Contents History 5 1. Geometry and Memory 8 1.1 Introduction 8 1.2 Conventional Geometry: Euclid to Einstein 8 1.3 Special and General Relativity 10 1.4 New Foundations to Geometry 12 1.5 The Memory Roles of Symmetry and Asymmetry 15 1.6 Basic Procedure for Recovering the Past 18 1.7 Architecture 21 2. A Process-Grammar for Shape 24 2.1 Curvature as Memory Storage 24 2.2 General Symmetry Axes 25 2.3 Symmetry-Curvature Duality 26 2.4 The Interaction Principle 27 2.5 Undoing Curvature Variation 28 2.6 Extensive Application 29 2.7 A Grammatical Decomposition of the Asymmetry Principle31 2.8 Process-Grammar and Asymmetry Principle 35 2.9 Scientific Applications of the Process-Grammar 36 2.10 Artistic Applications of the Process-Grammar 40 2.11 Architectural Applications of the Process-Grammar 41 3. Architecture as Maximal Memory Storage 54 3.1 Introduction 54 3.2 The Two Fundamental Principles 54 3.3 Groups 55 3.4 Generating a Shape by Transfer 56 3.5 Fiber and Control 58 3.6 Projection as Memory 59 3.7 Regularity in Classical Architecture 62 3.8 Breaking the Iso-Regularity 69 3.9 Reference Frames 70 3.10 New Theory of Symmetry-Breaking 70 3.11 Maximizing Memory Storage 72 3.12 Theory of Unfolding 75 4. Architecture and Computation 86 4.1 Introduction 86 4.2 New Foundations for Science 86 4.3 New Foundations for Art 89 4.4 New Foundations for Computation 90 4.5 What is a Building? 91