Leyton M. Shape as Memory: A Geometric Theory of Architecture

Basel: Birkhäuser – Publishers for Architecture. – 2006. – 92 p. In my published books and papers, I have developed new foundations to geometry that are directly opposed to the foundations to geometry that have existed from Euclid to modern physics, including Einstein. These new foundations imply an entire restructuring of science, the replacement of its separate systems of laws (e.g., in quantum mechanics, relativity, etc.) with a common system of inference rules that unfold the environment as a world of deep “forensic information.” In addition, there is a radical alteration in our understanding of design, and in particular, architecture: New foundations to geometry mean new foundations to architecture. In order to see this, we must first contrast the foundations of geometry, as they have existed for almost 3,000 years, with the entirely opposite foundations presented in my books. The following statement summarizes the basic difference. It is then followed by a more detailed explanation of this difference.History
Geometry and MemoryConventional Geometry: Euclid to Einstein
Special and General Relativity
New Foundations to Geometry
The Memory Roles of Symmetry and Asymmetry
Basic Procedure for Recovering the Past
ArchitectureA Process-Grammar for Shape
Curvature as Memory Storage
General Symmetry Axes
Symmetry-Curvature Duality
The Interaction Principle
Undoing Curvature Variation
Extensive Application
A Grammatical Decomposition of the Asymmetry Principle
Process-Grammar and Asymmetry Principle
Scientific Applications of the Process-Grammar
Artistic Applications of the Process-Grammar
Architectural Applications of the Process-GrammarArchitecture as Maximal Memory StorageThe Two Fundamental Principles
Groups
Generating a Shape by Transfer
Fiber and Control
Projection as Memory
Regularity in Classical Architecture
Breaking the Iso-Regularity
Reference Frames
New Theory of Symmetry-Breaking
Maximizing Memory Storage
Theory of UnfoldingArchitecture and ComputationNew Foundations for Science
New Foundations for Art
New Foundations for Computation
What is a Building?