Systems: Approaches, Theories, Applications: Including the Proceedings of the Eighth George Hudson Symposium Held at Plattsburgh, New York, April 11–12, 1975

207 Pages·1977·5.882 MB·English

by  Michael A. Arbib, Ernest G. Manes (auth.), William E. Hartnett (eds.)

SYSTEMS: APPROACHES, THEORIES, APPLICATIONS
EPISTEME
A SERIES IN THE FOUNDA TIONAL,
METHODOLOGICAL, PHILOSOPHICAL, PSYCHOLOGICAL,
SOCIOLOGICAL AND POLITICAL ASPECTS
OF THE SCIENCES, PURE AND APPLIED
Editor: MARIO BUNGE
Foundations and Philosophy of Science Unit, McGill University
Advisory Editorial Board:
RUTHERFORD ARIS, Chemistry, University of Minnesota
DANIEL E. BERLYNE, Psychology, University of Toronto
HUBERT M. BLALOCK, Sociology, University of Washington
GEORGE BUG LIARELLO, Engineering, Poly technic Institute of New York
No AM CHOMSKY, Linguistics,MIT
KARL W. DE UTSCH, Political science, Harvard University
B RUN 0 F R IT S C H, Economics, E. T.H. Zurich
E R WI N HIE BER T, History of science, Harvard University
ARISTID LINDENMA YER, Biology, University of Utrecht
JOHN MYHILL, Mathematics, SUNY at Buffalo
JOHN MAYNARD SMITH,Biology, University of Sussex
RAIMO TUOMELA, Philosophy, University of Helsinki
VOLUME 3
SYSTEMS:
APPROACHES, THEORIES,
APPLICATIONS
INCLUDING THE PROCEEDINGS
OF THE EIGHTH GEORGE HUDSON SYMPOSIUM
HELD AT PLATTSBURGH, NEW YORK,
APRIL 11-12,1975
Edited by
WILLIAM E. HARTNETT
Dept. of Mathematics, State University College, Plattsburgh, N. Y., U. S.A.
D. REIDEL PUBLISHING COMPANY
DORDRECHT-HOLLAND / BOSTON-U.S.A.
Library of Congress Cataloging in Publication Data
George H. Hudson Symposium, 8th, Plattsburgh, N. Y., 1975.
Systems: approaches, theories, applications.
(Episteme; v. 3)
Includes bibliographies and index.
1. System theory - Congresses. I. Hartnett, William, E. II.
Title.
Q295.G461975 003 77-22238
ISBN-13: 978-94-010-1241-6 e-ISBN-13: 978-94-010-1239-3
DOl: 10.1 007/978-94-010-1239-3
Published by D. Reidel Publishing Company,
P. O. Box 17, Dordrecht, Holland
Sold and distributed in the U. S. A., Canada, and Mexico
by D. Reidel Publishing Company, Inc.
Lincoln Building, 160 Old Derby Street, Hingham,
Mass. 02043, U.S.A.
All Rights Reserved
Copyright © 1977 by D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of the hardcover 1s t edition 1977
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any informational storage and
retrieval system, without written permission from the copyright owner
TABLE OF CONTENTS
PREFACE IX
ACKNOWLEDGEMENTS XI
NOTES ON THE CONTRIBUTORS XIII
1. A CATEGORY-THEORETIC APPROACH TO SYSTEMS IN A
FUZZY WORLD
by Michael A. Arbib and Ernest G. Manes
1. Machines in a Category 2
2. Fuzzy Machines 16
2. PARALLELISM, SLIDES, SCHEMAS, AND FRAMES
by Michael A. Arbib 27
1. Parallelism 27
2. Slides and Schemas 30
3. Frames and Schemas 33
4. Development 37
5. More on Parallelism 39
3. THE FUNDAMENTAL DUALITY OF SYSTEM THEORY
by E. S. Bainbridge 45
1. Introduction 45
2. Networks 47
3. Duality 51
4. Conclusion 60
4. TOWARDS A SYSTEMS METHODOLOGY OF SOCIAL CONTROL
PROCESSES
by Walter Buckley 63
VI TABLE OF CONTENTS
5 . STATES AND EVENTS
by Mario Bunge 71
1. Introduction 71
2. Properties and Predicates 73
3. Definition of a State Function 76
4. Law Statements 78
5. Lagrangian Law Schemata 80
6. State Spaces 82
7. Law Statements and Transformation Formulas 86
8. Events and Processes 89
9. Event Space 91
10. The Category of Events 92
11. Concluding Remarks 94
6. UNDERSTANDING SOCIAL AND ECONOMIC CHANGE IN THE
UNITED STATES
by Jay W. Forrester 97
1. System DynamiCS 98
2. Dynamics to Be Represented 104
3. Social and Economic Issues 109
4. Structure of the Model 114
5. Status, Schedule, Procedure 118
7. PATTERN DISCOVERY IN ACTIVITY ARRAYS
by George J. Klir 121
1. Introduction 121
2. Sampling Procedure 129
3. Evaluation of Masks 141
4. Reduction of ST-Structures 153
5. Conclusions 154
8. A PURPOSIVE BEHAVIOR MODEL
by Peter Milner 159
9. COMPLEXITY AND SYSTEM DESCRIPTIONS
by Robert Rosen 169
TABLE OF CONTENTS VII
10. CONCERNS, COMMENTS, AND SUGGESTIONS
by William E. Hartnett 177
1. Educational Concerns 177
2. Useful Mathematical Models 180
3. Problems of Applied Mathematics 180
4. Modeling 182
5. State Modeling of Objects 189
6. Questions 195
INDEX 199
PREFACE
For many years I have believed in a particular style of education for myself.
The idea is to focus on matters that you want to learn about, find a modest
amount of money, and then organize a symposium of those matters, inviting
knowledgeable individuals to participate - and, by extension - to come and
help with my education. The Eighth George Hudson Symposium held at
Plattsburgh, New York on April 11-12, 1975 was another attempt on my
part to learn something.
The ostensible reason for the Symposium was explained in the Announce
ment of the Symposium as follows:
Systems Theory is currently one of the exciting areas of intellectual activity, attracting
persons from diverse disciplines. In fact, it has almost become the prototype of inter
disciplinary effort. As such, it needs the interchange of ideas, viewpoints, and opinions
as a necessary condition for growth. This Symposium was convened to bring together a
number of persons- some of them experts and some beginners - for two days of con
centrated interaction on Systems Theory. The breadth of the interests of the invited
speakers can be noted from their "home" disciplines but space limitations forestall any
attempt to document their actual current interests which range from brain function to
political institutions to technoethics. The speakers were chosen for their expository and
interactive ability as well as for their work in Systems Theory and ample time has been
allowed for discussion with them.
The Symposium provided some measure of local interchange of ideas, view
points, and opinions; this publication is the global counterpart. For the most
part, the papers are those which were presented at the Symposium, in some
cases revised by the authors in the light of reactions and subsequent discus
sions. The paper by Bunge was prepared for the Symposium but he was not
able to attend. The papers by Forrester and by Bainbridge were added after
the Symposium. E. Manes gave a talk entitled 'A categorical catalyst: new
mathematical ideas in system theory' at the Symposium; by mutual agree
ment, no manuscript was prepared. The Arbib-Manes paper was background
for the Manes paper.
No central theme was set for the Symposium and hence the editor is
spared the task of showing (and the reader of accepting) how each paper
fits in with the central theme. Each paper speaks for itself and despite the
x
PREFACE
diversity of themes there are remarkable similarities of notions. One comment
should perhaps be made about the Arbib-Manes paper - more precisely,
about the title. In their paper - and elsewhere - fuzzy sets, fuzzy automata,
fuzzy machines, and fuzzy categories abound. In each case, fuzzy is an adjec
tive which adds something to the noun it modified. Reading again all of the
papers of this volume, I am convinced that "fuzzy" as in "fuzzy world" is
redundant. One might almost be tempted to say that the world is inherently
fuzzy. If such is indeed the case, I hope that this volume will help us deal
with the fuzz.
Plattsburgh, New York, US.A. WILLIAM E. HAR TNETT
March 1976
ACKNOWLEDGEMENTS
To D. Reidel Publishing Company and to Jaakko Hintikka, Editor of Synthese,
for permission to reprint 'A Category-Theoretic Approach to Systems in a
Fuzzy World', Michael A. Arbib and Ernest G. Manes, Synthese 30 (1975)
381-406.
To Jay W. Forrester for permission to print copyrighted material.
To the Faculty of Science and Mathematics, State University College,
Plattsburgh, New York, for funding the Eighth George Hudson Symposium
on Systems: Approaches, Theories, Applications, held at Plattsburgh on April
11-12,1975.
To Mario Bunge and to the Canada Council. To Bunge for haVing me as a
Research Associate during a very educational year and to the Council for
underwriting my weekly visits to McGill University. Their support provided
the gestation period for my paper.
To Carol Burnam, Secretary of the Department of Mathematics, for many
things, particularly for the loving care and attention she has given to my
work over the years. I am especially grateful for all the onerous tasks she has
undertaken in connection with the Eighth George Hudson Symposium and
the publication of this volume.
W.E.H.