Table Of ContentP r o m i s e
T h e
L i m i t s
a n d o f
C o m p u t e r
M o d e l i n g
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
P r o m i s e
T h e
L i m i t s
a n d o f
C o m p u t e r
M o d e l i n g
Charles Blilie
Trissential Consulting, USA
World Scientific
NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI
Published by
World Scientific Publishing Co. Pte. Ltd.
5 Toh Tuck Link, Singapore 596224
USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601
UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
THE PROMISE AND LIMITS OF COMPUTER MODELING
Copyright © 2007 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
electronic or mechanical, including photocopying, recording or any information storage and retrieval
system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright
Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to
photocopy is not required from the publisher.
ISBN-13 978-981-270-795-6
ISBN-10 981-270-795-6
Printed in Singapore.
Steven - The Promise and Limits.pmd 1 5/28/2007, 9:02 AM
Contents
Chapter 1 The Jade Mountain 1
Chapter 2 What are Models? 11
Kinds of Models 13
Models as Abstract Images 20
Why Build Models? 25
Simulations as Models in Motion 30
Chapter 3 The Modeling Process 37
Identification of Systems 39
Boundary Conditions and Interfaces 42
System Analysis I: Find System Components 46
System Analysis II: State Variables and
Transformations 50
Simulation Management: A Digression 57
Model Synthesis: Implementing, Verifying,
Validating 59
Summary: The Modeling Paradigm 62
Chapter 4 An Object-Oriented Universe 66
Modeling Through Object-Oriented Languages 68
Class Patterns 78
The Categories of Object-Oriented Reason 79
Cellular Automata as Micro-Objects 83
v
vi The Promise and Limits of Computer Modeling
Chapter 5 The Crossroads of Theory and Experiment 89
Models and the Synthesis of Data and Theory 92
Induction, Deduction, and the Socrates File 98
The Limits of Empiricism, Or, Will the Sun Rise
Tomorrow? 102
Summary: Modeling, Simulation, and the
Dynamic of Discovery 108
Chapter 6 Modeling the Appearances 110
Observables for Celestial Mechanics 112
Ptolemy and the Circular Motions of the Heavens 114
From Ptolemy to Copernicus 120
Kepler, Galileo, and the Extension of the
Heliocentric Model 124
Newton Completes the Classical Model 128
Extending the Newtonian Picture: The Discovery
of Neptune 130
Einstein’s Theory of Relativity and the Precession
of Mercury’s Perihelion 132
Summary: How Models Progress 134
Chapter 7 Laplace’s Mirage, or the Impossibility of the
Exact Calculation of the World 138
Intrinsic Limitations of Models and the
“Categories” 141
Extrinsic Limitations 152
Reductionism, Determinism, and Reality 156
Between Order and Randomness: Chaotic Systems 163
Summary: Laplace Humbled, but Not Destroyed 165
Chapter 8 Climates of Fact 167
Climate and Conceptual Models 169
Towards a More Detailed Model 174
Global Circulation Models 185
Validation and Climate Change 190
Contents vii
Chapter 9 Calculating War and Peace 202
Population Modeling 203
Predator-Prey Cycles 209
Why do Population Models Work? 212
Social and Economic Analogies 215
Chapter 10 From the Past into the Future: Is Historical
Simulation Possible? 220
Through the Lens of the Modeling Paradigm 221
Historical Order as Natural Order? 223
Not Nature, but Culture 230
Theory versus History: The Problem of the
Indeterminate and the Singular 234
Summary and a Modeling Thought-Experiment 237
Chapter 11 Virtual Reality … and Reality 240
The Interactive Image 243
Fictions, Simulations, and Cyberspace 247
Seeing is Believing? 248
Virtual Bodies 251
The Real and the Objective 253
Summary: The Mixed Success of VR 256
Notes and References 258
Index 273
TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk
Chapter 1
The Jade Mountain
Perhaps my favorite object in our local art museum is a Chinese jade
sculpture of a mountain. Although a massive piece of stone, it is truly
miniature compared to what it represents: tiny jade trees cling to its
diminutive cliffs; a procession of poets and scholars ascends its paths; its
rocks mimic the condensed shape of alpine crags. It is obviously a lofty
mountain; perhaps it is the distillation of a sacred place. The artist surely
intended it so. He created a microcosm that perfectly abstracts the
macrocosm.
To capture the world in miniature has long been a human dream. Or,
more accurately, to capture just that part of the world that is really
meaningful, to distill its essence, has driven both science and art forward
from the beginning. Such a blueprint or model of reality would grant
both the knowledge of its vast structure and the primary means to
manipulate it by, recalling Francis Bacon’s remark that “knowledge is
power.” It would provide the aesthetic and even spiritual satisfaction of
beholding reality in a single view. And this is, more or less, the aim of
every model ever built: to reduce reality to a smaller, yet more
concentrated form.
To jump in scale from the jade mountain to the world — to the whole
of reality — seems an impossible leap. Yet the advent of computer
modeling and simulation opens up this tantalizing possibility. Computer
scientist David Gelernter calls such comprehensive models mirror
worlds1:
“A Mirror World is some huge institution’s moving, true-to-life
mirror image trapped inside a computer -- where you can see and grasp it
whole. The thick, dense, busy sub-world that encompasses you is also,
1
