Michael Leyton (auth.)-Process Grammar_ The Basis of Morphology-Springer New York (2012).pdf

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Process Grammar: The Basis of Morphology
Michael Leyton
Process Grammar:
The Basis of Morphology
Michael Leyton
DIMACS Center for Discrete Mathematics
and Theoretical Computer Science
Rutgers University
Busch Campus
New Brunswick
NJ 08854
USA
mleyton@dimacs.rutgers.edu
ISBN 978-1-4614-1814-6
e-ISBN 978-1-4614-1815-3
DOI 10.1007/978-1-4614-1815-3
Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2011940966
© Springer Science+Business Media, LLC 2012
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY
10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection
with any form of information storage and retrieval, electronic adaptation, computer software, or by similar
or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are
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to proprietary rights.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Preface
The Process Grammar has been applied by scientists and engineers in many disci-
plines, including medical diagnosis (e.g., cardiac diagnosis); geology (e.g., the analysis
of volcanic islands); computer-aided design (to establish new CAD operators); meteo-
rology (to analyze weather patterns); biological anatomy (e.g., MRI human brain scans,
dental radiographs); engineering bridge design; chemical engineering; etc.
The Process Grammar is based on a theorem that I proved in the 1980s called the
Symmetry-Curvature Duality Theorem. Researchers have shown that this theorem
defines an enormous number of aspects of biology, e.g., anatomy with applications in
radiotherapy, surgery, and psychiatry, the tracking of DNA molecules, musculoskeletal
development, the morphology of leaves in botany, the morphology of fish, etc; also
geology, e.g., for the analysis of drainage patterns, etc; also graphics, e.g., for inter-
active rendering and cartoon vectorization, etc. The considerable applications of this
theorem demonstrate that the theorem is
fundamental to morphology.
Its importance
to morphology is explained by the Process Grammar.
In fact, every rule in the Process Grammar is an instance of a rule in a much larger sys-
tem, my New Foundations to Geometry, that I have elaborated in my book
A Generative
Theory of Shape
(Springer-Verlag, 550 pages).
Chapter 2 of the present book gives a brief introduction to these New Foundations,
so that the reader is then shown how the Process Grammar is an instance of these New
Foundations.
The central proposal of my New Foundations to Geometry is that shape is equivalent
to memory storage. Therefore, in the New Foundations, geometry is the mathematical
theory of memory storage, invented by the New Foundations. This opposes the Standard
Foundations to Geometry, which are based on the invariants program. My argument is
that invariants are memoryless.
The New Foundations to Geometry, being a generative theory of shape, define any
shape by a sequence of operations needed to create it. Furthermore, the New Foundations
require that this sequence be intelligent. In fact, the New Foundations gives a mathemat-
ical theory of intelligence, and base the entire New Foundations on this mathematical
theory. The two most basic principles of this mathematical theory of intelligence are
Maximization of Transfer and Maximization of Recoverability of the generative oper-
ations. The New Foundations give a Mathematical Theory of Transfer, and a Mathe-
matical Theory of Recoverability. In the Mathematical Theory of Transfer, transfer is
modeled by a group-theoretic structure called a wreath product. In the Mathematical
Theory of Recoverability, the fundamental claim is that the only recoverable operations
are symmetry-breaking ones. Furthermore, the Mathematical Theory of Recoverability
gives a mathematical theory of symmetry-breaking that is fundamentally opposed to
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