Table Of ContentBiomathematics
Volume 16
Managing Editor
S. A. Levin
Editorial Board
M.Arbib H.I.Bremermann I.Cowan W.M.Hirsch
S. Karlin 1. Keller K. Krickeberg R. C. Lewontin R. M. May
1. D. Murray A. Perelson T. Poggio L. A. Segel
Biomathematics
Managing Editor: S.A.Levin Editorial Board: M. Arbib,
H.J. Bremermann, J.Cowan,
W.M.Hirsch, S.Karlin, J.Keller,
K. Krickeberg, R. C. Lewontin,
R.M.May, J.D.Murray, A.Perelson,
T. Poggio, L. A. Segel
Volume 2 Volume 9
E. Batschelet W.J. Ewens
Introduction to Mathematics for Life Mathematical Population Genetics
Scientists
Volume 10
A. Okubo
Volume 3
M. Iosifescu, P. Tiiutu Diffusion and Ecological Problems:
Mathematical Models
Stochastic Processes and Applications in
Biology and Medicine
Volume 11
Part 1: Theory
B. G. Mirkin, S. N. Rodin
Graphs and Genes
Volume 4
Translated from the Russian by
M. Iosifescu, P. Tiiutu
H.L. Beus
Stochastic Processes and Applications in
Biology and Medicine Volume 12
Part 2: Models R. Gittins
Canonical Analysis
Volume 5 A Review with Applications in Ecology
A. Jacquard
Volume 13
The Genetic Structure of Populations
J. Impagliazzo
Translator: D. Charlesworth,
B. Charlesworth Deterministic Aspects of Mathematical
Demography
An Investigation of the Stable Theory of
Volume 6
Population including an Analysis of the
D. Smith, K. Keyfitz
Population Statistics of Denmark
Mathematical Demography
Selected Papers
Volume 14
c.J. Mode
Volume 7
Stochastic Processes in Demography and
E.R. Lewis
Their Computer Implementation
Network Models in Population Biology
Volume 15
Volume 8 D.L. DeAngelis, W.M. Post,
A. T. Winfree C.C. Travis
The Geometry of Biological Time Positive Feedback in Natural Systems
Complexity, Language, and Life:
Mathematical Approaches
Edited by
John L. Casti and Anders Karlqvist
Springer-Verlag
Berlin Heidelberg New York Tokyo
John L. Casti
International Institute for Applied Systems Analysis
2361 Laxenburg, Austria
Anders Karlqvist
Swedish Academy of Sciences
10110 Stockholm, Sweden
Mathematics Subject Classification (1980): 9202, 9302
ISBN-13:978-3-642-70955-5 e-ISBN-13:978-3-642-70953-1
DOl: 10.1007/978-3-642-70953-1
© International Institute for Applied Systems Analvsis, 1986
Softcover reprint of the hardcover 1st edition 1986
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, electronic, mechanical, photocopying,
recording or otherwise, without the prior permission of the copyright owner.
2141/3145-543210
Preface
In May 1984 the Swedish Council for Scientific Research convened
a small group of investigators at the scientific research station at
Abisko, Sweden, for the purpose of examining various conceptual
and mathematical views of the evolution of complex systems. The
stated theme of the meeting was deliberately kept vague, with only
the purpose of discussing alternative mathematically based
approaches to the modeling of evolving processes being given as a
guideline to the participants. In order to limit the scope to some
degree, it was decided to emphasize living rather than nonliving
processes and to invite participants from a range of disciplinary
specialities spanning the spectrum from pure and applied
mathematics to geography and analytic philosophy.
The results of the meeting were quite extraordinary; while there
was no intent to focus the papers and discussion into predefined
channels, an immediate self-organizing effect took place and the
deliberations quickly oriented themselves into three main
streams: conceptual and formal structures for characterizing sys
tem complexity; evolutionary processes in biology and ecology;
the emergence of complexity through evolution in natural lan
guages. The chapters presented in this volume are not the proceed
ings of the meeting. Following the meeting, the organizers felt that
the ideas and spirit of the gathering should be preserved in some
written form, so the participants were each requested to produce a
chapter, explicating the views they presented at Abisko, written
specifically for this volume. The results of this exercise form the
volume you hold in your hand.
Special thanks for their help in various phases of organizations
of the meeting and arrangement of the publication of this volume
are due to M. Olson, P. Sahlstrom, and R. Duis.
December 1985 John Casti, Vienna
Anders Karlqvist, Stockholm
The International Institute for App6ed Analysis
is a nongovernmental research institution, bringing together scien
tists from around the world to work on problems of common
concern. Situated in Laxenburg, Austria, IIASA was founded in
October 1972 by the academies of science and equivalent organi
zations of twelve countries. Its founders gave IIASA a unique
position outside national, disciplinary, and institutional bound
aries so that it might take the broadest possible view in pursuing its
objectives:
To promote international cooperation in solving problems arising
from social, economic, technological, and environmental
change
To create a network of institutions in the national member organi
zation countries and elsewhere for joint scientific research
To develop and formalize systems analysis and the sciences con
tributing to it, and promote the use of analytical techniques
needed to evaluate and address complex problems
To inform policy advisors and decision makers about the potential
application of the Institute's work to such problems
The Institute now has national member organizations in the
following countries:
Austria - The Austrian Academy of Sciences; Bulgaria - The
National Committee for Applied Systems Analysis and Manage
ment; ClIJUlda - The Canadian Committee for lIASA; Czecho
slol'akia - The Committee for IIASA of the Czechoslovak Socialist
Republic; Finland - The Finnish Committee for IIASA; France -
The French Association for the Development of Systems Analysis;
German Democratic Republic - The Academy of Sciences of the
German Democratic Republic; Federal Republic 01 Germany -
Association for the Advancement of IIASA; HUDgary - The
Hungarian Committee for Applied Systems Analysis; JtBIy - The
National Research Council; Japan - The Japan Committee for
IIASA; Netherlands - The Foundation lIASA - Netherlands;
Poland - The Polish Academy of Sciences; SwedeD - The Swedish
Council for Planning and Coordination of Research; UDiOD 01
Soriet Socialist Republics - The Academy of Sciences of the Union
of Soviet Socialist Republics; UDited States 01 America - The
American Academy of Arts' and Sciences;
List of Contributors
David Berlinski, Institut des Hautes Etudes Scientifiques,
35 Route de Chartres, 91440 Bures-sur-Yvette, France
John L. Casti, International Institute for Applied Systems
Analysis, A-2361 Laxenburg, Austria
Peter Gould, Department of Geography, College of Earth and
Mineral Sciences, The Pennsylvania State University,
302 Walker Building, University Park, Pennsylvania 16802,
USA
Ulf Grenander, Mittag-Leffler Institute, Auravagen 17, S-10262
Djursholm, Sweden
Jeffrey Johnson, Centre for Configurational Studies, Design
Discipline, Faculty of Technology, The Open University,
Walton Hall, Milton Keynes MK7 6AA, England
Howard H. Pattee, Department of Systems Science, T.J. Wat
son School of Engineering, State University of New York at
Binghampton, Binghampton NY 13901, USA
Robert Rosen, Department of Physiology and Biophysics,
Dalhousie University, Nova Scotia, Canada, B3H 4H7
Karl Sigmund, Institute of Mathematics, University of Vienna,
Strudelhofgasse 4, A-1090 Wien, Austria
Nils Chr. Stenseth, Zoological Institute, University of Oslo, PO
Box 1050, Blindern, Oslo 3, Norway
Rene Thorn, Institut des Hautes Etudes Scientifiques, 35 Route
de Chartres, 91440 Bures-sur-Yvette, France
Table of Contents
1. Allowing, forbidding, but not requiring:
a mathematic for a human world . . . . . 1
Peter Gould
2. A theory of stars in complex systems 21
Jeffrey Johnson
3. Pictures as complex systems 62
Ulf Grenander
4. A survey ofreplicator equations 88
Karl Sigmund
s.
Darwinian evolution in ecosystems: a survey of some
ideas and difficulties together with some possible solu-
tions . . . . . . . . . . . . . . . . . . . . . . . . .. 105
Nils Chr. Stenseth
6. On system complexity: identification, measurement,
and management ................... 146
John L. Casti
7. On information and complexity . . . . . . . . . . .. 174
Robert Rosen
8. Organs and tools: a common theory of morphogenesis . 197
Rene Thorn
9. Thelanguageoflife . . . . . . . . . . . . . . . . .. 231
David Berlinski
10. Universal principles of measurement and language
functions in evolving systems ............. 268
Howard H. Pattee
Introduction
John L. Casti and Anders Karlqvist
Complexity and the Evolution of Living Systems
One of the most evident features distinguishing living from nonliving systems
is the tendency for living processes to evolve ever more complex structural and
behavioral modes during the course of time. This characteristic has been observed
in lowly protozoa and in highly evolved linguistic and social communities. and has
been variously labeled "negentropy". "variety". "information". or just plain com
plexity. The understanding and explanation of the trend toward the complexifica
tion of living things forms the heart of any research program in the biological.
social. or behavioral sciences.
How does complexity emerge and what do we even mean when we speak of a
system as being complex? In everyday language. complexity is associated with
structural features such as large numbers of system components. high levels of
connectivity between sUbsystems. feedback and feedforward data paths that are
difficult to trace. and so on. Complexity is also associated with behavioral charac
teristics such as counterintuitive reactions. surprises. multiple modes of opera
tion. fast and slow system time scales. and irreproducible surprises. While the
structural features are. by and large. objective properties of the system per se.
the behavioral components of complexity are decidedly subjective: what is coun
terintuitive. surprising. and so on is as much a property of the system doing the
observing as it is a feature of the process under study. Thus. any mathematical
formulations of the notion of complexity must respect the subjective. as well as
the objective. aspects of the concept. In this volume. the chapters by Rosen and
Casti address both aspects of the complexity question. Casti argues that complex
ity emerges from the interaction between the system and its observer. while
Rosen introduces the idea of an activation-inhibition pattern to characterize the
informational interaction. and then uses this concept to speak of complexity.
Both of these chapters put forth strong arguments for the case that complexity of
living systems is a contingent. rather than intrinsic. property of the system. and
any theory of complexity management and control must start from this basis.
The explicit consideration of evolutionary processes in biology is taken up in
the chapters by Sigmund and Stenseth. Stenseth reviews the essential com
ponents of the Darwinian theory: reproduction. variation. inheritance. and selec
tion. and considers the issue of what kinds of mathematical models we need in
order to capture the Darwinian view in operational form. His conclusion is that the
numerous controversies surrounding the Darwinian paradigm in no way provide evi
dence for rejecting it. but rather point to the need to extend and improve our
