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.