The Best of Creative Computing Volume 1 (published 1976)
World Dynamics
the slums they replaced. In St. Louis it has even been
necessary to demolish some of the worst after they were
barely twenty years old. This situation is in stark contrast
to that found in engineering and the natural sciences. As
each Apollo flight blasted off to the moon, there was little
real doubt that it would work. Although a hundred million
dollar building or bridge may employ a new design, no one
expects collapse. The few failures are the exception.
In the midfifties with the aid of a Ford Foundation
grant, the Industrial Dynamics program was launched at
MIT in order to reduce these disparities. The aim was the
development of dynamic modeling techniques which would
promote understanding and prediction in the social
sciences. The first book evolving from this program,
"Industrial Dynamics" by Jay W. Forrester, appeared in
1961. This was followed by several others, but it was not
until the publication of Forrester's "World Dynamics" that
the efforts were greeted by extensive coverage in the
popular press. Most of the popular discussions actually
centered on the book "The Limits to Growth" by
Meadows, Meadows, Randers, and Behrens III which
employed an improved version of the world dynamics
model.
If one simply desires the results, then "The Limits to
Growth" is the book to read. For those who want to
understand the techniques, "World Dynamics" is the better
book, though its model is more primitive. In the latter,
knowledge of the systems dynamics approach is assumed.
This background can best be acquired through "Principles
of Systems."
"Principles of Systems" is an introduction to the
terminology and techniques used to model dynamic
systems. It begins by explaining the role of feedback loops
in systems, and goes on in Chapter Two to discuss both
positive and negative feedback loops of first and higher
orders. These ideas are illustrated with a model explaining
growth and saturation of sales. Unfortunately the model
used is more complicated than it should be so early in the
book.
In Chapter Three, the distinction between simulation
and analytical solutions is made. Although it has been
conceptually possible for many years to employ dynamic
models in such areas as business, this has actually been
attempted only since the development of economical
computers. Without computers we must resort to hand
simulations which are costly and lengthy or analytical
solutions which can be hard to obtain.
In later chapters we learn general principles for
developing dynamic models, the role of rates and levels, and
the necessity of alternating rates and levels. The reader is
shown how to express such models both as diagrams and as
sets of equations.
Dynamic models are actually sets of coupled differential
equations expressed in integral form. To solve these models
we begin with the initial values of the variables. After
choosing a suitable finite time interval, we evaluate the
equations to obtain the values of the variables at the new
time. This iteration continues until the behavior of the
model is known during the relevant time span. Though the
relationship between the dynamic models and differential
equations is mentioned, the book is remiss in not including
a chapter explaining how to translate between the two
notations.
The flows within models are classified into conserved
flows and information links. The importance of information
as connecting tissue in systems is stressed. lt is
information which alters flow rates.
Numerous diagrams, graphs, and tables contained in the
book do much to clarify the presentation. Over one half of
the book is a workbook containing both problems and
solutions. Many of the simulations are designed to be
iterated by hand. The others are intended to be run on
computer systems containing the DYNAMO compiler.
Unfortunately, most people do not have easy access to such
computers. Fortunately, it is fairly easy to translate the
DYNAMO notation into computer languages such as
BASIC. It would be helpful if the book included an explicit
discussion of this procedure.2 When undertaking such a
297
task, it is important to write subroutines to carry out
frequent calculations such as table interpolation and
graphing.
The book was written for college students beginning
their studies in the MIT systems dynamics program. It can
be read profitably by anyone having at least a good
understanding of high school algebra and familiarity with
any of the popular programming languages.
This is a good introduction to modeling dynamic
systems, but it can and should be updated as soon as
possible. It has been around too many years as the second
preliminary edition.
After reading "Principles of Systems", one is in a ggod
position to understand "World Dynamics". "World
Dynamics" is most useful if viewed not as a prediction of
the future, but rather as an illustration of the procedure for
constructing dynamic models. It is often surprising how few
variables are required to simulate complicated systems.
"World Dynamics" begins with a short discussion
encouraging the use of models in understanding behavior. It
then describes the actual model, and finally gives specific
results.
The world model contains five levels: population, capital
investment, natural resources, fraction of capital devoted to
agriculture, pollution, and the rates controlling these levels.
Since it is a highly aggregated model, factors such as
geographical dispersion and transportation are not included.
Although it is easy to offer suggestions for improving the
model, such improvements also complicate the model. Once
we understand modeling, it is always possible to construct
more realistic models if we are seriously interested in the
results.
Constituting over one fourth of the book, the third
chapter, contains the dependence of the rates on the levels in
both numerical and graphical form. The graphs are very
helpful in visualizing these relationships.
The fourth chapter includes the actual results of the
model. Most runs cover the time span from 1900 to 2100.
The results are also displayed in graphical form. After
exhibiting the basic model's behavior, a variety of
alternative assumptions are explored. It is important to
realize that this type of study does not give the best
strategy, but illuminates the consequences of alternative
strategies.
In the fifth chapter some obvious strategies are explored
and are found wanting. Often strategies looking good in the
short run have disastrous long term consequences.
For those seriously interested in dynamic models,
appendices B and C are particularly helpful because they
summarize the equations of the world model. These
equations are designed to be run on a DYNAMO compiler,
but, as previously mentioned, can be translated into BASIC
or other languages with a modest effort. Such an effort
probably gives a far better insight into the structure of
dynamic models than simply running the model on a
DYNAMO compiler.
The style is readable and the book is well laid out. There
are a few minor errors. For example, the rate controlling
the level capital-investment-in-agriculture fraction is missing
from the complete system diagram. This book can be read
and understood by anyone who has read "Principles of
Systems".
Should these books be bought? Yes, even though they
are slightly overpriced. As computers become cheaper and
faster, we can expect greater use of dynamic models. These
models will become a more integral part of the decision
making process on all levels. Bad models will always give
unreliable results even though they are computerized. Our
best hope for preventing abuse of these models is an
informed population understanding both their power and
their limitations.
William H. Rybolt
Babson Park, MA.
1 Asimov, Isaac, Foundation. Avon Books, New York, N. Y.
l97l.
2 Anderson, Jay Martin, Dynamic Modelling Using
FORTRAN IV. In Creative Computing, May-June 1975, p. 59.
