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EMERGENT SYMMETRIES: a Group Theoretic Analysis of an Exemplar of Late Modernism: the Smith House by Richard Meier

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EMERGENT SYMMETRIES: a Group Theoretic Analysis of an Exemplar of Late Modernism: the Smith House by Richard Meier EMERGENT SYMMETRIES: A Group Theoretic Analysis of an Exemplar of Late Modernism: the Smith House by Richard Meier A Thesis Presented to The Academic Faculty By Edouard Denis Din In Partial Fulfillment of the Requirements for the Degree Doctoral of Philosophy in Architecture Georgia Institute of Technology August, 2008 Copyright © 2008 by Edouard Din All rights reserved. EMERGENT SYMMETRIES: A Group Theoretic Analysis of an Exemplar of Late Modernism: the Smith House by Richard Meier Approved by: Dr. Athanassios Economou, Chair College of Architecture – Georgia Institute of Technology Prof. Charles Eastman, Co-Chair College of Architecture – Georgia Institute of Technology Dr. Terry Knight School of Architecture – Massachusetts Institute of Technology Dr. John Peponis College of Architecture – Georgia Institute of Technology Dr. Ellen Yi-Luen Do College of Architecture – Georgia Institute of Technology Date Approved by Chair: July 1st, 2008 ‘The diverse elements of Classical Architecture are organized into coherent wholes by means of geometric systems of proportion. Precise rules of axiality, symmetry, or formal sequence govern the organization of the whole with hierarchical distribution.’ ‘What Modern Architecture brings out, is the complexification of these systems by algebrization of their geometric relations.’ W. J. Mitchell, ‘The Logic of Architecture’ iii ACKNOWLEDGEMENTS Even if I would like to acknowledge the many people who have patiently directed and channeled my thoughts from the beginning to the end of this journey, the intellectual roots of this work firmly stand on the shoulders of three giants. Dr. Cheikh Anta Diop, stimulated much of the thinking and energy powering of my lifelong research. Dr. Thomas Brylawski, my advisor during my tenure at UNC Department of Mathematics at Chapel Hill, definitely channeled my focus on the language of abstract thinking and the study of patterns. Dr. Lionel March, whom I met in May 2001 during the Symposium on Space Syntax at Georgia Tech in Atlanta, provided me with an early impetus of the subject matter at the inception of this research. I would like to thank the members of my advisory committee, who constitute the human backbone of this dissertation. Dr. Athanassios Economou patiently guided me through the steps leading to the concretization of this dissertation and helped me buildup step by step the entire doctoral thesis. I highly appreciated Dr. Economou fine balance between giving me the freedom to pursue what fired me up and reining in my imagination when he got the better of me. Prof. Charles Eastman initiated me to the subtleties of Design Computing, and helped tremendously shaping up the foundations of the argument of the thesis. Dr. John Peponis demonstrated his support early on, and provided me with insightful feedback and invaluable insights. Dr. Ellen Yi- Luen Do gave me guidance and counsel and I would like to specially thank her for having faith and confidence in me. I thank the support of our institution, the College of Architecture of the Georgia Institute of Technology, and especially the Imagine Lab and its director Dr. Tolek Lesniewski, who, during the several years in which this endeavor lasted, provided me with moral support and useful assistance in digital visualization. I am indebted to my parents and family for inculcating in me the dedication and discipline to do whatever I undertake well, and most importantly, to Dr. Rebecca Din-Dzietham, and our children, James, Dora and Emma, who unconditionally stood by me during this journey. iv TABLE OF CONTENTS ACKNOWLEDGEMENTS iv LIST OF TABLES ix LIST IF FIGURES x SUMMARY xiv Chapter 1 Introduction ................................................................................ 1 1.1. Prelude ................................................................................................................ 1 1.2. Method ................................................................................................................ 2 1.3. Contribution ........................................................................................................ 3 1.4. Outline................................................................................................................. 4 Chapter 2 Formal systems in architectural design...................................... 6 2.1. Introduction......................................................................................................... 6 2.2. Formal systems ................................................................................................... 8 2.3. The structure of formal systems........................................................................ 10 2.3.1. Aesthetics machine .................................................................................................. 10 2.3.2. Design machine ....................................................................................................... 13 2.3.3. Vitruvian machine ................................................................................................... 13 2.4. Analysis and design systems............................................................................. 19 2.4.1. Analysis systems...................................................................................................... 19 2.4.2. Design systems ........................................................................................................ 22 2.5. Constructive and evocative systems ................................................................. 24 2.5.1. Constructive – Analysis systems ............................................................................. 25 2.5.2. Constructive – Design systems................................................................................ 29 2.5.3. Evocative – Analysis systems.................................................................................. 30 2.5.4. Evocative – Design systems .................................................................................... 35 v 2.6. Languages and configurations .......................................................................... 38 2.6.1. Proportion ................................................................................................................ 38 2.6.2. Symmetry................................................................................................................. 41 2.7. Summary........................................................................................................... 45 Chapter 3 Symmetry and Group Theory .................................................. 46 3.1. Introduction....................................................................................................... 46 3.2. A first encounter ............................................................................................... 47 3.3. Group structure................................................................................................. 50 3.3.1. Multiplication table.................................................................................................. 51 3.3.2. Group generators ..................................................................................................... 52 3.3.3. Pictorial representation ............................................................................................ 55 3.3.4. Subgroups ................................................................................................................ 56 3.3.5. Lattices..................................................................................................................... 60 3.3.6. Conjugacy................................................................................................................ 62 3.3.7. Isomorphism ............................................................................................................ 63 3.3.8. Counting non-equivalent configurations ................................................................. 66 3.4. Tracing histories................................................................................................68 3.5. Summary........................................................................................................... 73 Chapter 4 Abstraction, projection, weighting, layering............................ 75 4.1. Introduction....................................................................................................... 75 4.2. Representation................................................................................................... 76 4.2.1. Abstraction............................................................................................................... 76 4.2.2. Projection................................................................................................................. 77 4.2.3. Weighting ................................................................................................................ 80 4.2.4. Layering................................................................................................................... 82 4.3. Partial order....................................................................................................... 84 4.4. Model ................................................................................................................ 85 4.4.1. Stop mode................................................................................................................ 86 4.4.2. Rewind mode..........................................................................................................
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