1965), p.10. 49 The students of Egyptian temples had to swear not to speak of their knowledge and their learning outside of temples, and Pythagoras was no exception. But this knowledge is still evident in his teaching of the Pythagorean Theorem, the golden ratio, Tetraktys etc. 50 Brunes, The Secrets of Ancient Geometry--and Its Use, pp.236-239. 51 The Pentahedron is a Euclidian geometrical figure, which consists of five plane sides. The name comes from the Greek, penta (five) and hedron (faces). It consists of a square base and four conjoined equilateral triangles. 52 Martin Price and Peter Clayton, The Seven Wonders of the Ancient World (London: Routledge, 1988), p.7. 53 The location of the Great Pyramids is referred to by archaeologists as ‘the Giza necropolis’ or in Arabic as ‘The Giza Plateau’. M. Lehner and W. Wetterstrom, Giza Reports: Project History, Survey, Ceramics, and the Main Street and Gallery III.4 Operations (University of Michigan: Ancient Egypt Research Associates, 2007), p.21. 28

Figure 1.6 The Great Pyramids of Giza in Egypt.54

The precise arrangement of the structure used the principle of the ‘Golden section’ and the ‘polyhedral’ (from the Greek words, poly as many and hedral as face, and normally referring to a three-dimensional geometrical shape).55 56 In that case, the ancient Egyptians knew long before Pythagoras about the theorem (the theory of proportion). American mathematician and scientist, Martin Gardner (1914–2010) used the study of the structure of the pyramids to develop his conclusion. He claimed:

The Pyramid has been built so that the face of every side is equal to the square whose edge is the height of the pyramid… and the proportion of the height to twice the base is automatically a surprisingly correct value for π.57

This example of a precise geometrical structure designed by ancient man free of any machinery resulted in a specific and harmonic geometrical composition. In symbolic terms, the pyramid that is based on the shape of a triangle was placed second in importance to the sacred circle. The sacredness of the circle, above all other geometrical shapes for ancient man, came from their deity called Nun and is illustrated in Egyptian

54 Peter Tompkins and Livio Catullo Stecchini, Secrets of the Great Pyramid (1st edn.; New York,: Harper & Row, 1971), p.100. 55 Egyptians based their system of geometry on stone cutting but, as evident in today’s literature, the Greeks did not follow the same system. In fact, they found the Egyptian language barbaric and unreliable for years after their mathematical and technological growth. 56 J. O. Urmson, The Greek Philosophical Vocabulary (London: Duckworth, 1990). 57 Martin Gardner, In the Name of Science (New York: Putnam, 1952), p.185. 29 hieroglyphs in the form of a circle or point.58 In the text of pyramids, the reference to this deity as a protector and creator has been demonstrated in several areas.

Your offering-cake belongs to you, Nun and Naunet,

Who protects the gods, who guards the gods with your shadows.59

In today’s language, we refer to the same hollow or void symbol as the number ‘0’ and, in some places, to epitomise nothingness—and in ancient Egypt, it was from this nothingness that all form initiated. The apex of the pyramid symbolises rising from the secular form into the higher realm of creation. To emphasise the sacredness and superiority of its form, Egyptians applied gold or more durable materials to this part of the structure. The entire multifaceted dimension of the great pyramids comprises significant geometrical composition that represents ancient beliefs and sacred symbolism on their way to uncovering the source of creation. The ancient Greek historian Herodotus (484–425 BC) was the first thinker who thoroughly investigated the great pyramids and stated:

Twenty years were spent in erecting the pyramid itself: of this, which is square, each face is eight plethora (820 feet), and the height is the same; it is composed of polished stones, and jointed with the greatest exactness; none of the stones are less than thirty feet. This pyramid was built thus; in the form of steps, which some call crossae, other bomides.60

The reference to the Greek terms crossae and bomides at the end of the passage refers to a construction technique that can be translated as ‘battlements’ and ‘little altars’. In addition, Herodotus attests to earlier mentioned findings of the Golden section when he demonstrates the area of each triangular surface is equivalent to the square of the vertical height.

58 Nun or Nu, father of Sun God Re, believed to be the creator who began the universe. In some cases, it is translated to ‘primitive water’. Geraldine Pinch, Egyptian Mythology : A Guide to the Gods, Goddesses, and Traditions of Ancient Egypt (New York: Oxford University Press, 2004), p.173. 59 James P. Allen and Peter Der Manuelian, The Ancient Egyptian Pyramid Texts (Writings from the Ancient World; Atlanta: Society of Biblical Literature, 2005), p.301. 60 Herodotus and Harry Graham Carter, The Histories of Herodotus of Halicarnassus (World's Classics; Oxford University Press: London, 1962), p.131. 30

Figure 1.7 The Great Pyramids of Giza in Egypt: aerial view.61

Furthermore, there are certain numerological aspects of the great pyramids that clarify the purpose of their design. There are nine pyramids (Figure 1.7) in total, three great and six smaller in size. The occurrence of the number nine as the overall number of pyramids symbolises the Grand Ennead—the symbol of union and creation.62 According to The Leiden Papyrus X, this is: ‘The offspring of the nine-times-unity of neteru (or deities male/female)’.63

In contrast, there is the appearance of the number three, on the three-sided triangle, the three great pyramids and the chambers inside, which each signify the aspect of triune. ‘Establish the triangle and the problem is two thirds solved’.64 The sacredness of the number three and its divine position has been represented in different forms in many

61 Kathryn A. Bard, An Introduction to the Archaeology of Ancient Egypt (Oxford: Blackwell, 2008), 136. 62 In Egyptian mythology a cluster of nine deities begins with Atum, followed by Tefnut and Shu, who gave birth to Geb and Nut whose children are Osries, Isis, Nephthys and Set, called Grand Ennead. J.A. West, Serpent in the Sky: The High Wisdom of Ancient Egypt (London: Julian Press, 1987), pp.66-68. 63 C. Radcliffe, The Leyden and Stockholm Papyri, Greco-Egyptian Chemical Documents from the Early 4th Century Ad (Cincinnati: University of Cincinnati, 2002), p.50. 64 Pythagoras, The Golden Verses of the Pythagoreans : A New Translation of the Golden Verses (London: The Shrine of Wisdom, 1929), p.42. 31 traditions. In ancient Egypt, the doctrine of the Divine Triad began after the God Atum (‘formless’–referring to its source in watery chaos), and took shape in Osiris, Isis and Horus. Some researchers and archaeologists, based on their gathered evidence, have explained the meaning behind ancient Egyptian numerology and its symbolism. The American astrologist, Greg Nielsen (1949-) in his book Pyramid Power revealed:

The sides of the great Pyramid, facing the four cardinal points, signify extremities of dark and light (west and east) and the extremes of cold and heat (north and south). The base of the pyramid further represents to the student the four material elements of nature from which the body of man is formed: air, water, fire, soil. The face of the pyramid, being a triangle signifies the triune within every object in nature. The twelve signs of the zodiac appear also to be represented by the total number of lines and faces of the pyramid. The spiritual centres of man are represented by three main chambers of the pyramid as the heart, the brain, and the reproductive organ.65

There is another noteworthy aspect of the great pyramids, significant both metaphorically and geometrically. That is the angle of inclination above the horizon of the so-called airshaft in the south of the great pyramid of Giza, which is placed precisely on a 45-degree angle. The position of the sun in autumn, about mid-October, similarly reaches 45 degrees and consequently, at that time the sun’s position is exactly midway between sky and earth.

So far, this chapter has illustrated the importance of basic geometrical patterns and their existence throughout the very early era of civilisations. It has also been demonstrated how portions of the ancient geometric system—geometry applied as an image of the supremacy of God and as a reflection of the universe—are not similar to today’s application of geometry. As the French occultist, R. A. Schwaller de Lubicz elaborated in his thorough examination on sociological and architectural development in historical Egypt Before the Christian Era (BCE), the knowledge and awareness of techniques gave men social power, and that may have been the reason why ancient thinkers and rulers were quite protective and secretive about their learning—in order to preserve their position of superiority over others.66 Further study on the same subject are presented

65 Max Toth and Greg Nielsen, Pyramid Power : The Secret Energy of the Ancients Revealed (Wellingborough: Aquarian, 1988), p.29. 66 R. A. Schwaller de Lubicz, The Temple in Man: Sacred Architecture and the Perfect Ma n (Rochester: Inner Traditions press, 1998), p.47. 32 below, but in a different region and from a different outlook, to illustrate other approaches to applied geometry and its meaning in ancient architecture. The aim is to further support the observations already made about applied geometry and numerology in relation to ancient Egypt temples.

Number, Symbolism and Sacred Geometry in Hindu Temples

The construction of Hindu temples was based on circle, square and triangle patterns and founded in certain beliefs.

The Hindu temple is an imago mundi; its configuration is a semblance of the cosmogeneric procedure of finite space from the infinite; it is also a similitude of the production of time from Eternity. This symbolism is incorporated into the temple in a number of ways… 67

The Hindu temple is entrenched in the Vedic tradition and the architectural principles/rules dictated in the sacred treatises of India. The purpose of these rules is revealed in its form and proportion. Every element in a Hindu temple has a definite position and is set as a part of a complete whole.68 Wherever it stands, regardless of its size, age and material, the architectural ritual is to regulate all the elements based on a square form—as the Vastupurusamandala.69 The square is a result of a circular form. According to Indian architecture the perfect form of square and circle not only validates the plan of the Hindu temple but also harmonically regulates the vertical section and elevation. Nonetheless, the sacredness of the square is greater than that of the circle and consequently, the square is the fundamental form of Indian temple architecture.

67 A. Snodgrass, Architecture time and eternity (Delhi: Pradeep Kumar Print, 1990), p.128. 68 S. Kramrisch, The Hindu Temple (Delhi: Motilal Banarsidass Publisher, 1976), pp.7-8. 69 Vastupurusamandala compresses three key terms: ‘Vastu: the extent of existence in its ordered site is beheld in the likeness of the Purusa. Purusa: the origin and source of existence. The plan makes the site of the building in his image, which is his form. The plan of the building is in the likeness of the Purusa, or of the totality of manifestation. Mandala: denotes any closed polygon. Square is its essential form, it can be converted into triangle, hexagon, octagon and circle of equal area and retain its symbolism’. Kramrisch, 1976, pp.21-22. 33

Figure 1.8 Sri Yantra: Early coloured diagram.70

The composition of the Hindu temple was regulated precisely by religious principles and ritual diagrams. As such, the Sri Yantra formed in some Hindu temples is based on Kashmir Ś haivism, (Figure 1.8). Sri Yantra can translate as ‘glorious diagram’ or ‘divine instrument’.71 72 In eastern mysticism, the Sri Yantra is a sacred symbol to signify balance and control, but it is commonly a motif to signify the unification between male and female, bringing their energies into harmony free of any chaos and diversity.73 Its geometrical diagram is composed of nine interconnected equilateral and isosceles triangles that in the Indo-Arya language (the ancient Hindi language) are

70 Ajit Mookerjee and Philip S. Rawson, Yoga Art (Boston: New York Graphic Society, 1975), p.19. 71 The term Kaśmir Śhaivism refers to a Hindu philosophy on developing and nurturing the inner being and also creating harmony between opposite elements in the universe to achieve balance. 72 Yogani, Advanced Yoga Practices - Easy Lessons for Ecstatic Living, Volume 2 (Tennesse: Ayp Publishing, 2010), p.526. 73 In Hindu spiritual practice, the sacred representation of this symbol holds a very strong position in relation to mental and spiritual growth: ‘Sri Yantra, the diagrams in which energies are concentrated links visual parallels to the verbal mantras. They focus the energies of the meditator, and correlate all his previous efforts and knowledge into single divine images. The most important part is the Sri Yantra, composed of nine interpenetrating triangles, symbolizing male and female, which give rise to the circuits of other triangles. It presents a condensed image of the whole of creation’. Philip Rawson, Tantra : The Indian Cult of Ecstasy (London: Thames and Hudson, 1973), p.33. 34 called Navayoni.74 This interaction is the source of and outgrowth from bindu, or the spot that signified the meeting point of the earthly and the divine realms. From there the triangles appeared, four pointing downward and five pointing upward, delimited by a circle connecting eight petals of the lotus flower, within another circle that again connects sixteen petals of the lotus, all contained within a square.

In the middle are the power point (bindu), visualizing the highest, and the invisible, elusive centre from which the entire figure and the cosmos expand. The triangles are enclosed by two rows of (8 and 16) petals, representing the lotus of creation and reproductive vital force. The broken lines of the outer frame denote the figure to be a sanctuary with four openings to the regions of the universe.75

Microcosmically, there are even more figurative visual illustrations and symbolical significances attached to Sri Yantra. In order to justify my arguments in upcoming chapters of this thesis, it is necessary for me to review them here. Closer inspection reveals that the synchronisation of the major figures in Sri Yantra has been planned in a very careful and precise manner to generate hidden meaning and express veiled ideas that can only be understood by the attentive observer.

Within each triangle are two other triangles, of alternating opposing polarity in terms of the direction of pointing that represents male and female principles. Altogether, their overlaps constitute a total of 43 small triangles. Right through the middle of this is the 76 dot, the bindu, who is Śiva, the witness, or consciousness.

Also, by joining the petals in the first row of eight, the outline of the octagon comes to life, and if applying the same technique on the second row of sixteen petals, the shape of a hexadecagon appears, approaching the form of a circle. Numerically, the octagon is related to eternal existence (or God) and universal balance and, when applied to form a hexadecagon, it is a circle endeavouring to change its appearance and shape to a

74 The term Navayoni (Nava means the number nine and yoni means triangle) is one of the most sacred geometrical compositions which has been applied in ancient Hindu temple designs and ritual symbolism. Madhu Khanna, Yantra, the Tantric Symbol of Cosmic Unity (Rochester: Inner Traditions, 2003), p.81. 75 Kathleen Kuiper, The Culture of India (1st edn.; New York: Britannica Educational Pub., 2011), p.111. 76 Subhash Kak, Architecture of Knowledge : Quantum Mechanics, Neuroscience, Computers, and Consciousness (New Delhi: Centre for Studies in Civilization, 2004), p.6. 35 square.77 Thus, both geometrical shapes can be referred to as intermediary configurations.

In the Sri Yantra, due to their position in relation to the circle (believed to symbolise source, wholeness and divinity) and the square (believed to symbolise earth and immutability), the octagons emphasise their ability to act as progressive or transitional figures. The shape of the octagon found in Hindu temples was subsequently applied repetitively in art and architecture during the late Renaissance and Baroque eras.

These geometrical shapes are not only significant in Hindu temples. Throughout the history of architecture, the application of the mundane shapes of triangles, circles and squares created a metaphysical unity in a number of sacred buildings. The three-sided polygons ‘were conceived by the ancients to explain the secret order of the cosmos’.78 Because of its structural arrangement, the joining of three points is believed to symbolise the path to existence that unifies any division of those paths through it. In ancient Indian design, the triangle is a symbol of motherhood, or the mother of all forms.

Him who Strode, widely pacing, with three stepping forth over the realms of the earth for freedom and for life.79

In Hinduism, the number three symbolised Trimurti, or ‘three forms’, that come as one to stabilise the cosmic.80 Furthermore, it symbolised the Trinity. Triangles are also believed to symbolise heaven, and one of the four elements of classical belief—that of fire.81 The direction that the triangles point is symbolic, too. If the triangle is pointing upwards, it symbolises fire and if pointing downwards, it symbolises water. The important role of these dual elements, fire and water, is that the surroundings cannot be visible without fire, and conversely water brings flow and life to the lifeless.

77 J. Kappraff, Beyond Measure: A Guided Tour through Nature, Myth, and Number (Singapore: World Scientific, 2002), p.127. 78 Tompkins and Stecchini, Secrets of the Great Pyramid, p.119. 79 Hermann Grassmann, Rig-Veda (Leipzig: F. A. Brockhaus, 1876), p.105. 80 The Trimurti is an ancient Hindu belief in the three deities Brahma, Vishnu and Shiva – famously referred to as ‘the Hindu Triad’, which together shape and balance the Hindu Universe. Arvind Sharma, Classical Hindu Thought : An Introduction (Boston: Oxford University Press, 2000), p.21. 81 The origin of the four classical elements (earth, water, fire, air – later Aristotle added the fifth element aether) can be traced back to the tenth century before Plato. Plato, (428-348BC) the ancient Greek philosopher and mathematician was the first to describe these elements in his book Timaeus, section XIII, where he also assigned a regular solid to each element. 36

Consequently, placing these two contradictory elements together, just as male and female into one compositional figure, justifies the purpose of unification and harmonisation between the two. In addition, right in the centre of Sri Yantra where, as mentioned earlier, the bindu was located. One can also perceive an alternative representation of the ancient symbol of the eye looking right through the core triangle.

An equilateral triangle with an eye within symbolizes the Deity looking out from heaven. In Egypt it was changed to the all seeing eye of Orsis looking down from heaven.82

The same fundamental blueprint of the geometrical pattern of Sri Yantra formed the basis of the design of Hindu and Buddhist temples. It has been referred to as the most essential and sacred of all patterns, the ‘mirror of the cosmos’.83 Temples, such as the Kandariya temple in Khajuraho and Borobudur temple (Figures 1.9–1.10), applied these principles of configuration, not only in their plans but also their elevations.

Figure 1.9 Borobudur Temple in Central Java.84

82 James Churchward, The Sacred Symbols of Mu (New York: I. Washburn, 1939), p.142. 83 Martin Brauen, The Mandala : Sacred Circle in Tibetan Buddhism (1st edn.; New York: Shambhala; Random House, 1997), p.21. 84 Marcello and Anita Tranchini, 'Borobudur & Bali Photos', , accessed 7 December 2012. 37

Figure 1.10 Borobudur Temple: aerial view.85

The silhouette of a mountain reaching towards the sky is identical in overall form. The display of a common centre of gnomonic growth86 echoes the celestial and cosmic principle, and the same method can be found in Pythagoras' Tetraktys.87 88 As Robert Lawlor (1939–), Irish symbologist and mythographer and a member of Aurovill in India, states:

This is time as growth: an eternal expansion of growth upon growth, an evolution, and one might say, belonging to the conscious energies which transcend the forms and energies through which they manifest, a growth whose eternally enduring continuation is

85 Jan Fontein et al., Ancient Indonesian Art of the Central and Eastern Javanese Periods ([New York]: Asia Society; distributed by New York Graphic Society, 1971), p.28. 86 Gnomonic growth has been defined as an object or a shape that is in the progression of repeating itself systematically to become larger though preserving its original outline or shape during its development and maturation. D'arcy Wentworth Thompson, On Growth and Form (2d edn.; Cambridge: University Press, 1968), p.286. 87 The gnomonic growth has been defined as an object or a shape that is in the progression of repeating itself systematically to become larger though preserving its original outline or shape during its development and maturation process. D'arcy Wentworth Thompson, On Growth and Form (2d edn.; Cambridge: University Press, 1968), p.286. 88 The Tetraktys is an equilateral triangle formed by 10 points and was a major symbol of the Pythagoreans. The numerology of its composition 1, 2, 3, 4 and 10, individually and in sum, symbolised the sacred beliefs of Pythagoreans and was emphasised in several prayers, for example: ‘Bless us, divine number, thou who generated gods and men! O holy, holy Tetraktys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the key holder of all’. Tobias Dantzig and Joseph Mazur, Number : The Language of Science (The masterpiece science edition. edn.; New York: Pi Press, 2005), p.42. 38

at once mimicked and yet attested to in the growth of the cells, fibers and living nature. In this way through the form develops through the pulsating rhythmic expansion of gnomonic growth.89

It becomes evident that this successive growth bounded on four sides by the floor plan acted as a conducting instrument for the design of the elevation of Hindu temples, and in some cases the use of the Golden section to achieve the perfect, four-sided square.90 The whole structure is shaped as a step pyramid, rising on nine platforms and topped by a round pinnacle in the centre. The hierarchy between the levels is significant. The lowest six platforms are square and in some cases have offsets and niches next to straight walls that are mirrored on each platform. These first steps, or square platforms, represent Kamadhatu—or the realm of desire. Stepping up, the next five square platforms represent Rupadhatuor—the realm of earthly/mental mediations.91 Finally, the highest three platforms in the circle form represent Arupajhana, or the unearthly realm—the divine mediation. Throughout the centuries, further meaning and cultural beliefs influenced the form of the plan and volume of these sacred structures but the celestial order in which they believed, harmonically protected the fundamentals of the geometrical composition of the Sri Yantra.

Sri Yantra, in its formal content, is a visual masterpiece of abstraction, and must have been created through revelation rather than human ingenuity and craft.92

There are many more of these temples that demonstrate symbolic meanings and beliefs attached to their geometrical integration, but further description exceeds the scope of my thesis. In the following chapter, I include sections that address the ancient aspects of applied geometry and belief systems in order to illustrate the aims and notions of more current examples.

89 C. Bamford, Homage to Pythagoras: Rediscovering Sacred Science (New York: Lindisfarne Press, 1994), p.76. 90 The golden section or golden mean was first mentioned by Pythagoras, and in Greek is known as a ratio that is defined by the number of phi (φ) which is 1.61803. The result of applying it in art and architecture was to achieve aesthetic beauty. The Renaissance cosmologist and mathematician, Kepler, later called it ‘the divine proportion’. H. E. Huntley, The Divine Proportion: A Study in Mathematical Beauty (New York: Dover Publications, 1970), p.24. 91 C. P. S. Menon and L. N. G. Filon, Early Astronomy and Cosmology : A Reconstruction of the Earliest Cosmic System (History of Science Library; London: G. Allen & Unwin Ltd., 1932), p.52. 92 Ajit Mookerjee and Madhu Khanna, The Tantric Way : Art, Science, Ritual (London: Thames and Hudson, 1977), p.82. 39

Derivations of the Hindu Temple in Western Geometric Philosophy

To demonstrate a more recent approach to the ancients’ knowledge and their view on the creation of universe, the twentieth century Russian thinker, George Gurdjieff’s (1866–1949) theory provides a clear instance. His hypothesis is rooted deep in the old spiritual and symbolic teaching of east and west.

Everything in this universe can be weighed and measured. The Absolute is as material, as weighable and measurable, as the moon, or as man. If the Absolute is God it means that god can be weighed and measured, resolved into component elements, ‘calculated,’ and expressed in the form of a definite formula.93

Figure 1.11 The Enneagram diagram by Gurdjieff.94

In his demonstration of this particular area of fascination, he used various symbols such as the Enneagram (Figure 1.11)95 and the Ray of Creation.96 Gurdjieff used both symbols to explain his concept, ‘The Fourth Way’, which is a system for growth beyond the mind, body and emotional capacity, and attends to the issue of humans in relation to

93 B. Mouravieff, Gurdjieff, Ouspensky and Fragments (Devon: Praxis Research Institute Incorporated, 1997), p.86. 94 Anthony Blake, 'The Enneagram', , accessed 20 December 2012. 95 In the field of geometry, the term Enneagram is used to describe a nine-sided polygon, which sometimes appears in a shape of a nine-pointed star to signify unity and perfection in the universe. Enneagram comes from the ancient Greek tongue – Ennea: nine, and gram: illustration. 96 The symbol of Ray of Creation is a cosmological, systematic diagram that has been illustrated by Gurdjieff to clarify his attempt to teach the concepts of ‘the fourth way’ and the law of the universe. 40 the universe.97 In the Enneagram (Figure 1.11) the nine-pointed star inside a circle returns to some esoteric concepts in Islamic Sufi mysticism, and can also be traced back to the practice of fourth century Christian thinker, Evangrius Ponticus (345–399 AD), who spent his lifetime training in the temples of ancient Egypt in order to demonstrate the list of evil thoughts through numerology. He states, ‘The first thought of all is that of love of self; after this, the eight’.98

The Ray of Creation is another allegory to illustrate the concept of the formation of the universe through the use of numerology and past beliefs. The Ray of Creation is an eight level, orderly figure that communicates Gurdjieff’s law of octaves. It originated from the prevailing cosmological theory in ancient Greece called the ‘Geocentric model’,99 defining the relationship between the various levels of being that is progressive and diverse. The final stage is to reach the level of Absolute. For that reason, the Absolute is the unity between these levels, which demonstrates the creation of the universe as one amalgamated entity. Gurdjieff’s pupil, Peter D. Ouspensky (1878–1947), a Russian philosopher and esotericist, quoted Gurdjieff to explain the law of octaves:

The law of octaves in all its manifestations was known to ancient knowledge. Even our division of time, that is, the days of the week into workdays and Sundays, is connected with the same properties and inner conditions of our activity which depend upon the general law. The Biblical myth of the creation of the world in six days and of the seventh day in which God rested from his labours is also an expression of the law of octaves or an indication of it, though an incomplete one.100

Ouspensky further developed the idea of ‘The Fourth Way’ in his own terms, and placed this concept as a core concern of his research into finding the truth about creation and the well-preserved beliefs of the ancients. In his view, the only way to find the absolute truth is to look back into the history and civilisation of the East, and to understand their symbolism and the meaning behind it. Ouspensky believed that ancient

97 This idea demonstrates the comparison and relationship between Gurdjiff’s doctrine and Indian symbolism. 98 W. Harmless and R. R. Fitzgerald, 'The Sapphire Light of the Mind: The 'Skemmata' of Evagrius Ponticus ', Theological Studies, 62/3 (Sep 2001), p.498. 99 The Geocentric Model is the ancient belief that Earth is the centre of the universe with the other planets, and the sun and moon, circulating around the earth. 100 R.J. Defouw, The Enneagram in the Writings of Gurdjieff (Indianapolis: Dog Ear Publishing, LLC, 2011), p.47. 41 architectural works could be read just like a book—but with emotion. He further developed the doctrine of the fourth dimension in relation to Euclidian geometry; indicating how three-dimensional geometrical solids hold indefinite points, lines and surfaces that are hidden from the naked eye. Therefore, this existence of infinity is the stage of the fourth dimension.

The findings of Gurdjieff and Ouspensky on esoteric aspects of ancient symbolism, geometry and patterns of meaning in spiritual practices of the past influenced many thinkers around the world, including American architect, Claude Bragdon (1866–1946), who began to establish his view on the fourth dimension and the Hypercube. Bragdon was a theosophist before he became familiar with the idea of the fourth dimension and the possibility of its existence. Evidence for his development from theosophy into metaphysics is in his earlier writing. His 1912 work, Man the square: A higher space parable has more to do with his spiritual views than his 1920 work, New Concepts of time and space, which has a greater focus on scientific aspects of spirituality. In between these two works, Bragdon published other articles and books that clearly demonstrated his view on the progression from two dimensions to three dimensions, and then to a fourth. It is important to mention that the 1920s was a time of transformation of spiritual meaning, from within a religion to one founded in the pseudo-scientific approach of Ouspensky and Bragdon. This era was the point where religious spiritualism and its systems of meaning were threatened and eventually submerged.

Figure 1.12 Claude Bragdon: the projections made by a cube in traversing a plane.101

In the demonstration above (Figure 1.12), Bragdon illustrated what a three-dimensional cube (or any object or being) would understand of its higher dimension. Motion through space—or as Bragdon himself referred to it, through ‘the universe’—crosses the border of ‘reality’ at varying positions and shows the association between two and three dimensions that is the core to envisaging the transition to the fourth dimension. The concept of a higher dimension remained a theoretical concept until Albert Einstein’s theory of relativity surfaced in the late nineteenth century. This idea of a fourth dimension will be established further in Chapters Five and Six.

101 Claude Fayette Bragdon, A Primer of Higher Space (the Fourth Dimension) (Rochester: The Manas press, 1913), plate 30. 43

Conclusion

The first section of this chapter described several examples of the meaning revealed by geometrical patterns in the ancient eras. It demonstrated that the origins of geometrical patterns within the history of architecture had underlying but powerful meanings attached to them. These geometrical compositions it will be argued later are mute and ineffable elements in design practice today, lacking the meaning of their historical and cultural connections. The extent to which these residual meanings have changed applied geometry in modern architecture will continue to be evaluated in later chapters. What is the residual meaning and how is it discovered and expressed? In Chapter Two, I take this historical analysis a step further to find the answers to these questions by describing the expansion, transformation or expunging of earlier beliefs in applied geometry and analysing their role and value in architecture.

Chapter Two. On Architecture and Medieval Geometry

Chapter One described and analysed primitive beliefs that existed BCE, investigating ancient architecture in countries such as Egypt and India. This introducedthe application of special geometrical form to convey symbolic meaning in ancient civilisations. The focus now moves to the era between the birth of Christ and the Middle Ages (fifth century). The two key ideas presented in this chapter are based on theories that emerge from two texts, which later set clear guidelines for the production of art and architecture. These are De Civitate Dei, by St Augustine of Hippo (354–430), and Divine Comedy, by Dante (Durante degli Alighieri, 1265–1321).

Scrupulous examination of these two texts aims to form the main contention of this chapter, which is based on the subject of ‘meaning’ in relation to symbolism in architecture. It seems that what was valued as ‘meaning’ during the early Christian era, was motivated by sacred scriptures. In contrast, as generally understood in contemporary practice today, meaning in architecture does not need to have a spiritual aspect, nor is it always a simple expression of function. An example is the mission statement by the renowned architectural company, ‘Zaha Hadid Architects’. It states, ‘We create transformative culture, corporate, residential and other spaces that work in synchronicity with their surroundings’.102 Similar instances can be find by other well- known architectural firms that have defined different aspirational factors in their practice as designers (for example, Frank Gehry and Peter Eisenman). Visual illusion plays a large role in the ‘reading’ of their architecture. Whereas spiritual orthodoxies relied upon the ‘reading’ of buildings as visual texts to strongly convey their power, contemporary architecture strongly trusts the power of self-expression to generate an avant-garde design.103

102 Zaha Hadid, 'Zaha Hadid Architects', , accessed 12 June, 2011. 103 This claim can be justified through the study of the history of medieval cathedral buildings. Notre Dame in Paris is an obvious example of such cathedrals in that era which stood to represent authority, superiority and power through their architectural design. 45

The Beauty of Order, Harmony and Balance

In relation to the first hypothesis of my thesis, the intention of this chapter is to demonstrate the importance of the further development of, and a different approach to, the application of geometry in architecture. The evolution of architecture throughout these historical eras directly influenced the forthcoming transformations of both the inner and outer skins of any significant structures.

To grasp allusion and metaphor in architecture, a firm understanding is needed of the metaphors associated with building—provided by influential early religious works such as De Civitate Dei or The Divine Comedy. In particular, Augustine provides a metaphorical interpretation of the geometry of city plans. In his De Civitate Dei (City of God), the ‘grace’ of the Christian God is articulated in the layout of the town and this architectural expression becomes a spiritual lesson for its population.104

Is there a geometry that expresses the metaphor of the De Civitate Dei? The great thinkers of the Holy Roman Empire certainly believed so. It is common in architecture to merge metaphorical105 and literal106 interpretations, but can St Augustine’s book be taken literally, rather than metaphorically?107 To answer these questions, it is necessary to investigate how Augustine, in the De Civitate Dei, reached his geometrical and mathematical findings. The understanding of Augustine and his works by other scholars should be critiqued, and additionally the structure and geometry of the De Civitate Dei must be viewed in the way Augustine wished them to be perceived by one is to understand the implication for the design of buildings.

104 In this context, ‘grace’ given by God is the power and favour He shows to believers. 105 The term ‘metaphoric’ is used here to define a symbol, an expression or action that is a reflection of a belief or idea. Also, in this thesis this term is used to validate the idea that a non-literal representation and its real source/meaning only can be revealed to an informed beholder. This is based mainly on Saussurean tradition and the study of semiotics and the idea of signified and signifier. 106 The term ‘literal’ is used in this thesis to define the direct representation of an idea or belief: in other words, a method of visualization not influenced by the artist or architect, but only and accurately construct on a given idea or a text. 107 This is based on the idea that merging metaphors and a literal reading is common in architecture, for example the contemporary readings of Eisenman’s ‘The Fold’, and of Heidegger’s ‘Building Dwelling Thinking’. 46

The Representation of the Cross as an Architectural Symbol

For Augustine, numbers represented far more than purely a functional use in buildings; numbers were a way to decode spiritual meaning to reveal the unexplained mysteries of Christianity through their symbolism.

Philosophy has two principal instruments, the mind and its expression. The mind is enlightened by the Quadrivium (arithmetic, geometry, astronomy, and music), its expression, elegant, reasonably ornate, is provided by the Trivium (grammar, rhetoric and dialectic).108

Augustine emphasised that knowledge of the numbers found in sacred scripture is critical for understanding the order of the universe and the meaning of creation, as can be seen in this quote from The Wisdom of Solomon [Wisdom XI, 21]: ‘God orders everything in measure and number and weight’.109 Augustine reflected on this passage and wrote:

And, therefore, we must not despise the science of numbers, which, in many passages of Holy Scripture, is found to be of eminent service to the careful interpreter.110

In this chapter, I will explain in detail how numerology and geometry were used in the design of medieval era architecture. I shall also rely on additional evidence presented in the ground-breaking work of John James (1923-1993) on cathedrals. In doing so, the emphasis continues to highlight the reasons for the builder’s purposefully integrated geometry. As James explains:

In the middle ages people did not see that the instrumental function was the only attribute required of a building. Beyond the events and needs of our world lay the hierarchies of other beings and existences. This is not something we readily understand today, for where science provides the answers there are no mysteries. They believed that behind the superficial appearance of things lay a greater reality that would, if only it could be tapped, reveal the true nature of the universe. The ultimate mystery was as real to them as the laws of nature are to us. They not only tried to find ways to understand

108 Malcolm Miller, Chartres Cathedral (Pitkin Pictorials, London, 1980), p.126. 109 Augustine and J. Hammond Taylor, The Literal Meaning of Genesis, 2 vols. (New York: Paulist Press, 1982), p.108. 110 Augustine and J. W. C. Wand, St. Augustine's City of God (London: Oxford University Press, 1963), p.475. 47

them, but, as we do with scientific discoveries, attempted to apply what they had learnt to what they did. The results of their investigations were expressed in numbers and geometry, not unlike our formulae. They were applied to building so that the structure would reflect the Divine, and by reflecting it, illuminate man’s way.111

This critical perspective of architectural artefacts, recognised by James, further demonstrates that the secular world that shaped the foundation of our views of reality, was simply an unclear reflection for the medieval thinker, who believed instead that clarity could be found through the spiritual world.

111 John James, Chartres, The Masons Who Built a Legend (London, Routledge and Kegan Paul, 1982), p.66.

Figure 2.13 The Creation. Bible Moralisée, France, 1250.112

Figure 2.14 Geometrical analysis of ‘The Creation’, by the author.

112 G.B. Guest, Bible Moralisée (Isd, 1995). 49

Augustine’s teachings were based on his numerological beliefs and the sources from which they were derived. He believed in the Platonic and Pythagorean interpretations of numbers and geometry. Italian archaeologist, Gianluca Padovan (1948–) explained the influence of Plato’s works in relation to Augustine’s theology:

For Augustine, Plato’s account of the Creation in the Timaeus was a wonderful anticipation of Christian teaching. With its doctrine that the ultimate reality is in the immortal world of ideas and that the sensible world is its imperfect shadow, Platonism was for him supreme among philosophies.113

Testament to his partiality to Plato’s works is Augustine’s own passage in the De Civitate Dei: ‘There are none who come nearer to us than the Platonists’.114 The other viewpoint that helps us to understand the reason behind Augustine’s interest in numerology comes from Roman philosopher, Anicius Manlius Severinus Boethius— known simply as Boethius (480–525 AD). Boethius stressed the importance of understanding numbers in order to see the meaning behind the elements of the universe. He further explained that numbers could assist and direct the human mind to justify how the universe has been constructed and ordered. He said, ‘... geometry offers the notion of stable magnitude.’115

To enhance the above reflection, Augustine, in his other writings, openly expounded the eternal harmony that can be seen in architecture when it articulates the correct geometry and numbers and mirrors the design of the universe116 (Figures 2.13–2.14). Therefore, is it possible to reduce theology to geometry?

My conclusions support the overall hypothesis of this thesis, by demonstrating that belief systems, and their origins, were attached to selected geometrical compositions and numerological arrangements of architectural elements during the medieval era.

In the above passages, there is a noticeable resemblance between the thinking of Augustine and Plato. The German Neo-Hegelian philosopher, Richard Kroner (1884–

113 Gianluca Padovan, Civita Di Tarquinia : Indagini Speleologiche, Catalogazione E Studio Delle Cavità Artificiali Rinvenute Presso Il Pian Di Civita E Il Pian Della Regina (Oxford: Hadrian Books, 2002), p.304. 114 Augustine and Wand, St. Augustine's City of God, p.304. 115 Boethius and Michael Masi, Boethian Number Theory : A Translation of the De Institutione Arithmetica (with Introduction and Notes) (Amsterdam: Rodopi, 1983), p.72. 116 Augustine and Carroll Mason Sparrow, De Libero Arbitrio Voluntatis; St. Augustine on Free Will (Charlottesville: The Dietz Press, 1947). 50

1974) argued, ‘Without Plato’s Republic no De Civitate Dei could have been defined by St Augustine.’117 It is difficult to deny the impact of ancient Greek philosophy on the evolution of the Christian tradition, and it must be remembered that the earliest Christian thinkers harboured an undeniable affinity for Platonism. Emerging from the Dark Ages, Catholicism held Aristotelianism in the highest esteem, while the Protestant Reformation was in many ways a return to the Platonic school of thought.118 In fact, Plato’s Republic is a celebrated work that presents and justifies a political theory. Although in his writing Plato undeniably demonstrated the wrongness of democracy quite forcefully, at the same time he developed the idea of the earthly limitations of ownership. Plato claimed that:

It didn’t matter whether the ideal state exists, or ever will exist, because in heaven there is laid up a pattern of it to be seen by him who has eyes, and he who sees it will dwell there.119

Plato believed that the mortal world in which we live provides only a metaphysical reality, and only through spiritual meditation can we escape the illusion of mere appearances and recognise what is truly real.

On the other hand, the reason Augustine found Pythagoras so fascinating was the link Pythagoras posited between geometry and cosmological meanings; his representation of the number one as the ideal number, and the circle as the ideal shape are examples. According to Pythagoras, they both represent God and oneness and the perfection of creation. Christian teachers and philosophers use numbers and the meanings associated with them into their building design. In other words, mathematics is the key to explaining some points in the Bible. Egyptian theologian, Origen (184–253) wrote: ‘God made the world according to some definite number, predetermined by himself’.120 Therefore, it is no surprise to see that Augustine structured his book in the symbolic figure of the crucified Christ, and as it is presented in the following pages, he based its

117 Richard Kroner, Speculation and Revelation in the Age of Christian Philosophy (Philadelphia: Westminster Press, 1959), p.191. 118 Ibid. 119 Plato and Lee, The Republic, p.27. 120 Origen et al., On First Principles, 5 vols. (Sources Chrétiennes; Paris: Cerf, 1978), p.74. 51 form on numbers.121 To illustrate why he sought such a precise construction, in De Civitate Dei he elaborated on his approach:

It follows that the whole redeemed city, that is to say, the congregation or community of the saints, is offered to God as our sacrifice through the great High Priest, who offered Himself to God in His passion for us, that we might be members of this glorious head, according to the form of a servant.122

He gives this interpretation of the literary theology of the past that is clearly based on his philosophical and mathematical studies. For Augustine to build into De Civitate Dei, the motif of the crucified Christ was a natural act, since he sees them both (Cross and book) as a summary of God’s creation and a reflection of the universe generally. The significance of cruciform symbolism in De Civitate Dei is clearly and succinctly demonstrated in a sermon that illustrates the ideas expressed above:

That very cross contains in itself a great mystery; its position is such that it reaches to the heavens, its lower part adheres to the earth. Fixed in the depths it touches hell; its latitude seeks out the sides of the world, for by the suffering of the cross Christ profited the angels in heaven whose number had been diminished by the apostate angel but is daily filled up by the souls of the faithful; he profited us who are on earth, as well as those who because of original sin are held in hell. But he profited those, too, who lived in different parts of the world; the cross, laid down, reaches out to the four sides of the world, the east and the west, the north and the south. Thus Christ by his suffering draws to himself all peoples and subjects everything to himself as he said when rising from the dead, ‘all power is given to me in heaven and on earth’.123

Consequently, the geometric form of the cross and the meaning behind each of its elements can be related to the structure and the layout of the chapters of De Civitate Dei and to the contents of the book. The book ranges from the earthly city to heaven, and in the early chapters, it moves from Rome to Jerusalem in parallel with the storyline of past manifestations of God and the history of the earthly city. There are twelve books in De Civitate Dei and every book plays a specific part in the whole, but close examination

121 Ian S. Markham, Truth and the Reality of God : An Essay in Natural Theology (Edinburgh: T&T Clark, 1998), pp.30-35. 122 Augustine and Wand, St. Augustine's City of God, p.236. 123 Catholic Church. et al., The Missal of St. Augustine's Abbey, Canterbury : With Excerpts from the Antiphonary and Lectionary of the Same Monastery (Cambridge: University Press, 1896), p.120. 52 reveals that they fall into two groups. Historian, Deferrari (1878–1969) observed the development throughout the book:

The first ten are a reply to the enemies of the Church, who blamed the Christians for the evils that befell Rome; the last two give an account of the origin, history, and different ends of the two cities. Of the first ten, the first five are an answer to those who held that the gods were to be worshipped for the advantages of the present life, while the second five are directed against those who worshipped them for the life to come. Of the last twelve, the first four treat of the origin of the two cities, the second four of their progress or history, and the third four of their appointed ends.124

The fact that Augustine used numbers to unveil spiritual meanings should again be emphasised. Augustine wrote ‘Numbers are the Universal language offered by the deity to humans as confirmation of the truth.’125 This idea of using specific numbers as a foundation for his book’s structure came from Pythagoras. He also demonstrates in many of his writings that using numbers gives the ability to comprehend the consanguinity of everything, and effectively it reveals the secret of their relationship to divine grace. Augustine encapsulated this notion when he said, ‘the most hidden meanings are the sweetest’.126

The form of the cross also reminds man of the human figure, which itself is created by God, the perfect creature. Perhaps this is another reason why Augustine used this profound form as a template to give shape to his book. Mythologist, Joseph John Campbell (1904–1987) describes his view of the cross, which is also the generally accepted Christian definition:

…the vision of the Christian mystic, illuminated by faith, mounts upward from the cross on which the creator of logos dies to the starry firmament of Helios and Selene…and wherever he looks he sees the form of the cross imprinted on all things. It is as though the cross of his lord had enchanted the whole world. For him the form of

124 Roy J. Deferrari and M. Jerome Keeler, 'St. Augustine's ‘City of God’: Its Plan and Development', The American Journal of Philology, 50/2 (1929), p.117. 125 Karla Pollmann and Mark Vessey, Augustine and the Disciplines : From Cassiciacum to Confessions (New York: Oxford University Press, 2005), p.94. 126 Augustine and M. Dods, The Works of Aurelius Augustine, Bishop of Hippo. (15 Vols) (Edinburgh: T&T. Clarke Publication 1872), p.80. 53

the Cross is, first of all, the fundamental schema imprinted on the cosmos by God…Plato had written in the Timaeus of the world soul revealed in the celestial X…127

There is yet another interpretation of this form, the cross, which needs to be explained here to cover all different aspects of the structure of the cross. Sunderland writes, ‘Tau (or T) was the symbol for 300 in Greek and to the Christians T symbolised the Cross. Therefore 300 symbolized the Cross.’128 In 1961, Mâle argued that numerology and symbolism are more than just myths. They provide meaning for the curious human mind to understand what they see and make sense of what they have been told by God in the holy books.

The middle ages never doubted that numbers were endowed with some occult power. This doctrine came from the Fathers of the Church who inherited it from Neo-Platonic schools in which the genius of Pythagoras lived again. It is evident that St Augustine considered numbers as the thoughts of God.129

As is evident above, in De Civitate Dei, Augustine showed great attention to the numbers one, two, three, four, five, six, seven, ten and twelve. In addition to the demonstration given in earlier paragraphs, Augustine himself analysed each number and its significance as follows:

… six is a perfect number, for the number six is the first which is made up of its own parts, i.e., of its sixth, third, and half, which are respectively one, two, and three, and which make a total of six ... So again, in the number ten, four is a part, yet does not divide it; but one is an aliquot part, for it is a tenth; so it has a fifth, which is two; and a half, which is five. But these three parts, a tenth, a fifth, and a half, or one, two, and five, added together, do not make ten, but eight. Of the number twelve, again, the parts added together exceed the whole; for it has a twelfth, that is, one; a sixth, or two; a fourth, which is three; a third, which is four; and a half, which is six. But, on the seventh day, which number is also a perfect one, though for another reason, the rest of God is set forth, and then, too, we first hear of its being hallowed … Suffice it here to

127 Joseph Campbell, 'Papers from the Eranos Yearbook', The Bollingen series 30. (New York: Pantheon Books, 1954), p.372. 128 Robert Hyslop, Sunderland Sacramental Tokens (Sunderland: J.G. Campell, 1901), p.117. 129 Emile Mâle and Francis Palmer Smith, Twelfth Century Symbolism and Iconography as Influenced by Suger (Atlanta: The Lullwater press, 1941), p.10. 54

say, that three is the first whole number that is odd, four the first that is even, and of these two, seven is composed.130

Certain numbers signify the cruciform body of Christ because of their expression within geometric arrangements and of the apparently proper proportions of the human body. In De Civitate Dei, Augustine argues that Noah constructed the Ark based on the same numbers to convey the exactly corresponding proportions, and used the universal rule to maintain balance in its design. In De Civitate Dei, it is clearly explained how there is a direct connection between the dimensions of the cross, and the measurements of the Ark:

The Ark is without doubt a figure of the City of God wandering in this world, that is to say, the Church which is saved by means of the wood, on which hung the mediator of God and men, the man Christ Jesus ... And the door it received in its side is surely the wound made in the side of the Crucified when pierced by the lance, by which those enter who come to Him; for from it flowed the sacraments in which believers are initiated.131

In Genesis 6: 13–16, it clearly notes that God spells out the design, materiality and measurements of the Ark—even down to the size of its windows:

And God said to Noah, The end of all flesh is come before me; for the earth is filled with violence through them; and, behold, I will destroy them with the earth. Make thee an ark of gopher wood; rooms shalt thou make in the ark, and shalt pitch it within and without with pitch. The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits. A window shalt thou make to the ark, and in a cubit shalt thou finish it above; and the door of the ark shalt thou set in the side thereof; with lower, second, and third stories shalt thou make it.132

These kinds of geometrical compositions have also appeared in modernist architecture as will be shown in the discussion of Le Corbusier in Chapter five but apparently without the same meanings they had for Noah. It is interesting to consider their reappearance in new work in relation to cultural sources. Evidence from the modern era

130 Augustine and Wand, St. Augustine's City of God, p.284. 131 Augustine and William G. Most, A Digest of St. Augustine's City of God (Dubuque: Loras College Press, 1949), p.472. 132 Ernest G. Clarke, The Wisdom of Solomon (Cambridge: University Press, 1973). 55 will be reviewed in the upcoming chapters once the historical origins of the symbolism and meaning attached to major geometrical forms are demonstrated in these earlier chapters.

The Temple of Solomon is another example where Augustine showed how numbers relate to each of the decorations, pillars and various other architectural elements. These structural parts are accurately laid down by God throughout the Bible, up to the last book, ‘Revelations’. In Rev. 21:9, the De Civitate Dei is described as follows:

And he carried me away in the Spirit to a mountain great and high, and showed me the Holy City, Jerusalem, coming down out of heaven from God…12 It had a great, high wall with twelve gates and with twelve angels at the gates. On the gates were written the names of the twelve tribes of Israel. 13 There were three gates on the east, three on the north, three on the south and three on the west. 14 The wall of the city had twelve foundations, and on them were the names of the twelve apostles of the Lamb. 15 The angel who talked with me had a measuring rod of gold to measure the city, its gates and its walls. 16 The city was laid out like a square, as long as it was wide. He measured the city with the rod and found it to be 12,000 stadia in length, and as wide and high as it is long. 17 He measured its wall and it was 144 cubits thick, by man's measurement, which the angel was using…133

Of all the Christian writers, Augustine, with his precise and detailed analysis, thoroughly understood the story of Noah’s Ark. Also, as is evident in De Civitate Dei, he equally understood the design and structure of the Temple of Solomon. The similarities between the Ark and the Temple give us an insight into how Augustine wanted to depict the De Civitate Dei to his followers and interlocutors. He believed God wanted man to build in a way that reflected the structure of God’s own city, by keeping to the hallowed numbers that express the order and geometry of a perfect universe.

Medieval Architecture

The Divine Comedy, by Dante Alighieri, is an example of medieval metaphorical writing. The book is also a clear example of how literature is greatly influenced by early Christian architecture. Dante was an Italian Catholic poet, and the influence of his

133 J. B. Phillips, Bible. New Testament. Revelation. English. The Book of Revelation: A New Translation of the Apocalypse (London: The Macmillan Company, 1957). 56

Christian education are clearly apparent in his writing. In many respects, his book expresses the structure of the De Civitate Dei by using sacred geometry and numerology. Dante propounded a symbolic representation of the geometry that man seeks to perceive, either in the past or in the present. In The Divine Comedy, a description is given of the three realms of the journey of man after death, and of the architecture of each of those realms.

Figure 2.15 The Dantean Universe : illustration by M. Cactani, 1855.134

The geometric composition of a circular narrative (illustrated by Cactani in Figure 2.15) is used by Dante as if it were a universal language for communicating with mankind and

134 Chris Impey, The Living Cosmos : Our Search for Life in the Universe (Cambridge: Cambridge University Press, 2011), p.16. 57 to gratify the soul.135 The knowledge of this precise language can be learned, in part, through studying religious texts and ancient architecture.

Therefore, the timeless popularity of The Divine Comedy is due not only to Dante's rich and beautiful literary qualities, but also to his thorough knowledge of religious symbolism that illuminates the picture of the journey after life. English historian and scholar, Thomas Hart (1951–) viewed Dante’s planning of The Divine Comedy as follows:

The one involved overtly geometric constructions like the quadrant of Purgatory— 4.41–42, the other the references to propositions of Euclidean geometry in Paradiso 13.101–102 and 17.15. The evidence considered there led to a conclusion that was at first surprising, but which became as further patterns of this type emerged— increasingly insistent and in the end, by cumulative force, compelling: Dante must have planned and calculated the placement of such references, so that the verse-totals of resulting intervals would reflect, with a high degree of consistency and precision, characteristic mathematical properties of the geometric constructions referred to at those points.136

These reflections raise the probability that Dante might have undertaken at least a partial study of the architectural designs that existed around him, thus prompting spatial and geometrical motifs in his masterpiece, The Divine Comedy. These were more important in this poetical composition than its theological, theoretical and moral content. In The Banquet (Il Convivial) II.13 Dante stated:

Geometry moves between two things antithetical to it, namely the point and the circle— and I mean ‘circle’ in the broad sense of anything round, whether a solid body or a surface; for, as Euclid says, the point is its beginning, and as he says, the circle is its most perfect figure, which must therefore be conceived as its end. Therefore Geometry moves between the point and the circle as between its beginning and end, and these two

135 M. Cactani’s ‘The Dantean Universe’ appears unexpectedly foetal – with Heaven as the body, earth as the womb and hell as the foetus. Paradise seems to be the head. If such interpretation is correct about the secrets of the human body, M. Cactani probably also knew about Da Vinci’s dissections (to be reviewed in Chapter Three). What could be more timely than the transgressive novelty of the interior of the human body? But was this part of Dante’s idea or is it an eighteenth century elaboration? Both points are quite relevant and have the potential to motivate such an interpretation in the reading of The Divine Comedy. 136 Thomas Elwood Hart, 'The Cristo-Rhymes and Polyvalence as a Principle of Structure in Dante's "Commedia"', Dante Studies, with the Annual Report of the Dante Society, 105 (1987), p.3. 58

are antithetical to its certainty; for the point cannot be measured because of its indivisibility, and it is impossible to square the circle perfectly because of its arc, and so it cannot be measured exactly. Geometry is furthermore most white insofar as it is without taint of error and most certain both in itself and in its handmaid, which is called Perspective.137

What is evident in Dante’s work is the influence of the Bible and of Plato and Pythagoras, and as such, it was natural for him to express his literary talents through symbolism and numerology. As Portuguese musician and theorist, Luis De Freitas (1890–1955) explained:

Dante sums up and inspired shapes in diamantine form many of the fundamental ideas of a tradition that springs from a Platonic philosophy combined with an elaborate exegesis of biblical texts, namely Ezekiel's visions (the Ma’aseh Merkabah, or the ‘Work of the Chariot’, which together with the study of Genesis constitutes the fundamental base of Hokhmah Hakabbalah, the esoteric wisdom of the Kabbalistic tradition) as well as from a confirmed Sufi inspiration and possibly from teachings of the Kabbalah, as the vision of the car of Beatrice, so like the first vision of Ezekiel, whose name he invokes, seems to validate.138

Dante felt that his studies of the sacred forms (circle, square) and numbers around him gave him the onerous responsibility to educate and enlighten his readers and to convey deep meaning. With elaborate metaphors, The Divine Comedy articulates sacred beliefs through geometry and form.

To illustrate Dante’s understanding of sacred geometry and its significance, it is essential to analyse The Divine Comedy in same depth. This analysis requires studying the text as a whole rather than simply selecting lines at random. The book is open to any number of interpretations by different readers from different backgrounds. However, having a particular knowledge of sacred geometry and the mathematical laws propounded by scholars of the past produces an entirely different picture for the admirer of Dante’s work. With a full and complete understanding, what he really wished to convey—both expressly and implicitly—can be discerned. He confessed to the

137 Dante Alighieri and Richard H. Lansing, Dante's Il Convivio (the Banquet) (New York Garland, 1990), p.13. 138 L. De Freitas, '515--a Symmetric Number in Dante', Computers & Mathematics with Applications, 17/4-6 (1989), p.889. 59 importance of sacred geometry and mathematical laws in Paradise (iv, 41–42), where Beatrice tells Dante: ‘it is needful to speak thus to your faculty, since only through sense perception does it apprehend that which it afterwards makes fit for the intellect’.139

The structure of the book itself is purposely designed to create a likeness of the after- world by using sacred numerology. The book is a fusion of three sections—Hell, Purgatory and Paradise—each section having thirty-three cantos (divisions). There is also an introduction, making a total of one hundred divisions. On this matter, Annemaria Schimmel (1922–2003), German scholar and Orientalist wrote:

The pre-eminent numerological poet is Dante. Divine Comedy has a complex numerical structure based on the number 3: witness its terzarima and its 3 books consisting of 33 cantos each (the years of Christ's life). Along with an introductory canto (Christ died in his 34th year), this sums to 100 or 10 squared cantos, 10 being the number of the law and its commandments and the sum of the first 4 numbers (the Pythagoreans' tetraktys), and 100 being the ideal length of earthly life. Similarly Petrarch may be drawing on numerology as an organizing principle for his Rime and Trionfi (as well as on related calendrical schemata—natural and astrological, ecclesiastical and secular), and Boccaccio may be toying with the symbolism of 10 and 100 in his Decameron.140

The numbers 33 and 100 form the numerological foundation of the whole book, which demonstrates the importance of these numbers to the writer. Balanced against their literary usage, we can also find the same numbers in the architecture of the past. Hagia Sophia (constructed between 532–537 by Emperor Constantine) provides the closest example of this influence.141

Hagia Sophia’s historical significance originates from the period of its construction, at the time of the split in the Roman Christian Church into Roman Catholicism and the Orthodox Church. In the case of this Byzantine style building, the numbers 33 and 100 apply to the main structural features of the building (Figure 2.16 -2.17), with this sacred application designed to move the spirit of the beholder. American architect and scholar,

139 Gustave Doré and Robin May, Dante's Combined Works : The Divine Comedy (1st. edn.; Sedona, AZ: Star Rising Publisher, 2000), p.39. 140 Franz Carl Endres and Annemarie Schimmel, The Mystery of Numbers (New York Oxford University Press, 1993), p.24. 141 R.J. Mainstone, Hagia Sophia: Architecture, Structure, and Liturgy of Justinian's Great Church (London: Thames and Hudson, 2001). 60

Aarati Kanekar (1970–) related the design of Hagia Sophia to the numerology of Dante’s poem:

The dome of Hagia Sophia measures 100 in diameter in Byzantine feet and there are 100 cantos in The Divine Comedy. The narthex is 33 Byzantine feet in width and there are 33 cantos in each section of The Divine Comedy. These numerical relationships are further evidence that poem and building are subject to the same underlying tradition of formal meaningfulness. However, the more specific arrangement of space in the church holds greater interest from the point of view of the poem.142

142 Aarati Kanekar, 'From Building to Poem and Back: The Danteum as a Study in the Projection of Meaning across Symbolic Forms', The Journal of Architecture, (2005), p.138. 61

Figure 2.16 Byzantine architecture: Hagia Sophia, Istanbul. Ground floor plan.143 [Geometrical analysis by the author.]

Architectural elements are placed in relation to the square in the centre of building.

The three circles forming the floor plan are repeated in the configuration of section.

Figure 2.17 Hagia Sophia: Byzantine architecture, section through the centre.144 [Geometrical analysis by the author.]

Kanekar further explored the comparison between these two magnificent artistic milestones and presented a novel view:

For instance, in Hagia Sophia, Christ Pantocrator is in the heavenly sphere of the cupola, the Evangelic cycle is in the squinches, the theologians in the higher vaults, and finally the cycle of saints in the lowest—the terrestrial zone of the church. The higher an image is placed in the interior of the church, the more sacred it is considered to be.

143 Robert S. Nelson, Hagia Sophia, 1850-1950 : Holy Wisdom Modern Monument (Chicago: University of Chicago Press, 2004), plate.5. 144 Ibid. Front cover. 62

Centrality and distance from the physical ground plane seem to be especially significant. This centripetal geometry, which is also common in the mediaeval church, is of particular interest when explored in relation to the spatial scheme constructed in The Divine Comedy. In The Divine Comedy, much like the centralised churches, the same universe was disclosed as successive rings along an axis of descent or ascent, the axis being the route of Dante’s journey as well as the line of his narration of it.145

Another Dantean project, which differs from the Hagia Sophia design approach, is that of Italian architect, Giuseppe Terragni (1904–1943), who was designing during the Italian modernist movement. The literal translation of The Divine Comedy’s compositional structure orchestrated the entire spatial arrangement of Terragni’s design project.146 Even though this project was never built, it established a meaningful interpretation for architectural practice: the relationship between geometry and numerology in literature is used as a common denominator in architecture. Therefore, the synchronous dimension carries the meaning of what was initially intended by Dante into visual elements of Terragni’s ‘Danteum’.

Conclusion

There is a remarkably accurate transfer of the detail in the theoretical texts of Dante and St Augustine to the solid appearance of a building, which adds another layer of meaning to the process behind their designs—the translation of text into built form, or vice versa.

This chapter has identified the significance in medieval architecture of geometric forms such as circle, square and cross, and similarly the importance of numbers such as one, two, three and thirty-three, due to the meanings and beliefs attached to them. The incorporation of numerology and geometry continued to be crucial to the practice of many thinkers and believers throughout the following centuries. On the other hand, the idea formed during the early eras of a spiritual dimension attaching to geometrical shapes (as noted in the first two chapters) did not remain static; indeed, it transformed in meaning over time. This will be the main focus of the next two chapters.

145 Kanekar A, From Building to Poem and Back: The Danteum as a Study in the Projection of Meaning across Symbolic Forms (Georgia: Institute of Technology, 2000), p.139. 146 Thomas L. Schumacher, The Danteum, (Princeton: Princeton Architectural Press, 1993), pp.5-8.

Chapter Three. Religious Geometry in the European Renaissance

Myth, History and Elements in Geometric Structure

…in our life of experience, our own phenomenal life, we are accustomed to ascribe the value and name of actuality, reality, and truth, in contrast to art which lacks such reality and truth. But it is precisely this whole sphere of the empirical inner and outer world which is not the world of genuine actuality; on the contrary, we must call it, in a stricter sense than we call art, a pure appearance and a harsher deception.147

This quote by German philosopher G. W. F. Hegel (1770—1831) presents a philosophical view of the early Renaissance. Hegel discusses mankind’s spiritual need to reconcile his ‘inner’ (self) with ‘outer’ (nature) in order to engage fully with the world.148 Art and other creative practices provided us with the means through which this reconciliation could take place. The study of geometry helped many nations and cultures with different aspects of their everyday life. Sacred geometry, for instance, was used as a method for expressing a divine plan, often by allusion or metaphor, and was a feature of creative practices that became an obligation involving higher learning.

The Mesopotamians were the first to invent a system of proportion. One example is the pentagram, which originated in ancient Mesopotamia around 3000 BC, and at the time was referred to as ‘the heavenly body’ or the ‘star’.149 This relationship between symbol and referent is a cosmological one, made at a time when philosophy and science had not yet separated as they have today. In the first century BCE, Vitruvius created a scheme of proportions of the human body, which answered many of man’s questions regarding the physical body in relation to itself and the universe around him. The fact that a spiritual, masculine image also reflected a highly gendered, masculine social power structure (a masculine hegemony) was submerged within religious and cultural need to express a place for mankind in relation to the world.

Geometry as a contemplative practice is personified by an elegant and refined woman, for geometry functions as an intuitive, synthesizing, creative yet exact activity of the

147 Georg Wilhelm Friedrich Hegel and Bernard Bosanquet, Introductory Lectures on Aesthetics (London: Penguin Books, 1993), p.8. 148 Frederick C. Beiser, The Cambridge Companion to Hegel (Cambridge: Cambridge University Press, 1993). 149 L. Sprague De Camp, The Ancient Engineers ([1st edn. Garden City: Doubleday, 1963), p.18. 64

mind associated with the feminine principle. But when these geometric laws come to be applied in the technology of daily life they are represented by the rational, masculine principle: contemplative geometry is transformed into practical geometry.150

The calculations of Vitruvius’ scheme of proportions are based on a human figure in the centre of a circle, as indicated in Figure 3.18. One important aspect of this fifteenth century demonstration is that it appears as a static being, in comparison to a fourteenth century drawing by Leonardo Da Vinci that embeds meaning in positive action. Closer analysis of Vitruvian Man by Da Vinci will be presented later in this chapter.

Figure 3.18 Vitruvius’ description of ‘Human Proportion’.151

The use of mathematical proportions in relation to human form can also be seen in the work of the great Greek sculptor and architect, Polycleitus (second half of the fifth century BC). His statues Doryphorus and Diadumenus are great examples of the use of mathematical proportion. There is much to be said for Vitruvius’ approach when he wrote in his Roman Canon De Architectura about the idea of a circle with a human figure in the centre. This middle point is an ancient and sacred concept. The Lebanese

150 Robert Lawlor, Sacred Geometry, Philosophy and Practice, (London: Thames Hudson, 1982), 7. 151 Cesare Cesariano, Pollio Vitruvius, and Alessandro Rovetta, Vitruvio De Architectura : Libri Ii-Iv : I Materiali, I Templi, Gli Ordini (Milano: V & P Università, 2002), p.105. 65 born historian and mathematician, Zohor Shanan Idrisi (1945–) explains the roots of Vitruvius’ concept as follows:

Vitruvius relied upon the ancient sexagesimal system (related to number sixty) of calculation from which is derived our degree of sixty minutes and our minute of sixty seconds within a three hundred and sixty degree circle. This system of mensuration was bequeathed from Ancient Mesopotamia and Ancient Egypt to the Greeks.152

Major thinkers expressed great interest in Greco–Roman symbolism and methodology around the fifteenth century. As Renaissance scholars, they were inspired by Greek ideas, and their mission was to recover the methods that helped the Greeks to achieve results. Their attempts did not involve philosophical and scientific enquiry, rather the scholarly study of method in the writings and beliefs of the ancients. As historian, Peter Gay (1923–) argues, this strong interest in the ancients stemmed from a desire to rebel against a terrifying European Catholic Church. He argues that all modernism, which was built on the European Enlightenment, thus bears traces of paganism or atheism drawn from the ancient Greeks and built upon within European Renaissance Christianity. Noal Ward Gilbert notes:

The major historical achievement of the late Renaissance, it could almost be argued, was to hand on a more complete and accurate knowledge of the whole range of classical thought, from Plato and Aristotle to the Stoics, Sceptics and Epicureans, and their interpreters from late antiquity. This meant that the seventeenth century had a much richer and more stimulating philosophical tradition to draw upon or to reject.153

The most significant transformation in man’s beliefs was a heightened awareness of antiquity through new interpretations of the teachings of Aristotle and Plato. Scholars were acquiring new ideas from old sources by viewing them in a different light. An example is the work of Socrates (469–399 BC), who had rigorous and strict requirements for art, mathematics and geometry, and whose teaching exercised an influence on his most important pupil, Plato. Platonic thought became a significant source for Socrates’ methodology. The Renaissance drew upon Plato’s teachings to a

152 Zohor Shanan Idrisi, 'Decoding and Demystifying Da Vinci ', Foundation for Science Thechnology and Civilisation, 9/1 (2005), p.3. 153 Neal Ward Gilbert, Renaissance Concepts of Method (New York: Columbia University Press, 1960), p.24. 66 surprising degree. Architectural historian, Henry Millon (1927–2002) explains this interpretation of thoughts and beliefs as follows:

The other category of methodological thought, the scientific, was the contribution of Aristotle, who developed explicit criteria of demonstrative procedure that went beyond what Socrates had demanded of an art and that represented in a sense, a carrying out of the mathematical program of the older Plato. These two categories represent the poles of methodological thought and form a convenient scheme for orienting ourselves in the methodology of the Renaissance.154

In terms of the premise of my thesis, the importance of this section and the overall chapter is undeniable. Cosmological and mathematical development in this era resulted in a different approach to the practice of architects and artists of the Renaissance. Thus, grassroots analysis of particular beliefs or meanings attached to geometrical form provides a route to understanding the various symbolisms of the Renaissance era. In later sections I describe these changes in more detail and present imperative examples from which to draw clear conclusions to the two hypotheses of this dissertation.

Belief and De Re Belief

The Renaissance was a transitional period for philosophies, ideas and beliefs, moving from a focus on the past to the future. One might assume that all pre-Renaissance symbols are medieval and therefore need not merit attention, but in order to understand the true meaning and its origin, their importance is significant. The fifteenth and sixteenth centuries were a time of revived interest in Plato’s geometry and the rebirth of Pythagoras’ numerology. It was an era that saw the introduction of perspective in art by engineer and architect, Filippo Brunelleschi (1377–1446), and highly complex architecture involving sacred geometry. This period re-introduced the meanings and belief systems behind form, and the relationship between mathematics and universal order, emphasising them more fully than ever before. As Emmer (1993) explains:

Two major reasons forced Renaissance artists towards the pursuit of mathematics. First, painters needed to figure out how to depict three-dimensional scenes on a two- dimensional canvas. Second, philosophers and artists alike were convinced that

154 Henry A. Millon and Vittorio Magnago Lampugnani, The Renaissance from Brunelleschi to Michelangelo : The Representation of Architecture (London: Thames and Hudson, 1994), p.98. 67

mathematics was the true essence of the physical world and that the entire universe, including the arts, could be explained in geometric terms.155

One of the intellectuals of the period, Luca Bartolomeo de Pacioli (1446/7–1517), an Italian mathematician and geometer, wrote an exposition entitled De Divina Proportione (On The Divine Proportion).156 In all his studies, he aimed to demonstrate one thing: only through geometry can we see the human being as both human and divine. Reflecting on these two words, we can trace this belief back to ancient times. For example, this belief is referred to by the Egyptian π ratio and by the φ ratio of the Golden section. Pacioli deemed that the Renaissance received, and was influenced by, the ancient traditions and discoveries, and as a result created the most perfect art and designs of any era.

Pacioli’s works took much from the works of Piero della Francesca (c. 1415–1492), another early Renaissance Italian artist, mathematician and geometer. This influence most notably can be found in De Divina Proportione, where de Pacioli talks about solid geometry and its symbolic meanings. Italian historian and artist, Giorgio Vasari (1511– 1574), in his book Lives of the Painters, elaborated on the works of Francesca and describe him as the ‘greatest geometer of his time, or perhaps of any time’.157 Francesca studied the perspective of geometrical forms in depth, and the results of his research appear in his paintings, including the San Agostino Altarpiece and The Flagellation of Christ. Francesca’s findings are valuable for architecture because they are not based on perception or on a fixed point of view. However, American historian, Mark Peterson (1958–) critiques Vasari’s observations on these two Renaissance thinkers and reaffirms that:

In Piero's case, the story is of a lone mathematical researcher whose reputation has come to nothing because his work has been stolen by another and printed under his own name: Luca Pacioli. Vasari records not Piero's mathematical fame, as one might have thought, but rather his mathematical obscurity. When Piero's work is segregated from

155 Michele Emmer, The Visual Mind : Art and Mathematics (Cambridge: MIT Press, 1993), p.351. 156 He also wrote another influential text, Summa de Arithmetica, Geometria, Proportioni et Proportionalita (Venice, 1494) which was a revised version of Piero della Francesca’s work. 157 Giorgio Vasari and A. B. Hinds, The Lives of the Painters, Sculptors, and Architects, 4 vols. (Rev. edn. Everyman's Library. London: J.M. Dent, 1963), p.404. 68

Pacioli's work and correctly identified as the work of a different author, it takes on an integrity and intensity which appears altogether different.158

On the other hand, Pacioli, in De Divina Proportione, states:

The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilateral square.159

Reading through Leonardo Da Vinci’s (1452—1519) notebook, it appears that Luca Pacioli arrived in Milan in 1496, where he met Da Vinci. The two men began to work very closely, supporting one another with knowledge and skills.160 They exchanged ideas about various topics and Pacioli shared his findings on Platonic mathematical order, Divine Proportion, symmetries, mathematical roots, dichotomies, polarities and antitheses with Da Vinci.161 As a result of this collaboration, Da Vinci assisted Pacioli with illustrations of his book, De Divina Proportione, that were based on five regular Platonic solids and their properties (Figure 3.19). For these Renaissance men Pacioli and Da Vinci, the solids’ equal sides, unified parts and symmetrical structure branded them as being divine in their construction.

158 Mark Peterson, 'The Geometry of Piero Della Francesca', The Mathematical Intelligencer, 19/3 (1997), p.39 159 Luca Pacioli, Augusto Marinoni, and Biblioteca Ambrosiana, De Divina Proportione (Milano: Silvano, 1982), p.85. 160 Leonardo Da Vinci and Edward Maccurdy, The Notebooks of Leonardo Da Vinci, 2 vols. (New York: Reynal & Hitchcock, 1938), p.24. 161 Ibid., pp.24-25. 69

Earth Fire

Water Air

Universe

Figure 3.19 A dodecahedron from Luca Pacioli’s De Divina Proportione: and the universal emelents that each solid represents according to plato, illustration by Leonardo Da Vinci, 1509. 162

It is not known whether Pacioli acknowledged Francesca’s work, De Prospectiva Pigendi, in guiding his own findings. On the other hand, before the time of Pacioli and Da Vinci’s partnership, there is no evidence that Da Vinci himself had any formal awareness or any practical experience of geometry, proportion or symbolism. Moreover, it was not until later in life that Pacioli collaborated with Da Vinci to expand the concept of sacred geometry in art and architecture. As a result of their collaboration, Da Vinci produced an illustration called Vitruvian Man, based on the Roman Canon of Vitruvius. The origin and historical influences of Vitruvian Man and the significance of its geometrical elements will be further discussed in order to demonstrate its underlying belief system.

162 F.M. Bertato, A ‘De Divina Proportione’ : De Luca Pacioli (Tradução Anotada E Comentada) (Milan: Fábio Bertato, 1998), p.137. (The Latin inscription says: Dodecahedron Planum vacuum) 70

The works of Da Vinci centre on the geometric relationship of man to the universe (Figure 3.20). It is important to mention here that Da Vinci’s Vitruvian Man shows a dynamic image of a figure, with arms and legs in two positions, thereby multiplying the numbers of possible combinations of poses to sixteen.163 His image embeds meaning in positive action rather than static being. Therefore, it can be argued that besides the obvious purpose of the image, da Vinci emphasises action imbued with cosmic meaning. Note that other art works by da Vinci, such as the Mona Lisa and The Last Supper, also powerfully express geometrical forms and sacred proportions (Figure 3.21).

The Last Supper wall painting demonstrates something beyond a picture of Christ and the significant event this painting attempts to portray. The precise geometrical arrangement and intentional numerological composition enhances the overall work. In the painted interior, there are three arches right above the table, and three windows in the centre vanishing point164 (right behind the figure of Christ; there are also four openings either side of the interior)165. Moreover, the figures in this painting are placed in accordance with four identical circles. There are three figures inside each circle, and the main figure is right in the centre of the vertices. Christ bisects the sphere of matter, which consists of a Vesica piscis, whose centre coincides with his own navel. There are also three identical squares embedded in the geometrical arrangement of the painting (Figure 3.21).

163 Liviu Papadima, David Damrosch, and Theo D Haen, The Canonical Debate Today : Crossing Disciplinary and Cultural Boundaries (Amsterdam: Rodopi, 2011), pp.101-103. 164 Number Three symbolises the Christian doctrine of the Trinity that refers to three significance figures: the Father, the Son, and the Holy Spirit. 165 Number Four symbolises stability and the organic origin of all things; it also symbolises the four directions (north, south, east west) and the four ends of the cross. 71

Figure 3.20 Leonardo Da Vinci: Vitruvian Man—illustration, 1490.166

166 F. Zollner, Leonardo Da Vinci, 1452-1519 (Taschen America: LLC, 2000), p.36. 72

The figures in this painting are placed in accordance with four identical circles. There are three figures inside each circle, and the main figure is right in the centre of the vertices. There are also three identical squares embedded in the geometrical arrangement of the painting.

3 3 3 3

Figure 3.21 Leonardo Da Vinci: The Last Supper. Mural painting, late 1490.167 [Geometrical and numerological analysis by the author.]

At the same time (1509), Pacioli wrote Divina Proportione, introducing the Golden ratio and the theorems of Euclid. Da Vinci provided illustrations for this text for final publication, thereby gaining an opportunity to learn more about the great mathematicians and geometers of the past. Da Vinci used his primary tool—his strong drawing skills and articulation of geometrical designs in three-dimension—to assist him to communicate and to demonstrate his research and study of proportion. Obviously, such visual exploration benefited the expansion of his research to an elevated degree. (Interestingly, sophisticated mathematical drawing became common practice in architecture in ancient times; a good example is the precision seen in the construction of the pyramids of Egypt, as reviewed in Chapter One).

At the same time as Da Vinci was carrying on his research, Pacioli was researching the growth and progress of architectural design. An emphasis on proportion lies at the root of Renaissance aesthetics. It was as if human measurements and proportions were fundamental to the study of other related disciplines of classicism. Classical idealism is one of the main themes in theories of art and architecture that continue to be influential even today. The measure of all beauty, the perfection of anything in the world, was

167 Pinin Brambilla Barcilon and Pietro C. Marani, Leonardo : The Last Supper (Chicago: University of Chicago Press, 2001), p.85. 73 firmly based on the physically perfect man. For the Renaissance humanists, correct proportions in some way must have the ability to be translated into mathematical terms, and to communicate with universal theoretical perfections such as the square, the circle, and the Golden section. By applying these geometrical configurations, they were attempting to determine the relationship between the earthly and heavenly realms.

It is for this reason that da Vinci showed such passion for the study of human anatomy throughout his life, and applied this knowledge to his paintings and master works. Pacioli referred him to lost treatises on the human figure, and one of these was the work of Vitruvius on mathematics and architecture. Vitruvius’ beliefs relied upon the studies of the ancients. Da Vinci’s celebrated drawing, Vitruvian Man, combines words with an image to articulate the work of this first century Roman thinker, placing a man within two significant geometrical shapes: a circle and a square. American historian, Kenneth Keele researched and analysed the life and works of da Vinci, specifically Vitruvian Man, and he states:

Leonardo’s famous drawings of the Vitruvian proportions of a man’s body first standing inscribed in a square and then with feet and arms outspread inscribed in a circle provides an excellent early example of the way in which his studies of proportion fuse artistic and scientific objectives. It is Leonardo, not Vitruvius, who points out that ‘If you open the legs so as to reduce the stature by one-fourteenth and open and raise your arms so that your middle fingers touch the line through the top of the head, know that the centre of the extremities of the outspread limbs will be the umbilicus, and the space between the legs will make an equilateral triangle’ (Accademia, Venice). Here he provides one of his simplest illustrations of a shifting ‘centre of magnitude’ without a corresponding change of ‘centre of normal gravity’. This remains passing through the central line from the pit of the throat through the umbilicus and pubis between the legs. Leonardo repeatedly distinguishes these two different ‘centres’ of a body, i.e., the centres of ‘magnitude’ and ‘gravity’.168

Many other artists attempted to illustrate Vitruvius’ theory before da Vinci, but none could demonstrate the man’s position with two different figures in the same image. Vitruvian Man is simultaneously surrounded by both the circle and the square (Figure 3.22). The positioning of these two forms in relation to the man’s figure is intentional,

168 Kenneth D. Keele, Leonardo Da Vinci's Elements of the Science of Man (New York Academic Pub, 1983), p.196. 74 as the circle is centred on the navel while the square is centred on the genitals. The circle symbolises the divine realm and the square the earthly realm and their relation is a shift of centres illustrated in the downward motion. This represents a motion from divine to human progeniture, with both centres/realms/powers encompassed by the human being. The human figure, bounded at the same time by these two geometrical forms, assumes positions of the limbs that aim to demonstrate this dual connection, or double association. Upon closer inspection, it appears that the hands and feet of the figure touch the circle and square, but the hand can only reach to the square when it is straight, and the only time that both the geometrical figures are linked is when the arms are slightly raised.169 This composition forcefully expresses the deeper meaning of harmony and balance, incorporating Vitruvius’ emphasis on the link between these two shapes and the human body: ‘And just as the human body yields a circular outline, so 170 too a square figure may be found from it’. But there is no further evidence from Vitruvius to explain why these two geometrical elements were important in relation to human proportion. That is perhaps why Da Vinci undertook the difficult task of studying anatomy instead of adhering to a classical geometric ideal, achieving a clear and precise understanding of anatomical doctrine.

This work also reveals the human form as both human and divine; it can therefore be referred to as a representation of the universe as a whole. Centuries before the production of Vitruvian Man by Da Vinci, it was believed that man was created in God’s image. There is an obvious logical difficulty in likening man’s physical body to God, yet these physical proportions were believed to embody the divine order and replicate the semblance of heaven in accordance with theological bases.171 Therefore, proportion and measurement in architecture can represent the cosmic order and express a sense of harmony and balance, as discovered in antiquity by Pythagoras and Plato, whose ideas were extensively applied during the Renaissance—and applied to architecture in particular as the only way to produce acceptable building designs.

169 Gordon Campbell, Renaissance Art and Architecture (New York: Oxford University Press, 2004), p.98- 120 170 Pollio Vitruvius et al., De Architectura (Torino: Giulio Einaudi, 1997), p.29. 171 Ancient Egyptian structures (for example at the Temple of Luxor), Hindu temples and houses (based on the doctrine of Vastu-Purusha or human science architecture), early Christian churches as well as many twentieth century buildings (for example Le Corbusier’s The Modulor as a guideline for his design for Villa Stein) were all based on the proportions of the human body. Using the motif of man’s body to achieve ideal proportions in architecture is a continually important element for design and connects ancient, classical and modern architecture. 75

Invigorated by the Christian belief that Man as the image of God embodied the harmonies of the Universe, the Vitruvian figure inscribed in a square and a circle became a symbol of the mathematic sympathy between microcosm and macrocosm.172

In addition, da Vinci’s near contemporary, German artist and mathematician, Albrecht Dürer (1471–1528) also believed in geometrical methodology. Dürer’s approach was much more systematic and secular than da Vinci’s, relative to geometrical constructions, proportion and measurement. Dürer’s theoretical work Vier Bücher von Menschlicher Proportion (Four Books on Human Proportion) published in 1528, is the precise demonstration of five different types of human body (Figure 3.23)—not just male figures, but females and children too. The book is based mainly on his study of Vitruvius’s Ten Books on Architecture, published in 100 BC. Based on his extensive research of the construction of the human body, Dürer observed that:

Vitruvius, the ancient architect, whom the Romans employed upon great buildings, says, that whosoever desires to build should study the perfection of the human figure, for in it are discovered the most secret mysteries of Proportion. So, before I say anything about Architecture, I will state how a well-formed man should be made, and then about a woman, a child, and a horse. Any object may be proportioned out (literally, measured) in a similar way.173

Despite his exhaustive research, Dürer did not implement the proportional system of the Vitruvian Man in his analysis. Instead, he developed his own system based on imperial testing and favoured the methods of Ptolemy over Euclid. In his other work in Underweysung der Messung (Four Books on Measurement) published in 1522, Dürer precisely demonstrates his proportional system.174 Book One begins with a discussion of Euclid’s definitions of point, line, surface, and solid, and is primarily concerned with linear geometry. In Book Two, he describes triangles, rectangles, and regular polygons. Book Three begins the treatment of solids, but is devoted mainly to practical applications of these solids. It then gives an interesting exposition on architectural styles

172 Nigel Yates, Buildings, Faith, and Worship : The Liturgical Arrangement of Anglican Churches, 1600- 1900 (Oxford: Oxford University Press, 2000), p.209. 173 William Conway, Literary Remains of Albrecht Dürer (Cambridge: Cambridge University Press, 1899), p. 58. 174 Albrecht Dürer, Underweysung Der Messung, in De symmetria partium in rectis formis humanorum corporum (Nuremberg, 1532); Underweysung der Messung (Nuremberg, 1538), ed. David Price (Oakland, CA: Octavo, 2003) (digitised facsimile) 76 of columns, and techniques for constructing different types of sundials. Book Four contains an analysis of the properties of the polyhedra, and the book concludes with a detailed description of the art of perspective and its practical use for artists.

These two books on proportion/measurement and the human body became a valuable resource for many visionary artists who strove for modernity. Dürer’s mission through investigations into geometry, human proportions and architecture was to find a perfect and distinct system of measurement and proportion. For Dürer, that was the fundamental part of all arts.175

Figure 3.22 Albrecht Dürer: studies on the proportions of the female body, 1528.176

This analysis of Renaissance scholars is significant in relation to my first hypothesis, as it outlines the development and progression in geometry, and the evolution of past beliefs about the symbolism of certain geometrical forms (such as circle, square, cross and the principle of golden ratio). The origin of the idea of Da Vinci’s Vitruvian Man, its primary historical influences and the significance of its geometrical elements has also been delineated, as the symbolism of its design requires study and analysis in order

175 Jane Campbell Hutchison, Albrecht Dürer: A Guide to Research (New York and London: Garland, 1999), pp. 1–2. 176 Albrecht Dürer and Walter L. Strauss, The Human Figure; the Complete ‘Dresden Sketchbook.’ (New York: Dover Publications, 1972), p.91. 77 to understand and demonstrate the belief system behind it. The ideal proportions, as inspired by the human body in ancient times, set a guideline in the Renaissance—and many later eras—for architects aiming to achieve a similar balance and harmony in design to that achieved in past millennia.

Renaissance Architecture

The hypothesis of this work, though, is not only based on mathematical and geometrical underpinnings; it also connects these underpinnings to natural philosophy and metaphysics.177 Philosophy and metaphysics have many levels of belief, some highly educated and some less so. The relationship between belief and reality is highly culturally dependent. Astrology is one example of such a culturally dependent set of beliefs: extremely complex systems that, despite their rational organisation, have no foundation in observable reality, and yet have been steadfastly influential, especially in politics, religion and design. According to many ancient traditions, there is a belief in astrology that the human body is considered a microcosm to which is paired a macrocosm (the universe). A Buddhist tantric text contains the words ‘as without, so within’.178 ‘Without’ pertains to the universe as a whole, and ‘within’ refers to the parts of this whole. So this line clearly indicates the belief that the relationship between man and the universe is direct and undeviating. Similarly, in The Aurora, written by German theologian and mystic, Jakob Böhme (1575–1624) we can plainly see the significance of the human body itself as a whole in relation to its different parts:

The whole body with all its parts signifies heaven and earth. The interior ‘hollowness’ in man's body signifies the close connection between the stars and the earth. The hands signify God's omnipotence, since man makes with his hands what he pleases. The feet signify that near and far are one in God; let his feet take him near or far off—in nature he is neither near nor far off. The head signifies heaven.179

177 Natural philosophy, simply called science in the pre-Enlightenment period (fourteenth and fifteenth century), was used before science and philosophy separated into different fields. 178 Alex Wayman, Yoga of the Guhyasam Ajatantra : The Arcane Lore of Forty Verses : A Buddhist Tantra Commentary (1st edn. Delhi: Motilal Banarsidass, 1977), p.23. 179 Jakob Böhme, John Sparrow, and C. J. Barker, The Aurora (London: J. M. Watkins, 1914), p.143. 78

The elucidation by Böhme can resolve the concern mentioned earlier180 (the logical difficulty of seeing man’s body as the image of God). This can be explained in two different ways, each with their own justification. One is spiritual (invisible) or symbolic, and the other is corporeal (visible), or a literal representation. The first approach is typical orthodox religious theory. In The Aurora, Böhme wrote about Adam as an image of God before the Fall, and he explained further that this was because his inner body (spirit) and outer body were joined. In addition, if we apply measurements to this figure we can see that the foot is one fourth of the distance from the junction of the two legs to the heel. However, Vitruvius writes that the foot is one sixth of the entire human height. If we now refer to Böhme's testament above in The Aurora, the left foot in Da Vinci’s work symbolises the near, and the other foot, pointing straight ahead, symbolises the far.181

Furthermore, we need to examine this double link of literal presentation—the man’s figure inside both square and circle. The navel pinpoints the centre of the circle, and the junction of the legs occupies the centre of the square. But what is the significance of these two centres? As mentioned earlier, both geometrical figures have significant places in the history of geometry and mathematics. An example, which serves to better understand this composition and reveal the depth of its meaning, follows.

The significance of shapes, namely squares and circles, in different eras and different cultures, was mentioned in the previous chapter. In Chapter One, the analysis of both Sri Yantra, an Indian concept from Sanskrit, and the Great Pyramids in Egypt illustrated that geographically separated beliefs still symbolise a similarly significant meaning represented in the square and the circle. Even though the purposes of Vitruvian Man and the Sri Yantra are entirely different and represent products from a distinct era and culture (Da Vinci’s is a personal note generated in Italy in 1480, while the Sri Yantra, generated in Indian prehistory, is a didactic tool for monks), the study of their literal geometrical representation reaches clarity in two presented geometrical forms: circle and square. The Sri Yantra is made up of an outer circle that forms the boundaries of

180 The teaching and writing of Jakob Böhme caused great outrage and controversy among his contemporaries. The main doctrine of his works concentrated on evil in humanity, cosmology and the nature of revitalisation. Böhme's illustration entitled, ‘The Philosophical Sphere or the Wonder Eye of Eternity’ demonstrated the return of man to God only through cosmology. 181 These notions of paradox – the two in one; the joining of the inner and outer body – describe a key feature of the dialectic practices of modernism. 79 sacred space and holds the square mansion, symbolising the earthly life of man and representing different levels of human progression.

Ultimately, this composition stands on the within-without analogy. The mansion, or palace, radiates and grows out to touch the surrounding circle at four points, thereby forming a microcosm-macrocosm design similar to Vitruvian Man.

Figure 3.23 [L] Francesco Di Giorgio: Human body inscribed in a building plan, 1470.182

Figure 3.24 [R] Leonardo Da Vinci: Sketch of the plan of a church, 1490.183

Evidence of this collaboration or arrangement of circle and square includes the architectural works of Francesco di Giorgio (1439–1502), who related the proportions of building design to the human form (Figures 3.23 and 3.24). In doing so, di Giorgio learned that he could only partially rely on ancient influences, and that he needed to develop his studies further to create something original and different. However, bodily proportions provided a complete paradigm of the layout of cities, the plans and elevations of churches, and of the larger elements of the orders, and di Giorgio’s loyalty

182 Mark Wilson Jones, Principles of Roman Architecture (New Haven: Yale University Press, 2000), p.87. 183 Leonardo Da and Maccurdy, The Notebooks of Leonardo Da Vinci, p.51. 80 to the ancients made him unwilling to give up the sanction of antiquity. This is exemplified well when we observe his theory on entablature design.

It is to be known that coronas or cornices with its friezes and architrave were derived from the face or neck and breast of the human body. First, you divide the face in four parts from the top of the cranium to the lowest part of the chin. Of the first part, you make the upper cyma with its fillet, of the second the fascia. And the third is given to the ovolo. And the other, last, and fourth part bounded by the nose and chin is divided in three parts; of the first part, that bounded from the nose to the chin, the dentil moulding, and the other two parts the riversa and cyma placed below, bounded by its fillets. And from the chin and forking of the breast is given to the frieze. And from the forking of the throat to where the breast ends, the architrave is constituted. And so as the comb of the breast has four serried ribs, thus we will constitute four divisions of fillets and astragals.184

Conclusion

In Renaissance architectural theory and practice, geometry and meaning played very diverse roles compared to any other era. Applied geometry became the primary tool to envisage a conception, involving the marriage of theoretically inseparable elements such as a circle, square, or classical principles.

Early Renaissance beliefs and Vitruvian ideas formed the foundation of geometrical and mathematical theories in the art and architecture of the fourteenth to sixteenth centuries. It can be argued that the concept, symbolism and geometry of Vitruvian Man was the work of Pacioli, not Da Vinci, but it can also be claimed that Da Vinci began, from that time on, to examine every work from a geometrical point of view. As well as setting out the image of masculine hegemony, geometric projection and modernity, Vitruvian Man also lays out the form of ‘being’ for modern man, wherein religion and spirituality become a personal responsibility that led not only to classicism but also, and rather controversially, to Hegel’s romanticism.

‘…For architecture is the first to open the way for the adequate actuality of the god, and in his service it slaves away with objective nature in order to work it free from the

184 C. Kolb, 'The Giorgio, Francesco, Di Material in the Zichy-Codex', Journal of the Society of Architectural Historians, 47/2 (Jun 1988), p.135. 81

jungle of finitude and the monstrosity of chance. Thereby it levels a place for the god, forms his external environment, and builds for him his temple as the place for the inner composure of the spirit and its direction on its absolute objects’.185

Da Vinci has also been cited as the inspiration behind many of the early sixteenth century centralised churches. The centralised designs of Da Vinci, like the medieval baptisteries, carefully attest to what he refers to as redundant.186 On the other hand, the built forms that are said to be influenced by Da Vinci, such as the St. Peter’s project and Santa Maria delle Grazie (1497) by Donato Bramante (1444–1514) that have centralised planning, do not support what Da Vinci has rejected as a design belonging to medieval architecture.

My above remarks and my overall findings of this chapter are important to the first hypothesis of this thesis, because it explains the true origin of meaning attached to certain geometrical forms used during the Renaissance era. This early Renaissance development in mathematics and science, along with the evolution in belief systems attached to applied geometry and numerology in architecture, marked the beginning of revolutionary changes to the face of European art and architecture. Therefore in the next Chapter the beginning of Modern era will be demonstrated through the architecture of Baroque. The case studies are selected from late Renaissance from architects and architectural examples to cosmological and theological developments.

185 Hegel and Bosanquet, Introductory Lectures on Aesthetics, p.84. 186 Ludwig H. Heydenreich, Architecture in Italy 1400-1500 (New Haven: Yale university press, 1996), pp.102-105. 82

Chapter Four. On Geometry and Enlightenment Philosophy

Figure 4.25 Apollodorus of Damascus: The Pantheon, Rome, 126 AD.187

No aspect of building requires more ingenuity, care, industry, and diligence than the establishment and ornament of a temple. There is no doubt that a temple that delights the mind wonderfully, captivates it with grace and admiration will greatly encourage piety.188

In his above quotation, Italian Renaissance architect and scholar, Leon Battista Alberti (1404–1474) attests firmly to the importance of the temple in the architectural design world and its effect in revitalising the human mind. Then, how can a building made out of sand and stone have such an influence and, as Alberti suggests, ‘encourage piety’? As part of this thesis’ two hypothesis, my aim is to provide evidence that through symbolism and applied geometry in the design of temples of the past, it became possible to inspire the beholder to gaze into spiritual dimension in built form. Therefore, the objective of this chapter is to build on the last three chapters by progressing to the

187 Group Hoiol, 'Wikiarquitectura Building of the World', , accessed 14 November 2012. 188 Leon Battista Alberti et al., On the Art of Building in Ten Books, trans. Joseph Rykwert (London: MIT Press, 1988), p.194. 83 late Renaissance and Baroque eras, describing and analysing some architectural examples from these two unique periods. The examples have been selected based on their unique approach to past beliefs (spiritual and symbolism), innovative translation of theoretical bases into geometrical patterns, and their significance in the fifteenth century, which effectively changed the future of building design.

Beliefs, Culture and Composition

To begin, in the last chapter the focus was on theoretical/methodological findings in geometrical patterns and proportion from early Renaissance. It is necessary at this point to define the phrase ‘Renaissance’ that itself demonstrates the events of this era. It is derived from the Latin renāscī, meaning rebirth or revival. The rebirth of classical architecture first occurred in Italy during the early fifteenth century; it was at that time that Vitruvius’ book De Architecture and other classical literature were rediscovered.189

Vitruvius, a first century Roman architect, reminded his contemporaries of the classical era, of the principles and importance of architectural design and elegance. Behind the rediscovery of this masterpiece were scholars’ longing for innovative ideas, and those who were seeking recognition by the Catholic Church or, as they believed, the blessings and approval of God. For Italians to achieve a new society, they needed to base their works on ancient architecture and the written works of their ancestors (Figure 4.25).

At that time, Christianity was the major driving force for the most significant historical building works. The only place where one could view the high points of architecture, the symbolic arrangements of design features and the magnificent detailing, was in churches.

In 1517, the Protestant Reformation led by Martin Luther brought with it doubt and loss of trust in the teachings of the Roman Catholic Church. Luther’s followers did not believe that the Church should wield earthly power as its teachings suggested.

189 There are number of architects from early Renaissance to the latter part of the seventeenth century such as Brunelleschi, Alberti and Palladio who placed much emphasis on their classical findings. Anthony Grafton, Glenn W. Most, and Salvatore Settis, The Classical Tradition (Cambridge: Belknap, 2010), p.970. 84

For centuries before, the Church thrived as long as people remained ignorant, fearful, and deprived. In their desperation they were easy to control and subdue with promises expounded by the clergy of eternal happiness and life after death.190

At the same time, curiosity about medicine, history, science, astronomy and the physical world—as well as attentiveness to classical antiquity—was widespread among free thinkers and scholars, and this was an era of many key discoveries in diverse fields. One such scholar was Italian mathematician, astronomer and physicist, Galileo Galilei (1562–1642), who advocated a heliocentric theory of the universe.191 This theory was denounced by the Catholic Church as ‘false and contrary to Scripture’.192 Even after many warnings from the Church, Galileo published and defended his theory in his book, Dialogue Concerning the Two Chief World Systems. The realisation that the earth is not at the centre of the universe provoked many new ideas. Consequently, the Church found itself on very shaky ground.

Consequently, the highly influential Roman Catholic Church decided to change the architectural design of churches in order to maintain its congregations and propagate the faith. The architects who worked for the Catholic Church began to apply novel decoration, oversized and unusual shapes, dramatic styles and a celestial atmosphere in an attempt to capture the imagination and wonder of the people. This was also a time when various types of buildings emerged as architectural categories, for example private, business and public buildings. As a result, the application of geometrical patterns and significant spiritual symbolism extended beyond the walls of churches.

Each new building presented architects with the opportunity to use new design approaches and ideas. Churches became more open plan, for example, the Renaissance architectural idea to turn interior spaces into infinity strongly persisted throughout the era and to accommodate that, the medieval idea of having fewer columns developed further. There were also more figurative paintings of biblical scenes displayed, with sharper contrasts in lighting and reflections of natural forms. These dynamic styles and

190 Anthony Lingwood, 'Renaissance & Baroque', A Brief History of Interior Design (2012; Cork City, Ireland: Interiorize, 2012). 191 The term Heliocentric is the astronomical term, generated from the Greek words helios- ἥλιος and kentron- κέντρον, which translate to English as sun and centre. Heliocentric is a model to demonstrate the sun in the centre in around which all the other planets revolve around. Galileo Galilei was the first scholar to formally present the term and its significance. 192 Michael Sharratt and Galileo Galilei, Galileo : Decisive Innovator (Oxford: Blackwell, 1994), p.127. 85 changes were popularly referred to as Mannerism,193 which denotes ‘stylishness’. From there, we can discern the birth of the Baroque era and the transformation of applied geometry in architecture.

Baroque Architecture and the Beginning of Modernity

As the sixteenth century unfolded, the so-called ‘modern age’ began. This is to say that the architecture of that era is often referred to as the greatest disseminator of design knowledge to the modern age. The transition from High Renaissance to Baroque was influenced by major revolutionary forces: economic, political and social. The meaning of the word Baroque needs to be mentioned here, as the word clearly represents an actual style. It comes from an early Portuguese word barroco, a noun used to describe irregularly shaped pearls,194 and in Italian, Baroque means ‘enthusiastic’ and ‘lively’.

Jakob Burckhardt (1818–1897), art and cultural historian, described Baroque style as the decadent end of the Renaissance.195 On the other hand, prominent Swiss art critic, Heinrich Wölfflin (1864–1945), in his insightful book Principles of Art History, demonstrated the primary distinctions amid the art of the sixteenth and seventeenth centuries: ‘Baroque is neither a rise nor a decline from classical, but a totally different art’.196

Those studying the history of art and architecture in the Baroque era will see more complexity, more detail, more swirls and the larger scale of work on the interior and exterior of churches than in earlier periods. The purpose of all these innovations was to overwhelm, and in some cases to confuse the spectator and incite a feeling of awe. Based on new discoveries, ideas and philosophies in the sciences and humanities, Baroque deliberately allowed art to break from the strict rules set by the Church. The

193 The term ‘Mannerism’ belongs to the period in European art and architecture in the late sixteenth century. The style sought to represent a sense of beauty through exaggeration of human proportion and perspective. Arnold Hauser, The Social History of Art: Renaissance, Mannerism and Baroque (London: Routledge press, 1999), p.165. 194George L. Hersey, Architecture and Geometry in the Age of the Baroque (Chicago: University of Chicago Press, 2000), p.42. 195 Carl Jacob Christoph Burckardt, The Civilization of the Renaissance in Italy (United Kingdom: Penguin press, 1990) 196Heinrich Wölfflin and Marie Donald Mackie Hottinger, Principles of Art History: The Problem of the Development of Style in Later Art (New York: Dover, 1950), p.14. 86 geometrical patterns and symbolism based on spiritual beliefs became overshadowed by this revolution in scientific and mathematical discoveries.

Baroque was concerned with religious ecstasy, not simply as a decadent version of the Renaissance, but also the risky imagery of extremes. This is demonstrated in the sculpture by the Roman Baroque architect, Gian Lorenzo Bernini (1598–1680), titled Ecstasy of Saint Teresa in the Cornaro Chapel in Rome (Figure 4.26). A sense of motion has been achieved by using carved stone representations of fabric made to look as if the figure of Saint Teresa has a strong breeze blowing over her. Combined with her swooning pose, sunbursts and other religious symbols, Bernini’s sculpture suggests religious ecstasy.

Figure 4.26 Gianlorenzo Bernini: Ecstasy of Saint Teresa, Italy, 1645–1653.197

The sculpture of this period reaches its highest point in Bernini's pliable compositions. He said at one time that the most important thing for sculpture was to depict movement, and the living, wavelike, undulating lines of his creations are pure line for the sake of linear movement. His figures defy gravitational limitations and are often, as in his St. Teresa in

197 Helen Gardner, Fred S. Kleiner, and Richard G. Tansey, Gardner's Art through the Ages (Sydney: Thomson/Wadsworth, 2001), p.532. 87

Ecstasy, freely suspended in space. With his fluid, flamelike lines he goes as far as possible in the sculptural medium, and the restless Baroque spirit looks for further movement toward the more malleable media of painting and music.198

The Sacred Subject: Geometry as Mirror

By the sixteenth century, the Italian Renaissance had reached almost unsurpassed heights of cultural and intellectual achievement. The turbulent political climate in Italy was ideal for the spread of the High Renaissance and Mannerism, the latter style already showing tendencies towards the Baroque, with many aspects of Baroque art and design determined by religion.199

Figure 4.27 Francesco Borromini: San Carlino Alle Quattro Fontane, section engraving.200

198 William Fleming, 'The Element of Motion in Baroque Art and Music', Journal of Aesthetics and Art Criticism, 5/2 (1946), pp.121-28. 199 John Wyndham Pope-Hennessy, Italian High Renaissance & Baroque Sculpture (4th ed edn.; Oxford: Phaidon Press, 1996), p.480. 200 L. Steinberg, Borromini's San Carlino Alle Quattro Fontane: A Study in Multiple Form and Architectural Symbolism (Washington Garland Pub., 1977), p.58. 88

One of the main differences between Baroque and previous styles in architecture, especially that of the Renaissance era, was the effortless relationship between interior and exterior, which together were taken to be a whole, not as separate parts. Conversely, the architects of the Renaissance designed the inside and outside of a church entirely separately, with no connection in any respect. This ‘wholeness’ in Baroque design represented a new maturity in church architecture and fulfilled the aims of the Church to mirror the universe.

Baroque theorist and Italian architect, Francesco Borromini (1599–1667), produced great examples of complex applied geometric systems to his outstanding architectural designs, but in a different way to his contemporaries. The first building he designed independently—his masterpiece—is a church in Rome, San Carlino alle Quattro Fontane (San Carlino), 1641. It is a renowned piece of Baroque architecture (Figure 4.27).

This church is such a strong statement of a passionate, artistic determination that to traditionalists of the neo-classical age, it has been described as ‘grand delirium’,201 and ‘wilfully complex’.202 To this day, there is no agreement on the forms that made up San Carlino’s plan. However, from reading different interpretations of Borromini’s intentions, one point that all sources agree upon is that San Carlino is structurally complex in the service of a symbol, and the underlying meaning of this building can be read in the juxtaposition of different forms. However, this can only be achieved if they are read closely as a whole.

201 Francesco Milizia and Eliza Taylor Tr Cresy, The Lives of Celebrated Architects, Ancient and Modern: With Historical and Critical Observations on Their Works, and on the Principles of the Art, 2 vols. (London: J. Taylor, 1826), p.179. 202 Dagobert Frey, Architecture of the Renaissance, from Brunelleschi to Michael Angelo [Microform] : 160 Reproductions with Text and Catalogue (Hague: G. Naeff, 1925), p.7. 89

Vesica piscis forming the major planning of the building.

Two equilateral triangles determined the centre of the two circles inside the Vesica piscis.

Figure 4.28 Borromini: San Carlino alle Quattro Fontane, floor plan, Rome.203 Analysis by the author.

In the church’s ground floor plan, there are barely any straight lines. Burckhardt analysed it as a ‘combination of ellipse, semi-circle and irrationally projected space’.204 Reading the elliptical shape in the long axis, we can see three interlocking circular lozenges. It seems as though his design cannot be analysed in depth two-dimensionally; only with three-dimensional observation can we see the whole picture. Observing its structure closely, we can see much intentional complexity in the planning of this two- storey church. On the floor plan drawing, Borromini used only simple geometrical figures: two circles overlapping the two equilateral triangles and all of these embedded inside the Vesica piscis, an intersection of two circles (Figure 4.28).205

Consequently, the result is in the form of an oval. The centrepiece of this building is an oval-shaped dome placed on the level with an oval opening in the middle, which pleases the eye. Looking more closely at the domed ceiling, the cement casting patterns

203 S. Grundmann and U. Fürst, The Architecture of Rome: An Architectural History in 400 Presentations (Berlin: Ed. Axel Menges, 1998), p.208. 204 Cornelius Gurlitt, History of the Baroque Style in Italy (Stuttgart: Ebner & Seubert, 1887), p.82. 205 This figure demonstrates the geometrical composition, which is based on the intersection of circles in relation to the same central point. 90 contained by the oval have a wide range of deep-set, engraved geometrical shapes; interlocking octagons and hexagons that bear crosses all the way across the surface. There are eight crosses surrounding the central oval and similarly, eight crosses are encompassed by the outer oval and entablature.

Vesica piscis, generated from the marriage of two circles, is also the symbol of Jesus and is often referred to as ‘Jesus fish’. Vesica piscis accurately means ‘bladder of a fish’ in Latin, and in Greek ‘ichthys’ (ΙΧΘΥΣ) is the word for fish and was used by

Augustine to signify Jesus. His reference to Ichthys is a contraction for ‘Ίησοῦς Χριστός, 206 Θεοῦ Υἱός, Σωτήρ’, in English ‘Jesus Christ, Son of God and Saviour’. During Jesus’ lifetime, he was also referred to as ‘the fisher of men’s souls’. For example, in Matthew 4:19 ‘And Jesus said unto them, Come after me, and I will make you become fishers of men’.207

It seems that Borromini may have intended the viewers to sense a relationship between San Carlino and a Renaissance church. The same central dome and four semi-domes flanking it are there, but they have been constructed in such a way that they appear to have yielded to pressure from two sides. Spatially, the result is a sense of flow and fusion between the compartments instead of the emphasis on the clearly defined units, which was characteristic of high Renaissance buildings.208

Moreover, out of all the geometrical figures that have been mentioned above, the most potent is the equilateral triangle. Throughout history, it has been a symbol of power held in the highest respect. In ancient Greece, the numerical and geometrical significance of this figure was the holy composition, and people would even swear their vows by it. Likewise, ancient Romans considered this form a symbol of justice, unity and righteousness.

The equilateral triangle is also a sacred symbol of the Deity, being the same in its form as the ancient Greek delta, or letter ‘D’. The Phoenician letter ‘D’, as well as the

206 Augustine and Wand, St. Augustine's City of God, p.23. 207 Guest, Bible Moralisee. 208 Helen Gardner, Art through the Ages (4th edn.; New York: Harcourt, Brace, 1959). 91

Egyptian, was of a similar form. The equilateral triangle in Greek tongue, as well as many other ancient languages, was thus the initial letter of the name of Deity.209

Similarly, the reason for this belief also came from the structure of the form that has three equal angles and three equal sides. At that time the equilateral triangle, or τετρακτύς (or Tetraktys), stood for the Greek word tetra (four) and tys (lines). The composition of the Tetraktys has its own numerical value and it symbolises the universe as it was perceived in the Pythagorean period (Figure 4.29). For Pythagoras, numbers and forms were used to depict universal and divine principles as real as light and gravity. Pythagoreans have a number of prayers that address the significance and holiness of the Tetraktys. Parallel to that, Tetraktys also shows the importance of numerology, geometry and order for Pythagoras followers. These claims take form in the passage below:

Bless us, divine number, thou who generated gods and men! O holy, holy Tetraktys, thou that contains the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never- swerving, the never-tiring holy ten, the key holder of all.210

Figure 4.29 Pythagorean mystical symbol Tetraktys, consisting of four rows and ten points (Illustrated by the author)

209 Robert Hewitt Brown, Stellar Theology and Masonic Astronomy: Or, the Origin and Meaning of Ancient and Modern Mysteries Explained (New York,: D. Appleton, 1882), p.150. 210 Dantzig and Mazur, Number : The Language of Science, p.42. 92

The Tetraktys figure is formed by placing one point on top of a triangle or pyramid and below that another two points, followed by three on the next level and then the last row with four points. The figure symbolises unity, starting from one and passing through four rows or levels and returning to one. The progression from unity to multiplicity by using numerological order to model this universal wholeness defines the philosophy of Pythagoras as one of analogy.211

In a way, this composition suggests that unity underlies diversity and multiplicity. In addition, it illustrates a unity of the parts to create a whole. This is the foundation of the tetrahedron: a Platonic solid with four faces and four vertices. Plato in Timaeus referred to it as a symbol of fire.212 This is pagan Greek geometry on the one hand yet on the other, there are Christian orthodox geometric metaphors. For example, the equilateral triangle was used to represent the Holy Trinity and the unity of the Father, Son and Holy Spirit. These three names have been repeated many times in liturgical writings. ‘Go therefore and make disciples of all nations, baptising them in the name of the Father and of the Son and of the Holy Spirit’.213 Borromini appropriately applied this representation of an equilateral triangle in his design for San Carlino and his later work, the church of San Ivo (1642–1650).

Enlightenment Architecture

Speculating on the geometrical organisation of Borromini’s works, I sensed throughout that for him, the circle was not a closed figure expressing perfection but a potentiality of the form ‘circle’. Borromini applied the circle in his designs as a creative centre and viewed the oval as a consequence of the circle’s growth. They tackle one another, and are surrogates for each other.

Moreover, another important element in Borromini’s design is that it is based on circular form, as is the creation of his domes. The dome is incorporated within every other geometrical feature of the church, with the circles within the cupola and the ovals

211 Christoph Riedweg, Pythagoras : His Life, Teaching, and Influence (Ithaca: Cornell University Press, 2005), p.83. 212 The Greek terminology Tetrahedron translates to tetra (as number four)-hedron (seats), or a four sided figure and is usually refered to as a three dimensional triangle. M. Hazewinkel, Encyclopaedia of Mathematics, Supplement I (Auckland: Springer, 2010), p.446. 213 Robert H. Mounce, The Book of Revelation (Revised edition. edn.; Grand Rapids: Eerdmans, 1998). Matt.28:16-20. 93 within the church as a whole representing one form, when all the interpenetrating forms of the structure are recognised in the shapes of the coffers.

In other words, he sees the oval as a circle in motion. Borromini’s correlation of circle and oval occurred only a few years after Kepler had arranged both circle and ellipse in a continuous series of geometrical sections. This near simultaneity may or may not be accidental, but one thing is certain: the visual evidence of Borromini’s work suggests that his original response correlates with the most advanced scientific thinking of his time, towards the characteristics of continuity among previously defined geometric forms. The circle is the familiar medieval symbol of the sun, and the sun is a symbol of wisdom. The circle is also the main feature in the Temple Minerva Medica in Rome.214 For Borromini’s planning, learning from past examples, especially the models from antiquity in Rome, was the imperative answer (Figure 4.30).

214 The fourth century Roman Temple of Minerva Medica is located in the rione Esquilino in Rome. The circular shape of the dome’s interior (characteristic of the Pantheon structure) and the decagonal structure are the important elements of this temple architecture. 94

Figure 4.30 Borromini: pencil sketch of Minerva Medica in 1643. There are dimensions and grids illustrated on this sketch.215

In the case of Borromini’s conception for his designs, he embodied not one theme but three thematic symbols. It was indeed the Minerva Medica (Figure 4.30) but it was also the moment of Pentecost; under the beliefs to eternity, the Church was the house wherein the Holy Spirit descended upon the apostles, whose statues originally filled the twelve niches in the lower zone of the building. Thirdly, the decoration throughout was shown to refer to the papacy as the earthly mediator of divine wisdom.216

Another aspect is the numerical kinship between San Carlino and St Peter’s217 (designed by number of architects and artists including Italian architect, Donato Bramante (1444– 1514), Swiss-Italian architect Carlo Maderno (1556–1629), and Gian Lorenzo Bernini (1598–1680)) (Figure 4.31).

The relevance of this affinity to the hypothesis of this thesis (in relation to spiritual meaning attached to applied geometry in architectural form) is to understand the source

215 E. Debenedetti, L'arte Per I Giubilei E Tra I Giubilei Del Settecento (The University of Virginia: Bonsignori, 2000).Fig. 145. 216 Steinberg, Borromini's San Carlino Alle Quattro Fontane: A Study in Multiple Form and Architectural Symbolism, p.391. 217 St Peter’s Basilica remains one of most important places for Christian believers of the world from renaissance time until today. 95 of Boromini’s belief in symbolism of geometrical patterns, and the major influence on his designs. Therefore, in a later section of the chapter I describe in more detail how these geometric patterns have evolved and been used in architectural design without their initial attached meaning.

Figure 4.31 Maderno: St Peter, Carlo Maderno, façade constructed in 1506, Rome.218

It is as though Borromini systematically reduced the dimensions of the chapel of St Peter’s to render his own creation. The internal octagon under the dome at San Carlino is equal to the diameter of the dome of St Peter’s (Figures 4.32–4.33). In reading Borromini’s biography, it is evident that Borromini studied the structure of St Peter’s in detail and reflected it in his own work.219

Borromini suggests that San Carlino, envisaged as a smaller scale Basilica, was to be a symbol of the Church of St Peter’s. One example is the way that San Carlino reduced St Peter’s design by lowering the drum inside the extended barrel vaults of the Greek cross, with the exception that Borromini’s illusionist coffering represents just such barrel vaults, as if it is invoking the absented elements by suggestion (Figure 4.32).

218 J.L. Varriano, Italian Baroque and Rococo Architecture (London: Oxford University Press, 1986), p.36. 219 Anthony Blunt, Borromini (Cambridge: Belknap Press of Harvard University, 1979). 96

The coffering in San Carlino in form of Greek cross and octagon.

The eight-sided octagon placed together Vesica piscis and the other major elements of San Carlino ceiling.

There are sixteen columns in the main interior space those caring the load of the oval dome.

Figure 4.32 Borromini: San Carlino alle Quattro Fontane, dome, Rome (analysis by the Author).220

220 Ibid. p.52. 97

Figure 4.33 Bernini: St Peter’s dome, Rome.221

It seems that Borromini may have intended beholders to sense a relationship between San Carlino and a Renaissance church. The same central dome and four flanking half- domes are there, but they have been constructed in such a way that they appear to have yielded to pressure from two sides (Figure 4.32).

The result spatially is a sense of flow and fusion between the compartments instead of the emphasis on the clearly defined units which was characteristic of high Renaissance building.222

Following on from his above explanation, German art historian, Eberhard Hempel (1886–1967) continued his observations on San Carlino as an image of a Basilica’s crossing and in conclusion, he called it the ‘refectory’. The other obvious similarity is that St Peter’s dome designed by Michelangelo and San Carlino’s dome aperture both measure exactly 186 Cubit at their bases.223 The octagonal theme shows strongly in the church plan, stretched by four axes across the chapel. Interestingly, the diagonal wall

221 Varriano, Italian Baroque and Rococo Architecture, p.75. 222 Eberhard Hempel, Francesco Borromini (Wien: A. Schroll & Co., 1924), p.400. 223 The term Cubit is the standard Roman unit of measurement that comes from the Latin word, ‘Elbow’ which is about 46 cm. 98 sections of the interior are designed to create the landing place of an octagonal crossing, equivalent to the landing place of St Peter’s (Figure 4.34)..

The octagon embody the other geometrical forms those symbolised the three realms in the dome of St Peter church. Heaven (circle), earth (square) and Jesus Christ (Greek Cross).

The Greek cross that forms the eight sided shape (octagon) forming the dome of St Peter designed by Bramante. The design has been aspired by the Pantheon. The dome is supported by four piers.

Figure 4.34 Bramante: St Peter, floor plan, Rome.224

This, and the structural octagon traced in the plans, puts beyond doubt that the octagon is materially present in San Carlino and is essential to its interpretation. The columns of San Carlino number sixteen in total and they are positioned and clustered in a way that they support the three overlapping rhythms of the structure. All sixteen columns have been applied to express a symbolic sense: they carry the church ‘as a geometric trinity’.225 In the case of the dome’s decoration, ‘the honeycomb patterns’226 of its stucco refers back to St Peter’s octagonal structure, so that once again we can compare it with the Basilica. The numerology of its proportions the broad face design of its

224 Varriano, Italian Baroque and Rococo Architecture, p.21. 225 Leo Steinberg, Borromini’s San Carlino Alle Quattro Fontane: a study in multiple from and architectural symbolism (New York: Garland Press, 1977), p.73. 226 Hempel, Francesco Borromini, p.380. 99 triangular vaulting under the dome, and the surface expression of the San Carlino dome are all references to St Peter’s.

The dome coffering performs precisely those elements that compose the main structure. This pattern is a kind of metaphorical representation in architecture of the divine progression. Light is directed from the centre of the dome as the focal source of light in the immediate interior, beside four octagons on the four corners of the oval dome, which are open to the outside and provide additional luminosity. The eye is gradually led along the vertical interior line towards the ceiling and all the way to the dome. This gradual movement finally arrives as a light at the Holy Spirit in a very symbolic way. Moreover, this beautiful and steady unfolding of geometrical order shows that Borromini does not only apply it to produce form, but to generate an architectural space as a whole. On the other hand, this configuration on its own, symbolically, expresses the concept of progression from earthly life towards the perfection of the divine through the process of spiritual enlightenment.

Astronomical nova to Keplerian composition

The hidden dimension mentioned above has been referred to by many ancient religions as ‘axis mundi’, or a cosmic axis that connects heaven and earth, in other words, a communication line between lower and higher realms. Ultimately as described above, geometry becomes a vital tool to link mankind and a Higher Power. In the same way, when Galileo was asked to describe his book on cosmology, he spoke of geometry and its implications:

…. but we cannot understand the universe if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.227

The reason behind the hidden order of Borromini’s planning and his unwillingness to reveal the groundwork of geometrical configurations of his building, is to allow the

227 Galileo Galilei, Johannes Kepler, and Edward Stafford Carlos, The Sidereal Messenger of Galileo Galilei and a Part of the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries (London: Rivingtons, 1880), p.171. 100 viewer to decode the real meaning behind the obvious external features of the structure unaided. Borromini was trained by the Roman Baroque architect, Gian Lorenzo Bernini (1598–1680), who designed the main interior spaces of St Peter’s Basilica. It was during his apprenticeship that Borromini’s interest in ancient mathematics and geometry was developed. He became exposed to the works of Galileo and his study of divine geometry and cosmology.

Even though there is no hard evidence or explicit acknowledgment of this exposure, it is clearly illustrated in his architectural style and in particular, the influence of Neo- Platonism developed by German astronomer and key seventeenth century figure, Johannes Kepler (1571–1630). Borromini was quite receptive to Kepler’s mathematical and cosmological theory and translated it into his practice. In the Astronomia Nova (the New Astronomy) of 1609, Kepler expounded his solar system theory with its introduction to elliptical orbits around the sun (Figure 4.35). Even though Borromini’s suns or circles in oval orbits are from a later date, they directly relate to Kepler’s views on the order and composition of the universe.

Figure 4.35 Kepler: Laws of planetary motion, oval orbits.228

One can say with certainty that Borromini used ovals and circles in his designs in a manner quite unlike any other architect in history. Borromini pictured a microcosmic vision of the universe in his church designs in the same way as his contemporaries,

228 David C. Knight, Johannes Kepler and Planetary Motion (London: Chatto & Windus, 1965), p.48. 101

Galileo and Kepler wrote about universal order and ultimate truth. This can only be understood through the study of the celestial realm based on divine geometry (Figure 4.35).

Hence, San Carlino was planned and organised through a strict geometrical composition and that in itself represented the inbuilt structure of the universe as a whole; indeed, it was where meaning and form come together as a narrative framework (Figure 4.36).

Figure 4.36 Johannes Kepler: Mysterium Cosmographicum, diagram of the planetary spheres, 1596.229

It seems to me that Borromini moved away from the idea of proportions of the human body and their relation to architecture as a representative model of the universe. I also suggest the epistemology in Borromini’s work is evidence of his awareness of Kepler’s cosmology. For example, it was Kepler who first revealed, in Astronomia Nova, that the planets revolve in elliptical orbits with the sun at a central point, instead of the older

229 J.R. Voelkel, The Composition of Kepler's ‘Astronomia Nova’ (Princeton Princeton University Press, 2001), p.35. 102 belief that they move in a circular path.230 He also believed that the sun is at the heart of the universe and is the main cause of the planets revolving. Therefore, Borromini was also influenced by Kepler’s elliptical planetary orbits for the dome of San Carlino and the opening in the middle of the dome, which symbolises the sun. In addition, the significance of this symbolic figure has been mentioned in a biblical passage: ‘she [Wisdom] is the brightness of eternal light ... she is more beautiful than the sun’.231 And here in San Carlino, we can see the sun surrounded by the eight crosses and eight octagons.

230 Johannes Kepler and William H. Donahue, New Astronomy (Cambridge: Cambridge University Press, 1992), p.132. 231 Phillips, Bible. New Testament. Revelation. English. The Book of Revelation: A New Translation of the Apocalypse.Wisdom 7:26, p.29 103

Figure 4.37 Borromini: San Carlino, façade, Rome.232

San Carlino is a church that was conceived as Christ’s mystic body by analogy with St Peter’s, the earthly house of worship. Within Borromini’s oval and cross rested a dual iconological meaning for what the Church stands for, as the symbol of the body of Christ, and as a Christianised planet/Orb—as old as Christianity itself. The followers of Christ referred to the body of Christ as follows in Colossians (1:24): ‘Now I rejoice in my sufferings for your sake, and fill up on my part that which is lacking of the afflictions of Christ in my flesh for his body's sake, which is the church’.233 Both symbols are embedded in the structure in such a way that they do not appear openly to viewers, but subtly suggest to them the structure of St Peter’s. The parallel between the

232 Varriano, Italian Baroque and Rococo Architecture, p.53. 233 Catholic University of America., New Catholic Encyclopedia (2nd edn.; Washington: Thomson/Gale, 2003). 104 church and the body of Christ, the building that stands to represent the house of God, is a microcosm of the Church universal.

The bravery of Borromini’s architectural symbolism reflects the methodologies introduced by early theological thinkers and Church fathers such as St Cyprian, who asserted that the structure of the church building should be ‘in ternary form, since it is essentially a symbol of the trinity’,234 or Tertullian, who claimed the Church stands for ‘the body of the three Persons’.235 On subsequent examination, it becomes clear that Borromini’s design and exegesis for San Carlino applied very important elements to signify Jesus Christ and the heavenly realm.

Conclusion

In relation to the two hypotheses I present in this study, (1) The identification and investigation into the geometrical patterns such as oval, octagon, Vesica piscis and cross that has been presented to architectural form during the Baroque era. Some have been inherited from the past and symbolises the same belief, while others represent a meaning using a different/new geometrical forms; and (2) Due to the critical scientific development and also the significant evolvement of the Church during the sixteenth and seventeenth centuries, the elimination and replacement of number of past geometrical patterns and their symbolism occurred in built forms.

In the previous three chapters, of this thesis my investigation into early architecture introduced a number of types of structures, geometrical forms, beliefs, meanings and the role of spirituality. These meanings conveyed through geometrical patterns endured for many centuries and shaped significant architecture, buildings and theory. In this chapter, I described and explained the vivid change in application of geometry during the 16th and 17th centuries. A purely spiritual proposed milieu conflicted with new discoveries that provoked the new forms and techniques in building design. This was the beginning of modern era in the world of art and architecture. In the next chapter, my historical study continues towards the nineteenth century and the rise of secularity and technology.

234 Henri De Lubac, The Splendor of the Church (San Francisco: Ignatius Press, 1999), p.29. 235 Ibid. p.39. 105

Chapter Five. On Modernism and its Sources in Geometry

Figure 5.38 Le Corbusier: en la Acropolis Atenas (Acropolis in Athens), 1911.236

For the artist, mathematics does not consist of the various branches of mathematics. It is not necessarily a matter of calculation but rather of the presence of a sovereign power; a law of infinite resonance, consonance, organisation. Rigour is nothing other than that which truly results in a work of art, whether it be a Leonardo drawing, or the fearsome exactness of the Parthenon, or the unity in a Cezanne, or the law which determines a tree, the unitary splendour of roots, trunk, branches, leaves, flowers, and fruit. Chance has no place in nature. Once one has understood what mathematics is—in the philosophical sense—thereafter one can discern it in all its works. Rigours, and exactness, are the means behind achieving solutions, the cause behind character, the rationale behind harmony.237

By using mathematics, it is possible to unlock the mysteries of geometry and explore the coherence of numbers in order to understand how the universe works. Artists and architects have often looked to mathematical formulas for creative inspiration in their own quest to unearth the mysteries of the universe. This is one of the key ideas I will present in this chapter, which will be determined through examples of linear thinking

236 L. Corbusier and I. Žaknić, Journey to the East (London: MIT Press, 2007), p.80. 237 Corbusier Le, Peter De Francia, and Anna Bostock, The Modulor : A Harmonious Measure to the Human Scale, Universally Applicable to Architecture and Mechanics ([2nd edn.; London: Faber and Faber, 1961), p.32. 106 through the nineteenth and early twentieth centuries. This is to provide evidence in relation to my second hypothesis that geometrical patterns during this era were applied in architectural milieus without any attachment to past symbolism of spiritual meaning or beliefs. Rather, the architects sought to discourage such representation. The purpose is to give a synopsis of the evolution of architectural form, philosophical interpretation of spiritual beliefs, and their antecedents. This is the point of transition from the once claimed religious spiritualism attached to geometrical shapes, to the more secular spiritualism of Platonism.

Wars, Revolution and Nihilism

Charles-Édouard Jeanneret (1887–1965), better known as Le Corbusier, was arguably the most influential architect of the twentieth century. He saw science as a means to improve technology, and he considered technology to be the foundation for his creative practice.

His ethos towards geometry and, more generally, shapes, was an essential part of his philosophy, as well as its application to metaphysics, and even theology. To Le Corbusier, mathematics was almost a religion, and his deference to it above all other disciplines was based on one key reason: mathematics is the only way to enlighten man with the most fundamental laws of the universe, which rise above the precision of anything else. That is also how designers of the great monuments from antiquity, the Middle Ages and the Renaissance brought harmony to their masterpieces. Thus, to take architectural design beyond the present requires mathematics and geometry; only then can structures be described beyond doubt as being ‘modern’ in a similar way to architectural classics such as the Parthenon (Figure 5.1).

It is impossible to appreciate symbolism and belief systems in twentieth century modernist architecture without first coming to terms with the work of Le Corbusier. His influence has extended over many regions and generations, and an assessment of his influence is a complex matter because it is based on subjectivity, that is varies according to one’s point of view. Nevertheless, evaluations and judgements of any kind are preferably based upon thorough analytical scrutiny rather than on contemporary criticism. Critics need to understand the existence of an avant-garde that changed the concept of art (both in practice and in theory). The tendency in earlier and contemporary 107 generations to indulge him was seen by Le Corbusier as an unquestionable fact of the modern era, which saw through many historical themes with greater depth and different views. Those waiting for such new ideas praised that dutifully.

To effectively examine the way Le Corbusier, as an artist, architect and theorist, compressed so many levels of meaning into his work, I find it necessary to reference the architecture he experienced and the symbolic associations that shaped his creative thinking. Le Corbusier’s activities as a professional cannot be distinguished from the influence of tradition, society, nature or culture upon him. That is why the forms he created gained authenticity from a social and political vision. He translated these influences through the language of his own ethos, creating a unique architectural style yet detaching the meaning belonging to traditional symbols and building forms.

Many thinkers and artists born in the late nineteenth century regarded themselves as prophets, and Le Corbusier was no exception. He strove to teach the truth and reveal the ‘essence of the times’ to his audiences through his writings, buildings and sculptures. He attempted to embed in his modernist architectural ideals such as timelessness, because he viewed architecture as superior to any other form of art or even spirituality.

He struggled with the practices of many so-called avant-garde architects and scholars and attempted to create something less temporal and more timeless, which Frank Lloyd Wright called ‘the law and order inherent in all great architecture’.238 Interestingly, in many of his earlier writings and practices, Le Corbusier’s emphasis was on the philosophy that most exemplary art of the present must indeed be rooted in the past; in other words, that rebuilding and renewal of architecture in his time should extend its concepts back to its roots. This belief was upheld by a number of architects, although few conveyed it effectively in their designs. Indeed, American architect and scholar Anthony Vidler (1941–), elaborated on the same idea: ‘We must return to the source, to the principle and to the type’.239 This is not only relevant for an architect to consider, but is emphasised as a responsibility.

238 Frank Lloyd Wright and Frederick Albert Gutheim, Frank Lloyd Wright on Architecture : Selected Writings 1894-1940 (New York: Duell, Sloan and Pearce, 1941). 239 Anthony. Vidler, The Idea of Type: The Transformation of the Academic Ideal, 1750-1830 (New York MIT Press, 1977). 108

In appraising Le Corbusier’s work as a modernist thinker, it is imperative to examine his journey of learning. It is evident in his oeuvre that he was fascinated by the writings of Henry Provensal and Edouard Schure, whose discourses extensively deliberated classical culture and religion. In addition, he travelled, read widely, learned and wrote much about ancient architecture and the lessons to be learned from the pyramid of Cestius, the Colosseum, Ancient Roman structures and the Grand Mosque at Bursa. The pure representation of these bold structures studied by Le Corbusier are presented through simple yet powerful geometrical compositions from the designers, who were quite aware of the symbolic nature of these behemoths.

In the very early stages of his professional development, Le Corbusier undertook trips to various countries and pilgrimages to many great buildings, including the Acropolis in 1911. He later reflected on his journeys and the design principles of historical buildings (Figure 5.39), and discerned ‘in the diversity of the races the fundamental unity of human nature’.240 He perceived the universal principles that perfected those great buildings and accordingly believed that if anyone wished to achieve such perfection, he must follow the same path that resulted in the creation of the Parthenon. Above all, what is stressed in the following quotation and in many other writings of his is standardisation:

We must see the establishment of standards so we can face up to the problem of perfection. The Parthenon is a product of selection applied to a standard. Architecture works on standard. Standards are a matter of logic, of analysis, of scrupulous study: they are based on a problem well posted. Experimentation definitively fixed the standard.241

This emphasis on creating a standardised system/common proportion for any milieus is to create a sense of unity and control, regardless of style. The result of this belief was his work, The Modulor, a product for modern design. For Le Corbusier, this ideal proportional system precisely corresponds to the quest of the contemporary culture and industrial revolution of his time.

240 Stanislaus Von Moos, Le Corbusier, Elements of a Synthesis (Cambridge, Mass: MIT Press, 1979). 241 Le Corbusier and Frederick Etchells, Towards a New Architecture (Reprinted and enlarged from the 1931 edn.; London: Architectural Press, 1987), p.178. 109

I selected this particular architect and his practice as a major example in proving the contentions of my thesis because of Le Corbusier’s obvious shift, even his aggressive approach towards design of building forms serves to reiterate the true meaning of symbolism presented by geometrical forms in architecture. What was Le Corbusier’s understanding of past beliefs, and was it successfully translated in his work?

Figure 5.39 Le Corbusier: Notre Dame, Paris.242

Numerological Mysticism, Golden Section and Modern Architecture

In an essay by Italian historian, Pierre Vaisse (1930–2001) about Le Corbusier and his obsession with Gothic architecture, Vaisse declared that Le Corbusier’s fascination with buildings from that era was only in relation to the meaning and symbolism of Gothic structures rather than its construction methods. It is worth mentioning here that Le Corbusier was also captivated by the buildings in Pompeii. Based on his sketches and

242 Ibid. p.78. 110 notes, it is evident that he analysed and illustrated those buildings with reference to their geometrical composition and arrangement (Figure 5.40).

For him, this was a way to convey a sense of unity between different elements (harmony) and generated order. It is seen as essential for the architect in pursuit of beauty and an intensity of meaning, to produce symbolism using numbers and geometry. The medieval mind was informed by a set of spiritual beliefs that dictated architectural design, for example the numeric ordering of façade elements.

Figure 5.40 Le Corbusier sketches. Left is the Casa delle Nozze d’Argento, Pompeii, 1911. To the right is the house of Sallustius, Pompeii, Italy.243

For Le Corbusier, however, Gothic cathedrals embodied esoteric traditions going back to the time of Pythagoras and his fascination with the mysticism of numerology. In addition, his interest in mathematics was fuelled by reading Pythagoras’ works, in order to understand the extent of this influential discipline on his own work.

Gothic architecture is not, fundamentally, based on spheres, cones and cylinders. Only the nave is an expression of a simple form, but of a complex geometry of the second order (intersecting arches). It is for that reason that a cathedral is not very beautiful and that we search in it for compensations of a subjective kind outside plastic art. A cathedral interests us as the ingenious solution of a difficult problem, but a problem of which the postulates have been badly stated because they do not proceed from the great

243 Ibid. p.218. 111

primary forms. The cathedral is not a plastic work; it is a drama; a fight against the force of gravity, which is a sensation of a sentimental nature.244

Reading the above quote by Le Corbusier, a question arises: How and what did he draw from the mathematical teachings of Pythagoras and Gothic architecture into his own work in the age of machine, and the intellectual conditions of capitalist industrial technoscience? In the following section, evidence will be provided on what was retained and what was erased from these learnings for Le Corbusier, and the influential factors that affected the process.

From Gothic cathedrals, Le Corbusier learned about the integral relationship between the chronological ordering of geometry, as this influenced the form and construction of these buildings and how they come together harmoniously. The ‘Golden section’ or ‘Golden mean’ was the fundamental methodology used in design of Gothic cathedrals. Conversely, Pythagorean numerology taught him about the role of harmonies and proportions; the great sense of rhythms embedded in Pythagorean numerology. Le Corbusier witnessed and experienced these methods. But through time, in his prolonged attempts to apply the Golden mean to produce his own legacy; he reduced the Golden mean into rational numbers, detached from its past symbolical meaning (refer to Chapter one and three). Le Corbusier shifted the initial status of ‘Golden ratio’, from absolute and universals into relative standards and immediate environment related. Effectively, his milieus lacked the metaphysical implications of the ancient systems. The selected examples of Le Corbusier’s interpretation of the ancient system, Open Hand, The Modulor, Carpenter Centre and Villa Schwob. I will analyse each of these works later in this chapter.

On the other hand, there was another significant influence in the architectural practice and form-making of Le Corbusier. Paul Turner, who studied and researched Le Corbusier’s life, affirmed that he was radically influenced by eighteenth century German philosophy (that is, deism and the revolution in rationalism).245 Most important was Le Corbusier’s exposure to the works of German philosopher, Friedrich Nietzsche (1844–1900), especially his ‘Will to Power’. Nietzschean thoughts carried the views of rebellious polemicists, who in their bold and radical approach discarded the ‘existing

244 Ibid. p.105. 245 Paul Venable Turner, The Education of Le Corbusier, (New York: Garland, 1977), pp.37-59. 112 world’ as we know it.246 That was Le Corbusier’s first exposure to dialectical thinking and it supported his existing ideas on the tragic view of mankind in his time and the deepening of spiritual origins. He opposed the practitioners of Art Nouveau for their lack of firm standards, and functionalists for their lack of lyrical views. Thus, Le Corbusier carried out his observations on the necessity of secret Greek teachings on the great gods of art; the duality of Apollo and Dionysus, being partially rational and partially poetic.

His philosophical readings and search for new truths left deep marks in his self- awareness as an architect, artist and writer for the rest of his career. At the same time, in many ways he began to put into perspective his prophetic mission of regenerating mankind and bringing salvation.

I have borrowed my adjectives from the Greeks, who developed their mystical doctrines of art through plausible embodiments, not through purely conceptual means. We are made to recognize the tremendous split, as regards both origins and objectives, between the plastic, Apollonian arts and the non-visual art of music inspired by Dionysus. The two creative tendencies developed alongside one another, usually in fierce opposition, each by its taunts forcing the other to more energetic production, which the term art but feebly denominates: until at last, by the thaumaturgy of an Hellenic act of will, the pair accepted the yoke of marriage ...247

Le Corbusier’s understanding of his role as an artist draws much from Nietzsche’s concept of Übermensch, and the role model for a person who seeks meaning.248 In fact, he borrowed greatly from Nietzsche on the theme of the ‘Open Hand’ for his 1930 painting and 1950 cover of the book Poesiesur Alger and the 1952 monument in Chandigarh, India. This theme of the Open Hand (Figure 5.41) can be seen as Le Corbusier’s ideogram for a seer who destroys for the sake of mankind’s rejuvenation and growth.

246 Nietzsche in his book ‘Thus Spake Zarathustra’ demonstrated the belief that ‘mankind ‘ was reaching the end and the only way to surpass it was through evolution and it is beyond man to achieve that (in Nietzsche writing ‘ ‘man’ only represents ‘person’ and not a specific gender). Friedrich Wilhelm Nietzsche, T. Common, and O. Levy, Thus Spake Zarathustra (London, 1967). 247 Friedrich Wilhelm Nietzsche, Raymond Geuss, and Ronald Speirs, The Birth of Tragedy and Other Writings (Cambridge: Cambridge University Press, 1999), p.23. 248 The German word Übermensch used by Nietzsche simply means over person/person or one who surpasses. In Nietzsche, the anti-religious view is of Übermensch not as the saviour but as a destroyer. ‘The waters of religion are ebbing away and leaving behind swamps or stagnant pools’. Friedrich Wilhelm Nietzsche and Eliseo Vivas, Schopenhauer as Educator (Chicago,: Regenery, 1965), p.4. 113

Conversely, it also symbolises Le Corbusier’s egoism and his belief in the power of modernism and age of machines, just like a large-scale modernist painting. The 14-metre high revolving Open Hand monument in Chandigarh, with an eye carved in the centre of the palm gazing over the city and reaching upward towards heaven, is titled ‘Open to give; Open to receive’. This monument’s conception can be perceived in two ways: as a floating, Picasso-style dove of peace, and as Zarathustran symbolism. In the second part of Nietzsche’s book, when the lonely saint, Zarathustra returns to his cave to hide from men, he declares:

His soul, however, became impatient and full of longing for those whom he loved: because he had still much to give them. For this is hardest of all: to close the open hand out of love, and keep modest as a giver.249

249 Friedrich Wilhelm Nietzsche and R. J. Hollingdale, A Nietzsche Reader (Harmondsworth: Penguin, 1977), p.244. 114

Figure 5.41 Le Corbusier: Open Hand, Chandigarh.250

For Le Corbusier, this is emblematic of universal harmony in this tragic period in history, and was perhaps the starting point for Europe’s moral regeneration in the wake of the Second World War.

At the age of 15, when he enrolled at La Chaux-de-Fonds art school, an institution that was based on encouraging invention, developing knowledge in ornamentation and perfecting good values for future artists and decorators, Le Corbusier met his lifetime master, Charles L’Eplatte. Little is known about L’Eplatte, but one thing is evident from his student’s writing; his teaching revolved around the importance of understanding nature and its underlying structure. He was also a great believer in translating natural forms into an art of abstract geometrical motifs. He was a passionate admirer of John Ruskin’s medievalism and from his study of Ruskin’s works and, in particular his ‘Elements of Drawing’, L’Eplatte encouraged his students to examine nature in great detail and try to abstract the results of their observations and then study how order in the natural world can advance the human representation of ideas. Le Corbusier described

250 Fellow Banner, 'Aging Modernism ', , accessed 25th June 2011. 115

Ruskin as ‘the geometrician and algebraist of flowers’.251 Thus, Le Corbusier found geometry not only in the architecture of the past, but also in nature.

Figure 14.42 Le Corbusier: Study of pine trees (1905–06).252

It is important to mention here that in L’Eplatte’s asked students to closely study and reproduce Ruskin’s ‘folklore of the fir tree’ and from minute observation of its upright position and pyramidal shadow, Le Corbusier saw an emblem of moral order. The influence of his master’s teaching can be clearly observed through Le Corbusier’s conceptual drawings and sketches that capture the underlying shapes of plants with swirls and curves. However, he found it hard to find examples of what he had been told was important, as he lacked an affinity for nature.

In the early stages of his research life as a young architect, Le Corbusier came across the not-so-popular German thinker and architect Henry Provensal (1868–1934), author of Towards Universal Harmony. Le Corbusier found Provensal’s views were in accord with his own. Provensal addressed architecture as ‘the cubic, harmonious expression of thought’ and suggested new leadership was urgently needed to reintegrate spiritual knowledge.253 He also expressed apprehension for future generations facing the rapid advance of materialism and modernism. One of the most important areas of his writing that Le Corbusier paid close attention to was on the laws of absolute, divulged through

251 Le Corbusier, The Decorative Art of Today, (London: The Architectural Press, 1987), p.132. 252 H. Allen Brooks, Le Corbusier’s Formative Years: Charles-Edouard Jeanneret at La Chaux-de-Fonds, (Chicago: The University of Chicago Press, 1997), p.139. 253 William J. R. Curtis, Le Corbusier : Ideas and Forms (London: Phaidon, 2006), p.23. 116 divine principles of numerological unity and harmony. He cites Pythagoras as the father and prophet of mystical numerology, as well as Plato’s Simile of the Cave when he talks of ‘the quality of an idea that is reproduced in a symbolic form’.254

For Le Corbusier, Pythagoras went far beyond the teaching of numbers. He defined each number and its principle, in relation to law and active forces in the universe. Nevertheless, he said that its basic principles were contained in the first four numbers (Number 1,2,3 and 4), since ‘by adding or multiplying them we find all the others’.255

The influence of all this early philosophical reading is evident in Le Corbusier’s application of ‘harmonic rapports’ and ‘visual proportion’ to his early designs. To this modern architect and thinker, beauty was far more important than practical and functional considerations that could be achieved using proportion, which reflects its underlying meanings.

One of the other major features in Le Corbusier’s revolutionary works was his search for truth in music and theatre. He grew up in a family of musicians; his mother was a conventional piano instructor and his brother a professional musician and composer. To him architecture, like music, was an expression of a natural human impulse and an expression of the human spirit seeking the sublime.256

In 1917, as recorded in his ‘Œuvres complètes’, he watched an unorthodox ballet in a Paris theatre performed to music by composer Stravinsky called The Firebird. He interpreted this as a decline in the values that he was brought up with in the art school of La Chaux-de-Fonds. In comparison, Stravinsky’s The Rite of Spring in 1913 was for him an outstanding work of modern music: moving, inspirational and formative. It was around the same time that his brother Albert, in collaboration with Adolphe Appia, invented a new drama production that they called ‘Espaces Rythmiques.

One of the characteristics of this new style was its universality and pure rhythm, free of any decoration that might cause restrictions for a performer’s movements. Appia states

254 Charles Jencks and Corbusier Le, Le Corbusier and the Continual Revolution in Architecture (New York: Monacelli, 2000), p.33. 255 Paul Venable Turner, The Education of Le Corbusier (The University of Michigan: Garland Pub., 1977), p.108. 256 The reference to spirit here is not the usual understanding of spirituality. For Le Corbusier it means spirit in the German Romantic way, a nationalistic identity born out of moral action. 117 that ‘Without gesticulating body, the staging remains mute’.257 This involves the translation of music into something tangible, being the movement of a performer’s body. Aware of his brother’s discovery of the way to make music somatic, Le Corbusier applied similar thinking to architecture to make it more experiential. He did this by exploring the rhythms of proportions within the composition of forms (that is the movement of architecture as anchored geometry). For him, this was the very essence of design; the need to communicate beauty to the user of these spaces through the mathematical beauty of geometry. Professor Max Risselada (1953–) reviewed the life of Le Corbusier and in 1910, after confirming that Le Corbusier was influenced by ‘Espaces Rythmiques’, Risselada stated:

In much the same way as movement and gesture were aimed at making the heart of the music audible, the ‘promenade architecture’ had a purpose of making the core of the architecture tangible.258

One of the outcomes of his studies was the creation of a system that became known as The Modulor (Figure 5.43). In 1920 in pre-war Europe, during his purist period,259 Le Corbusier and Amedee Ozenfant (1886–1966) developed a passion for geometrical forms and mathematics. They called themselves purists and wrote a manifesto titled Après Le Cubism (translated English title After Cubism), continuing with a series of essays over five years and the magazine L’Esprit Nouveau.

257 Adolphe Appia, The Work of Living Art; a Theory of the Theatre (Coral Gables: University of Miami Press, 1960), p.115. 258 M. Risselada, A. Loos, and J. Van De Beek, Raumplan Versus Plan Libre: Adolf Loos and Le Corbusier (Rotterdom: 010 Publishers, 2008), p.165. 259 One of the bases for the purist vision or purism movement is anti-ornamentation. This ideology encourages the liner, clear and uncomplicated geometrical pattern in architectural milieus. There is no secret or hidden meaning. It is just what beholder sees. The appearance of aesthetic through modern functionality defined Le Corbusier purist approach. 118

Figure 5.43 Le Corbusier: The Modulor, 1948.260

The main argument of this essay series, under the heading ‘Living Aesthetics’, was to develop their idea of Purism and further justify the necessity of its elements including pure forms, proportion, order, geometry and structure. This anti-cubist notion of purism was due to cubism’s bizarre ambiguity and ornamental aspects, which helped them to present purism in favour of logic or in other words, as an art of the ‘intellect’. Interestingly, this ‘criminalisation’ of ornamentation in architecture derived from Adolf Loos (1870–1933) who stated in 1908:

The evolution of culture is synonymous with the removal of ornament from utilitarian objects ... Not only is ornament produced by criminals but also a crime is committed through the fact that ornament inflicts serious injury on people’s health, on the national budget and hence on cultural evolution ... Freedom from ornament is a sign of spiritual strength.261

260 Moos, Le Corbusier, Elements of a Synthesis, p.314. 261Adolf Loos, Adolf Opel, and Michael Mitchell, Ornament and Crime : Selected Essays (Riverside: Ariadne Press, 1998), p.20. 119

Loos himself formed the fundamentals of his idea after spending four years working in America and studying the works of architect Louis Sullivan. His antagonism towards Art Nouveau grew from this experience, although he admired every element of the German Werkbund, or mass production. Although Sullivan applied decoration to his structures, he still encouraged simplicity and plainness.

It could only benefit us if for a time we were to abandon ornament and concentrate entirely on the erection of buildings that were finely shaped and charming in their sobriety.262

Le Corbusier and Ozenfant believed that certain geometrical forms and proportions create a visual idiom, the beauty of which can be expressed through architecture. This idea comes from their study of Pierodella Francesca and, more generally, Renaissance building design and applied geometry. This period was familiar to Le Corbusier because of his earlier readings of Provensal on the sudden fading of Renaissance spirituality, which he believed had anchored that society. This connected with his concern of a similar loss of faith in modern civilisation as evidenced in, for example, materialism and ‘meaninglessness’ in art.263 He also rejected ornamentation and saw the task of contemporary architecture as a paring down of architectural elements to the pure geometry of Plato and the numerological order of Pythagoras.

An exploration of Russian theorist and artist, Wassily Kandinsky (1866–1944), one of the key figures of early nineteenth century abstraction, explains more clearly what I have discussed and what is to follow. Kandinsky is well known for his pure abstraction in art, and his research on ‘inner necessity’ through spirituality. One aspect of his work concerning the spiritual in art, which is most relevant to Le Corbusier designs, is Kandinsky’s Point and Line to Plane work. In that work, he spoke of escaping attachment to tradition through the pursuit of non-objectivity in art.264 For Kandinsky, the age of machines and rapid changes in society required a creativity that was compatible with this new age of energy and dynamism.

262 H. Morrison, Louis Sullivan - Prophet of Modern Architecture (London: Smyth Press, 2007), p.168. 263 In Provensal’s theory of life, the natural phenomena that can be expressed in art and architecture can create ‘supreme intelligence’. ‘In Paul Turner's opinion some of the ideas to be found in Provensal can be found almost intact in Le Corbusier's work’. F. Samuel, Le Corbusier: Architect and Feminist (Hoboken: Wiley-Academy, 2004), p.61. 264 W. Kandinsky, Point and Line to Plane (New York: Dover Publications, 1979). 120

The geometric line is an invisible thing. It is the track made by the moving point; that is, its product. It is created by movement—specifically through the destruction of the intense self-contained repose of the point. Here, the leap out of the static to the dynamic occurs…. The forces coming from without which transform the point into a line, can be very diverse. The variation in lines depends upon the number of these forces and upon their combinations.265

The emergence of modernist ideology influenced many other contemporary artists and architects worldwide, and it was a common belief that a universal language of geometry would infuse the utopian reaction that would be delivered through mechanisation. Modernism was a secular, spiritual movement responding to the chaos of political conflict and class divisions. On the other hand, purism played a different role to post- war avant-gardes such as the Russian constructivists of the 1920s, with their ideological extremism, or the Dadaists with their post-war pessimism. Le Corbusier believed in revolution and renewing design principles to suit the age of the machine, but at the same time advocated reinstating lessons from tradition to generate innovation, an idea in line with the philosophy of purism. Galison (1955–) studied the nineteenth century modernist thinkers and stated:

The modernist manifesto declaimed: one group of combatants, holding fast to traditional social forms, cultivates traditional attitudes of metaphysics and theology whose content has long since been superseded; while the other group ... faces modern times, rejects these views and takes its stand on the grounds of empirical science.266

Le Corbusier’s celebrated statement, ‘A house is a machine for living in’267 can be misinterpreted when taken literally, but looking at his practice and writings, his true intention becomes clear. He did not mean to reduce the dwelling to just a soulless yet useful object, what he really meant was to design an inspiring and practical analogue of universal order. The appropriate example here is his simple comparison in Vers une architecture (Towards an Architecture) between ancient and modern—the relationship of the Basilica at Paestum (sixth century) to a Humber automobile (1907) and the Parthenon (fifth century BC) to a Delage sports car (1921). He then comments on these

265 Ibid. p.57. 266 Peter Galison, Gerald James Holton, and S. S. Schweber, Einstein for the 21st Century : His Legacy in Science, Art, and Modern Culture (Princeton: Princeton University Press, 2008), p.26. 267 Corbusier Le and Frederick Etchells, The City of Tomorrow and Its Planning (London: Architectural Press, 1987), p.90. 121 creations: ‘Our great buildings have already reached their highest potential while machines are still developing and growing’.268 Further, he concluded that the development of science and machines (for example, motorcars) challenged architects to design buildings that by necessity required that they look beyond the Parthenon or the Basilica for guiding architectural principles.

The modernism both groups had in mind would not stop at the traditional boundaries of science or art; they would reform fundamental aspects of daily life. We witness the spirit of the scientific world-conception penetrating in growing measure the forms of personal and public life, in education, upbringing, architecture, and the shaping of economic and social life according to rational principles.269

He dedicates a whole section of his book to the significance of the Parthenon alone under the heading ‘Architecture, pure creation of the mind’. To him, the Parthenon was a pure creation; every element of its structure was alive and full of energy and a symbol of perfect harmony, even in relation to its surroundings. If one takes the time to study Le Corbusier’s words, the struggle to see the Parthenon in relation to the art and architecture of his own time is expressed quite poetically, and the unshakable grounds of his argument are palpable:

... You employ stone, wood and concrete, and with these materials you build houses and palaces. That is construction. Ingenuity is at work.

But suddenly you touch my heart, you do me good, I am happy and I say: ‘This is beautiful’. That is Architecture. Art enters in.

My house is practical. I thank you, as I might thank Railway engineers, or the Telephone service. You have not touched my heart.

But suppose that walls rise towards heaven in such a way that I am moved. I perceive your intentions. Your mood has been gentle, brutal, charming or noble. The stones you have erected tell me so.

You fix me to the place and my eyes regard it. They behold something which expresses a thought. A thought which reveals itself without word or sound, but solely by means of

268 Corbusier and Etchells, Towards a New Architecture, p.230-232. 269 Rudolf Carnap, The Logical Structure of the World; Pseudoproblems in Philosophy (Berkeley,: University of California Press, 1967), p.340. 122

shapes which stand in a certain relationship to one another. These shapes are such that they are clearly revealed in light. The relationships between them have not necessarily any reference to what is practical or descriptive. They are a mathematical creation of your mind. They are the Language of Architecture. By the use of raw materials and starting from conditions more or less utilitarian, you have established certain relationships which have aroused my emotions.

This is Architecture.270

Later in the same section, he compares building elements with the arrangement of human facial features and gives a reasoned explanation for the beauty of a face. However, reason and rationality are more than skin deep; they are rooted deep down in our being, hence Le Corbusier’s desire to discover the universal principle to set it as fundamental to his architectural work, which became the basis of his radical variations of style over the course of his life. In The Lesson of Rome, he gave an illustration of great ancient buildings and five prisms (cylinder, pyramid, cube, oblong and sphere) that present each building’s pure geometrical shape, along with the perennial values that made those buildings symbols of beauty.

Le Corbusier’s aesthetic vision was grounded in seeing regular geometric forms as the source of architectural beauty. For Le Corbusier, the path to making meaningful and harmonious architecture lay in combining modern technology with geometric principles that invoked ancient mathematical systems and their inherent spirituality. All these shapes and elements are a mathematical creation of the mind, not combined in any particular way. They are the language of architecture.

Production of Forms and Geometric Numbers

It could be argued that Le Corbusier strongly disliked Roman architecture because in his view the works from that era were like an answer that misunderstands the question—in other words, a false and unsophisticated representation of a belief. For Le Corbusier, a more identifiable relationship between geometry and spirituality occurred later in the Gothic period, as could be evidenced in the regulating lines on Gothic cathedrals, such as Notre Dame in Paris (1163–1345). Through his analysis of Notre Dame and many

270 Corbusier and Etchells, Towards a New Architecture, p.203.

123 other major ancient structures, he learned that a unified façade comes to life through geometrical and compositional laws underpinned with primordial principles (i.e., ‘regulating lines’) based on harmonic order and proportion. As a case in point, he used these proportional rules and universal measurements to design his revolutionary Villa Schwob in La Chaux-de-Fonds (1916) without being derivative but rather fresh and refined (Figure 5.44). These primordial physical laws gave this building a subliminal potency.

Figure 5.44 Le Corbusier: Villa Schwob, back elevation, Chaux-de-Fonds.271

The living room is placed in the heart of the villa, right at the centre of the cross that extends in to the four directions of the villa. The number four is a significant number in the design of this building: four oval windows on the north façade, four interior columns, etc. A huge, blank square canvas on the north façade is located right in the middle of the rectangular brick wall with two oval windows on each side, framed by apses on the western and eastern sides.

The plan of the villa is a composition of Platonic pure solids: square and circle. Perfect symmetry appears in every aspect of its design. All the pure Platonic forms that are used to configure the design are connected by regulating lines created by applying the right

271 Ibid. p.84. 124 angle from Michelangelo’s Capitol in Rome and Pythagoras’ Golden section with its underlying cosmic order. With an open mind, one can experience the pure rhythms of this building. The design of Villa Schwob is influenced by elements from classicism to Andrea Palladio (1508–1580) to Auguste Perret (1874–1954), and similarly draws its energy from the use of regulating lines, which Le Corbusier focused on during his life as an architect and theorist.

The Second World War brought the opportunity for Le Corbusier to return to his research, part of which was theorising the issues of proportion and coming up with an adequate solution. He became exposed to the works of Romanian mathematician and historian, Matila Ghyka (1881–1965), and German psychologist, Adolf Zeising (1810– 1876), whose main area of study was anthropometrics, and who was the first to point out the Golden ratio seen in the veins of leaves. Both thinkers’ findings helped him to integrate what he had learned from history, Greek design laws, universal principles, the Golden section, human dimensions, regulating lines, and harmonic order. This integrated system was eventually given the title of The Modulor.

There is a geometry of art as there is a geometry of life, and, as the Greeks had guessed, they happen to be the same.272

The Modulor, deriving from the Latin word modulāri or module, describes measurement and abstract mathematical symbolism and is based on the Golden ratio that governs both microcosm and macrocosm. The case study discussion in this chapter aims to demonstrate Le Corbusier’s thinking patterns that inspired and effectively drove his well-known influential, progressive designs during his life. After Le Corbusier, this then translated into further changes in numerological geometrical beliefs in architecture.

As discussed earlier in this chapter, Le Corbusier invented The Modulor during his purist phase and its main purpose was to create a standardised universal measuring system to attain divine beauty in architectural and mechanical design. It is a combination of abstract numerical laws and human proportions. The idea emerged when in 1940, the French Vichy regime—for reasons of burgeoning industrialisation and the problems that might emerge in the construction industry—decided to set up an organisation under the name ‘the French Association for Standardisation’. Le Corbusier

272 Matila C. Ghyka, The Geometry of Art and Life (New York: Dover Publications, 1977), p.154. 125 was never invited to be a member of this organisation, which allowed architects and engineers to work hand-in-hand with politicians to put in place standards to rebuild a city. This rejection motivated him to set up a research organisation called ASCORAL (Assemblée de constructeurs pour une rénovation architecturale), which included architects and engineers who soon started working on various projects.

The system that became The Modulor was one of the research topics appointed to a young assistant named Gerald Hanning. He was instructed by Le Corbusier to look into the research on proportion using the Golden section, the system inherent in nature, the geometry of the great buildings of the past, and in relation to man. Two words were key to this final research: harmony and efficiency. The other important aspect for Le Corbusier was to create a universal standardisation framework. This may explain the motivation behind employing Hanning as the main researcher on this project, a bright Englishman who at the time was working for a French organisation.

A young art curator, Elisa Maillard joined Hanning to continue the research on this topic. Interestingly, Hanning found it hard to clarify whether The Modulor was Le Corbusier’s work or his own, because of his intense research into the project. It is important to note that Le Corbusier’s mathematical expertise was not strong and it can be seen from his notebook that when he was writing and working on The Modulor, he would often listen to Bach and relied upon the works of Ghyka, but stressed more and more the mythical aspects of the project. He soon realised he needed someone with a strong mathematical and geometrical background, which was when he brought Sorbonne mathematician, Rene Taton (1915–2004) into a partnership.273 Even though there was much disagreement between the two, Taton’s involvement hastened the completion of The Modulor. When visiting Albert Einstein in America, Le Corbusier showed him his completed work on The Modulor. Einstein reflected on it and later wrote him a letter stating:

273 Rene Taton has been credited not only for helping to finalise The Modulor but also for working out the calculations for the shape of Le Corbusier’s Notre Dame du Haut in 1954. 126

It is a scale of proportion which makes the bad difficult and the good easy ... this weapon shoots straight: in the matter of dimensioning, of proportion, it makes your task more certain.274

In 1951, Le Corbusier attended a conference entitled Da Divina Proportion. Rudolf Wittkower, whose main research was on Palladian proportions, presented a paper on Vitruvian systems, which was a breath of fresh air for Le Corbusier’s research. What they achieved was Vitruvian Man without any connection to theological beliefs, instead using vitalist and organic beliefs.

As indicated above, Vitruvian tradition depicted how man is placed within a geometric figure that symbolises the universe as a whole, while The Modulor demonstrates the anthropometric in relation to the immediate space or environment. Its attempt to create a common level between an average-sized and muscled human and elementary geometry is illustrated by a man standing tall, stretching one arm straight up and spreading his legs shoulder width. His navel lines up exactly with the edge of a small square and the middle of the larger square, within which the whole figure and the rest of the illustration is placed.

The measurements and division are in accordance with the Golden ratio and the applied numbers are based on Fibonacci numbers. The curving circular pattern on either side of the figure is sequenced in relation to the measurements. The figure of a muscled human itself comes across as humorous and is far from the way Leonardo Da Vinci depicted his ideal man. In contrast, the deformity of the human figure in The Modulor advocates the importance of the geometrical composition and the mathematical system attached to it, instead of being simply representative of a body.

Reading The Modulor, one is reminded of universal order in Ruskin’s book on the Gothic revival, Seven Lamps of Architecture (1849). He used Ruskin’s language to speak of a higher order in geometry that expressed a moral and spiritual point of view. The reference to spirituality for Le Corbusier and other modern thinkers in the age of the machine was not about theology, rather, it was the search for a secular spirituality.

274 Keith Micklewright, Drawing : Mastering the Language of Visual Expression (New York: Harry N. Abrams, 2005), p.58. 127

In the statement below, Le Corbusier affirms how his view of the world has been influenced by Ruskin’s views on the moral characteristics of architecture:

He gave a demonstration of honesty to a population gorged with the first fruits of the nascent machine age: go to San Giovanni e Paolo in Venice and take a very long ladder with you; lean it against the grandest tomb–that of the Vendramin; climb up to the top of the ladder and look at the head of the Vendramin, seen in profile as it lies on the catafalque. Lean over and look at the other side of the head, behind the profile. This other side is not carved. Disaster! Cheating! Falsehood! Treason! Everything is false in this sumptuous, enormous tomb… !

This was how Ruskin shook our young minds profoundly with his exhortation ... Ruskin had softened our hearts.275

The Carpenter Centre, which Le Corbusier designed in 1963—one of his last designs— fully reflects what he established in The Modulor and its manifesto of architectural elements (Figure 5.45). As architectural historian, Eduard Franz Sekler famously observed, this building showed ‘the magnificent, knowledgeable and correct play of volumes under light’.276 Looking at his conceptual stage sketches, it appears Le Corbusier was no longer trying to advocate a milieu in the classical language of pure mathematics of his earlier purist practice.

The geometrical forms in the Carpenter Centre become less similar to Le Corbusier’s previous designs, instead the design composition took an unusual approach of abstraction and graphical interpretation of the regular form of circle and square. The floor plan properties have a more irregular shape of two lung-like masses; reminding one of Le Corbusier’s drawings from 1950–1951 (Figure 5.46). The strange architectural elements of exposed curving concrete slabs, angles brise-soleil and the exchange of the void and solid spaces are all strategically placed on the angled grid of the surrounding milieus. The Carpenter Centre exhibits a design opportunity of innovation and subjective content. A design that is drawn from its program and represents a resistance to project man-made surroundings does not carry any attachment from past beliefs. The compositional forms attest to what is relevant to Le Corbusier

275 Corbusier Le, The Decorative Art of Today (London: The Architectural Press, 1987), p.132. 276 E.F. Sekler and W.J.R. Curtis, Le Corbusier at Work: The Genesis of the Carpenter Center for the Visual Arts (Harvard University Press, 1978), p.160. 128 and project an immediate impression: a building with a creative vision and abstract values.

Figure 5.45 Le Corbusier: Carpenter Centre, Cambridge, Massachusetts.277

277 Ibid. p.345. 129

Figure 5.46 Le Corbusier: Cow with calf, 1950, View of landscape passing over Colombia from aeroplane, 1951.278

Conclusion

At the beginning of Le Corbusier’s career, his extensive reading and research are echoed in his assertion that nature’s ‘invariability’ is connected with Pythagorean numerology and also with the laws of cosmic order that result in pure harmony. Le Corbusier’s interest in mathematics was almost like a religion that could respond to his concerns about existence and universal order. Thus, his endless attempts to take the architecture of his time beyond the present was not only to create something modern, rather it was to make it ‘remote from its time’, just as the Parthenon was also timeless. One can say that the highest duty of an artist is to take man to the spiritual realm, and in order to do so it has to represent divine forms. It is impossible for the artist to do this unless he can unify art and mathematics, or marry sensibility with logic. The successful outcome is the appearance of true beauty in art that is eternal and universal.

278 Iain Fraser, Rod Henmi. Envisioning Architecture, (New York: Van Nostrand Press, 1994), p.3. 130

It is fascinating to study Le Corbusier’s personal history and architectural journey, and his attempt to coordinate traditional geometry with a non-Euclidean world. By focusing on humans in their environment, not just universals, Le Corbusier shifted from Calvinism and absolutism to Catholicism and relativism. Through The Modulor, he attempted new numerical and geometric combinations, which is the older system of proportion and might be called ‘one-track systems’. Its elements are extremely simple: square, double square and divisions that are blended into a system of mean ratios, creating symmetry from two divergent series of irrational numbers derived from the Golden section. Whatever one may think, it is a coherent synthesis of ancient and modern geometry, including the proportions of plane geometry used in the Middle Ages, the arithmetical proportions of the Renaissance. In tandem with these were Le Corbusier’s dual system of irrational magnitudes, with its dependency on and reiteration of Pythagorean-Platonic concepts, which were the primordial basis of geometry.279

In the next Chapter I tested the two hypothesises in relation to historical development of Russian architecture. The grass roots study of Russian primeval milieus, and the effect of major political conflicts explained the rise of 1920s movement in art, architecture and philosophy. Furthermore the idea of abstraction and secularity is the significant study of this Chapter to lead to the new age of architectural design and use of geometrical pattern. In the way that the creative minds of twenty and twenty-first century, break, fold, overlapped and segmented the historically believed spiritual meaning and symbolical function of Geometrical pattern; welcomed the new age of architectural design.

279 L. Corbusier, Modulor 2, 1955: (Let the User Speak Next) (M.I.T. Press, 1968), p.142-144. 131

Chapter Six. From Early Russian History to the Age of Avant-gardism

Symbol and Universals in Architecture

Not the old, not the new, but the necessary.280

In the first five chapters of this thesis, I have focused on a historical study of the development of the use of geometry in architecture. The key objective has been to demonstrate the theme of historical influences that informed and transformed the use of geometry in architecture over the centuries, as well as a critical examination of the meaning attached to these geometrical forms. This chapter and Chapter Seven present and discuss examples of key architectural figures from the twentieth century through to present day. In the selected case studies, I used three significant indicators to test my thesis’ second hypothesis, including: (1) the revolution in meaning of spirituality; (2) social developments; and (3) rapid technological/scientific growth.

Current research on architectural design varies in terms of its focus. Although the literature reviewed has considered some important issues pertaining to functionality and aesthetics, there are nevertheless significant gaps in present discourse relative to meaning, forms and geometrical patterns. Aspects that have been shown to have a negative effect on the theoretical evaluation of architectural milieus include: (1) the neglect of historical evidence; (2) the awareness of past symbolism; and (3) a lack of emphasis on meaning as an important aspect of design for humankind. The following discussion will fill these gaps.

My focus in this chapter is Russia’s architectural and political history, as this relates to the rise of abstraction and secular beliefs. I will thereby offer a grass roots analysis of the various external forces that have contributed to major changes in architectural approaches to applied geometry and meanings, as these have been identified throughout the history of architecture. This chapter also seeks to open up new perspectives of understanding on selected, prominent creative minds of the 1920s, and major movements resulting from past practice of Russian architects and social and political changes.

280 Norbert Lynton, Tatlin’s Tower: Monument to Revolution (London: Yale University press, 2008), p.97. 132

The investigation of material, volume, and construction made it possible for us in 1918, in an artistic form, to begin to combine materials like iron and glass, the materials of modern Classicism, comparable in their severity with the marble of antiquity. In this way an opportunity emerges of uniting purely artistic forms with utilitarian intentions.281

In the above quotation, Vladimir Tatlin, the key figure of the Constructive movement, refers to the birth of a new approach to art and architecture in the 1920s. This new approach pertains to the attempt of constructivists to attain a utopian form of design, influenced by socio-political conflicts and functionalism. In the age of machines, the forward-looking approach of Tatlin was to dispense with the carcass of old beliefs; he perceived these as neither relevant nor necessary to the modern era.

281 Andra Papadakēs, Catherine Cooke, The Avant -garde: Russian architecture in the twenties (The University of California: Academy Edition, 1991), p.23. 133

Figure 6.47 Left, Albrecht Dürer: Melencolia I, engraving, 1514.282

Figure 6.48 Right, El Lissitzky: Tatlin working on the Monument to the Third Internationa, 1922.283

In twentieth century Russia, the thinker, who was also regarded as a god, was the creator (of a thought or milieu). Historically speaking, the thinker was also believed to have a duty to follow the pattern of the heavenly realm. The symbolic representation of the same instruments across different eras and belief systems is apparent in Dürer’s engraving, Melencolia I (figure 6.47) and in El Lissitzky’s photomontage (figure 6.48) of Tatlin working on his masterpiece (I discuss this work later in this chapter.)

In Dürer’s work, an angelic figure is seen contemplating with, compass in hand, a sphere at her feet, surrounded by different elements from Platonic and Pythagorean teaching. In contrast to this mystic image from the Renaissance era, in Lissitzky’s representation we have a modern man constructing while standing on a stool with a compass in front of his eyes (symbolising the over-precise dimensioning and scaling),284

282 Horst Woldemar Janson, Anthony Fanson, History of Art: The Western Tradition (Venice: Pearson Education Publication, 2003), p.62. 283 John Milner, Vladimir Tatlin and the Russian Avant Garde (London: Yale University Press, 1984), p.168. 284 The concept of placing the ancient measuring tool, compasses, in the eye could be trace back to Renaissance teaching by Leon Alberti, Michelangelo, Gian Pietro Bellori, Federico Zuccari and many other theorists from that era. ‘... You have the compass and ruler in your eyes, and judgment and 134 and the mathematical formula of infinity at his feet. In his pursuit of creativity, he is combining the abstract and fractural interpretation of elements from Dürer’s image. In comparison, these two influential images portray a battle between the spiritual and the secular.285

However, before attempting an analysis of Tatlin’s particular teachings, we first need to investigate the culture and beliefs of the Russian constructivist thinkers, artists and architects. To define the term ‘constructivism’ requires recognition of a number of different associations, which are remote from constructivism’s initial intention. To do this, a brief excursion into Russian history and architecture is necessary in order to comprehend past practice and understand the derivation of new movement design development and response to past beliefs.

Transformation of Multi-domes, Wooden Churches to Man’s Forgotten Reality

The purpose of below historical analysis in to the design of Russian’s sacred building is to understand the development of geometrical patterns and meaning in that region. That will translate into clear recognition of how leading contemporary artists and architect establish their teachings that lead to an historical movement.

The development of architecture in Russia evolved via a range of socio-cultural influences over a considerable period, particularly a history of invasion and territorial changes that affected, and were subsequently reproduced in Russian culture. Undoubtedly, the vast territorial extent of Russia and its distinct geographical position resulted in unique relations between both east and west, which largely accounted for these historical transformations. Prior to the October Revolution in 1917, the attacks of the Mongols in 1220 and the Tartars in 1380 were the most influential and destructive events in the cultural, social and political history of Russia. As a result of these

practice in your hands’. Roland E. Fleischer, Susan Scott Munshower, The Age of Rembrandt, Studies in Seventeenth-Century Dutch Painting (Pennsylvania: Aldus Corporation, 1988), p.193. 285 The term secular is from the Latin sēculāris that can translate to something earthly and attached to tangible realm. The approach to this ideology of Secularity in this thesis is connected directly to the application geometrical forms and meaning attached to it in the field of architectural theory. The study of German philosopher Theodor W. Adorno (1903-1969) especially his book Aesthetic Theory in 1970, demonstrate the idea of secularity for the creative minds of the modern era. 135 harrowing events, Russia found itself three centuries behind other European countries in terms of development.

Figure 6.49 The wooden Church of Transfiguration in Kizhi, west view, Russia, 1714.286

Folk traditions in art and architecture in Russia, characterised by an affection for decoration and woodwork (Figure 6.49), changed after the acceptance of Christianity from the Eastern Orthodox Church in Byzantium (Istanbul) in 988 AD. The transition from paganism to Christianity brought with it the influence of Roman architecture and introduced symbolism into Russian art and architecture. Russian architecture responded to these external influences, which also merged with vernacular traditions that reflected different regional cultural, topographic or landscape differences.

286 William Craft Brumfield, A History of Russian Architecture (Cambridge: Cambridge University Press, 1993). plate.80. 136

For example, the complex rectangular wooden church designs of eighteenth century Russia were created from ideas rooted in folklore and tradition. These churches were designed to ‘house God’, meaning to house immortality, which became an architectural type that was repeated for many decades in northern Russia. An examination of some design elements from past centuries shows their influence on many prominent architects and artists of that district who, in turn, inspired the beliefs of many other current designers and creative minds.

The common practice of architects up to the seventeenth century was to design without any documentation or drawings.287 Rather, design was a tradition, passed on from generation to generation by word of mouth. A major symbolic configuration and recognisable trait of church designs up to the eleventh century were the multi-cupola churches with their numerological associations embedded in the design as will be discussed below. Unlike Byzantine domes, which were large, extensive and lightly inclined, Russian domes were smaller, more spherically shaped, and placed on a slimmer drum. This diverse design famously referred to as an onion shaped dome that symbolises God as the dome, Christ as the ‘drum’, and the blaze of prayers reaching towards the celestial heavens as the axis mundi surmounting the cupola.288 Architecture historian, Henri Frankfort (1897–1954) explains how this planning arrangement had its roots in ancient Egyptian belief:

The world mountain is placed in the centre of the world: at a point where the ‘world axis’ passes. The axis continued upwards (through the crest of the world mountain) is marked with the position of the Polar Star; its continuation downwards points to the location of an entry to the Underworld (Hades). The base of the mountain is the ‘hub of the universe’. The world mountain has three parts Gods live on its top. Evil spirits inhabit its foot—they belong to the realm of the dead. Humankind lives in its middle, the earth level.289

Under the Tartar invasion, a major change appeared in the design of churches. The drums that the domes were set upon rose ever higher, to form the figure of warriors in

287 Historians until the middle of the twentieth century assumed this because they could not find the drawings. Later research determined they were carefully hidden in secret places such as the tops of columns, in order to stop other masons copying them. 288 Doris Bradbury, The Russian Orthodox Church (Moscow: Progress, 1982), p.7-10. 289 Alexander A. Barabanov, 'Man and Architecture: Semantics of Relations', Urban Bodies, 7/1 (2002), p.10. 137 armour. Those warriors symbolised protection and in some cases, churches were built to celebrate military victories, or to show defence of the motherland. The rest of the building was affected with, for example, the insertion of loophole shaped windows. This transformation appeared on single dome as well as multi-domed churches.

Figure 6.50 Eastern façade of Saint Sophia Cathedral, Kiev in Russia, 1037.290

The first application of the multi-domed form was in Kiev, Russia (Figure 6.50) with this form of design reaching its prime during the fifteenth and sixteenth centuries. The application of two, three, five, seven, nine and thirteen cupolas occurred, at the same time preserving the pyramidal silhouette, which attested to the influence of Roman and Greek beliefs. Numerology was an important design determinant and aesthetic metaphor in multi-domed churches. The number two represents the two natures of Jesus Christ; three symbolises the Father, Son and Holy Spirit; five for God and the four evangelists, or Christ’s five wounds during the crucifixion; seven stands for the seven sacraments; nine for the nine heavenly hierarchies,; and thirteen for Christ and his twelve disciples.

290 George Heard Hamilton, The Art and Architecture of Russia (New York: Penguin, 1983), p.26. 138

Figure 6.51 Kizhi Pogost, Lake Onega in the Republic of Karelia, Russia,1714.291

One outstanding example of a multi-domed church is Kizhi Pogost, Russia (Figure 6.53), which has a total of 33 domes, which signify Christ’s earthly life of 33 years. These multi-cupolas were harmonically arranged and placed into the overall plan of the church to create a dynamic and visually pleasing pattern of the construction as a whole. (An extended analysis of this rhythmic motif is beyond the scope of my research for this thesis).

Another design trend that occurred in the fifteenth century was tent-shaped roof churches with their surrounding elevated pyramidal towers in the shape of an equilateral triangle, symbolising the Trinity. Another design was created from an octagonal base that was popular in Moscow and surrounding regions for many years. The appearance of the number nine, with eight sides of the tent and the centre crown can be seen here in Figure 6.51. This arrangement also represents number eight plus one, which symbolises 292 Theotókos, or ‘The one who gave birth to God’.

Also seen in these churches is the eight-pointed star that has a cross climbing through the centre of the building up to the crown of the tent roof form. Historically, the tent-

291 S.J. Kelley, Wood Structures: A Global Forum on the Treatment, Conservation, and Repair of Cultural Heritage (Philadephia: ASTM, 2000), p.30. 292 Gwendolyn Leick, A Dictionary of Ancient near Eastern Architecture (London: Routledge, 1988), p.160. 139 shaped roof developed through triangulated forms that evolved in Russian churches. However, this combined with the curved-sided equilateral triangle, adopted from European Gothic architecture and symbolised the manifestation of God’s divine will on earth. In contrast, the application of multi-cupolas was never utilised by European Gothic architects.293

St Basil Cathedral (or Trinity Cathedral) at the Red Square in Moscow (1555–1561) clearly demonstrates the many allegorical aspects of church architecture that have been mentioned above. Its octagonal floor plan defining the eight domes with the ninth, tent- roofed dome right in the centre (Figure 6.52), is a metaphor for the Book of Revelation of St. John and symbolises New Jerusalem, or the earthly motif of the heavenly city with the icon of the Mother of God watching over Red Square and protecting the city. One could also say that this arrangement symbolised the eight battles over eight continuous days (1552) of Tsar Ivan with Russo Kazan. To honour his conquest, Ivan ordered the building of this cathedral, which was designed in such a way that it represented this dual meaning.

293 Hamilton, The Art and Architecture of Russia, p.177. 140

Figure 6.52 Saint Basil’s Cathedral, Red Square in Moscow, 1555.294

Throughout the eleventh century and until the middle of the sixteenth century, Kievian and Novgorodian Russian building practitioners were heavily influenced by Byzantine art and design and, more generally, Greek architecture.295 A clear example of this is the thirteen-domed orthodox cathedral of St. Sophia in Novgorod (Holy Wisdom of God) (1045–1050). In the mid-twelfth century, Russian architects realised that they needed to apply some changes to those sacred compositions in order to create buildings compatible with the climate of their particular regions, which was entirely different to

294 D. O. Shvidkovski, Ekaterina Shorban, and Antony Wood, Russian Architecture and the West (New Haven Yale University Press, 2007), p.138. 295 Kievian or to be exact Kievian Rus was the most significant political period established during the medieval era and the central state in Russia. Novgorodian was the second biggest state of Russia during the medieval time and in 882 become a part of Kievian Rus Empire. Both Kievian and Novgorodian have been referred to as chosen for cultural, social, political and social change in Russia. 141 the Mediterranean environment. Although any major modification was taboo in the eyes of the Church, gradually it became convinced that changes were needed to protect the construction from the harsh temperatures. This led to further distinctive forms and structures and a recognisable identity to Russian churches of this era. The general view as to why these geometrical configurations were significant and are still relevant today is a matter that needs special attention and precise understanding.

As American scholar and researcher, David M. Petras argued, the intentional arrangement of geometrical patterns in the design of twelfth century Russian churches was to reinforce the sensory experience, which a beholder can explain by glancing at this geometrical pattern as akin to stepping out of mortal time into a heavenly realm of eternity.296 These buildings are imbued with a sense of divine vision of the cosmos, balance, union and resolution that is both spiritual but also boldly logical. This interpretation of early Russian churches is based on how geometry and spirituality coalesced with vernacular traditions under the influence of historical and cultural forces.

The sublime character, geometrical arrangements and aesthetic beauty of these buildings and their symbolic forms was a product not just of tradition and the copying of standards, but evolved through the interpretation of individuals creatively expressing their imagination and influenced almost unconsciously by a historical genealogy. To better comprehend this, I believe it is useful to consider the idea of the ‘sublime’.

During the Enlightenment era, many thinkers such as George Berkeley (1685–1753) and David Hume (1711–1776) wrote about the sublime in depth. However, it was German philosopher, Immanuel Kant (1724–1804) who clearly outlined the idea of the sublime in his Critique of Practical Reason:

Two things fill the mind with ever new and increasing admiration and awe, the more often and steadily we reflect upon them: the starry heavens above me and the moral law within me. I do not seek or conjecture either of them as if they were veiled obscurities or extravagances beyond the horizon of my vision; I see them before me and connect them immediately with the consciousness of my existence. The first starts at the place that I occupy in the external world of the senses, and extends the connection in which I stand into the limitless magnitude of worlds upon worlds, systems upon systems, as

296 David M. Petras, The Typikon of the Patriach Alexis: The Studies of Novgorod-St. Sophia 1136 (Michigan: star printing, 1991), p.41. 142

well as into the boundless times of their periodic motion, their beginning and continuation. The second begins with my invisible self, my personality, and displays to me a world that has true infinity, but which can only be detected through the understanding, and with which ... I know myself to be in not, as in the first case, merely contingent, but universal and necessary connection. The first perspective of a countless multitude of worlds as it were annihilates my importance as an animal creature, which must give the matter out of which it has grown back to the planet (a mere speck in the cosmos) after it has been (one knows not how) furnished with life-force for a short time.297

Vernacular Russian churches were designed to inspire human contemplation on the sublime, on the awe of ‘limitless magnitude’ and ‘boundless time’, which required the unification of reason in terms of geometry and construction with intuition and poetics in order to design a deeply symbolic building. It is not surprising that these buildings remained in the collective cultural mindset of later Russian designers, as they represented a spiritual vision that would become an ideological utopia. Moreover, these buildings have an ability to be viewed without words and for many, can be expressed and understood as a universal language as a theoretical instrument to reinstate to man his forgotten reality.

The Virtues of Building: Architecture Beyond Building

To add to the enduring political and social conflicts in Russia, the after-effects of World War I (WWI) and World War II should also be mentioned, although the extent of social depression and psychological aftermath is immeasurable. However, I believe a review of the revolution it caused in humankind’s view to spirituality and theological principles is vital to the first hypothesis of my thesis insofar as it relates to the twentieth century— or even to current practices of architects. The new production of geometrical forms, to show political and social depression, mutely indicates what is beyond illustration on a canvas or a constructed milieu.

In Russia, architectural practices were entirely for the benefit of the aristocracy and this did not change until the October Revolution in 1917. Architecture was further divorced from social reality, as it was solely the province of royalty and the aristocracy, although

297Immanuel Kant, H. W. Cassirer, and Ronald Weitzman, Critique of Practical Reason (Milwaukee: Marquette University Press, 1998), p.269. 143 ironically, it was nominated by the Soviets as one of the ideals of Marxism. The resistance to Russian medieval methodology in 1861 shaped a much stronger movement towards a more persistent and meticulous appreciation of medieval Russian architecture.298

This controversial rebellion in art and architecture happened at the same time as the arts and crafts movement in other European countries, and it was as much of a trajectory in Russia as it was elsewhere. After WWI, the reproduction of architectural design rebelled against more international influences and interpretations of expressionism, cubism and abstraction. To break away from reality (and also traditional thinking), avant-garde architects in Russia used machines as a prominent model for their designs. The emphasis was on the mind that has to be considered as creator of new forms, divorced from traditional beliefs. Therefore, the logic of the machine and mathematical reasoning became the paradigm of thinking for utopian designers. It was a time of coalition between abstract painting and geometrical production for the physical building. This alienation of forms and composition was impersonal and free of any human sentiment.299

In the early twentieth century, the word ‘construction’ in Russia defined a radical movement in the world of creativity. For constructivists, geometrical patterns and materiality were clearly the indicating elements to illustrate different conceptual viewpoints, instead of expressing it through words/theoretically or formally. In that respect, the Russian language gave obvious indication to the real meaning of this movement. For Russians, the term construction in a building context is stroitel’stvo, which comes from the nuance, stroit, referring purely to the physical process of building and the materiality of milieus. There is another Russian word, konstruktsiia (конструкция), which also translates to ‘construction’ in English. However, конструкция in it is origin refers to the idea/structure/framework of buildings. The combination of these two vernacular terms delineated the basic logical paradigm of

298 Thomas Sanders, Historiography of Imperial Russia : The Profession and Writing of History in a Multinational State (Armonk, N.Y.: M.E. Sharpe, 1999), p.497-499. 299 Marian Moffett, Michael W. Fazio, and Lawrence Wodehouse, A World History of Architecture (2nd edn.; London: Laurence King, 2009), p.380-384. 144 thinking (intellectual category and ordering of thoughts) for constructivists in the ‘first machine age’.300

The term constructivism was first associated with the experimental practice of Russian architect and sculptor Vladimir Tatlin (1885–1953). It was at this time that art and architecture were aligned with radical political thought in Russia, and effectively became the instrument for the reformation of social, cultural and industrial demands after the fall of the tsar. The challenge of unifying the presentation of art or architecture with life or, in other words creating the novel artistic reality at that time, became a tragedy.301 The chief paradigm to this combination is Tatlin’s designed monument to the Third International. Tatlin’s design was considered a milestone project based on the constructivist theme of geometrical composition and emotionless minimalism; at the same time, it served as a reminder of the tent-shaped domes (Figure 6.53).

In his desire to project dynamism in his work and to symbolise the era as one of revolution and the freedom of humankind, Tatlin combined the cylinder frame, diagonal trusses and the spiral forms that rotate, merge and move promptly to the top of the monument. This provided a unifying formal theme in the monument. The pyramidal form of Talin’s design echoed the hidden meaning of microcosm and macrocosm—in a way that mechanical parts are distinct from the whole, yet are related to the whole monument.

Similarly, the geometrical configuration signified progression, energy or modernity and was used by visionary thinkers among his contemporaries. This symbolism attracted a significant audience and draw attention from a society exhausted by the effects by war, to see it as the spirit of the new age.

300 Reyner Banha, Theory And Design In The First Machine Age (London: the MIT press, 1980) 301 As the responsibility of artists and architects is not to create and design in accordance with other political and social changes but to attend to the need of humankind as a whole. 145

Figure 6.53 Vladmir Tatlin: Model of the Monument to the Third International, 1919.302

The demonstration of this abstract expression through geometrical shapes has been applied to generate conscious stimulation of the utopian idea to reinstate to man his humanity and the positive direction to renew civilisation. Therefore, it is no surprise that the articulation of the idealistic social and aesthetic visions by which to recompose humanity on further inventive and autonomous principles, was practised by many Russian architects for many years after 1918. An ideal example can be found in the art and ideology of Russian artist and designer, El Lissitzky (1890–1941). The uniqueness of his recognition and realisation of Russia’s most pressing needs made his works dominant for many decades. Even though their motivation of creating a new world in

302 Ibid. p.370. 146 the design industry had been justified, the question is whether they achieved what they strived towards, or whether their goals were misinterpreted.

Lissitzky’s creative productions were deeply affected by the constructivist movement and the self-defining theory of the vision of totality. His self-contained hypotheses of art were unlike those of Kazimir Malevich, another avant-garde Russian artist whose practice was intensely affected by spiritual beliefs and whose mission to achieve metaphysical transformation set the course of modernity in Russia and later on influenced the other regions way of thinking. It was a proposition for a new way of life that was free of any dependency on old beliefs or tradition. Meanwhile, Lissitzky and a few other thinkers referred to Malevich’s execution of different geometric abstractions with a set of assumptions about history, nature and creativity.

These abstractions have never been precisely explained but were loosely defined as what Lissitzky meant by those terms and their significance in relation to forms. It seems the word nature has been used as a reference to anything irrational, changeable or subjective, as a vague and arbitrary definition for the alienation of man from his natural being. The use of abstract geometrical shapes in his art came across as a tool for Lissitzky to reinforce the alienation based on geometrical forms, producing historical significance that could assist in bringing back human creativity and logic. The emphasis on the unavoidable attempts of man to attain a better life is repeated consistently in the writings of Lissitzky and his contemporaries and reflected in his designs.

On the other hand, through the production of machinery and industrial techniques that history made available, man came to rely less on nature. The transposition of nature into a man-made environment could be demonstrated by utilising technology and transforming it in the form of art. The ‘First Machine Age’, especially for Lissitzky, was an ‘expression’ of man’s total control over the natural environment and his effect upon it. Consequently, society was brought closer to manufacturing a better world because the rationality and certainty in this new age of machine could be substituted for the beliefs in natural and spiritual base values.

Theo van Doesburg (1883–1931), the founder of the Dutch movement, De Stijl in Netherlands in 1927, articulated his idea about nature and the machine age as follows:

147

The same is true of the individual, organic life function. We are convinced that it is a sign of ‘higher civilization’ when these organic functions are transformed into mechanical functions, and we already more or less despise those who function organically in complete naturalness. This contempt is directed chiefly towards the complete identification with organic nature. What we miss in ‘natural’ man is: opposition, contrast, resistance, struggle—in a word, spirit.303

To consider Lissitzky or architects and artists like him as only producers of images or instrumental design is an underestimation of their works, for they were more active in production of theory.304 However, the originality of their theories is another matter that can be summarised by a brief deliberation on their productions, who learned from history and elements from other philosophers and were transformed into a new context that they called their own. In particular, Lissitzky’s purpose was not to produce an original idea but to articulate ‘a New Vision for a New Man in New Society’ in order to achieve salvation.305 His attempts to introduce mathematics as a vital element in art to establish modernity and the sense of a highly intelligent game, demonstrates the artist’s polemical view to formulate his own rules and his refusal to apply accepted visual symbols from the past. Provocation of the sense of curiosity became possible for Lissitzky through the play of mathematical composition of geometrical shapes in some of his earlier works, which ironically were formalist without the awareness of the history of meaning in geometry.

Lissitzky diligently incorporated ancient Greek methodology of proportion (arithmetic ratio and proportion) and of perspective (vanishing point) into his work in a way that was free of any attachment to any past application; he created a new universe breaking the dogma and claims of the old universe. Lissitzky created his own Vitruvian Man in Proun 43, and on the cover of Ma art magazine, his ideal man is stretching inside a circle shaped boundary—except this time there is no square, but a rectangle. Stepping back, one can see that the whole composition in both works has been placed inside a square. However, the true fascination comes with the realisation that the circle is not fully closed, as if allowing the man to claim his freedom and escape from this divine

303 Theo Van Doesburg and A. Petersen, De Stijl (Amst, 1968), p.203. 304 Reviewing the key texts of El Lissitzky there is little theory in the form of writing, the main production of his theory being through his unscripted artwork. 305 El Lissitzky and Sophie Lissitzky-Kuppers, El Lissitzky: Life, Letters, Texts (London,: Thames & Hudson, 1968), p.18. 148 realm into the earthly life of the square. What Lissitzky had in common with other constructivist architects was the aim to rebuild life through the manifestation of art.

Lissitzky’s ongoing search to find a new scientific device to advance his creations significantly distinguished him from other utopian thinkers of his time. One of his earlier collaborations was with German born Russian mathematician and geometrician, Hermann Minkowski (1864–1909), who was Einstein’s mentor. This can be found in Proun G7, which drew so much from Minkowski’s symbolic continuum diagram in which space and time are united into hyperbolas. This influence has been repeatedly applied and followed by Lissitzky but surprisingly, all credit has been given to Einstein’s theory of relativity instead of to the work of Minkowski. The combination of scientific methodologies of non-Euclidian geometry and imaginary numbers formed Minkowski’s idea to move on from the old belief of physical space in order to experience virtual space. As he put it:

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.306

There is another aspect to these thinkers’ ideological progression that I believe needs to be reviewed and examined in order to have a refined overall view of this critical era for architecture theory. The concept of unnoticed dimension was formulated in the nineteenth century as ‘Fourth dimension and Non-Euclidean geometry’. Chapters One and Five introduced the topic of a fourth dimension, which has been explained by philosophers and architects such as Ouspensky, Hinton and Bragdon. In addition, French mathematician, Henri Poincare (1854–1912) made a great contribution to the subject of the fourth dimension, by adding the higher dimension to the objects through ‘several perspectives from several points of view, … and in that sense we may say the fourth dimension is imaginable’.307

Here, many Russian architects made reference to this belief and attempted to apply it to their works as a popular and modern culture. The meaning of fourth dimension remained notorious and never achieved a universally agreed definition. Among various

306 F. W. Lanchester and H. Minkowski, Relativity : An Elementary Explanation of the Space-Time Relations as Established by Minkowski, and a Discusson of Gravitational Theory Based Thereon (London: Constable & co., limited, 1935), p.32. 307 Henri Poincare, Science and Method (The Origins of Modern Philosophy of Science, 1830-1914; London: Routledge/Thoemmes Press, 1996), p.89-90. 149 examples, the most popular belief was the scientific aspect that the fourth dimension defined time and speed for many thinkers, while others believed it represented the spiritual and non-earthly realm—something that can only be felt or experienced through human senses.

This mystical meaning and its sense of modernity attracted creative minds who believed this new dimension would be a new tool for progress and illuminated thought. Malevich accepted and followed this spiritual dimension through his art practice. In the beginning, Lissitzky had a similar vision to Malevich but later, in 1905, he began to see the fourth dimension in terms of the space timeframe, or one could say the physics theory of Einstein. Furthermore, Van Doesburg succeeded in seeing the importance in both definitions of the fourth dimension as an experience that a spectator can undertake while travelling through the built environment. For all these thinkers, the main tool to express this alternative dimension was geometry. By using this ancient conduit as a visual language in a way that revolutionised what these configurations had always stood for, they transformed the view of the traditional belief of the universe.

For Lissitzky in particular, educating architecture in the uproar of post-revolutionary Russia was an opportunity to invigorate this new geometrical expression, machine like, with renewed political ideas. He justified through his writing and practical works that geometry is a foundation for the suprematist’s way of communication, in order to merge rationality with imagination. Thus, according to Lissitzky, the inventive mind of a suprematist designer should subsequently see this as a technique, not as a style that advances progression towards utopia. The attractive subject of mechanical art and clear order/geometry for Lissitzky was as strong as it was for Le Corbusier’s belief on the subject of the perfection of machines. As Le Corbusier said in 1923, ‘the house is a machine for living in’.308 Surprisingly, also in 1923, Lissitzky similarly wrote:

The vitality the uniformity the monumental quality the accuracy and the beauty of machine created by the economy of the age ... A house is a device for living in, just as a car or an airplane is a device for travelling in.309

308 Corbusier and Etchells, Towards a New Architecture, p.108. 309 Lissitzky and Lissitzky-Kuppers, El Lissitzky: Life, Letters, Texts, p.333. 150

Rather, the machine was the way to bring nature under man’s control. To both these thinkers, machines were the closest lead to achieving perfection in social order and a good life. A good life was one that can satisfy man’s physical and psychological needs through the rhythmic organisation of their surroundings, and that is architecture.

One of the influential figures on the topic of the fourth dimension was British mathematician, Charles Howard Hinton (1853–1907), who published an article entitled What is the Fourth Dimension? This work formed much of Lissitzky’s production to allow the observer to see not only the forms but also to control his mental visualisation or sensual experience beyond what is already on the surface. This visionary approach was more a psychological effect than a physiological one.

For Lissitzky, applying an axonometric view on most of his works, especially his Proun Room project, was a way to express more than simply three-dimensional views or make a dynamic image and create a liveable object. His main concern was to demonstrate the idea of ‘doubling’. To express this idea, Lissitzky used axonometric projection to present the Proun Room (Figure 6.54). The relative motion felt in the two-dimensional panels is undeniable; it is as if the image is following the eyes of the observer in any direction he moves. The relation between different forms and their arrangement is directly and concisely interlinked with the surrounding space to demonstrate the image in a sense of macro and generate a virtual space for the spectator, which depends on the strength of his imagination to perceive the fourth dimension.

We can only change the form of our physical space but not its structure, i.e. its three- dimensionality ... Only a mirage may be capable of giving us such an illusion.310

310 Ibid. p.359. 151

Figure 6.54 El Lissitzky: Proun Room, 1923.311

For Lissitzky, the Proun series was a point of transition linking two-dimensional art and architecture. It illustrated the symbolic sense of illusion in his Proun project and demonstrated his thirst for moving away from the limited two-dimensional surfaces. He wrote:

The painter’s canvas was too limited for me ... We begin our work on the two- dimensional surface, we then pass onto the three-dimensional model constructions and to the needs of life ... Through Proun we have now come to architecture—which is not accidental.312

Lissitzky’s final decision to move away from painting after Proun 99 was because he could not truly express movement and because suprematism and futurism were just an illusion of motion.313 This led him to architecture and the generation of his Proun Room in 1923, Room for Constructivist in 1926, and Hangover Room in 1928. The continuous change throughout these spaces is compelling and dynamic. The revolutionary nature of his work owed much to his knowledge of the theory of relativity and ongoing

311 N. Perloff and B.M. Reed, Situating El Lissitzky: Vitebsk, Berlin, Moscow (Los Angeles: Getty Publications, 2003), p.49. 312 Lissitzky and Lissitzky-Kuppers, El Lissitzky: Life, Letters, Texts, p.329. 313 Ibid. pp.340-342. 152

314 nourishment from Minkowski’s world. For Lissitzky, the future of humankind was solidly dependent on scientific understanding and progression.

Public Architecture and Chaos in the Age of Machines and Fine Arts

So we arrive at the conception that a great deal of biological and human behaviour is beyond the principles of utility, homeostasis and stimulus response, and that is precisely this which is characteristic of human and cultural activities. Such a new look opens new perspective not only in theory but also in practical applications.315

In 1972, Rem Koolhaas, together with Madelon Vriesendorp, Elia Zenghelis and Zoe Zenghelis, worked on the project called Exodus or ‘the voluntary prisoners of architecture’ (Figure 6.55).316 It was Koolhass’ last project in Europe before he departed for America. From his point of view, this project was more about an anti-capital of the twentieth century (London). A landing strip of strong urban allure enclosed by two walls protected from the rest of the metropolis runs through the centre of London. This project can be considered the end to the futuristic architecture of the 1960s.

The twofold aim of this project was firstly to point out the ideological resistance between old and new, besides expressing the true face of the upcoming features of London and the soullessness of the metropolitan ideal. The chance of escape from the new commune and the fear of being prisoners of this machine, dominated society. For Koolhass, this was also a reflection on Berlin, which he had personally experienced in 1971. To him, the Berlin Wall was an architecturally utopian manifesto that was both a rejection and an acceptance of any likelihood of moulding society (politically, culturally, psychologically) by architecture. Exodus on the other hand, was designed as an anti-utopian architectural project that carried a very strong symbolic meaning: architecture can both destroy, make inhabitable or ugly and equally, it has the ability to rebuild and beautify society.

314 Ibid. pp.330-332. 315 Ludwig Von Bertalanffy, General System Theory (New York: G.Braziller, 1968), p.115. 316 Lieven De Cauter, The Capsular Civilization : On the City in the Age of Fear (Rotterdam: NAi Publishers, 2004). 153

Figure 6.55 Rem Koolhaas and Elia Zenghelis, Exodus, or ‘The Voluntary Prisoners of Architecture’, London, 1972.317

The advancement in science and technology during the early twentieth century has transformed the position of architecture in relation to mankind. The rejection of Platonic pure geometry or the Pythagorean ordering system and Cartesian forms had to be applied in order to make way for new thinking. Russian avant-garde theoretical and formal experimentation and production became a fascinating learning curve for many architects of today. It was the constructivists’ attempts to act on the fusion of physical, abstract forms and philosophical implication of an era that is rapidly changing is of the highest importance as a point of reference.

In 1916, Kazimir Malevich (1879–1935) launched his controversial painting project called ‘Suprematism’, and stated with much confidence that it would change the world and herald the beginning of a new era for art (Figure 6.56). The manifesto of suprematism about a ‘white state of mind’ and a ‘non-objective world’ was projected by its followers as the only way to guide man to experience the purity of his true

317 Rem Koolhaas et al., Rem Koolhaas/Oma (Düsseldorf: teNeues, 2002). 154 existence.318 Malevich’s philosophy was an abstract one aimed to free man from the restrictions of the phenomenal world.

I say to all: reject love, reject aestheticism, reject the trunks of wisdom, for in the new culture your wisdom is laughable and insignificant. I have untied the knot of wisdom and set free the consciousness of colour! Remove from yourselves quickly the hardened skin of centuries, so that you can catch up with us more easily. I have overcome the impossible and formed gulfs with my breathing. You are in the nets of the horizon, like fish! We, the Suprematists, throw open the way to you. Hurry! For tomorrow you will not recognize us.319

In the beginning, production of this style appeared to be some kind of strange mysticism that was eventually banned by the Communist authorities (Alexandre Nikolayevich Benois, Russian historian alleged it to be a ‘sermon of nothingness and destruction’).320 However, the influence of its principles lived on to shape the later movement of constructivism and continues to inspire numerous artists and designers today. Malevich was returning modernism to its origins by applying active figures to demonstrate a surreal landscape and flowing space. The primary motifs for this development were the circle, square and cross. According to Hadid, her graduation project (Architekton Hotel) was based on Malevich’s two-dimensional paintings and transformed the elements from his works into a hotel located in London, right across the Thames River.321 Hadid took the research further along Malevich’s suprematism route when he moved from the two- dimensional practice of his movement to three-dimensional (art to architecture).

318 Fischer Fine Art Limited, Russian Suprematist and Constructivist Art, 1910-1930 : [Catalogue of an Exhibition Held at] Fischer Fine Art Limited, London, March-April, 1976 (London: Fischer Fine Art Ltd, 1976), p.8. 319 Matthew Drutt and Kazimir Severinovich Malevich, Kazimir Malevich : Suprematism (New York: Thames & Hudson, 2003), p.40. 320 Carnegie Library - Pittsburgh, Monthly Bulletin of the Carnegie Library of Pittsburgh (Pittsburgh: The Library, 1918). 321 Gordana Fontana Giusti, Zaha Hadid works: Process, Sketches and Drawings (London: Thames & Hudson, 2004), p.81. 155

Figure 6.56 Kazimir Malevich painting: Suprematism, No.85, oil on canvas, Krasnodar Museum of Art, Russia, 1916.322

One of Malevich’s most influential works was his stage design (1913) for the Russian Futurist play, Victory over the Sun. In this work, he determined the idea of Black Square (Figure 6.57), and the floating in nothingness of space. However, looking at Hadid’s design and the painting that she produced for the hotel, which was based on Malevich’s elementarism, it is more potential or abstract architecture than practical or real architecture. Malevich called this the ‘non-objective reality’. He declared that ‘the forms of suprematism have nothing to do with technology of the earth’s surface’.323

322 John Milner and Kazimir Severinovich Malevich, Kazimir Malevich and the Art of Geometry (New Haven: Yale University Press, 1996), p.161. 323 Ibid. p.210. 156

Figure 6.57 Kazimir Malevich: Black Square, oil on canvas, State Russian Museum, St. Petersburg, Russia 1915.324

Figure 6.58 Zaha Hadid: Horizontal Tektonik, acrylic on cartridge, London, England, 1977.325

324 Ibid. p.128. 157

In contrast, Hadid’s painting (Figure 6.58) incorporates pure geometric figures and the composition of many systematic layers. Having said that, Hadid indeed envisions and brings to life to Malevich’s suprematist ideology as a transformation of the art and architectural world. She diverts the theory of the return to the origin of modernism in a way that is capable of detaching itself from theology or strict rules. As a result, it is evident that most of her works are about experimentation, conceptual progress, and disengagement from any principle. Her mission to raise the two-dimensional figures in the already executed suprematist paintings into a building is achieved by borrowing the different elements or figurative movements from the painting for each project she is working on. In terms of my second hypothesis this developments in architectural thinking and creation of building transformed the design world.

Figure 6.59 Zaha Hadid: MAXXI, Rome, Italy, 2010.326

Hadid’s 1999 project, the Hoenheim-North Terminus and Car Park in France, is slanted and prismatic, while the MAXXI National Museum of the 21st Century Arts (Figure 6.59) is rectilinear and sinuous. Many more examples of her projects substantiate the diversity and inclusiveness of the forms and her design ideology.

325 Zaha Hadid, Patrik Schumacher, and Gordana Fontana-Giusti, Zaha Hadid Complete Works, 4 vols. (London: Thames & Hudson, 2004), p.19. 326 Z.H. Architects, Maxxi: Zaha Hadid Architects: Museum of XXI Century Arts (Rizzoli, 2010), p.83. 158

Malevich’s approach to humanity and universal principles was mystical and theological, and his mission was to develop a radical art form that could have a place in man’s history. One can trace Malevich’s concepts methodically back to French styles of cubo futurism and transrational realism before the gloominess of Russian futurism. His philosophy in art was to produce a work that is an individual interpretation of creation. In his book, The Non-Objective World, he referred to his revolutionary creation of a black box as the ‘image of God as the essence of his perfection on a new path for today’s fresh beginning’.327 Malevich stated that suprematism adjoins unorthodox components to his avant-garde art that originates from the experience of man’s creation (modern technology) of his era. On the other hand, by observing his works closely, it is apparent that the other quest upon which he placed just as much emphasis, was to invent a sensory experience of modernism or technology and discover spiritual effects beyond the physical. The titles of his works such as The Aviator, Aeroplane Flying, The Non- Stop Station, The Knife Sharpener, and many more demonstrate his intention. For her part, Hadid translates such theological beliefs and earthly modern elements into her works through the idea of microcosm and macrocosm, the architecture of vibrant and abstract form reaching for totality and true perfection. She is creating space that expresses sensation of modernity but is still open to interpretation—or even to misinterpretation. Umberto Eco explained his view on the openness of her works as ‘the poetic of the open work tends to encourage acts of conscious freedom to multiply possibility and rejects definitive messages’.328

Conclusion

One can interpret Russian avant-garde’s representation in the twentieth century as the ‘secular spiritualism’ that strived to achieve freedom from attachment to any set principles or any familiar symbolism. Rather, it stands for exclusivity and impression. Moreover, the standpoint that is clearly drawn is a resistance or even denial to seek out meaning in their designs. If this art were associated to any symbolism or attached meanings, it would have been referred to as less avant-garde, less modern, and even outdated. As Naum Gabo comments:

327 Kazimir Severinovich Malevich, The Non-Objective World (Chicago,: P. Theobald, 1959), p.92. 328 Umberto Eco, The Open Work (Cambridge, Mass.: Harvard University Press, 1989), p.3. 159

Either build functional houses and bridges or create pure art, not both. Don’t confuse one with the other. Such art is not pure constructive art but merely an imitation of the machine.329

This is a clear instance of Russian architects’ way of thinking and advocating their point of views at the time of the first machine age. The core concept of their argument was to separate art from life, also theory/thinking and practice/doing. The twentieth century Russian architects’ insistence on openly refusing to evoke past or present values resulted in producing geometrical patterns belongs to no-time. Rather, the alienation in art and architecture of Russian constructivist geometrical patterns became a way to introduce the far future.

In this chapter, I analysed the two hypotheses of this thesis to see whether it support my thesis. The analysis does not reject my hypotheses. An investigation of the early 1990s movement of constructivism led me to review and understand the architecture of early Russian vernacular churches and political history of Russia. This chapter has demonstrated the geometrical patterns that were used to symbolise the spiritual meaning or other beliefs in historical Russian churches (hypothesis number one), and how it has been changed or forgotten through time under political and social devastation or developments (hypothesis number 2).

The form and composition those constructivists’ creative minds and their admirers produced aimed to leave the meaning and theory of their work inconclusive for the beholder, or maybe for the beholder to decide what it meant. In other words, their works were concerned with ‘becoming’ rather than ‘being’. Consequently, there was no overwhelming meaning for the beholder. This was the utopian design; the base concept for architects was the non-objective art and the study of material construction, which resulted in reflecting nothing but these constructivist projects intended to function as complex social organisms.

In the next Chapter the investigation will continue to question the second hypothesis and follow the narration of Deconstructivist practice and ideology. The discussion of this chapter concludes in the second age of machine and the rapid growth of digitalisation profoundly influenced architects and the form of milieus.

329 Naum Gabo, Modern Architecture: A critical history (London: Thames and Hudson, 1985), p.169. 160

Chapter Seven. Implications for Design Today

Figure 7.60 Bernard Tschumi: Parc de la Villetter, Paris, 1982.330

It may be that we have become so feckless as a people that we no longer care how things do work, but only what kind of quick, easy outer impression they give. If so, there is little hope for our cities or probably for much else in our society.331

Political and economic upheaval, war and social events of the early twentieth century caused an evolution in the world of architecture. Modernist architects tended to reject the concept of meaning and introduced geometrical patterns and pure lines to achieve freedom of expression in their unusual, yet interesting design work. Rather than represent symbolic form, they created gestures. The Platonic notion of geometry and idea as the paradigm of the universal realm and pure form was no longer an important consideration for creative minds. The Russian avant-garde rejected past beliefs (tradition) by rebelling against classical design principles in which the balanced, hierarchical relation between forms created a unified, meaningful whole. The dream of architects to create a pure form that contributed harmoniously to a building’s structure, thereby guaranteeing meaningful symbolism that can please the mind and spirit of humankind, had become a nightmare for the modern man.

330 Omnibus Volume, Deconstruction (London: academy edition, 1989), p.174. 331 Jane Jacobs, The Death And Life Of Great American Cities (New York: Random House, 1961), p.71. 161

The Machine and the Guilt of Meaning

With the rise of postmodernism in the late twentieth century, the idea of geometry as being representative of spirituality or religion shifted to a more secular kind of spiritualism, which I describe in this chapter. Analysis of the work of certain celebrated architects from the early twenty-first century (such as Rem Koolhaas, Zaha Hadid and Peter Eisenman), along with the theoretical work of influential philosophers such as Ferdinand de Saussure and Jacques Derrida, allows closer examination of architectural deconstructivism. Parallel to the revolution of deconstructivism, I further investigate the beginning of computational creativity in the era of information technology. The aim is to demonstrate how geometrical forms (as identified in earlier chapters) in late twentieth and twenty-first century architecture have reformed, and to what extent contemporary architects understand the historical and spiritual meaning attached to these forms.

The importance of my arguments in this chapter in relation to the second hypothesis of this thesis (that architects use geometric patterns without understanding their origins and attached meanings) is to demonstrate recent events in architecture in relation to geometric patterns and meanings. Also significant is my investigation into how architects lack an understanding of the embedded spiritual meaning when applying geometric patterns to their work. In this chapter, I will show how creative minds influence historical geometrical form by breaking and deforming them, and detaching them from any set beliefs or symbolism. Notwithstanding, meaning and symbolism in the design of buildings is an important characteristic, as the Polish architect and scholar, Rykwert affirms:

Through Semantic study of environment we can discover the means of discoursing in our buildings. Only that we will be able to appeal to the common man again. … If memory and association are starved visually by architects, then the result must be malaise and a rejection of the environment which they created.332

The lack of emphasis on meaning and symbolism is noticeable, not only in the physical design works of these architects, it is also apparent in the theoretical writings of twenty- first century architectural design scholars. On the other hand, distinguished architects and theorists have reached out to other fields in their prolonged search for creating new

332 Joseph Rykwert, Meaning And Building, The Necessity Of Artifice (New York: Rizzoli, 1982), p.16. 162 forms and methods to disguise meaning. Fine art and philosophy appear to have become the relevant fields to fulfil this desire.

Deconstruction of Geometry and Architecture of Rebellion

During the 1980s, London-based architect Zaha Hadid (1950–) proposed that modernity was an incomplete movement that had not reached its full potential and deserved to be revisited and developed.333 Like many architects in the postmodern era, Hadid believed that idealism behind the word ‘modernism’ had led to a soulless style. This questioning of modernism by architects of the 1980s occurred under the influence of the seductive consumer culture of the late twentieth century. Hadid began to move away from the utilitarian, universal principles of modernism and rejected ancient aesthetics as no longer important in design. She saw a need to move away from the eclecticism and myth cultivated in architecture in order to achieve a more utopian style.

Importantly, Hadid reprised the work of the 1920s Russian constructivists with its revolutionary heroes. She directly transposed the ‘visual language’ of constructivism into her design methodology. Other architects of the time were following a similar path, particularly Dutch architect, Rem Koolhaas (1944–) and Greek architect, Elia Zenghelis 334 (1937–) of the OMA.

However, Hadid responded with a more aggressive avant-gardism. She placed her architecture in the framework of Kasimir Malevich’s Suprematism, El Lissitsky’s Proun Room experiments and Russian Rationalism, which became the precursor to her utopian works after 1980 (I demonstrated this approach in detail in Chapter Six). Hadid provides us with some sense of the role that Russian constructivists’ works has played in inspiring and informing her designs. In 1988, Hadid, along with seven other prominent architects, was invited to the Museum of Modern Art in New York to take part in an exhibition curated by postmodern American architect, Philip Johnson. The

333 Zaha Hadid is an Iraqi born contemporary architect who started her education in mathematics at the American University in Lebanon. She moved to London in 1972 after the political changes in her home country and attended the Architectural Association School. It was there she met her influential teacher, Dutch architect Rem Koolhaas (1944-). P. Schumacher and G.F. Giusti, Zaha Hadid (Virginia: Rizzoli, 2004), p.15-18. 334 OMA (Office for Metropolitan Architecture) was established in 1975, and is based in Rotterdam in Netherlands. The founders of this organisation include, Rem Koolhaas, Elia Zanghelis, Medelon Vriesendorp and Zoe Zanghelish.Berlage Instituut, Hunch: The Berlage Institute Report (Delft: Berlage Institute, 2005), p.150. 163 title of this exhibition was deconstructivist Architecture. Besides attaching the term ‘deconstruction’ to the practice of building designers, this exhibition gave a new identity to the involved architects. The projects in this exhibition tended to disturb the beholder’s thinking, not by dismantling a milieu but through radical bent of architectural tradition and engaging the conflicting ideas into the design composition. In a relatively short time, deconstruction, the new movement, formed the new paradigm of thinking. Those architects designated ‘deconstructivists’ followed the modern thinkers in various fields such as political and social, written and practical, with perhaps irrelevant references to architecture. It is rather like the way Robert Venturi (1925–) in the following passage sets the atmosphere:

I like elements which are hybrid rather than ‘pure’, compromising rather than ‘clean’, distorted rather than ‘straightforward’, ambiguous rather than ‘articulated’, perverse as well as impersonal, boring as well as ‘interesting’, conventional rather than ‘designed’, accommodating rather than excluding, vestigial as well as innovating, inconsistent and equivocal rather than direct and clear.335

There are circumstances in which deconstruction can be transferred from philosophy to architecture. The principles of modernism suggest that the style is the inheritor of the Enlightenment. The difference is that the theological symbolism and mythical belief of the Enlightenment era has been replaced by faith in the power of reason. But can reason formulate artistic concepts in art and architecture? And if so, what would be the result of such a production in the field of art?

Zaha Hadid has fought against all the set boundaries and principles. Her design solutions are very far from reality or rationality of any practical response in many aspects. She strove to eliminate those forms or symbolic geometric shapes that had been incorporated in the architecture of the past. Instead, she aimed to introduce a new era in architecture and design with the ability to conquer the traditional assumptions of earlier periods (Figure 7.61).

335 Robert Venturi, Complexity and Contradiction in Architecture (London: Architectural Press, 1977), p.16 164

Figure 7.61 Zaha Hadid: Grand Buildings, Trafalgar Square London, England, acrylic on canvas, 1985.336

In order for Hadid to become acclaimed as a successful architect, she often sacrificed the meaning and social responsibility of architecture for functionality. Even though she claimed in many of her interviews that her designs considered humanity and were designed with the users’ requirements in mind, in practice, she certainly did not follow the same line.337 The idea of liberation from the existing universal order and consequently having to invent a new order in every project was a constant battle for Hadid and many of her contemporaries. In 1983, she stated:

We can no longer fulfil our obligations as architects if we carry on as cake decorators. Our role is far greater than that. We, the authors of architecture, have to take on the task of reinvestigating Modernity ... there is only one way and that is to go forward along the path paved by the experiments of the early Modernists.338

The symbolic use of the term ‘modernity’ at that time was just another pretext for the alienation of twentieth-century architecture and pushed it far from collective necessity. On the contrary, the industrial pressure on designers and thinkers for a non-utopian

336 Zaha Hadid and Ivorypress Space, 'Dezeen Magazine', , accessed 6th January 2012. 337 After intense research, this thesis can state that there is a lack of theoretical texts by or about Hadid. Most of the reflection on her projects has been compiled through short audio interviews or assembled by her business partner Patrik Schumacher, and only after the completion of the project. 338International Union Of Architects, Planetary Architecture Two. International Architect Magazine (London: International Architect Publishing Ltd., 1984), p.16. 165 notion of any inventions, encouraged the production of such illusionistic and seductive manifestations. Hadid’s attentiveness and openness to such profitable requests defined her distinct social vision and artistic vernacular, which owed much to her Russian constructivist forerunners.

In general, individual desire and self-expression has come to play the main role in forming the language of architecture today, in comparison to the past where the core purpose was the generation of a meaningful composition of set beliefs among the population of society. Designers’ self-expression has often resulted in the loss of the harmonious designs of the past and has continued to add to the general population’s disconnection with the designs.

The sublimity in Hadid’s designs is purely autonomous.339 In relation to her projects, sublimity is not merely a reflection of what has been already inherent in something; it involves the various emotional reactions towards what man sees, and embodies a powerful amalgamation of universal and individual images, experiences, sentiment, and facts. There is a sense of freedom in the state of ‘the sublime’ that is unchained from any dictated reasons. Therefore, the sublimity of aesthetic linguistics, the principle of morality, and the assembly of the universe at large, are closely interwoven and effectively interconnected. My main concern with the topic of sublimity in relation to this thesis is to demonstrate clearly how deep-rooted beliefs can be altered via different influential factors that lie in the conscious or unconscious mind of man.

339 The term ‘autonomous’ has been applied here in relation to Hadid’s works based on Theodor Adorno’s (1903-1969) definition of this term in his book ‘Aesthetic Theory’. He believed that autonomy in the field of art (and effectively architecture) has cultural and social dimensions, which began after the era of Enlightenment when art became detached from cathedrals and aristocratic influences. ‘By crystallising in itself as something unique to itself, rather than complying with existing social norms and qualifying as 'socially useful', it criticises society by merely existing ... through its refusal of society, which is equivalent to sublimation through the law of form, autonomous art makes itself a vehicle of ideology.’ Theodor W. Adorno and Rolf Tiedeman, Aesthetic Theory (Minneapolis: University of Minnesota Press, 1997), p.296. 166

Architecture as Proposition of Becoming

Figure 7.62 Benoit Mandelbrot: Four stages in the construction of the Koch snowflake.340

In 1975, French-American mathematician, Benoit Mandelbrot, published a book called Les objects fractals, forme, hasardet dimension (Figure 7.62).341 In the introduction to his book, he clearly states the distinction between Euclidian geometry and fractal geometry in the context of art and architecture.342 He refers to modern architecture such as that of Mies van der Rohe and criticises the lack of textural progression and harmony with the space it occupies. This new method of fragmentation and irregularity in mathematics and geometry changed the traditional application of pure geometry in architecture in order to achieve an organic and more complex shape.

Not long after this publication and its translation into English, the American architect Peter Eisenman (1932–) designed House 11a (Figure 6.63). In that design, the words and methods of fractal geometry and fractal scaling were developed into core thematic motifs. It was then he first developed the idea of ‘L’ in his designs, which itself is the fragment of a square, and symbolised unbalanced geometrical forms in any composition of perhaps a symmetrical and stable design. It is also an emblem for the in-between position. He explained his design process using the concept of fractal scaling as:

Three destabilizing concepts: discontinuity, which confronts the metaphysics of presence; recursivity, which confronts origin; and self-similarity, which confronts representation and the aesthetic object.343

340 B.B. Mandelbrot, The Fractal Geometry of Nature (New York: W.H. Freeman, 1983), p.173. 341 In 1977 translated to English by the title, Fractals: Form, Chance and Dimension. And in 1982 was revised and published under the title, The Fractal Geometry of Nature. 342 Mandelbrot, The Fractal Geometry of Nature, p.23-25. 343 P. Eisenman and T. Nakamura, Architecture + Urbanism, Peter Eisenman (the University of California: A+U Pub. Co., August,1988), p.70. 167

Figure 7.63 Peter Eisenman: House 11a, produced during the Cannaregio design seminar in Venice, Italy, 1978.344

Prior to any further analysis on his work, it is necessary to consider the origins of his study and professional development to justify the importance of his works in the contemporary practice of architecture. The way in which Eisenman changed the design ideology that he practised during the 1960s and 1970s was criticised by many of his contemporaries. He became the most prominent practitioner in his writing and most manifestly through his practice as an architect. This mode shifted from his earlier concerns about aesthetic autonomy, orthodox architecture, late modernist use of form and the dominance of self-expression, and transformed him into a Poststructuralist/post- phenomenologist advocate. Eisenman himself described his design process as a research into the generation of form as a specific manipulation of meaning within a culture, or the syntactic dimension of architecture.

One important aspect of his detailed study of classical architecture is the generation of representation and sign.345 Eisenman’s fascination with the Renaissance era and the

344 Peter Eisenman, Bedard, Jean-Francois, Balfour, Alan, Cities of Artificial Excavation : The Work of Peter Eisenman, 1978-1988 (Montréal: Canadian Centre for Architecture, 1994), p.55. 345 Eisenman’s interest in sign and symbolism expanded later on in his professional life once he was introduced to the works of Saussure and Derrida. Through the study of these two traditions, he attempted to break the norm in its application and produce an original representation. 168 semantic dimensions of the building from that time brought him to a clear understanding of the linkage between form and meaning. The external meaning of geometrical forms, in complete or part of structure, in his view was the greatest aspect of any buildings treated as significant in their design and mediation. To him, the semantic change in architecture was truly executed over the classical and even modern era, and the long-held belief in human physical form being included in the universal order was no longer applicable to architecture. That was the point in his professional life where he moved from the traditional approach of symbolism, expressional meaning and semiotics to the more avant-garde strategy of syntactic dimension within architecture.

It is essential to remember that Eisenman’s earlier architectural projects, such as his houses of the 1960s through to the 1970s, were following modernist and influenced by the more classical belief of the relation between the human form and the dwelling. The reason for his earlier approach to design was the core idea of provoking the spirit of architecture, or the autonomy in the method to pursue an architectural essence. An important aspect of Eisenman’s early work was his belief in the core function of architecture as the projection of geometry in space (space in his case meaning what bounds an area, such as ceiling, floor and walls). The ‘formalism’ or linear/rectilinear arrangement of his earlier projects, in comparison to his later works, is a more complex variation of formalism and is evidence of his views of architecture. In House III (1971) the proportion and scale of the design is suggesting development in accordance with the doctrines of Vitruvian Man’s dimensions.

This architecture would necessarily create anxiety and a distance, for it would no longer be under man’s control. Man and object would be independent and the relationship between them would have to be worked out anew.346

The symbolism in architecture, or as Eisenman suggests above, signs in architecture, can be refined through the elimination of meaning, making and symbolic function of the architectural object.

For Eisenman, architecture had to be independent of any simulation or representation of traditional cosmology, culture and rituals. His work for autonomous architecture saw

346 Peter Eisenman, Eisenman inside Out : Selected Writings, 1963-1988 (New Haven: Yale University Press, 2004), p.218. 169 that creating the architectural form was not logically consistent and the attached meaning was derived from the issue of logical interface of formal notions.347 These matters were addressed in House I through the design of form and space in order to create a structure that is neither unintentional nor peripheral to the initial and core idea of the work.

This project for Eisenman was a detailed experiment of a physical environment by applying a logically consistent method, free of any attachment to external meaning or even symbolic function. American art and architecture critic, Rosalind E Krauss (1941– ), in a reflection on Eisenman’s early works, wrote an outstanding essay: Death of a Hermeneutic Phantom: Materialization of the Sign in the work of Peter Eisenman.348 In that essay, Eisenman’s Houses I and II were analysed in order to demonstrate they were a classical example of twentieth-century architectural symbolism, which has its roots in the Russian non-objective universe or nihilism, and also shows the transformation of modern or avant-garde architecture from clear and transparent design into a more opaque design (Figure 7.64 and 7.65).

347 The idea of autonomy in architecture was first revealed by German philosopher Immanuel Kant (1727-1804) and extended by Viennese architecture historian Emil Kaufmann (1891-1953). 348 P. Eisenman, R.E. Krauss, and M. Tafuri, Houses of Cards (Oxford University Press, 1987), p.180 170

Figure 7.64 Peter Eisenman’s, House I, Princeton, 1967.349

Figure 7.65 Peter Eisenman’s, House II, Hardwick, Vermont, 1970.350

349 Studio Led by Nicolas Simon & Max Turnheim., 'École Architects Est', , accessed 2nd June 2011. 350 Ibid. 171

For Eisenman, solidity and transparency, and the distinction between the two, made it possible to set apart what is art and what is not. His emphasis on the outward appearance and symbolism in applied geometry is the process of inwardly referencing to its own laws and forms, and logically distancing itself from everything else. One of the important figures with whom Eisenman famously pursued a dialogue was Colin Rowe (1920–1999), a British born architecture historian and theorist who had a great influence on architects’ opaque path of thoughts. Rowe collaborated with an American artist, Robert Slutzky (1929–2005) in one of his papers called Transparency: Literal and Phenomenal. In this paper, they examined the allegorical quality of the two kinds of transparency, physical and virtual, or as they called them, literal and phenomenal. They wrote:

Transparency, however, implies more than an optical characteristic; it implies a broader spatial order. Transparency means a simultaneous perception of different spatial locations. Space not only recedes but fluctuates in a continuous activity.351

In terms of transparency in architecture, the formation of such contention appears between frontally structural materials or configurations such as glazing, or the simple void between multiple storeys and the hidden realm of meaning in substance. Rowe further reflected on the topic of transparency and studied in detail in Le Corbusier’s Villa Garche. He wrote:

There is a continuous dialectic between fact and implication. The reality of deep space is constantly opposed to the inference of shallow space; and by means of the resultant tension, reading after reading is enforced.352

Subsequently, this phenomenal transparency constitutes the true quality of any forms. As for Eisenman’s study of Rowe’s theory, it cemented his diverse conceptual ideology in architectural design—the appearance of forms and their deeper reality. On the other hand, Rowe was the one who actually encouraged Eisenman to study Le Corbusier’s works and the uncanny similarity to his building models, in order to gain a better understanding of modern architecture. Eisenman’s observation of this modern architectural practice showed him the methods of producing structures and forms of

351 C. Rowe, As I Was Saying, Volume 1: Recollections and Miscellaneous Essays (Cambridge: Library of Congress Publication, 1996), p.160. 352 Ibid. p.41. 172 conceptual and abstract appearance. In addition, he saw the modern exploration of geometrical forms at both the symbolical level and the conceptual interpretation of their phenomenal transparency. Eisenman’s findings have been asserted clearly in the conceptual process of his ‘houses’ project, through a fundamental formal association that influences humankind’s deep emotional receptivity in relation to the environment he is in.

Figure 7.66 Andrea Palladio: Villa Rotonda, Vicenza, 1570.353

In relation to Eisenman’s works on the experimental houses, the designs appeared exaggeratedly formalistic and contrived. The density in his work was amplified through the idea that applied geometry can express the various levels of meaning, which can only become clear to knowledgeable observers. In his validation of this design method or theory, he indicated the metaphorical link between Palladian nine squares (Figure 6.66) and the semantic model.354 Eisenman’s early drawings and diagrams for his projects clearly illustrated the significance of formalism in the nine square grid and principally the matter of humanity in the form of architecture.1 This was another lesson

353 Kim Williams, Giovanni Giaconi, and Andrea Palladio, The Villas of Palladio (1st edn.; New York: Princeton Architectural Press, 2003), p.130. 354 Villa Rotonda’s floor plan and recurrence of nine squares in different configuration in other designs of Andrea Palladio. 173 from Rowe that suggested Renaissance design methods were the superior model to follow in order to achieve true proportion and harmony in building ratio that is in a measure of the human body. Rowe quoted English architect, Sir Christopher Wren (1632–1723) as follows:

There are two causes of beauty natural and customary. Natural is from geometry consisting in uniformity, that is equality and proportion. Customary beauty is begotten by the use, as familiarity breeds a love for things not in themselves lovely. Geometrical figures are naturally more beautiful than irregular ones …355

The result of Rowe’s studies of Eisenman’s works is an illusionistic creation that affects viewers visually and intellectually. It was then that the symbolic aspect of his design practice was replaced by his new discovery of syntactics. After exhausting his belief in symbols, Eisenman took a different turn in his practice and study in order to achieve utopia; he discovered an interest in linguistic theory and architecture design.

Historically, the practice of architecture has struggled to find common ground with linguistic theory. Moreover, if it was applied or directed to merge, the results were not entirely encouraging. This syntactical dimension of practice derived from Eisenman’s study of the works on universal grammar by Noam Chomsky (1928–) the American historian and linguist. Ironically, for Eisenman there was no literal way to form the basic hypothesis from his study of Chomsky’s theory; the only possible approach seemed to be in a metaphorical fashion. The study of the existence of form instead of the study of underlying knowledge of the same form drew his attention to the linguistic concept and deep structure.356 In 1971, Eisenman composed and published an essay based on Chomsky’s syntax titled, From Object to Relationship II: Casa Giuliani Frigerio: Giuseppe Terragni Casa Del Fascio. In that essay, he explained:

In Architecture both types of relationships exist simultaneously. There is a surface aspect essentially concerned with the sensual qualities of the object: that is aspects of its surface, texture, color, shape, which engender responses that are essentially perceptual. There is

355 Colin Rowe, The Mathematics of the Ideal Villa, and Other Essays (Cambridge: MIT Press, 1976), p.2. 356 The term is used in linguistics and refers to any two or more sentences which carry the same meaning, Marina K. Burt, From Deep to Surface Structure : An Introduction to Transformational Syntax (New York: Harper & Row, 1971) explained the term as ‘In transformational grammar, the underlying syntactic structure (or level) of a sentence’. In Architecture, this term applies to non-visible surface structure and represents the conceptual significance of architectural/structural forms. 174

also a deep aspect concerned with conceptual relationships, which are not sensually perceived; such as frontality, obliqueness, recession, elongation, compression, and shear, which are understood in the mind. These are attributes, which accrue to relationship between objects, rather than to the physical presence of the objects themselves.357

Therefore, building is the manifestation of this relationship and a demonstration of the transformation from conceptual to physical. Eisenman’s work was on syntax as a system to make this process free of any attachment to tradition or cultural belief. To him, this was the logical process to generate form and most importantly, to fulfil the quest for autonomous architecture. However, by the early 1990s it became obvious to the progressive architect that his earlier work, especially his theoretical writing, was apparently a fictionalisation of unreal history and in general, it was an allegory of what he used to emphasise as the logic of autonomy. He had to replace what he had professed for many years as his notion of architecture and the visual independence of his practice. After such a realisation, he began to look for a way to revolutionise and heighten his avant-garde way of thinking.

It was during this time that Eisenman’s research introduced him to Jacques Derrida’s (1930–2004) theory of deconstruction and exposed him to this theorist’s idea of the philosophy of language, aesthetic and semiotics. There are numerous different translations of the term deconstruction that aim to attach the concept to various fields or past beliefs. In architecture, this term is collectively used when the abstraction, disturbance and distortion of pure geometrical forms are set in an order, which cannot really be called order itself. The work of contemporary architects such as Frank Gehry, Daniel Libeskind, Rem Koolhaas, Peter Eisenman, Zaha Hadid, and Bernard Tschumi illustrate this so-called ‘style’.358 Derrida’s definition of deconstruction is:

Deconstruction cannot be restricted or immediately pass to a neutralization: it must, through a double gesture, a double science, a double writing–put into practice a reversal of the classical opposition and a general displacement of the system. It is on that

357 Peter Eisenman, Written into the Void: Selected Writings, 1990-2004 (New Haven: Yale University Press, 2007), p.177. 358 Bart Van Der Straeten, 'The Uncanny and the Architecture of Deconstruction', Image & Narrative, 17/5 (1997). 175

condition alone that deconstruction will provide the means of intervening in the field of oppositions it criticizes and that is also a field of non-discursive forces.359

For the purpose of this argument, and specifically to understand the deconstructivist thinking in late twentieth-century architecture, it is vital to review, clarify and justify the reasons why the topics of philosophy and linguistics need to be mentioned here. In the design practice of many recent architects who seek utopia, the desperation to find new forms leads them to seek their answers in theory and philosophy.

In reading British historian Jonathan Rée’s book on Western Philosophy, he explained that when man first started a series of questions on various areas such as existence, reality, language and nature, it was the birth of philosophy. Philosophy originates from Greek terminology meaning ‘love of wisdom’ and is been referred to by some as ‘love of argument’.360 From the beginning of history, as long as culture and civilisation has existed, when intellectuals started to consolidate their way of thinking, a philosophical statement was concerned mostly with the connection between thought and its true representation while searching for a reference to existence and meaning. Later, they rephrased their enquiries after isolating them from other influential fields such as religion, politics, and science, to the more refined question of the vernacular (talk of ideas) in relation to the universe (talk of meaning). In some cases, philosophy is a polemic device to literature inscribed about the same matters. In those cases where philosophy is a polemic device, it can only result in an unfinished discussion or illogical argument.

While ancient philosophers simply sought truth but knew that truth could be found in a number of ways, modern philosophers are ‘system builders’, which they believe are truth generators. For example, the German philosopher, Immanuel Kant built a system of analysis and synthesis within his ‘Critiques’, with the third critique being about aesthetics, The Critique of Judgment.361 And then there is Derrida, who without holding to any dispute or thesis, is merely associated with his precursor not through the same subject matter but simply on similarity and dialectical tradition. Derrida was mistakenly

359 Jonathan Derrida. Culler, On Deconstruction : Theory and Criticism after Structuralism (London: Routledge & Kegan Paul, 1983), p.86. 360 J. O. Urmson and Jonathan Rae, The Concise Encyclopedia of Western Philosophy and Philosophers (London: Routledge, 1991), p.39. 361 Immanuel Kant, The Critique of Judgment (New York: Cambridge University Press, 2000) 176 referred to as the philosopher of language but in between his written lines, he protests against this label. He claims his distrust pf writing, or language in general, and sees it as an impurity of philosophy. The heart of philosophy is a transparent representation of facts in relation to an argument or exhibition of an idea. Consequently, to communicate these represented facts to others and to demonstrate the true meaning of any concept, the philosopher must write. It is an illumination of any unnecessary confusion for the readers, and of any writing that requests more writing. Derrida keeps his philosophy in its sense of direction and significance.

There is therefore good and bad writing: the good and natural is the divine inscription in the heart and the soul ... A modification well within the Platonic diagram: writing of the interior and of the exterior, as there is a voice of the soul and a voice of the body… The good writing has therefore always been comprehended. Comprehended, therefore, within a totality, and enveloped in a volume or a book. The idea of the book is the idea of totality, finite or infinite, of the signifier. This totality of the signifier cannot be a totality, unless a totality constituted by the signified pre-exists it, supervises its inscriptions and its signs, and is independent of it in its ideality ... If I distinguish the text from the book, I shall say that the destruction of the book as it is now under way in all domains, denudes the surface of the text.362

Following this, the re-establishment and re-examination of Kant’s writing and thoughts became the core idea of Derrida’s fundamental concept, but again without giving an account of anything. He found the Kantian philosophical image an illusionistic way of thought, and Derrida’s challenge of Kant works was related to the fundamental nature and purpose of language and philosophy. He attempted to work against the force of writing a book about the philosophy of language or reinterpreting others’ books, instead engaging in generating a game with the different writings of philosophers who thought they had written about language. However, he never admitted his exact view was with the concern of language, nor did he articulate his apprehension about representation and reality being far similar to the Enlightenment position in relation to years of dispute and writing about deity and man.

This insistence that we need to transform ourselves in the way we see, express and teach, led Derrida to the notion of deconstruction. He studied the works of Ferdinand de

362 Jacques Derrida and Gayatri Chakravorty Spivak, Of Grammatology (Baltimore: Johns Hopkins University Press, 1976), p.17. 177

Saussure (1857–1913) in semiotics and linguistics, which clearly modelled linguistic signs and how to attach meaning to a sign. Sign is not connected to physical events outside of itself; the arbitration of sign is determined by the linkage between signified and signifier.363 It is important to mention here, that everything surrounding man in his everyday life operates through signs. Man would not have any immediate cognition of the present object without sign or symbols.

This demonstration of the theory of sign was a vital finding for even a contemporary architect to understand how to add meaning to geometric forms and what that meaning contained in itself. The unconscious reaction of man to formulate meaning for a sign comes from individual familiarity with that sign, which is influenced by man’s experience, memory, education and belief. On the other hand, the polysemies (many meanings) of a sign make it uncontrollable in the way it can attach itself to a large number of meanings. Therefore, the core concern of semiotics for Saussure was to demonstrate a systematic and meaningful use of sign so that it involved all the other signs, and consequently conveyed value to the sign as a whole.

To think of a sign as nothing more, would be to isolate it from the system to which it belongs. It would be to suppose that a start could be made with individual signs, and a system constructed by putting them together. On the contrary, the system as a united whole is the starting point, from which it becomes possible, by a process of analysis, to identify its constituent elements.364

Reading Saussure and learning about the purpose of his theory helped Derrida to firm his faith in deconstruction. In relation to his theory, he witnessed that language can apply to Saussure’s formula, and factually stated that language is a form. He protested the need to conquer ‘the book’ because its lack in presenting totality as the signifier independently does not have the ability to be whole unless its signifier exists prior to that, and then the representation of signifier as a totality and sign becomes probable. He then agrees that the word within a text or the connection of the word within it, produces

363 Saussure formulates a diagram that demonstrates the sign consists of two sides, which composes its meaning as a whole in linguistics: Signified and signifier. Just like two sides of a coin, each side is as perfect as the other side and they are indivisible. Ferdinand De Saussure et al., Course in General Linguistics (London: Fontana, 1974), p.67. 364 Ibid. p.114. 178 the total meaning and the meaning does not come from a mystical foundation. ‘There is nothing outside the text’.365

Although there are speculations about the similarity of thoughts on semiotics between Derrida and Saussure, there are many unnoted lessons for Derrida’s philosophy that are rooted in the primary value of Saussure’s theory. Saussure creates a new metaphysics of the sign system, detached from any relationship to any origin or field. For Derrida, playing with his terms was a justification of the autonomy in his own philosophy. The evidence for such a claim is embedded in Derrida’s writings and debates, for example, in his 1971 essay White Mythology, where he illustrated the connection between ancient and modern signs:

While acknowledging the specific function of a term within its system, we must not, however, take the signifier as perfectly conventional. Doubtless Hegel's Idea, for example, is not Plato's Idea; doubtless the effects of the system are irreducible and must be read as such. But the word Idea is not an arbitrary X, and it bears a traditional burden that continues Plato's system in Hegel's system. It must also be examined as such, by means of a stratified reading: neither pure etymology nor a pure origin, neither a homogeneous continuum nor an absolute synchronism or a simple interiority of a system to itself.366

Returning to Eisenman and the lessons learned from Derrida’s philosophy, one of the most significant works of Derrida, which was closely studied by Eisenman, was his essay, Plato Pharmacy. In this essay, which can be referred to as a foundation text of deconstruction, Derrida remarks on the principle of specific Socratic law that rules the reality of the Eidos.367 He argued that the ability of two parts to recount to one another is by one communicating or referring in the same sense to the other part and not through their division, just like the relationship between writing and ideas. Through the Crito, 368 the generalisation of such a concept can become simpler. This dilemma has repeatedly become an apprehension in architecture, art and in the deconstructive view of

365 Derrida and Spivak, Of Grammatology, p.158. 366 J. Derrida, Margins of Philosophy (University of Chicago Press, 1982), p.254. 367 The term Eidos is of Greek origin and used in Plato’s theory of form. It comes from the verb Eido, which means ‘to see’. Plato used Eidos to demonstrate the meaning of ‘idea’ and the primary substance of things. 368 This ancient Greek terminology was used by Plato and refers to a short but vital conversation. Crito also was the name of a lifelong friend of Socrates and their philosophical dialogue. 179 both. In addition, Derrida demonstrates the conception of presence and absence in terms of seeking the absolute truth. To illustrate this more clearly, he discusses the nature of speech and writing.

According to Socrates, speech operates with the living words; it contains a spirit, but against that, writing is just an image of the already exhausted and soulless words and nothing more. Without speech, there is no writing. Therefore, Socrates concludes that speech is an accurate approach to the absolute truth, and writing is coupled with the representation of speech and belongs to the art of signifying the absolute truth, although 369 it appears only as an outline of the absence or presence of that truth. Plato refers to ‘writing’ as Pharmakon, an ancient, complex Greek term that stands for cure and intoxicant. In his view, writing cannot be controlled and has an ability to be quite misleading and open to reinterpretation of the original living narrator’s true meaning.

He, who speaks in contrast, is not controlled by any pre-established pattern, he is better able to conduct his signs; he is there to accentuate them, to inflect them, retain them, or set them loose according to the demands of the moment, the nature of the desired effect, the hold he has on the listener.370

The above passage is a crucial statement to explain deconstruction and also to exhibit Derrida’s interpretation of what he had garnered from earlier philosophers. The coherency of one argument reveals an underlying belief system and true meaning, expressed only through speech and the living word. Derrida calls this preference and superiority of speech, Phonocentrism, and describes writing as merely the derivative medium of communication.371 Derrida’s delineation of Phonocentrism is derived from German philosopher, Martin Heidegger’s (1889–1976) writings on metaphysical epoch. Even though Derrida criticised Heidegger’s approach to this notion of Phonocentrism in

369 In fact, Socrates himself only breathes through the written words in ancient Greek Philosophical scripts. He is known only through his written thoughts and records. 370 Jacques Derrida and Barbara Johnson, Dissemination (London: Continuum, 2004), p.116. 371 Jacques Derrida, Writing and Difference (Chicago: University of Chicago Press, 1978). 180 relation to the word ‘being’,372 it was a justifiable introduction to establishing his theory for modern philosophy.373

This scheme of différance374 between two communication methods in terms of Derrida’s ideology of deconstruction, as described above, is a short leap from Hegel’s analogy to synthesis or between-ness.375 And if the corporeal structure of architecture no longer represents the account of real and existent buildings, then the drawings of the buildings are the only authentic representations of designer’s concept. In other words, in the field of architecture, as the design grows from two-dimensional to three- dimensional, its preliminary idea fades away.

Instigated in 1985, The Choral Works,376 was a joint venture of Eisenman and Derrida developing ideas for a larger project in Paris called Parc de la Villette. The project was synchronised by another deconstructivist architect, Bernard Tschumui (1944–), who won the design of this project in 1982 and who was also influenced by Derrida’s philosophy. This question of whether the authored project is translating the written theory into a physical form was the work of an architect and philosopher or vice versa. Evidently, this is a philosophical thought that solidified the foundation of the architectural concept and initial idea. The title Choral was initiated from Derrida while he was writing an essay based on Plato’s Chora theory (described below), and this idea was transferred to Eisenman once he became involved in the project.

372 The notion of word ‘being’ in Heidegger’s works refers to possibility of generalisation; however, Derrida criticized such generalization and independency of ‘being’ placed more emphasis on the sense of ‘being’ and its dependency. 373 Joshua Kates, Essential History: Jacques Derrida and the Development of Deconstruction (Evanston: Northwestern university Press, 2005), pp165-167. 374 This term was first used by Derrida in his paper ‘Cogito et Histoire de la folie’ (English translation ‘Cogito and the history of madness’. Chicago: University of Chicago Press, 1978). It comes from the French term differe which itself represents sameness that is not identical. 375 The root of this concept is in Buddhism and the search to find the middle ground in order to end the suffering of humankind. In the Noble Eightfold Path, one of the principal teachings of Buddha, this third approach has been demonstrated. The middle path; it gives vision Avoiding both these extremes, the Perfect One has realized the Middle Path; it gives vision, gives knowledge, and leads to calm, to insight, to enlightenment. David Rose, Buddhism (Dunstable: Folens, 1995), p.142. 376 It is from the term Chora. Plato in Timaeus first mentioned This Greek terminology. This Platonic notion is used to describe the space or site and sometimes the place in space and later was considered one of the primary formulations of spatial planning in the West. Eisenman suggested the title Chora for this project to portray this collaborative work that has a musical sense to it. 181

In Timaeus, Plato differentiates three basic forms of existence. The first existent model form can only be understood beneath the notion of reason and functions in relation to universal principles—this form is logical and intelligible. The second form is a replica model of the first form and is in direct contact with man’s senses. But the third and final form is Chora, and is completely different from the first two forms. Chora offers the 377 original attitude and laws for exciting things. It gives ability to originals to function and sometimes mix, but as a result it might change at different times. Therefore, in Plato’s Timaeus, Chora conveys the motive that indicates the associations that may result between the original and its latent being. For him, it is an original and changing status wherein the substance and perceptible arrive into life, just like existence and progression of identity after birth. In other words, Chora is like a space for creation that everything transitions through, although nothing is contained in this space. Yet, Plato later refuted Chora due to its undermining of the two earlier forms, claiming it was immeasurable in relation to two statutes of the universe. Derrida explained the term in his essay titled Khora as:

Neither present nor absent, active or passive, the good nor evil, living nor nonliving—but rather a theological and nonhuman—khora is not even a receptacle. Khora has no meaning or essence, no identity to fall back upon. She/it receives all without becoming anything, which is why she/it can become the subject of neither a philosopheme nor mytheme.378

For Derrida and Eisenman, as two men who attempted to revolutionise Western traditions in philosophy and architecture, their selection of Chora as a theme for their garden project was the most suitable of all. Clearly, such a theme could not have been represented in the material form or in a physical form due to its unrepresentative state. The endeavour was to dispute the supremacy of presence and absence, as it had been approached traditionally in architecture and theory through the in-between condition of Chora. Even though Derrida works reached a result that took the wholeness to pieces, or in some cases structured unorthodox geometry, he instead witnessed the new interpretation of his idea through fractal and broken geometry. It was a new stage of architecture and complexity.

377 Plato and Oskar Piest, Timeaus (New York,: Liberal Arts Press, 1959), pp.113-123 378 Jacques Derrida and Thomas Dutoit, On the Name (Stanford: Stanford University Press, 1995), p.90. 182

One of the most important aspects in architectural design for both thinkers was not to create any material structure or monuments for the visitors, thereby producing an evolving space for the users in which they could experience fragments of Chora through their physical performances while sensually observing the unseen in the garden. The idea of creation and erasure of movement through the garden evokes Chora. This place of absence is a familiar experience for man, the cosmic moment it transpires from the theories of creation. Derrida and Eisenman proposed to incorporate materials such as sand, water, glass and mirrors, which have the ability to permit traces and also to be changed or even erased with the visitors’ will to do so. Therefore, the garden is under constant change by its participants throughout time, with different meanings and forms; there is nothing permanent in there. ‘Place is not; place is to be’.379

Eisenman used this concept in his other projects, Arrows Eros, Eros and other Errors: Romeo & Juliet (1986), in relation to the castle of the Montagues and Capulets in Verona, where the main architectural design focused on the aspects of ‘absence’ and ‘presence’ of Chora. But Derrida protested about these additional readings of his theory, finding such an approach gave insufficient understanding of Chora and Plato’s cosmological belief.380 He persistently endeavoured to explain to Eisenman this view of the difference between the absent and the present, seeing in between the two and not concentrating on each independently. This latter concentration he felt resulted in a misinterpretation of what this sacred theme really referred to.381

379 E.S. Casey, The Fate of Place: A Philosophical History (Los Angeles: University of California Press, 1997), p.320. 380 Eisenman, Written into the Void: Selected Writings, 1990-2004, p.160. 381 Through the reading of Derrida’s letter to Eisenman such emphasis on the sacredness of the term Chora and the value of that to its initial explorer becomes obvious. I have questioned you in a non-circuitous fashion about God and Man. I was thinking about the Sky and the Earth. What does architecture, and primarily yours, have to see and do with experience, that is to say, with the voyage that makes its way outside of Earth? What distinguishes your architectural space from that of the temple, indeed of the synagogue (by this word I mean a Greek word used for a Jewish concept)? If you were to construct a place of worship, Buddhist, for example, or a cathedral, a mosque, a synagogue (hypotheses that you are not obliged to accept), what would be your primary concern today? Naturally, this question concerns also your interpretation of chora in ‘our’ ‘work’, if one can say in quotations our work ‘in common’. I am not sure that you have detheologized and deontologized chora in as radical a way as I would have wished. Jacques Derrida and Hilary P. Hanel, 'A Letter to Peter Eisenman', Assemblage, The MIT Press, 12 (Aug., 1990).

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On this later project, Eisenman engaged his other point of interest: human scale. Traditionally, the human body was a datum for architecture; true proportion and scale could be learned only through knowledge of the human body. Besides this lesson, he evolved the idea that this bodily being of a human symbolises origin, recursion and presence.

Figure 7.67 Peter Eisenman: Diagrams of transformation of House IV, 1971.382

The other unique aspect to the designs of Eisenman was his method of drawing. His application of axonometric drawings instead of perspective drawings, in his three- dimensional communication technique illustrated his emphasis on making the reading of his design in a more complicated and opaque term (Figure 7.67). It is rather more abstract and far from the reality that can be demonstrated graphically in perspective view drawing. On the other hand, the measurement in axonometric drawings is accurate and therefore has an ability to be read in relation to floor plan, sections and elevations. Such interpretations of Eisenman’s work can be referred back to his belief and teaching on self-sufficiency and autonomy in architecture in order to attain to the true meaning of architecture.

Computerisation of Architecture

It may be that we have become so feckless as a people that we no longer care how things do work, but only what kind of quick, easy outer impression they give. If so, there is little

382 Peter Eisenman, Diagram Diaries (London: Thames & Hudson, 1999), p.29. 184

hope for our cities or probably for much else in our society. But I do not think this is so.383

In the most popular period of deconstructivist design production, the rapid growth of information technology and advancement of the digital world draws the attention of creative minds. The booming of the digital world overshadowed these architects’ theoretical and philosophical research. The powerful tools of digital drafting and visualisation have generated advanced and new geometrical forms that might draw far from intended purpose. It could be argued that being in fashion, using high technology becomes the priority in any milieu, rather than a matter of meaning in relation to geometrical patterns and intellectual aesthetics.384 Within this new encompassing framework, architects such as Zaha Hadid, Daniel Libeskind, Peter Eisenman, and Frank Gehry embrace the opportunity of computer-aided design to add complexity and depth to their designs. As a result, the rationality that came through digitalisation in architectural language pronounced a theoretical challenge for thinkers who seek meaningful design.

Having abandoned the discourse of style, the architecture of modern times is characterized by its capacity to take advantage of the specific achievements of the same modernity: the innovations offered it by present day science and technology. The relationship between new technology and new architecture even comprises a fundamental datum of what are referred to as avant-garde architecture, so fundamental as to constitute a dominant albeit diffuse motif in the figuration of new architectures.385

In a radical departure from centuries’ old traditions of architecture design and principles, computer generated forms do not carry the same meaning as the conventional drawing of the past designs. Instead, the computer influences the logic behind any lines and geometrical patterns. A digital mind calculates and provides the range of possibilities of geometrical composition in a precise and buildable manner. This process has profoundly evolved the position of architects as creators of form.

383 Jane Jacobs, The death and life of great American cities (Michigan: Random House, 1961), p.71. 384 In architecture, the reference to aesthetic generally explained in two forms: (1) experiential aesthetics and (2) intellectual aesthetics. Experiential aesthetic relate to the subconscious responses to built form and intellectual aesthetics define by conscious responses, it is affiliated with the designer intended meaning embedded in the milieu. Helmut Leder, Benno Belke and Dorothee Augustin, The model of aesthetic appreciation and aesthetic judgments (British journal of psychology, 2004) 385 Ignasi de Sola Morales, Differences: Topographies of contemporary architecture (Cambridge: MIT Press, 1997), p.117. 185

Adopted by mostly every architect, the dynamic transformation of geometrical forms has overthrown past beliefs and theological symbolism in architecture. In other words, conceptual digitalisation has become the norm in the world of art and architecture, in the form of theory or practice. The general argument is that the digital age is generating a very different kind of architecture. Digital technologies are empowering a direct correspondence between what can be designed and what can be built, at the same time prioritising other issues such as given law and standards, software compatibility with designer intent, production cost, implementation plan and control of data.

Today, discretisation of design in many aspects can be analysed, codified and tested using stealthy processes implemented by computers. Nevertheless, the problem with such precise, prompt, quantitative design processes is the rationalistic determinism that can intimidate freedom of expression and a creative mind. According to the humanistic position, the design comes to life through the different sensual and intellectual considerations.386 Such a theoretical view towards the design process discards digitalisation as a promising tool that is finite and limiting in relation to the human mind. However, the fast growth of such a convenient tool, which has the ability to illustrate complex geometries in a fraction of the time, convinces the creative mind to eliminate what was previously believed to be important principles in built form. The spiritual beliefs and geometrical symbolism for today’s architects has become less relevant, and for some viewed as absurdly standing as merely a product of the unsophisticated early centuries of human history. Computer generated forms have become more relevant productions for twenty-first century avant-garde architects to achieve utopian design.

386 The example of that can be a designer intuition, past experiences, choice and influences from external factors. 186

Figure 7.68 Frank Gehry: The Guggenheim Museum, Bilboa, 1997, CAD modelling.387

In digitally mediated design, the Guggenheim Museum by Frank Gehry in Bilbao is a prominent example (Figure 7.68). The heterogeneously parametric design by Gehry theorises new direction and proposes different techniques in creating forms of materialisation, fabrication and manufacturing. Every aspect of this design and many of Gehry’s other buildings are using digital technology as a gestural design procedure (drawn, calculated, communicated, presented and built). Beyond the postmodern sensibility of complexity through heterotopia, or complex hybrid, the Guggenheim’s new geometric approaches are free of prior formalisms, such as linguistic formalisms.388

Conclusion

This current era in architectural design is defined by computationally-based design developments with an emphasis on variability and experimentation rather than stability, morphology and an understanding of the urban typology. The quest for fast growing urban populations and relative infrastructure do not allow contingency for history and reflection of meaning. The position of designer as a creator of form and meaning has

387 Gehry Partners, LLP, 2008, accessed 1 September 2014, http://www.dac.dk 388 Bruce Lindsey, Digital Gehry: Material Resistance/Digital construction (Berlin: Birkhauser Press, 2001), p.72. 187 faded away; instead, the focus is on fast, economical design solutions. Similar to the Baroque era (as demonstrated in Chapter Four) thinkers and architects have been trying to create a milieu detached from the Cartesian grid and conventional norms of beauty in architecture. The resemblance between new digital architects and Baroque philosophy are certainly numerous. Gilles Deleuze (1925–1995) attested to that when he referred to new architecture as Neo-Baroque.389

For Baroque architects, the historical understanding and application of geometrical form was not developed for a coherent or common methodology to architecture itself. The geometrical forms were previously applied as an instrument to symbolise meaning. Nevertheless, the condition from which architecture suffers today can be found in their collaboration between architecture and its use of geometry and number similar to development during Baroque era or, in other words, during the early modern period. Therefore, I argue that the challenge modern architecture faces has its roots in the historical process beginning with Galilean astronomical speculation, and Newton’s natural philosophy. The transformation of conceptual design during that era brought architecture from the realm of art to the realm of science. Consequently, mathematical certainty became a core foundation for creative minds whenever making decisions for design solutions.

Today more than ever, the world of science and design are consolidated. The doctrine of reason/rationalism has entered the world of conception, expression and form. For contemporary architects, finding a connection and harmony among self-expression and collective necessity has become a daunting task. Deconstructive thinking by architects has been expressed in the physical form of a building and thus articulates the underlying geometric ideas that have been formulated, and which arise from the theory of philosophy, a range of complex and fractal geometrical ideas and fashionable concepts. Australian-based scholar, architect and planner, Jon Lang elaborates on the same issue in today’s practice of contemporary architects, stating:

The understanding and conversing about meaning, spiritual beliefs and geometrical symbolism, for many architects considered irrelevant and synonymous with insanity and

389 Deleuze, Gilles, The Fold: Leibniz and the Baroque (Minneapolis: University of Minneapolis Press, 1993), p.96.

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illusion. Though certainty and true reality regarded as a theory based on science and high technology. In recent theories if an architect design a milieu that carries meaning and provoke emotional reaction it is a work of art and not architecture. And architecture, especially, must eliminate participation in fine arts; it has to be, before anything else, a paradigm of efficient and economical construction.390

This Chapter built on my previous argument in Chapter Six to test the second hypothesis investigation and study of postmodernism and deconstructivism. The new way to formalise utopian geometrical forms and philosophy, redounded past beliefs and approaches in architecture. Furthermore, the spiritual meaning or dimensions that were previously symbolised through particular geometrical forms (sphere, cube, tetrahedron, etc.) were forgotten or replaced with new meanings. The ideas of abstraction, semiotic and fold, were formulated by philosophers but architects used their relevancy to develop concepts and forms for their own design solutions.

The final part of this thesis is the Conclusion to this thesis and also follows the discussion of this Chapter. This section also summarises the seven Chapters, and elaborates on the results of overall study. All those results strongly support the claims made in this thesis; consequently the level of confidence in two hypothesis is strengthen.

390 Jon Lang and Walter Moleski, Functionalism Revisited, Architectural Theory and Practice and the Behavioral Sciences (Burlington: Ashgate Publication Limited, 2010), p.286. 189

Conclusion

In this thesis, I have presented a detailed account of the spiritual meanings and symbolic functions attached to geometrical shapes used in architectural design throughout recorded history. Over time, the cultures for which these meanings and symbols had value may have disappeared, or in some cases, the belief or meaning has changed due to social, political, philosophical or other influential impacts. In their design planning and use of geometrical patterns, the architects consciously or subconsciously stopped acknowledging or identifying with the historical or original meaning that once gave significance to these geometric forms.

As a result, the meaning and significance of the beliefs attached to a particular geometrical symbolism have diverged, or have simply been erased from contemporary architectural theory. The historical research method I used in this thesis exposed the theoretical ideas through an examination of these ancestries. This qualitative approach used historical evidence, spanning a wide range of geographical locations and eras to form a theoretical argument—but my thesis is about much more than history itself. My aim was to demonstrate how architecture over the centuries, including architectural geometry, was influenced by, amongst other things, the juxtaposition or convergence of critical political, theological, economic and social occurrences worldwide. By understanding the meanings attached to specific geometric shapes throughout history, we can examine what, if any, residual meaning remains for today’s architects designing the world’s future in built form.

Importantly, architecture is a three-dimensional interpretation of two-dimensional geometry, which is transformed when historically specific material and constructional choices are influenced by social, cultural, economic or religious forces. Geometry carries meanings that throughout history have provided architects and designers not only with inspiration, but also with a solid reference guide. In addition, geometry has always been a visual language that has guided civilisations and societies who are conversant with, if not implicitly, its referents, providing a collectively recognisable paradigm for architects to design within. For example, in chapter two of the ‘Divine Comedy’, I explained how Dante Alighieri reduced the theological beliefs of his time into geometrical shapes. This became a much-prized example for late Renaissance architects and artists. Dante’s poetic construction of the three realms—Inferno, 190

Purgatory, Paradise—was composed from the view of both inside and outside the sphere. On his journey to Paradise, he traversed multiple stages, each designated with specific numbers, all of which influenced the planning of a number of churches.

For the men of the Renaissance this architecture with its strict geometry, its harmonic order, its formal serenity, and the sphere of the dome revealed the perfection, the truth and goodness of God.391

My thesis has demonstrated how meaning in architectural geometry has evolved through time, adapting and transforming under the influences of the various eras and, in particular, to any changes in spirituality, politics, economics and science. Interestingly, as I reviewed in earlier chapters, the same meanings were used in different geographical places to signify similar geometric shapes. For example, in Chapters One and Two, I explained the symbolism of the ‘equilateral triangle’ in ancient Egypt, Sri Yantra in Hindu tradition, and Pythagorean Tetraktys in Greece. All these cultures chose a particular geometrical shape—the triangle—assigning it equally important symbolic power, which was aligned to a religion.

By evaluating architecture as the formal realisation of ancient belief systems, we start to see geometry as an evolving symbolic language that began (although not exclusively) in ancient Egypt, extending to ‘early Paganism’ in Greece and from there, to the early Christian era and subsequently through time after Christ. However, just as belief systems, societies and mathematical knowledge evolved, so too geometry and symbolism changed in concert with both the spiritual and scientific search for truth. A number of influential scholars developed geometry, directed by the search for a mathematical system that would allow them to comprehend truth in the universe—a language of universal truth. For example, Pythagoras, Plato and Dante all attempted to understand the laws and order of the universe, seeking to discover answers to deeper questions of human existence that have been sought for centuries.

In the much more secular twentieth century, symbolism does appear in modern architecture but is significantly detached from the meanings it held for ancient societies. This was largely due to the emphasis on artistic freedom and the rise of ‘abstraction’,

391 Rudolf Wittkower, Architectural Principles in the Age of Humanism (London: Academy Editions, 1973), p.29. 191 when artists and architects no longer viewed themselves as serving the vested interests of religion. Geometry was stripped of its spiritual meaning, and this continued into the postmodern era when design became iterations of abstraction intensified by deconstructivist ideology, which led to a much less formal approach to the application of geometry.

When I discovered what we now call ‘Deconstructive architecture’ … were in fact deconstructing the essentials of tradition, and were criticising everything that subordinated architecture to everything else-the value of, let's say, usefulness or beauty or living—‘habite’—etc, not in order to build something else that would be useless or ugly or uninhabitable, but to free architecture from those external finalities, extraneous goals.392

There were nevertheless many exceptions of modern architects exploring geometrical symbolism. For example, as I argued in Chapter Five, the architect Le Corbusier criticised the buildings of Ancient Rome, which to him were an answer that misunderstood the question; in other words, a false and unsophisticated representation of a belief. However, through his study of Roman architecture and many more major ancient structures, Le Corbusier took two ideas that became core principles in his architectural oeuvre—harmony and efficiency. So ultimately for Le Corbusier, architecture came to life by creating plans, façades or three-dimensional shapes that were unified through geometrical and compositional laws, and underpinned by ancient principles based on harmonic order and proportion.

As discussed in Chapter Two, some meanings have spiritual aspects that adhere to geometrical patterns applied to form a milieu, and in some cases the result of this built form is not related to its cultural context. These ‘spiritual’ meanings give a quality of symbolism and meaningfulness to a specific geometrical form. Consequently, I have addressed this postmodern ‘re-enchantment’ of meaning that is possibly attached to premodern ideas of anthropomorphic approaches to art and architecture. The origin of ancient belief systems and theological acceptance, or even animism, is all included in my postmodern approach.

392 Jacques Derrida, Alan Bass, and Christopher Norris, Positions (London: Continuum, 2004), p.8. 192

Furthermore, I have argued that modernism was a secular, spiritual movement reacting to the chaos of industrial revolution, political conflict and class divisions. In the age of modernity, architecture can be viewed as a rebirth of ancient symbolism, but not standing for the same significants. It was an era of representation and invention.

Figure C.69 Le Corbusier: Villa Schwob, La Chaux-de-Fonds, Switzerland, 1916. Floor plan.393 Geometrical analysis by the author.394

In this thesis, I have demonstrated how architects work in a specific socio-historical context that influences their thinking—but they also work with geometry and its perceived and inherent traditions, whether they choose to understand and engage with these or not.

For example, in the late twentieth and early twenty-first centuries—the eras of postmodernism to deconstructivism—has seen an emergence of a ‘secular spiritualism’ or ‘secular Platonism’ in which geometric forms once understood within a historical or religious context are now being claimed for different purposes. The thrust of certain

393 Mavi Boncuk, 'Le Corbusier ‘Voyage D'orient’ 1911', , accessed 10th February 2012.

394 This is one of the earlier projects of Le Corbusier that determine his take from primitive principles and the lessons learnt from history.

193 architectural experiments has been to try to break away from, or at least to break down, past beliefs to reveal classical so-called perfect orders with a view to bringing out of them new compositional possibilities. Cues taken from Russian constructivism have provided enough power to show that relations need not follow classical arrangements or oppositions.395 In his detailed study of deconstructivist architects’ designs and applied geometry, American postmodern architect Philip Johnson (1906-2005), who founded the Department of Architecture and Design at the Museum of Modern Art in New York City, affirmed:

Deconstructivist architect gains all of its designs force by challenging the very values of harmony, unity, and stability, proposing instead that flaws are intrinsic to the structure. They cannot be removed without destroying it; they are, indeed, structural.396

In Chapter Six, using practical and theoretical examples, I investigated the proposition that the deconstructivist use of geometry has a spiritual dimension, albeit concealed within its secular spiritualism in the actual shapes used. Compositions that fold, bend, twist and break the symmetrical geometry suggest a protest against and frustration with the underlying rules and meaning of geometrical symbolism inherited over time. Despite their protests, deconstructivists continue to demonstrate meaning in architecture, but not in the same way as in pre-modern history. Geometric abstraction now symbolises ‘aesthetic’ freedom, which in this secular capitalist age also represents its meaning.

When an architect designs a building, whether it is a simple dwelling or a vast sacred complex, he or she does so for a number of identifiable and meaningful reasons. This raison d’être for an architect ranges from the practical to the metaphysical, and only together can the multitude of reasons for its construction and use be completely explained. The role of an architect is thus multifaceted, as they must in part be social scientists, considering how the living spaces they create will affect and influence the culture, customs and interpersonal relationships of a community; they are also in part social engineers, creating designs that will affect the character, nature and mindset of their users.

395 Omnibus Volume, Deconstruction (London: Academy editions, 1989), p.35. 396 Philip Johnson, Mark Wigley, Deconstructivist Architecture (New York: Museum of Modern Art, 1988), p.11. 194

Man-made buildings historically have meaning behind their symbolic functions. In this thesis, I have demonstrated the symbolic and ritual role of applied geometry and the relationship between form and meaning in both spiritual and secular contexts. The understanding and application of applied geometry is a fundamental skill for any architect to master in order to practise building design. My research has shown that, despite the philosophical critique it received in the middle of the twentieth century, applied geometry is still fundamental to most cultural models for building design. Geometry is always present in the plan and the shape of a building. It orders everything and, though not always visible to the naked eye, geometry suggests how we spatially move and interact with others. Geometry is less seen, more sensed, bringing scale, harmony and balance through an experiential aesthetic. Hence, it may rightly be described as the science of space.

New trends in architecture must acknowledge the imagination, traditions, achievements and discoveries of the past and, consequently, recognise the ancient understanding of geometrical forms and their significance so that practitioners can transform them into contemporary use. The designs of today will thus be able to harmonise, stimulate, enhance, interpret and lend meanings to solid structures.

In Chapter Five of this thesis I demonstrated how aesthetics is directly related to both the conscious and unconscious mind. Humanity’s deep-rooted beliefs change over time, as does their interpretation and the use of geometric principles. For example, I discussed the battle between reason and imagination in Kant’s distinction between the beautiful and the sublime in his work, The Critique of Judgment, as for him this changed the perception of form. Interpreting an object, form, scene or architecture through ideas such as the beautiful and sublime, transforms the qualitative aspects of what is perceived by a sense of the infinite ‘quantitative aspects’ that are beyond the visible form. Kant writes:

It is a very sublime thing in human nature to be determined to actions directly by a pure law of reason, and even the illusion wherein the subjective element of this intellectual determinability of the will is held to be sensuous and an effect of a particular sensuous feeling (an ‘intellectual feeling’ being self-contradictory) partakes of this sublimity.397

397 Kant, Cassirer, and Weitzman, Critique of Practical Reason, P.221. 195

In this age of ‘secular spiritualism’, we have seen geometry uncoupled from spiritualism or tradition with its symbolic meanings. Architects no longer feel attached or obliged to explore or replicate the underlying geometric principles of the past. If one views neo- constructivist (deconstructivist) architectural design in contrast to premodern/classical architecture and principles, one can suggest that aesthetic freedom allows them a value free engagement with geometry. This raises the question, are traditional meanings in geometry still important in architecture? I believe there has been and always will be a close relationship between geometry and architecture, and to ensure that new buildings are not devoid of meaning and symbolism, the history and traditions of geometry should remain a vibrant source of aesthetics.

The Contribution of the thesis to Knowledge

My study contributes to the general understanding of the historical, theoretical and practical aspects of architecture. This is achieved by analysing the built form in relation to its geometrical patterns, symbolism and by developing a theoretical, spiritual and phenomenological basis for this relationship. In addition, my thesis contributes to an appreciation of the role of geometry and, in particular, its meaning in architecture. It identifies the various influences that forced design decisions throughout different eras. Furthermore, my study investigated the gaps in current theoretical research, and a deficiency in comprehension of how and why architects use particular geometrical patterns in their designs.

The objective of my study was to provide support for two hypotheses. Firstly, that spiritual meanings were formerly embedded in architectural forms but over the centuries of political, religious and social upheaval and cultural development, they were gradually forgotten. Secondly, the hypothesis that modern day architects are incorporating geometrical patterns into their designs without understanding their spiritual origins or meanings.

My research was intended to find meaning and spiritual dimension represented by different geometrical forms through precise analysis of historical architectural examples. In the thesis, I aimed to explore whether these attached meanings continue to represent the original beliefs throughout the history of architecture. What I found was that geometrical forms have evolved and, over time, various forces have created a 196 tendency to transform the philosophy of producing meaningful milieus for humankind. In short, in some instances in today’s architecture, there is an absence of its sense of symbolism, meaning, and soul.

Limitations of the Thesis

This study was primarily concerned with specific geometrical patterns and those identified as significant have been discussed in detail as selected case studies. The analysis presented has focused on how spiritual meaning is represented through built form. The findings of my study were limited to sample of examples and to European architecture and theory. I have addressed only the most important influences that caused the evolution of particular geometrical patterns had a significant impact on the work of notable architects, and only specific eras were considered.

Within the limitations of historical, geographical and theoretical scope, my thesis does not focus on psychological testing in relation to the two main hypotheses, especially the Gestalt laws of visual organisation. I also wish to make it clear that I deliberately refrained from intense examination of contemporary digital architecture as part of this current thesis. The next step in research on the topic will forms the second machine age, the age of information technology in architecture, and the position of meaning and applied geometry within these themes.

197

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212 Appendix B

List of Publications by Author

Hosseinabadi, S, 2014, ‘Architecture From Derridean's Semiotic To Deconstructivism’, ARCHTHEO 14/Theory of Architecture Conference, DAKAM Publication, Istanbul, Turkey

Hosseinabadi, S, 2013, ‘Glory of Infinite absent’, REHAB, International conference, Tomar, Portugal ISBN 978-989-8734-02-0, [Refereed Article]

Hosseinabadi, S, 2012, ‘Platonic Divine’, The International Journal of Arts & Sciences (IJAS), Volume 05, Number 02, Harvard University Publication, Boston, USA, ISSN: 1943-6114, [Refereed Article]

Hosseinabadi, S, 2012, Alienation and deconstructivism, Conference of the International Journal of Arts & Sciences, 5, (2) pp. 91-92. ISSN 2649-7111, [Refereed Article]

Hosseinabadi, S, 2011, ‘Multi-dimensionality in Architecture’, Proceedings of the Art and Architecture around 1400: Global and regional perspective, University of Maribor, Slovenia, international colloquium under auspices of CIHA, ISBN 978-961- 6656-91-7, [Refereed Article]

Hosseinabadi, S, 2011, ‘The Modernity of Le Corbusier’ , Proceedings of the International Conference Contemporary architecture: Beyond Corbusierism, Young Architecture Festival (YAF), Chandigrah, India, ISBN: 978-9350-59002-7

Hosseinabadi, S, 2010, ‘4th Dimension in Architecture’, Proceedings of the Image Conference, The International journal of the image, volume 1, number 1, Common Ground publishing, Los Angeles, USA ISSN: 2154-7857, [Refereed Article]

212