Professor Michael Leyton
Books by Michael Leyton:
Leyton's book "A Generative Theory of Shape" (Springer, 554 pages).
The book gives extensive applications
of the theory to CAD/CAM, human and machine vision, robotics,
software engineering, and physics. In CAD, lengthy chapters are
presented on mechanical and architectural design. For example,
using the theory of unfolding groups, the book works in detail
through the main stages of mechanical CAD/CAM: part-design, assembly
and machining. And within part-design, an extensive algebraic
analysis is given of sketching, alignment, dimensioning, resolution,
editing, sweeping, feature-addition, and intent-management. In
robotics, several levels of analysis are developed for manipulator
structure and kinematics. In software, a new theory is given
of the principal factors such as text and class structure, object
creation and modification, as well as inheritance and hierarchy
prediction. In physics, a new theory is given of the conservation
laws, and motion decomposition theorems in classical and quantum
The full book can be viewed electronically at the Springer website:
Leyton's book on paintings, published by Springer (Sept 2006).
Leyton's book on morphology (Springer, 544 pages)..
Leyton's book "Symmetry, Causality, Mind" (MIT Press, 630 pages).
"This is a remarkable book. Its claim is that perception is none other than the recovery of causal history. One cannot but be struck by the depth, novelty and brilliance of Leyton's accounts, page after page, of even the most minute and ordinary of perceptual phenomena - claims which contradict virtually every previous treatment of these phenonena." Professor Eleanor Rosch, University of California, Berkeley.
"Leyton's work is a most engaging and utterly original treatment of some classical problems in perception and cognition." Professor Barbara Landau, Johns Hopkins University.
"This is a superb book. The writing is extraordinarily clear and the theory is very original. It challenges the reader to think about basic questions and presents new concepts and bold new principles that give a new perspective on visual perception in particular and cognitive representation more generally." Wayne Wickelgren, Professor, Columbia University.
For ordering information on the book, at Amazon books, click: Leyton's book at Amazon.com
Leyton's book on architecture, published by Birkhauser (July 2006).
Description of Book:
In his mathematical books and papers, Michael Leyton has developed new foundations to geometry that are directly opposed to the conventional foundations that have existed for almost 3,000 years, from Euclid to modern physics, including Einstein. Whereas the conventional foundations minimize the memory contained in the geometric object, these new foundations maximize it. A fundamental conclusion is that shape is equivalent to memory storage.
In this book, Leyton shows that his new foundations for geometry result in new foundations for architecture. Whereas architecture, for thousands of years, has been based on the minimization of memory storage the aim of conventional geometry the new architecture he proposes is based on the maximization of memory storage the aim of the new geometry. He elaborates the structural principles by which buildings can be designed as maximal memory stores. This reformulates the relation of architecture to computation: the computational process becomes one in which the mind undergoes self-creation by reading and writing itself as history. The architectural principles proposed by Leyton are the means by which buildings can be read and written as the self-creation of mind. Leyton illustrates these new architectural principles with his own administration buildings.
Leyton's Published Musical Compositions
The scores of Leyton's string quartets are currently being published. The first to be published was String Quartet #5, shown below.
Susan Kay on Leyton's string
Leyton's Scientific and Mathematical Influence
Leyton's mathematical work on shape has been used by scientists in over 40 disciplines including: radiology, meteorology, computer vision, chemical engineering, geology, computer-aided design, robotics, anatomy, botany, urban planning, forensic science, software engineering, architecture, abductive reasoning, linguistics, mechanical engineering, computer graphics, control theory, electromagnetism, thermodynamics, quantum field theory, archaeology, etc.
As an example: Leyton's Symmetry-Curvature Duality Theorem has been applied by scientists in over 40 disciplines, including: MRI human brain scans, dental radiographs, transmission electron microscopy, blood-cell analysis, neuronal growth models, DNA molecule-tracking, grasp determination in robotics, geological formation of volcanic islands, interactive rendering, cartoon vectorization, drainage patterns, musculoskeletal development, botanical leaf analysis, human facial expression, shock scaffolds, weather prediction, molecular dynamics, shape skeletonization, etc.
original paper proving this theorem can be viewed at Symmetry-Curvature
Another example is his Process-Grammar, which he invented in 1987. This recovers the past history of an object; e.g., the history of growth, deformation, morphology, design, etc.
Leyton's extensive theory of CAD, solid-modeling, object-oriented programming, mechanical engineering, has aroused great interest from all these disciplines, as can be seen on the web by the many invitations he has received from the major conferences in these areas. You can view a comprehensive mathematical elaboration of his theory in his Springer book mentioned above, A Generative Theory of Shape. The conceptual elaboration of his work is given in his other books in MIT Press and Birkhauser.
Professor Leyton is president of the following two societies:
He is also on the governing board of the Institute for the Fundamental Reseach in Music, in Zurich; the MittelEuorpa foundation in Bolzano Italy.
Leyton receives several invitations a year to give conference addresses in a wide range of disciplines: Computer vision, Mechanical Engineering, Mathematics, Computer-Aided Design, Cognitive Science, Aritificial Intelligence, Music Theory, Semiotics, Art, etc.
Recent invited conference addresses include:
Keynote address: Society for
Applied Systems Research
Leyton's Artistic Exhibitions
Leyton is a well-known artist. His paintings, sculptures, and architectural projects, have been featured in international design journals and invited exhibitions. The following site gives you access to a large selection of Leyton's works:
Eric Wiener of the East Village
Guide, New York, writes:
Leyton's current work
Leyton is currently writing a 4-volume work on the foundations of science, with particular emphasis on quantum mechanics. He also continues to work on the structure of software, as well as interoperability and large-scale engineering systems integration, in the mechanical/aerospace industry.
Recent published work includes:
DIMACS Center for Discrete Mathematics,
& Theoretical Computer Science,
Rutgers University, Busch Campus,
New Brunswick, NJ 08854,