Some Basic Concepts in System Dynamics - Creative Learning ...

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D-4894 - 5 -Some Basic Concepts in System DynamicsbyJay W. ForresterIn its full development, system dynamics is a discipline with the scope ofscience, education, law, engineering, or medicine. On the other hand, it isbecoming clear that teachers in ordinary K-12 schools can make enough progressin two or three years to achieve major improvement in students’ thinking, selfreliance, and enthusiasm for learning.1. THE NATURE OF SYSTEMSMany principles form the foundation of system dynamics and become a basisfor thinking in all endeavors.1.1. Feedback LoopsHere we touch on the natureof feedback loops. People seldomrealize the pervasive existence offeedback loops in controllingeverything that changes throughtime. Most people think in linear,nonfeedback terms. For example,in Figure 1, people see a problem,Figure 1decide on an action, expect aresult, and believe that is the endof the issue. Figure 1 illustratesthe framework within which mostdiscussions are debated in thepress, business, and government.Copyright © 2009by Jay W. ForresterPermission granted to reproduceFor noncommercial and educational purposes

- 6 - D-4894InformationaboutproblemClosed-loop Structureof the WorldActionFigure 2ResultA-4293JWF34However, a far morerealistic perception would beFigure 2 in which a problemleads to action that produces aresult that creates futureproblems and actions. There isno beginning or end.We live in a complex of nestedfeedback loops. Every action,every change in nature, is setwithin a network of feedbackloops. Feedback loops are thestructures within which allchanges occur.JWF35Filling a glass of water isnot merely a matter of waterflowing into the glass. There is acontrol of how much water. Thatcontrol is the feedback loop fromwater level to eye to hand tofaucet to water flow and back towater level. Such closed loopscontrol all action everywhere.Figure 3

D-4894 - 7 -1.2. Simplest Feedback LoopFigure 4 shows the simplest possiblefeedback system. In the figure are twosymbols—a stock, and a flow. The stockis an accumulation, or integration, or level,to choose terminology from differentfields. The flow changes the amount in thestock. The flow is determined by astatement that tells how the flow iscontrolled by the value of the stock incomparison to a goal. All systems,everywhere, consist of these two kinds ofconcepts—stocks and flows—and noneother. Such a statement, that there two andonly two kinds of variables in a system, ispowerful in simplifying our view of theworld. People familiar with accountingstatements, as in annual reports ofcorporations, will recognize the twoFigure 4classes of variables. A financial report ispresented on two different pages—thebalance sheet and the profit and loss statement. All numbers on the balance sheetare stocks representing accumulations that have evolved over time. The profit andloss statement represents the flows that cause the stocks to change. There is nocomparably important third page, only the page representing stocks and the pagerepresenting flows. That structure of an accounting statement represents afundamental truth about all systems. Water in a bathtub is a stock; the flow ofwater changes the stock. A person’s reputation is a stock that is changed by theflow of good and bad actions by that person. The degree of frustration in a groupis a stock that gradually changes in response to surrounding pressures.2. FROM SIMPLE TO COMPLEX SYSTEMSThe basic feedback loop in Figure 4 is too simple to represent real-worldsituations. But simple loops have more serious shortcomings—they are misleadingand teach the wrong lessons. Most of our intuitive learning comes from verysimple systems. The truths learned from simple systems are often completely

- 8 - D-4894opposite from the behavior of more complex systems. A person understands fillinga water glass, as in Figure 3. But, if we go to a system that is only five times as!JWF037B"#$%&'()complicated, as in Figure 5, intuition fails. A person cannot look at Figure 5and anticipate the behavior of the pictured system.Figure 5 from World Dynamics is five times more complicated than Figure 4in the sense that it has five stocks—the rectangles in the figure. The figure showshow rapidly apparent complexity increases as more system stocks are added.Mathematicians would describe Figure 5 as a fifth-order, nonlinear, dynamicsystem. No one can predict the behavior by studying the diagram or its underlying

D-4894 - 9 -equations. Only by using computer simulation can the implied behavior berevealed.Figure 5 displays interactions between population, capital equipment,agriculture, resources, and pollution. The diagram links multiple disciplines. Aproper study of systems must usually break down the boundaries betweenacademic disciplines. As stated by Gordon S. Brown, former dean of engineeringat MIT, “The message is in the feedback, and the feedback is inherentlyinterdisciplinary.”3. EVERYONE USES MODELSI sometimes ask an audience how many use models for all their decisions.No one responds. How then, I ask, do they make decisions? They quickly see thatall decisions are made on the basis of mental models. No one’s head contains afamily, city, school, country, or business. Decisions are based only on assumptionsabout separate parts of real systems, and trying by intuition to fit those fragmentsof knowledge into an estimate of how things change and what will be theconsequences of a proposed action.ModelsAll actions based on modelsMental modelsBasis of human activity.Major strength:Tremendous store ofinformationMajor weakness:Unreliable in handlingcomplexity and dynamicchange.JWF12Figure 63.1. Computer Models andMental ModelsSystem dynamics builds two-waycommunication between mental modelsand simulation models. Mental modelsare the basis for everyday decisions.Mental models contain tremendousstores of information. But the humanmind is unreliable in understanding whatthe available information means in termsof behavior. Computer simulationmeshes nicely with mental models bytaking the mentally stored informationand then displaying the dynamicconsequences.Such mental models belong to the same class as the computer models usedin system dynamics. In fact a system dynamics model is often built fromassumptions in the mental models. Mental models are rich and often sufficiently

- 10 - D-4894Computer SimulationMake mental models explicitDiscover inconsistenciesDetermine future implicationsImprove mental modelsaccurate about the pieces of asystem—what information is available,who is connected to whom, what aredifferent people trying to achieve. Butmental models are entirely unreliablein deducing what behavior will resultfrom the known pieces of a complexsystem. On the other hand, a computersimulation can, without doubt, revealthe behavior implicit in the structurefrom which it is constructed.Figure 7JWF154. WORKING WITH COMPUTER MODELSThe translation of a mental model to a system dynamics simulation modelmoves through several stages.1. A model must be created with no logical inconsistencies.All variables must be defined. None can be defined more than once.Equations must be unambiguous. Units of measure should be thesame on both sides of an equation. Most system dynamics softwareapplications check for and find such logical errors.2. When a model is first simulated, the results may be absurd.Simulated behavior may be impossible. Inventories, or water in abathtub, or students in the school may go negative; negative valuesoften have no real-world meaning. One goes back to refine the modeland make the structure more realistic and more robust.3. As a model becomes better, surprising behavior often doesnot reveal model errors but instead begins to tell something about reallife that was not previously realized. I have usually had such newinsights from models. One example arose from the model in myUrban Dynamics book dealing with the growth and stagnation incities. One weekend I added a job-training program to the model. Itwas a perfect job-training program in the sense that it simply tookpeople out of the unskilled and underemployed category and put them

D-4894 - 11 -in skilled labor; and, furthermore, no charge was assigned so it costnothing.The perfect job-training program caused unemployment in themodel to go up. The increase in unemployment surprised me until Ispent a day discovering what the model was doing, after which theresult seemed plausible. I took the computer runs back to formermayor John Collins and the several people from Boston business andpolitics that had been working with me. They looked at the risingunemployment as a result of introducing job training in silence forseveral minutes until one said, “Oh, Detroit has the best job-trainingprogram in the country and the most rapidly rising unemploymentrate!” Later I went to people in the business of running job-trainingprograms and asked if they had ever heard of a situation where jobtraining could increase unemployment. Their answer, “Of course,when that happens we go to another city.”The job-training program in the model was defeated by threeforces: 1) before the program, businesses had been dipping into theunskilled and unemployed pool as necessary to obtain employees.The job-training program substituted for the training that businesseswould have done, so training by businesses stopped. About half of thetraining program was neutralized by such substitution; 2) the programincreased the number of skilled workers thereby increasingunemployment among skilled workers and resulted in increaseddownward flow back to the unskilled-unemployed pool. Nearlyanother half of the training was lost through the increased downwardmobility; 3) and last, the training program had high public visibilityand attracted unemployed from other cities, even though the programhad not created significant new jobs. Forces within the systemneutralized the training program and the public visibility of theprogram attracted additional people who would increase unemployed.Another situation of first learning about real life from a simulation modelarose when a student modeled the behavior of insulin and glucose in variousaspects of diabetes. In response to an experiment simulated within the model, hegot a result from his computer patient that had never been reported in the medicalliterature. Was there something wrong with the model? He showed the results todoctors doing diabetes research. After studying what was happening in the model,their response was, “We had a patient like that once, but always thought there was

- 12 - D-4894a mistake in the measurements.” This process had identified a new medicalsyndrome.5. SOURCES OF INFORMATIONMentaldata baseConsider the available databases,or sources of information from whichwe can build computer simulationmodels.JWF13Writtendata baseNumericaldata baseSources of InformationFigure 8I suggest that the world’s storeof information lies primarily inpeople’s heads—the mental database.As a test of that statement, considerany institution, for example, yourcorporation or your school system.Imagine that at 10 o’clock somemorning every person suddenly leavesand is replaced by a person who canread but has no experience in thesystem. You instruct your replacementto follow the instructions and policystatements in your office and carry onfor you. Chaos would result. Ourfamilies, schools, businesses andcountries operate on the information inpeople’s heads gained from participation, apprenticeship, and on-the-job learning.The mental database is vastly richer than the written database in the form of books,magazines, and newspapers. In turn, the written database is far more informativeabout how society operates than the numerically recorded information.System dynamics modeling should build on all available information,including the voluminous mental database. By contrast, most analyses in the socialsciences have been limited to information that has been numerically recorded. Thenumerical information is an extremely small part of all the information that isavailable.

D-4894 - 13 -6. GENERIC OR TRANSFERABLE STRUCTURESGeneric StructuresTransferable between:Past and presentFrom one setting to anotherA small number cover a widerange ofsituationsWhen understood in one setting,they are understood in allsettingsBasis for effective educationJWF7Many structures of levelsand rates are found repeatedly.They are “generic structures”because they are found in manydifferent situations, even inentirely different fields ofapplication. If a particularstructure is understood in onesetting, it is understood in allsettings. Generic structuresprovide a person with power tomove between situations with thelearning in one area being appliedto other situations.Figure 9In education, afterunderstanding a collection of basicdynamic structures, a student canquickly draw on one to understanda new situation if its structure hasbeen encountered previously.

- 14 - D-48946.1. Generic Structure of a Clock and Economic Business CycleVelocityEmploymentChange inpositionProductionrate less salesAccelerationHiring rateFigure 10PositionInventoryA-3865Ad.5JWF39Figure 10shows two sets ofnomenclature. Thelabels above thebars relate to theswinging pendulumof a clock. Thelabels below thebars describeinventory andemployment inmanufacturing.With appropriatechoices of parametervalues, the structurewill exhibit theoscillation of a onesecondclock pendulum, or alternatively the several-year interval between peaks ofa business cycle. The single loop with two levels as in Figure 10 results in only asustained oscillation. Additional structure is necessary to represent friction in apendulum or the forces that might change the amplitude of business cycles. Aswinging pendulum and the central core of the production-inventory business cyclehave the same oscillatory structure.In my own experience with transferability of structure, I was meeting with agroup of medical doctors and pharmacologists in Palo Alto one day. A topic cameup that was not on the agenda. They began to talk about a doctor who was doingan experimental treatment, which clearly those present did not approve. They haddescribed the experiment but had said nothing of the results when I suggested anoutcome. I told them that if I were to judge that medical experiment on the basisof the kind of behavior that we had seen in the Urban Dynamics model of cities, Iwould guess the treatment would cause atrophy of the pancreas. They said,“You’re right. That’s exactly what’s happening.” There was enough

D-4894 - 15 -transferability of structure between the two systems to justify suggesting themedical outcome.For dramatic, personal-experience learning, computer structures can beconverted into games with people making the decisions that would control theflows in a model. A distribution system from manufacturer, through distributorand retailer, to customers has been played by hundreds of thousands of peoplearound the world to drive home the way in which people can interact to createinstability. Other games show the dynamics of producing great depressions some45 to 80 years apart, and still others show how companies can grow so rapidly thatthey cause their own failure.7. DIFFERENTIAL EQUATIONS VS. INTEGRATIONOne might ask how it is now possible to teach behavior of complex dynamicsystems in K-12 when the subject has usually been reserved for college andgraduate schools. The answer lies in having realized that the mathematics ofdifferential equations has been standing in the way.Differential equations are difficult, confusing, weak, and unrealistic. Theyoften mislead students as to the nature of systems. Mathematicians have haddifficulty defining a derivative and there is a reason. Derivatives do not existexcept in a mathematician’s imagination. Nowhere in nature does nature take aderivative. Nature only integrates, that is, accumulates in stocks. Casting behaviorin terms of differential equations leaves many students with an ambiguous or evenreversed sense of the direction of causality. I have had MIT students argue thatwater flows out of the faucet because the level of water in the glass is rising; thatseems natural to them if the flow has been defined as the derivative of the waterlevel in the glass.Any child who can fill a water glass or take toys from a playmate knowswhat accumulation means. The stocks in a system dynamics model (the rectanglesin Figures 4 and 5) are the integrations (accumulations). By approaching dynamicsthrough the window of accumulation, students can deal with high-order dynamicsystems without ever discovering that their elders consider such to be verydifficult.

- 16 - D-4894An MIT undergraduate working to develop system dynamics materials forK-12 education observed:In my differential equations class we used calculus to figure out thebehavior of populations. I realized just how much simpler system dynamicsmade that thought process. Whereas only college students can understandsuch phenomena using math, elementary scholars can understand the samethings by using system dynamics modeling. It’s really amazing.”This paper has given only a glimpse of the principles and concepts that makeup an understanding of complex social and economic systems. Furthermore, anunderstanding of systems will not be internalized just by reading about them. Welook forward to the time when an education from kindergarten through college willcreate citizens and leaders who can create far more satisfactory human andenvironmental systems.8. MORE ON SYSTEM DYNAMICSStudy materials are available from the Creative Learning Exchange. Manydownloads of the K-12 information come from corporations that use the materialfor internal training. Exactly the same material can be used anywhere from the 5 thgrade to chief executive officers; it is new to all.Creative Learning Exchangehttp://clexchange.orgMs. Lees Stuntz, Director27 Central StreetActon, MA 01720tel: 978-635-9797fax: 978-635-3737email: stuntzln@clexchange.orgLook on the web site or ask about the list of available materials to bedownloaded and the “Road Maps,” which is a self-study introduction to systemdynamics. Also go to:sysdyn.clexchange.orgfor the assignments and solutions for the Guided Study Program in SystemDynamicsInternet discussion group: Send a message tolistserv@sysdyn.clexchange.org with the line “subscribe k-12sd first-name last-

D-4894 - 17 -name” as the only thing in the message’s body (no footer, no signature, etc.) Thesubject line is immaterial. “First-name” and “last-name” are your first and lastnames.Pegasus Communications, Inc.One Moody StreetWaltham, MA 02453-5339tel: 781-398-9700fax: 781-894-7026Alfeld, Louis Edward, and Alan K. Graham. 1976. Introduction to Urban Dynamics. Waltham,MA: Pegasus Communications. 333 pp.Fisher, Diana M. 2001. Lessons in Mathematics: A Dynamic Approach. Lebanon, NH: iseeSystems.Fisher, Diana M. 2004. Modeling Dynamic Systems: Lessons for a First Course. Lebanon, NH:isee Systems.Forrester, Jay W. 1961. Industrial Dynamics. Waltham, MA: Pegasus Communications. 464 pp.Forrester, Jay W. 1968. Principles of Systems. (2 nd ed.). Waltham, MA: PegasusCommunications. 391 pp.Forrester, Jay W. 1969. Urban Dynamics. Waltham, MA: Pegasus Communications. 285 pp.Forrester, Jay W. 1971. World Dynamics. (1973 second ed.). Waltham, MA: PegasusCommunications. 144 pp. Second edition has an added chapter on physical vs. social limits.Forrester, Jay W. 1975. Collected Papers of Jay W. Forrester. Waltham, MA: PegasusCommunications. 284 pp.Goodman, Michael R. 1974. Study Notes in System Dynamics. Waltham, MA: PegasusCommunications. 388 pp.Mass, Nathaniel J., ed., 1974. Readings in Urban Dynamics: Volume I, Waltham, MA: PegasusCommunications, 303 pp.Meadows, Dennis L. 1970. Dynamics of Commodity Production Cycles. Waltham, MA: PegasusCommunications. 104 pp.Meadows, Dennis L., et al. 1974. Dynamics of Growth in a Finite World. Waltham, MA:Pegasus Communications. 637 pp.Meadows, Dennis L., and Donella H. Meadows, ed., 1973. Toward Global Equilibrium:Collected Papers, Waltham, MA: Pegasus Communications, 358 pp.Randers, Jorgen, ed., 1980. Elements of the System Dynamics Method, Waltham, MA: PegasusCommunications, 488 pp.Richardson, G. P. (1991). Feedback Thought in Social Science and Systems Theory. Waltham,MA: Pegasus Communications.Schroeder, Walter W., III, Robert E. Sweeney, and Louis Edward Alfeld, ed., 1975. Readings inUrban Dynamics: Volume 2, Waltham, MA: Pegasus Communications, 305 pp.