TIMS Studies in the Management Sciences 14 (1980) 75-89© North-Holland Publishing Company

TIME IN SYSTEM DYNAMICS *

Lewis J. PERELMANJet Propulsion Laboratory

System dynamics studies the behavior of systems through time. Yet time itself rarely isdiscussed in the existing literature of the field. Alternative concepts of time come from New-tonian mechanics and from modern thermodynamics; system dynamics mixes these two con-cepts in a way which may be problematical. Another issue involving time is the selection of thetime horizon of the model run. The length of the time horizon affects the policy implicationsof the simulation, yet no clear rule exists for selecting the time horizon. These problems withthe treatment of time in modeling influence the practical application of system dynamics topolicy management.

1. Introduction

People complain about time being short, going fast. But when it seems to go slowly they com-plain that it drags. Let us consider the people, not the supposed movement of time.

Idries Shah

"Feedback systems are of interest because of the way they act through time."This simple statement by Jay Forrester (1968, pp. 2-7) defines one of the majorgoals of system dynamics. System behavior traced through a flow of time is thefocus of all system dynamics research. Yet, to my knowledge, the literature ofsystem dynamics uniformly has taken for granted the concept of time on which themethodology is based. Time is the canvas on which all system dynamics models arepainted; though the design of the model often is debated, the nature of the canvasrarely is noticed.

The following discussion deals with the meaning and structure of time in systemdynamics, not only as a theoretical issue but also in terms of the intellectual,emotional, and ethical interests of system dynamics practitioners as human beings.I address the subject from the perspective of a professional policy analyst, whoworks as an advisor to the management of public bureaucracies, and who uses

* The author is indebted to Dennis Meadows. Donella Meadows, Herman Daly, NicholasGeorgescu-Roegen, and Arthur Harkins for their comments on early drafts of this paper and toGerda Whitney for her editorial assistance. The views expressed are the author's and do notnecessarily represent those of any other individual (If or uaruza t iori.

76 L.J. Perelman, Time ill system dvnamics

system dynamics models as one basis for the evaluation and development of publicpolicies. My experience indicates that the treatment of time is important to theeffectiveness of system dynamics in the process of "policy management" - i.e., aconsciously systematic approach to real-world decision making. The issues raisedhere arc too complex to resolve in so short a space. Rather, my goal is to call atten-tion to some questions relevant to the development of system dynamics which Ibelieve have not been sufficiently addressed in the existing literature of the field. Ihope to provoke the interest of the generalists and specialists who need to colla-borate on finding the answers.

2 _Concepts of time

Discussions of time in system dynamics literature deal with time constants ofsystem behavior, the time increment of each iteration of the simulation, and thetotal time span of the simulation run. But the existing literature assumes that theterm "time" refers to a single concept which is universally understood andaccepted. Practitioners of the methodology may not realize how limited andvulnerable an assumption this is. Among non-Western language groups and culturesare found vastly different conceptions of "time" and "dynamic behavior":

There is no boundary between past Trobriand existence and the present; he can indicate that anaction is completed, but this does not mean that the action is past; it may be completed andpresent or timeless. Where we would say "Many years ago" and use the past tense, the Tro-briander will say, "In my father's childhood" and use nontemporal verbs: he places the eventsituationally , not temporally. Past, present, and fu ture are presented linguistically as the same... (Lee, 1973, p. 139)

More germane to the present discussion is the fact that even within the domain ofcontemporary Western science, at least two major concepts of time are employed(Georgescu-Rcegen , 1971, Ch. 5), and confusion between these can cause seriousmethodological problems. The first of these two concepts, labelled "t", derivesfrom Newtonian mechanics and represents a slice taken out of the universal flow ofTime for the purpose of studying the behavior of a mechanical system. The natureof "t" is that it is assumed reversible and uniform. To develop the Newtonian lawsof mechanics, one has to assume, first, that in any equation where "t" appears thesubstitution of "minus t" will predict motion exactly in reverse. A motion pictureof a frictionless, swinging pendulum portrays physically realistic movement whetherrun forward or in reverse; the change in the sign of "t" does not violate Newton'sLaws. Second, one has to assume that all time intervals, "delta t", of the samelength are identical. This is to say the pendulum swings the same way in 1777 or in1977. (As noted later, this also implies that the informs lion content of the systemis conserved.)

The second concept of time, "T", comes from the development of thermo-

L.J. Perelman, Time in system dynamics 77

dynamics. The essential argument of the Second Law of Thermodynamics, orEntropy Law, is that every transformation of a real system produces a change in theuniverse which is both qualitative and irrevocable. The motion picture of a thermo-dynamic process cannot be run in reverse and present a realistic image: spilled milkdoes not flow back into the bottle, and a house of cards does not spontaneouslyspring forth from a random jumble. Real Time, the Time of our consciousness andour experience of the real world, is unidirectional and evolutionary. Unidirectionalbecause the degradations of heat, friction, and other phenomena of decay are irre-vocable and occur only one way. Evolutionary because irrevocable change leavesmilestones in the path of Time which create a history.

The relationship between the theories of entropy and of evolution has been anintimate and sometimes paradoxical one which has been influenced by the dualconcepts of time. In the 19th century, Sir Charles Lyell's studies of fossil organismsin geological strata strongly suggested a pattern of progressive development of formand complexity through Time. In order to formulate a theory of geological evolu-tion, Lyell postulated the principle of uniformitarianism.

The problem confronting Lyell was much like a system dynamics problem. Hehad two types of empirical information available: information describing the geolo-gical structure of the earth (mountains, deserts, rivers, oceans, forests, etc.) andinformation describing the forces affecting the dynamic behavior of that structure(wind, rain, vulcanism, biological processes, etc.). In effect, Lyell had a collectionof level variables and rate variables. Lyell's problem was to explain the relationshipbetween geological structure and physical forces in a continuous model of geophy-sical evolution - i.e., a model for explaining the dynamic behavior of the geologicalsystem through time.

Since Lyell's model had to incorporate an extremely long time interval, he hadto make assumptions about the nature of time in his model which were incor-porated in the principle of uniformitarianism. The elements of the principleassumed that the forces operating on the earth's crust in the present were the sameand the only forces that had done so since the origin of the system. The principleassumed, second, that these forces operated in the same way, at the same rate,uniformly throughout the entire previous history of the system. In effect, then, theprinciple of uniformitarianism was related to conservation of information. Theprinciple meant that all the information necessary to describe the dynamic behaviorof the system was present in every state of the system, past and future. Theimportance of uniformitarianism in solving Lyell's "modeling" problem now shouldbe clear. The principle permitted Lyell, beginning with a description of the presentstate of the system and of the rate and direction of certain dynamic forces, toextrapolate the impacts of those forces backward ill time to the origin. The resultsof this reverse extrapolation were both a theory (or model) of geophysicalevolution and an estimate for the age of the earth.

The principle of uniformitarianism served as the Rosetta Stone needed to decodethe story engraved in the earth's crust. But the assumptions were basically an exten-

78 L.l. Perelman, Time ill svsrem dynamics

sion of the Newtonian concept of time to the study of terrestrial evolution. Lyelltreated the earth's crust as a giant clock which could be run backward or forwardwith predictable results. His theory conflicted with the vision of planetary historyin the developing field of thermodynamics. Lord Kelvin's calculations of the heatflow from the earth's interior indicated a lifetime for the earth much less thanwhat seemed to be required by the evolutionary theories of Lyell, Darwin, andothers. This contradiction was removed by the subsequent discovery of radioactiv-ity, a heat source unrecognized by Kelvin, but a basic conflict in the perception ofthe behavior of systems through Time remained. The Entropy Law also contra-dicted (though not explicitly until the next century) the conservation of inforrna-tion implied in uniformitarianism.

Uniformitarianism leads to a view of system behavior through time as progres-sive, developmental. The Entropy Law portrays the same behavior as a downhillslide toward inevitable decay. The paradox of biological evolution, where so-called"self-organizing systems" appear to behave through Time in a manner contrary tothe rule of the Entropy Law, was resolved by the modern discoveries of cellularbiochemistry. At the level of the living cell, it has been demonstrated that the ther-modynamic price of structural evolution is paid in full (Monod, 1971). We mustnow view T as a "truer" concept of time than t, at least in the sense of providing amore realistic context for the study of real-world systems. Uniformitarianism and tare still useful in studying some aspects of system behavior, but are less compre-hensive explanatory principles than T.

Modern thermodynamic, quantum, and relativity theories have led to a dramati-cally different view of reality from that of classical science. Yet the modern scienti-fic revolution is more evident in the natural sciences than in the social sciences,which still seem largely based on the concepts of classical mechanics, includingNewtonian time. That quantum and relativity theory have affected social science solittle may not be very surprising since they deal with aspects of reality far removedfrom the mainstream of our ordinary human experience. But the same is not true ofthermodynamics.

The Entropy Law is a central feature of the world of our ordinary consciousnessand experience, as Georgescu-Roegen (1971, p. 10) has observed:

We know that people can live even if deprived of sight, or of hearing, or of the sense of smell ortaste. But we know of no one able to live without the feeling which under various forms regu-lates the activities directly related with the maintenance of the physical organisms. In the caseof a mammal this feeling includes not only the sensations of cold and warm but also the pangsof hunger and the contentment after a meal, the feeling of being tired and that of being rested,and many others of the same kind. Things are not stretched, therefore, if one argues that theentropic feeling, in its conscious and unconscious manifestations, is the fundamental aspect oflife from amoeba to man.

In spite of (and perhaps because of) the ubiquitous impact of the Entropy Law onhuman experience, we commonly ignore or deny its existence. Tyro inventors con-

L.J. Perelman, Time in system dynamics 79

tinually apply for patents on perpetual motion devices. Prestigious economists insistthere are no physical limits to material growth. Politicians avoid mentioning declin-ing resource quality as a cause of monetary inflation.

Our social sciences generally are undergoing a crisis of credibility, partly as aconsequence of their failure to accommodate the reality of the Entropy Law. Whyhas this happened? A major part of the reason may be the ambiguous time dimen-sion of our systems studies.

Social scientists embracing uniformitarianism need not feel imprisoned by thepast nor, more important, disturbed by a sense of responsibility to the future. Whenall temporal boundaries arc arbitrary, one can draw them as close to one's imme-diate interests as desired. The problems of the past are dead, and the problems ofthe future can take care of themselves. We have a kind of intergenerational liber-tarianism at work. Once the entropic concept of irrevocability is discarded, allgenerations are created equal; each has an equal right and responsibility to maxi-mize its own welfare.

Also, the two concepts of time lead to different approaches to the study and useof history in social analysis. In the uniformitarian view, historical and contempo-rary social processes are homologous. Thus one can and presumably should followSantayana's advice and apply the lessons of history exactly to today's problems. Inthe thermodynamic view, history is evolutionary, and all events are essentiallyunprecendented. The relationship of past system behavior to present and futurebehavior is metaphorical but not homologous.

Once one abandons uniformitarianism and embraces the thermodynamicconcept of Time, things become messy and sometimes painful. The cause of acurrent problem may lie in the distant past, and therefore may be insoluble bycurrent actions. The solution to a problem within one future time horizon maycontain the seeds of catastrophe in a longer time horizon. Conversely, a near-termdisaster may be the best hope for the long-term future. The study of history is nolonger a search for precedents but a quest for understanding the causal relationshipsbetween system structure and behavior.

System dynamics is intensely affected by the ambiguity of the scientific concep-tion of time. Philosophically, the methodology is highly thermodynamic. The non-uniformitarian perspective discussed in the preceding paragraphs is common to thebasic literature of system dynamics. But the treatment of time in the programmingof system dynamics models is strictly Newtonian. This contradiction may be aserious flaw or a creative synthesis. Certainly some of the important controversiesabout system dynamics are directly related to its ambiguous time concept.

One of these issues, and perhaps the most important. is the matter of irreversibil-ity. System dynamics models at least conceptually can be run backwards toproduce exactly the same trajectory in reverse. (In practice, round-off error wouldcause some divergence, but a sufficiently large computer and sufficiently small timeincrement, dt, usually could make this effect insignificant.] The problem is that thebehavior so described is patently unrealistic from a thermodynamic perspective (the

80 L.J. Perelman, Time ill system dynamics

spilled milk flowing back into the bottle) and if pressed far enough will generateimpossible historical events (the milk bottle eventually forcing its contents backinto the cow). This kind of reverse projection was used by Cole and others of theSussex group to attack the validity of the WORLD 2 and WORLD 3 models(F orrester , 1971; Meadows et al., 1972; Cole et al., 1973, p. 113). Meadows and hisassociates responded by arguing that running the models backwards simply violatedthe rules of the methodology, ignored attributes of the computation process, andtherefore proved nothing (Cole et al., 1973, .p, 221).

In exploring the same example, Wils and Senge (1973) tied the thermodynamicparadox of reverse projection to the properties of "forward convergent" models;that is, models in which certain relationships among state variables converge to anequilibrium value which is essentially independent of initial conditions. Relatingreverse projection to the information theory version of the Entropy Law, Wils andSenge observed:

... The convergence of state trajectories is an en tropic process in the following sense. Givenany finite amount of uncertainty in the precise system state, as the trajectories converge, ourability to know where the system came from diminishes. This occurs because the number ofdifferent trajectories which fall within our range of uncertainty increases with time. Conversely,when time runs backwards, the second law of thermodynamics predicts that information willalways increase. If a forward convergent system is run backwards, our knowledge of the pasthistory of the system increases as the trajectories diverge. As time moves backwards past historybecomes less ambiguous because, for any finite range of uncertainty in the current state, thenumber of possible state trajectories within that range decreases.

In other words, even when ordinary computational noise is eliminated, reverseprojection of models which are forward convergent (a common but not essentialfeature) ultimately must force the system state description beyond the limits ofirreducible uncertainty because of the logic of the Entropy Law. Reverse projectioninevitably requires the creation of new information, a process of which no com-puter is capable. This is precisely the error introduced by the uniformitarian hypo-thesis, which assumes conservation of information throughout all states of thesystem. At least in forward convergent models, the conceptual error of using New-tonian time generally will not be evident in forward projections; while the totalinformation content actually is conserved, the growing surplus of informationusually has no obvious effect on the output of the model. On the other hand, theinformation deficit implied by reverse projection ultimately becomes egregious asthe projection is extended before t = 0, that is, as the computer begins to addinformation to what the modeler supplied.

But the problem of reversibility or irreversibility runs deeper. Many of the criticsof the WORLD models have observed that system dynamics does not authenticallyrepresent social behavior because the model systems do not "learn." That is, thesystems do not alter their own structure in response to past experience or in antici-pation of future problems. (The critics presume real social systems do this; pessi-

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mists might debate it, but the view is at least plausible.) Even when the modeledsystems pass points of crisis or catastrophe, they continue to carry out the same setof policies established initially. Because the model has "learned" nothing in thecourse of its run, it can be run backwards and will unwind the identical sequence ofevents in reverse. (This is disregarding the errors mentioned above.) In simple terms,system dynamics models change, but they do not evolve. (An excellent discussionof this distinction is in Watzlawick et al., 1974.)

Partly in response to this problem, Mesarovic and Pestel (1974) developed analternative methodology for studying the Club of Rome's "problematiquehumaine." Using more complicated coding and man-machine interaction, theirmethodology permitted simulation of adaptive social learning and evolutionary,irreversible types of system change.

Making system dynamics models irreversible is not intrinsically difficult. Severalmethodological tactics could achieve this, starting with the simple expedient ofaltering the DYNAMO compiler to prevent model reversal. But the problem may bevery thorny to solve at its root, which is that the method uses reversible, mechani-cal time to describe the behavior of evolutionary, thermodynamic systems. Theproblem may be impossible to solve without radically transforming the basicmethodology, and very possibly there by losing the method's elegant simplicity. Thisis illustrated by the efforts of Mesarovic and Pestel. Although their modelingmethod may refelct more closely the evolutionary behavior of thermodynamicsystems, it does so at the cost of an extreme complexity which makes their modelinscru table to those not directly involved in its construction, and therefore makesreplication and counteranalysis by other researchers extremely difficult. Signifi-cantly, the policy implications of their "problernatique " study were virtuallyidentical to those derived from the simpler and more accessible WORLD models ofForrester and Meadows. A practical approach to the problem of reversibility maybe greater incorporation of gaming and Monte Carlo methods in system dynamicssimulations. The "Debug" mode of DYNAMO also could be used to simulate someof the features of social learning. System dynamics models can be constructed sothat behavioral goals are a function of the system's past history. This tactic doesnot fully capture the stochastic quality of evolutionary processes, but still mayoffer a more authentic simula,tion of social system behavior. In this case theproblem becomes one of having an adequate hypothesis about the nature of sociallearning; getting a group of social scientists to agree on a proper hypothesis couldbe difficult.

Perhaps these and other techniques can be combined to develop systemdynamics models which authentically simulate the irreversible processes of socialevolution. However, the simplicity and usefulness of system dynamics should beprotected. We should keep in mind that just because the real world is irreversible,this does not mean that an irreversible model is necessarily better than a reversibleone. The real world is irreversible because of the novelty introduced by spontane-ous transformations, purchased at the ':OSt of growing entropy. Since novelty

82 L.J. Perelman, Time in system dynamics

necessarily cannot be predicted, no model ever can simulate true system evolution.The utility of system dynamics probably will be improved less by irreversiblemodels than by practitioners sensitive to the ambiguous concept of time.

3. Time boundaries

The definition of problems and solutions in any system is dependent on thestipulation of the system's boundary. This is evidently so in the case of thegeographical or topological boundary of the system. No less is it so in the case ofthe temporal boundary of a dynamic system. No scientist, engineer, or otherproblem-solver aspires to solve all of the universe's problems simultaneously. Wedraw boundaries around the systems that interest us in order to exclude a host ofproblems and focus our attention on a few or just one. We get away with this exclu-sion pretty well in the spatial dimensions, with time held constant. Most of thesystems that concern us are approximately isolated, at least to the degree that wecan specify exogenous inputs and disregard outputs of the system that go "else-where." The temporal boundary is more troubling; so much so that I sense most ofus have difficulty recognizing, much less talking about it.

The question of choosing temporal boundaries exists on two levels. At the super-ficial level, it is a rather dry, methodological issue: Over what time span shall thebehavior of a particular system be studied? But this question also has meaning at amore profound level, leading us to ask: What is the role of the systems analyst?How does he relate to the systems he studies'? Of course, the mere existence of afield like system dynamics .as a profession, the fact of grants and contracts andconsultations with decision-makers, implicitly raises such philosophical issues. But,for me, the simple act of defining temporal boundaries uniquely evokes the ethical,metaphysical, and social roots of the methodology.

The existing literature of system dynamics contains very little discussion of themethodological issue of how one chooses the temporal boundary of a system to bemodeled. The lack of commentary on the selection of temporal boundaries may beindicative of one of two things. Either the step is so trivial in the modeling process,it warrants little comment. Or the question entails psychologically disturbing factorswhich repel modelers from coming to grips with it. One of the few comments onthe choice of temporal boundaries is this by Meadows et al. (1974, p. 90):

The time horizon of a model is the period over which the modeler is interested in the system'sbehavior. That period usually corresponds either to the time required for the system to mani-fest a behavior mode of interest or the time required for the system to respond fully to someproposed new set of policies.

What this suggests is that the selection of temporal boundary is as arbitrary as theselection of spatial boundary. But the more we think about this, the more we mustrealize it is not so.

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The definition of problems and solutions is necessarily an anthropocentricphenomenon. There are no problems in nature. Only humans (or whatever is theuniversal equivalent of verbally conscious, intelligent beings) have problems andseek to solve them. This already makes the temporal boundary troublesome. Whenwe draw our system boundaries in space, we are comforted by two things. We candraw the spatial boundary so that it includes what concerns us and excludes whatdoes not concern us. The definitions of the system and the problem are completelya function of the problem-solver's interest. And in a strong epistemological sense,we can know what our interests are. Because we can know what concerns us, wecan proceed in some rational way to draw a system boundary which reflects ourconcern. The second thing that comforts us is that, as problem-solvers, we havemany contemporaries, and among them are many who will disagree with us. Withina shared paradigm of values and concerns, debate and criticism regarding problemdefinition, spatial boundaries, and problem-solving procedures help each researcherto find solutions to the problems of general interest. Our contemporaries workingin alternative paradigms assuage us with the knowledge that important problems wemay have excluded from our system of interest are being attacked by someone else.

In the time dimension we are on less secure ground. There is no way to define atime horizon for nonmechanical systems without raising questions about origin,destiny, purpose, and value. As soon as we take the question of defining the timehorizon of a system seriously, we are plunged into ethics and metaphysics; andnothing could make a problem-solver who fancies himself "pragmatic" moreuncomfortable.

3.1. Ethics and metaphysics of the time dimension

When we define the temporal horizons of a system, we get no disagreemcn t fromeither the dead or the unborn. Among both our precursors and our posterity, thosewho share our particular paradigm have no ability to correct our errors, and thosewhose concerns are different or contrary have no recourse in the present. Few cul-tures stress responsibility to the past; we speak facetiously about our actionsmaking our ancestors "turn over in their graves," but we don't take the moral impli-cations of this very seriously. The ethical dilemma of our relationship to posterity ismore serious. Our posterity is totally at our mercy; our every act may influencetheir fate. At the same time, it is their condition that imbues our own existencewith purpose. The choice of the future temporal boundary of any nonmechanicalsystem is inevitably an ethical decision.

We know the assumption that a system is spatially isolated breaks down at somelevel of precision, but it is a safe assumption for most practical purposes. Theassumption that a system is temporally isolated is far more risky. The system mustbe excised from both its ancestry and its posterity. In the context of Newtoniantime and causation this may be prudent. but in thermodynamic, evolutionary timeand causation, it is perilous.

84 L.J. Perelman, Time in system dynamics

3.2. The case of "limits to growth"

One of the motives behind the research for the Club of Rome by Forrester andMeadows (Forrester, 1971; D.H. Meadows et al., 1972) was the fact that conven-tional econometric models either studied static situations, or made projections onlya few months or years into the future. Within the time horizon of one to five years,the macro-problem of "limits to growth" simply does not appear. Within the 200-year timespan Forrester and Meadows elected to study, limits to growth becameevident. Many of the critics of their work picked on this issue. They argued thatsince conventional econometric models were not very accurate over a span of even afew months, the projections of Forrester and Meadows could not possibly beaccurate over a century in advance. The counterargument was that conventionaleconomics is too short-sighted; by discounting the future, it reduces the presentvalue of the economic welfare of even our grandchildren to virtually nothing; and itdisregards the long-term destructive consequences of short-term economic"progress." In a five-year time horizon, limits to growth are invisible; in a 200-yeartime horizon, they become evident. But in a longer time horizon, limits to growthmay seem to disappear again. If one assesses the future prospects of humankind inthe time frame of the expected lifetime of our planet and solar system (anotherseveral billion years), "this sort of time scale makes fears about the long-termeffects of a nuclear war or of other disasters seem rather ridiculous" (Berry, 1974,p. 33). Even in a lO,OOO-year perspective, limits to growth do not seem to be much

. of a problem. Within the next ten millenia, humankind conceivably will haveacquired the ability to colonize most of this solar system, and perhaps will havediscovered the means for rapid interstellar travel. Alternatively, if one dismisses thepossibility of space colonization, the earth for the remainder of its expected life-time must be considered closed, save for the flux of solar energy. The implicationof the Entropy Law then becomes inescapable: The pet political platform of neo-Malthusians, the establishment of J.S. Mills's "stationary state," is physicallyimpossible. The assumption of a closed earth permits only declining futures forhumankind and the only choice before us is between rapid decline and slow decline(see Georgescu-Roegen , 1975).

Whatever the prospects may be for an extraterrestrial economy, simply thinkingabout the problem of growth limits in a time horizon much longer than a centurycompels us to consider a crucial question: If we were to succeed in establishing aglobal sta tionary state, then what'?

The argument for demographic and economic equilibrium (the so-called neo-Malthusian argument) presumes a moral obligation of the present generation tofuture generations. What is the temporal boundary of such an obligation? Theanswer appears paradoxical. Are we responsible for all future generations or only alimited number? If we conserve nonrenewable resources for all future generations,they never are used at all. In a sense, the future thus "colonizes" the present. Butrestricting our responsibility to N generations leaves the N + 1 generation holding

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the bag. If we use our limited and irretrievable stores of low entropy at any nonzerorate, we ultimately must destroy them, depriving all future generations beyond theNth of their use. Thus the present "colonizes" the future. If some future generationis going to be impoverished as a result of our prodigality, why not the next one?Why not abandon all future welfare for the sake of present enjoyment? Any assess-ment of the problem of limits to growth in a much longer time horizon than severaldecades complicates and perhaps undermines the rationale for neo-Malthusian advo-cacy of a stationary state. Consideration of the very-long-term future thus threatensthe intellectual and political interests of many neo-Malthusians, including thisauthor. Not surprisingly, many of us feel motivated to dismiss the relevance of thevery long term.

But is our disregard for the very -long-term perspective intellectually sound?Meadows et al. present a two-point argument for omitting the distant future fromcurrent analyses. Specifically, in the development of the WORLD 3 model, it wasdecided not to extend the analysis beyond the year 2100 "because the validity ofmany important assumptions sor far into the future is questionable and becauseinformation about developments that might occur beyond the year 2100 couldhave little impact on present-day decisions." (D.L. Meadows et al., 1974, p. 9.)

The first reason given is technically true but is not a valid justification forabandoning consideration of the very long term. All our assumptions and beliefsabout the future are probabilistic in nature. To each we implicitly or explicitlyassign a probability, form zero to 100%, reflecting our confidence in its provingcorrect. Our confidence in any assumption about the future generally decreases aswe probe further ahead in Time. Undeniably, many if not most of our assumptionsbecome highly questionable beyond the medium to long term. But it is importantto keep in mind that many assumptions retain a high level of our confidence wellinto the very long term. The assumption that our sun will explode in about 6 billionyears is one of these; the assumption that the Entropy Law will continue to bevalid in our sector of the universe is another. Modern physics, astronomy, biology,and geology have provided us with "information" about the most distant horizonsof Time in which we have significant if not perfect confidence.

This kind of knowledge is germane to many current economic, political, andpersonal decisions. Energy policies are formulated on the basis of knowledge aboutthe very -long-term life cycles of fossil fuels or decay times of radioactive materials.Industrial projects are delayed or blocked in consideration of the evolutionarysignificance of endangered species or unique geological formations. Very-long-termpersisten t poUution and climatological trends are matters of serious public interest.Men send messages by radio or spececraft to unknown civilizations many light yearsaway.

The second of these reasons, that very-long-term studies have little impact, seemsfalse to me and I believe few futurists would accept it as valid. A widely respectedbook by Polak (1973) argues that the "image of the future" has a profoundinfluence on a society's day-to-day behavior. OUf ordinary human experience

86 L.J. Perelman, Time in system dynamics

supports this view. The existence of organized religions demonstrates how relevantconceptions of the distant future are to contemporary human decisions. Theevidence is overwhelming that our beliefs about the future profoundly affect ourcurrent actions, regardless of how rational or irrational, probable or improbable ourbeliefs may be. Even the belief that the very-long-term future is inscrutable orirrelevant to present decisions has a significant impact.

Students of system dynamics must recognize that the stipulation of temporalboundaries is not an arbitrary or trivial act. The choice of time horizons is anexpression of an intimate, personal image of the future. The choice inevitably raisesthe dilemma of the individual researcher's relationship and responsibility to futuregenerations. There is no single or simple solution to this dilemma. However, aminimal approach for the purposes of system dynamics would be to establish a setof ethical criteria for defining "reasonable" time constants in model construction.At least modelers should make their personal values and judgment of long-termresponsibility explicit.

4. Time in practice

Were system dynamics purely an abstract, self-contained intellectual activity, thetemporal boundary issue would be of little importance. Because system dynamics isalso a political process (a process for creating policies), temporal boundaries are cru-cial. Current political forces assure some "balance of power" in the spatial!structural dimensions of modeling. But the temporal dimension is regulated only bythe time horizons of current political incentive structures. System dynamics' verytlexibility increases the burden on its practitioners. Other policy research methodshave intrinsic obstacles to employing very large (or very small) time constants,making temporal boundary questions largely moot. Since system dynamics modelscan incorporate time constants of virtually any size, questions of the scope andmeaning of time are unavoidable, even if they be answered by default.

The system dynamics researcher does not ply his trade in a vacuum. On thecontrary, professional system dynamicists are overwhelmingly concerned withinfluencing social policy. This being so, applying a mathematical scalpel to the lineof Time and carving out an interval of "interest" is also defining a zone of responsi-bility. Since there is no way to receive feedback from either the past or future, thisis a double responsibility because each analyst must enforce it himself.

Many of us deprecate the conventional econometrician's habit of discounting thefuture, and of dealing with a time horizon of a few months or at most a couple ofdecades. But who is to say that a time horizon of 50, 100, or 300 years is not"shortsighted"? Perhaps we should be considering time constants of 1,000, or10,000, or a billion years. Intuitively, we feel this is impracticable or incorrect. Butthere is now no methodological justification for omitting very-long-term considera-tions from the development of current policies. Such a justification would be, in

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effect, an ergodic theory of history: Beyond a certain span of time, no differencemakes any difference. If we want to lean on such a theory, Forrester's philosophyof system dynamics seems to require that it be made explicit. So far, this has notbeen done.

Perhaps the main reason for the tendency to dismiss very-long-term behaviormodes from models is not because the resulting policies would make no differencein the long run but rather that they would make no difference in the short run.That is, system dynamicists are probably disinclined to deal with problems in morethan a 50- to 100-year time horizon because the grant/ contract/ consulting marketoffers no incentive for doing so. The aftermath of the WORLD 2 and WORLD 3efforts indicates little effective demand for the services of those who want to solveeven the next century's crises. As a rule of thumb, we can say that the lucrativenessof policy research as a vocation is inversely proportional to the largest timeconstant of the problems attacked. Consultants who can increase a corporation'sprofits in the next quarter are likely to acquire a more prodigious income thanthose who, perhaps, can increase the survival chances of the corporation president'sgrandchildren.

System dynamics must be addressed primarily as a practical tool of policymanagement, and as part of a very imperfect and very human political process. Themajor concern of system dynamics practitioners today is the interface betweentheory and practice. Inspired by Forrester, students of system dynamics have littleinterest in model-building as an academic enterprise but urgently want the method'sproducts to influence the policy management process. Bridging the gap betweentheory and practice is a matter of over-riding interest.

Concepts and boundaries of time can be viewed as an extremely abstract, almostethereal subject. Yet the meaning and treatment of time is an important pragmaticissue in the application of system dynamics in practice. In fact, the commonproblems related to time that practitioners encounter in using system dynamics areso mundane that they may be difficult to connect to the theoretical issues discussedabove.

For example, not long ago I recommended to the director of the state agency inwhich I was employed that we do a fairly limited system dynamics study of severallong-term trends relevant to our area of responsibility. My proposal was based onmy desire to adapt a model already developed as an academic exercise (at Dart-mouth) in order to bring it into the policy-making process. I felt that the model hadproduced some useful insights and should be applied to decision-making in ourstate. My director's response was: Since no one can predict what will happen in thenext 30 years, there was no reason to spend the taxpayers' dollars on studying ourpolicies over such a long time period.

The simplistic but common currency of the policy management process is goodand bad results, and these are always a function of Time. Decision-makers in realorganizations define their problems in terms of good and bad outcomes in theframework of their own peculiar short and long-term objectives. Within this world

88 L.J. Perelman, Time in system dynamics

of mundane choices, the temporal quality and structure of a model significantlydetermines the kind of advice the decision-maker will derive from it. This is a prac-tical and ethical problem for the policy analyst and planner. One of my previousemployers sought analysis and recommendations on alternative actions he couldand had to take. As a staff analyst, I believed policy options should be evaluated ina time frame of several decades, at least. My director (an experienced and respectedadministrator) chose to evaluate them in a time frame of several months - particu-larly the time from the present to the next election. His view was not cynical, butsimply practical. Bridging this kind of gap is vital to the success of system dynamicsin affecting political decisions. There is no simple solution to this problem but Ibelieve better understanding of the nature of the architecture of Time in the studyof system dynamics would be helpful.

5. Conclusion

Studied seriously, the time dimension of system dynamics raises many questionsabout the meaning of models, about their role in the policy management process,and about the profession of the modeler. Practitioners and theorists of the fieldneed to pursue these questions more deeply and thoroughly than I have been ableto here. Our current understanding of time in system dynamics is sharply dividedbetween the pragmatic knowledge of modelers, analysts, and policy makers and thesubtle theoretical knowledge of philosophers, mathematicians, physicists, and otherscholars who have specialized in the study of time. Both sources must be tapped toimprove the treatment of time in system dynamics as it is applied in practice.

Meanwhile, we should recognize that the conception of time and the choice oftemporal boundaries in modeling dynamic systems are methodological expressionsof the modeler's intimate image of the future. Such elements of the modelingprocess should not be treated lightly; these images of the future have a profoundinfluence on personal and social life. Students of the field should be encouraged toapproach the time dimension of system dynamics with sensitivity, reflection, andsome caution.

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