4th International Conference on Integrating GIS and Environmental Modeling (GIS/EM4):
Problems, Prospects and Research Needs. Banff, Alberta, Canada, September 2 - 8, 2000.

The geography of time and ignorance

Dynamics and uncertainty in integrated urban-environmental process models

GIS/EM4

Helen Couclelis
XiaoHang Liu

Abstract

Interest in integrated models of social and environmental processes is growing rapidly. Most of the models in that category involve coupling together individual components representing relevant human and physical phenomena and processes. However, integrating subsystem models developed from within different disciplinary perspectives and modeling traditions may pose many new challenges. This paper examines some issues of potential logical incompatibility raised by the very different underlying conceptualizations of time and uncertainty in models representing relevant aspects of urban, socioeconomic and natural systems. We begin with a discussion of two radically different conceptions of time (Newtonian time and ‘real’ time), and the ensuing notion of ignorance, which is broader and deeper than uncertainty. The significance of these notions for model prediction is then examined. We arrive at the surprising conclusion that models can predict the future only to the extent that they are not about the future. Next, we propose a three-part typology of system descriptions and discuss to what extent prediction is possible within each of them. We refine that typology into three, qualitatively different generic models that can be represented within a temporal GIS. The concluding discussion speculates on the implications of that framework for coupling together models of different types and points to some future research in this area.

Keywords

Model prediction, integrated models, Newtonian time, real time, system description levels, temporal GIS

Introduction

We see the world as an inextricable mix of pattern and noise. Pattern consists of what is typical, stable, recurring, repeatable, predictable. The noise is our ignorance. We have several words for it: surprising, atypical, uncharacteristic, unexpected, unpredictable, counter-intuitive, mind-boggling, miraculous. There is a temporal dimension to our ignorance in that, standing at the ‘now’ point we generally see the noise increase exponentially in both the directions of future and past (though the rates are usually different). There are exceptions to the rule but more on this later. The point is that time and ignorance are related through change: time brings change and change inevitably invalidates some of the things we know now.

For a small child everything that happens is a source of wonder. We envy the child’s blissful ignorance of how the world works. As we grow up experience, practical knowledge, formal education, intelligence, common sense and intuition all help us to see the patterns in the noise, and thus to lead lives, engage in activities and make future plans reasonably well sheltered from major surprises. We all have a good sense of why things happen the way they do in both the natural and the social world around us. Limiting the unexpected is largely a matter of grasping how human nature and social practices as well as how the laws of physics happen to work. Indeed, over relatively short periods social and institutional structures contribute stability on a par with some of the most reliable natural processes. (Each year tax time is as predictable as the arrival of spring.) Technology also heavily contributes to pattern by creating stable, predictable environments and conditions so that most roads can be expected to still be drivable in bad weather, most dams to still stand following a moderate quake, and most airlines to get us to the meeting in time to give our presentation.

When experience, knowledge, education, intelligence, common sense and intuition are not enough we need to use models. Models are meant to tease a little extra pattern out of the noise by weaving together things we already know or think we can guess into new things that expand the range of what is expected and predictable. This process of ignorance reduction through inferring unknown facts from known facts is called prediction, a term which, in the general sense, does not concern only the future but also the filling of gaps in knowledge about the present and the past. Prediction in the broad sense thus includes everything from strict logical inference to prophesy, through interpolation, extrapolation, retrodiction, prognosis, forecasting, speculation, gut feeling and educated guess. No matter what criterion is used, clearly not all predictions are born equal.

Prediction, or the reduction of ignorance, is the main reason why we build models. A major role of models is indeed to help reduce our ignorance about what is, was, and especially what will be. Models help infer consequences from known or conjectured facts based on the more stable known elements – the patterns – in the environment. There are many kinds of models just as there are many different kinds of predictions and model predictions vary greatly in usefulness and reliability from on type of model to the next. Assessing the predictive quality of individual models is a well-established research domain. This paper deals with some additional problems arising when we attempt to integrate two or more very different types of models, as is increasingly necessary in the environmental modeling field.

Following a more detailed problem statement, this paper examines the themes of time, ignorance and prediction as these may relate to environmental models. The next section develops a general conceptual framework for describing and classifying models (better: specifications of large complex systems) with qualitatively different predictive properties. We then refine that typology into three different generic conceptual models that can be represented within a temporal GIS. The concluding discussion speculates on the implications of that framework for coupling together models of different types and points to some future useful research in this area.

Problem statement

The prototypical example of the problem discussed in this paper would be the development of integrated urban-environmental models, where intentional human actions, socioeconomic forces, the structural and material properties of the built environment, and physical and biological processes interact with one another and must be represented within a single modeling framework. It is likely that models built on the basis of significantly different conceptual frameworks will produce unreliable results when coupled together, regardless of whether the coupling is loose or tight. While this may not be a problem when the models in question stem from cognate fields (say, a rainfall model feeding into a runoff model), issues of mutual incompatibility may arise when the disciplinary perspectives within which the component models have been developed are far apart. This can easily be the case when trying to integrate physical and socioeconomic (in particular urban) system models: for example, urban periphery growth and fire hazard models; traffic flow and toxic plume release models; or models of land use change and impacts on biota.

It is widely acknowledged that the reliability of model predictions can vary substantially from one domain to the next, with models of physical processes being in general the most reliable and models of human decisions and socioeconomic processes the least so. But is this just a matter of varying degrees of uncertainty in the predictions, or are there some fundamental qualitative differences in how models in different domains infer new facts from old? If the latter is the case, what special problems may arise when combining models whose rationales for prediction may differ significantly?

This paper takes a first step in answering the practical question of the do’s and don’ts of model coupling by highlighting some key qualitative differences among three very general classes of predictive models. These differences are largely based on underlying alternative conceptions of time, and so this is the topic we turn to next.

Background

"Real" time and 'real' ingorance

This paper borrows its title from a book by O'Driscoll and Rizzo (1985) entitled ‘The Economics of Time and Ignorance’. These authors examine the nature of prediction in economics and conclude that under no circumstances can prediction be complete because of the existence of ‘real’ time and ‘real’ ignorance. The authors contrast ‘real’ time to Newtonian time which is simply a framework for ordering events, a line against which events can be mapped as either points or intervals. A basic property of time-as-framework is that it does not in itself affect events. In other words, Newtonian time does not bring change, it only serves to register change as it happens. The passage of time is merely movement or position along the time line. Time is fully analogous to (Newtonian, absolute) space, and has the same three basic properties: homogeneity (all time-points are the same except for their position along the time line); continuous divisibility (implying that neighboring time points are independent of one another); and causal inertness (time is independent of its contents: in itself it causes nothing). Thus even in a dynamic model based on Newtonian time it is the present as we know it that is sent rolling along the time line. As the great economist F. H. Hahn observed, in such models “the future is merely the unfolding of a tapestry that exists now.” (Original emphasis, cited in O’Driscoll and Rizzo, p. 52).

‘Real’ time by contrast is characterized by the properties of dynamic continuity, heterogeneity, and causal efficacy. Dynamic continuity is based of the two aspects of memory and expectation. The meaning of each moment depends on its place in the context of what we remember of the past and expect for the future, just as in the experience of music each note can only be appreciated relative to those heard a moment before and those anticipated yet to come. More generally the timing of an event changes its nature to the extent that the unique context of other events within which it occurs affects its role in the determination of subsequent events. This is the case, for example, with economic agents whose response to events today depends on what they learned yesterday (which includes the responses of other agents to yesterday’s events), as well as on what they expect to happen tomorrow (which includes how they expect other agents will act). The property of heterogeneity of real time follows from dynamic continuity in that no two instants can be the same, each one relating to a different set of preceding and succeeding moments and their remembered or anticipated contents. This makes events in real time genuinely non-repeatable. Thus non-repeatability emerges from an event’s temporal ‘place value’ - its order in the flow of events. Causal efficacy is a further corollary of the above in that dynamic, heterogeneous time is causing actions and events to be different now from what they would have been under the same conditions some time earlier or later.

Real time is much closer to the psychological intuition of a dynamic flow of ever-changing experiences than to the traditional scientific view of a directed axis used as a framework for pegging events. Its significance is obvious for social science problems involving intentional agents such as the economics models discussed in O’Driscoll and Rizzo (1985). However what this conception of time addresses is not just human cognition and action but more generally historicity, or the claim that the nature of any phenomenon depends to some extent on its place within a process of historical development. A good example from natural science would be the significance of a particular mutation in an organism, which may or may not have an evolutionary value depending on the timing (and placing) of its appearance. The fact that it is impossible to predict future speciation in biology is further evidence that the processes of evolution work in real time.

In recent years research on time has blossomed within the geographic information science community (Langran 1992, Barrera et al.1991, Worboys 1995, Vasiliev 1997, Egenhofer and Golledge 1998). Several models of time have been proposed in the context of ‘temporal GIS’ beyond linear time: cyclic time, branching time, totally- and partially ordered time, valid and transaction time, clock- vs. event-driven time, etc. (see Frank 1998). Each of these brings some useful modification to the simple time-line of classical physics but the characteristic ‘causal inertness’ of Newtonian time remains: time is still the neutral framework against which independently unfolding events are projected, sorted and measured. None of these models (with the possible exception of some interpretations of branching time) approaches the dynamic, causally efficient conception of real time that O’Driscoll and Rizzo (1985) believe to be so important in economics and the social sciences in general. Indeed, a strong case can be made that human decisions are made at least in part in real time. But, as mentioned above, the notion of real time is not restricted to human phenomena and may affect modeling efforts in several domains of environmental science.

The bottom line is that anything happening in real time is genuinely unique and unpredictable and is thus associated with ‘real’, i.e. irreducible, uncertainty – or ignorance. The reason why we can predict at all is because the world appears to be a mix of typical, stable, recurring features and unique ones, and the first kind of features (the pattern in the noise) can be the stuff of formal or informal models. But ‘pattern’ is just a metaphor: what do we mean by that?

Prediction and time

To understand the significance of real (or, for that matter, Newtonian) time for model prediction we need to consider the epistemological roots of prediction itself. What justifies a belief that a statement about the future (or about an unknown aspect of the present or the past) may be reliable? The answer is to be sought in the concept of determination, defined by Bunge (1959, p.7) as ‘constant and unique connection between things and events’. Every model determines an answer or family of answers in that sense. But there are many different kinds of determination, each with different logical credentials. Bunge (1959) distinguishes at least eight, of which causal, statistical, and teleological determination are perhaps the best known.

The key point discussed in this section is that much of determination, and thus prediction, has little or nothing to do with time. Bunge (1959, p.312 ff) discusses several mechanisms used in science for the derivation or ‘prediction’ of unknown facts from known facts. Here is a slightly adapted list:

1. Logical inference includes deduction, induction and abduction.

2. Structural laws help predict new properties from the known properties of material or formal structures (e.g., properties of chemical elements can be deduced from their place in the periodic table).

3. Phenomenological laws predict phenomena on the basis of known constant associations (e.g., the laws of geometrical optics).

4. Functional laws infer functional properties of a system from knowledge of the functional role of the parts and their interconnections (e.g,wingless birds cannot fly).

5. Statistical laws help derive collective properties of classes of events from an analysis of such classes.

6. Mechanical laws extrapolate future (or past) states on the basis of known current states and relations (e.g, the Newtonian laws of universal gravitation).

A moment of thought will show that at least the first five of these inference principles are genuinely atemporal, and the sixth is the one that gave birth to Newtonian time. They all help postulate determinations or ‘constant and unique connections between things and events’ (or classes of events in the stochastic case) regardless of when these events may be happening. Reference to temporality is indirect: whenever, if/then, usually when… To turn these statements into temporal predictions, ordering and cross-referencing events along a linear continuum is all that is needed: before-after, in 1856, in 2010. They work backwards and forwards and for however long the particular kind of determination may be expected to hold. For them the future (and the past) is indeed ‘the unfolding of a tapestry that exists now’.

In addition to the above inference principles familiar from mainstream science there are other, more informal ones that contribute to the stability and continuity of everyday life: habits, customs, settings, rituals, social and institutional rules and practices – in short, the sources of the daily, weekly, and annual routines we all rely on. A large number of social science models can be built and fairly reliable predictions can be made about the future based on things people are doing now. Although not atemporal in the same sense as mechanical laws these principles too are of and about the present.

The surprising implication is this: models can predict the future to the extent that they are not about the future. We can indeed predict many aspects of what is to come because events are constrained by several different kinds of determination that are in themselves outside of time. Some of these constraints are empirical: the life expectancy of a particular population, the rate of growth of a tree species, the time it takes to plan and build a major freeway. The range of variation of these quantities may be assumed to remain fixed for the foreseeable future. Other constraints are systemic or formal: once a system has been defined in some particular way, at some particular level of abstraction, all kinds of conceivable predictions about its domain of application become thereby impossible.

Which brings us back to ‘real’ time: in real time, time itself – qua temporal position - is a determinant of events. Our predictive devices, based as they are on either strict but atemporal forms of determination (or perhaps on more or less reliable speculations about what ‘usually’, ‘lately’, or ‘currently’ may be the case), can say nothing about possibilities that are a function of futures not yet realized or even thought of. But is real time relevant to integrated environmental modeling? Since real time presupposes an agent capable of anticipation and memory, the answer is positive to the extent that such agents have a place in environmental systems. The next section generalizes the notion of an agent acting in real time and places it at the center of a general typology of integrated environmental models.

A typology of integrated environmental models

A characteristic of very large, complex systems, as environmental systems usually are, is that they admit of several different partial descriptions (Casti 1989). More specifically, they admit of an ordered sequence of descriptions along a formal hierarchy of systems specifications of increasing functional detail (Zeigler et al. 2000). Along similar lines Couclelis (1984) distinguishes three levels of description in very large systems (VLS) on the basis of how each of them relates to the rest of the world (the model’s environment). The latter of course includes the part of the VLS that is not explicitly modeled at that level. The key criterion for the classification is the absence, explicit consideration, or implicit incorporation in the description of a regulator. The regulator is a special subsystem that is either coupled or tightly integrated with the system of interest and which interacts with that system according to goals and rules of action of its own, causing forms of behavior not deducible from the model’s internal structure. In more contemporary terms the regulator could be an intentional agent acting on the system according to principles that may be known or unknown to the observer.

A mechanical example of a system with an explicit regulator (Type II) would be a model of a device controlled by a thermostat (a reactive agent). In the environmental domain, this could be the model of a forest managed by an agency whose goals (e.g., optimize logging income while preserving ecological health) can be explicitly modeled. Note that the same managed forest could also be viewed as a Type I system (no regulator), with the intentional interventions of the managing agency being perhaps captured in some statistical relationship between tree birth, growth and depletion. A Type III description by contrast may attempt to model the group interactions among forest managers resulting in more flexible goals and policies contingent upon how each of the key participants may be viewing the broader context of these decisions at each point in time. This would be analogous to the discussion of the behavior of economic agents (who are cognitive agents) in O’Driscoll and Rizzo (1985), and all of these authors’ arguments pointing towards unique events occurring in real time would be applicable here also.

Figure 1. The three types of system description (Adapted from Couclelis 1984, p. 334)

With respect to prediction we may summarize the key properties of these three types (or levels) of system descriptions very simply as follows. System behavior described as Type I is predictable in deterministic or probabilistic terms; system behavior described as Type II is also predictable deterministically or probabilistically if the response rules (ends and means) of the regulator are known; system behavior described as Type III is for the most part not predictable, though the detailed structure of the model may be valuable in many other respects (e.g., for running ‘what if’ scenarios). These three types of formulations have qualitative different predictive properties due to different prior structures. Couclelis (1984) calls prior structure that aspect of a model that is responsible for its predictive ability. The prior structure captures the ‘pattern’ in the system modeled and everything that is not part of it is by definition unpredictable noise. It is similar to Bunge’s (1959) notion of structural determination mentioned earlier except that here the structure is seen to belong to the description rather than to the real system studied. Thus different descriptions of the same real system will have different prior structures. The concept of structural prior is fully developed in Couclelis (1984) and will not be elaborated here.

For the purposes of this paper, prior structure may best be viewed as the union of the diverse sets of constraints, both empirical and formal, that limit what can possibly be observed in any particular domain at some particular level of analysis. It consists of two parts: a ‘historical’ prior that incorporates all the empirical information about factual aspects of the system - natural, biological, social, cultural and institutional - that may be assumed to remain basically the same at the level of resolution of the model and over the period examined. The second class of constraints that make up a model’s prior structure is the ‘structural’ prior. This reflects the non-empirical elements that go into the construction of a model, such as the properties of the mathematical and logical tools used and the conventions of measurement assumed in its formulation. Though the notion of structural prior is grounded in modern model theory and information theory, the idea that the properties of our formal and observational tools have a lot to do with how we see the world has been used much earlier in theoretical physics to derive fundamental properties of the physical world (or of our knowledge of it). In the words of the great physicist Sir Arthur Eddington (1974), the size of the mesh of our fishing net has quite a bit to do with the kind of fish we can expect to catch. Among other things, the structural prior explains how very similar model structures are sometimes developed about phenomena in very different domains (e.g., equilibrium models or chaos models). A more extensive discussion of system modeling principles can be found in Couclelis (2000).

Towards implementing the integrated model typology

The model outlined here is an extension of the one presented in Allen et al. (1995). These authors describe a generic conceptual model for representing causal links within a temporal GIS using an extended Entity-Relationship formalism. The entities included in the model are: Objects and their States, Events, Agents, and Conditions. The relationships are: Produces, Is-Part-Of, Conditions. Time is represented through special symbols indicating that a given entity evolves (in attributes, geometry, location, or existence status). The model is hierarchical and allows the representation of uncertainty. Its appeal in the context of the present discussion is its simplicity but especially the fact that its elements map in a fairly straightforward manner onto the key concepts discussed in this paper. In particular the element ‘Agent’, defined by Allen et al. (1995) as an intentional entity whose actions cause, but are not caused by events, is functionally equivalent (anthropomorphism aside) to the notion of an explicit system regulator discussed above.

Some modifications are necessary in order to adapt that model to the typology described in the previous section. First and obviously, not one but three generic structures are needed to represent to the three types of systems distinguished earlier: system with no regulator, with external regulator, with internal regulator. Second, the restriction of determination to causal links and causal production is insufficient for the representation of environmental models where as we saw, many kinds of determination beyond causality are equally relevant. Third, in order to accommodate a concept of real time, time-dependence should not be restricted to entities but also apply to relations (relations too can change in a system evolving in real time). Fourth, event and other agents can affect the behavior of agents (Type III level description). Fifth, in keeping with the notion of prior structure, the entity type ‘conditions’ will be here interpreted as ‘constraints’. The modified version of the model proposed by Allen et al. (1995) is schematically illustrated in Figure 2.

Figure 2. Conceptual data models for Type I, II and III system descriptions.

Conclusions and future research

This paper explored the epistemological basis of prediction in complex environmental models. It argued that qualitative differences in predictive ability among different types of models are largely based on differences in the implicit or explicit treatment of time in these models. The surprising conclusion is that models can predict the future only to the extent that they are not about the future but about atemporal forms of determination that can be expected to hold indefinitely within the model’s time horizon. In particular, models that implicitly or explicitly include agents capable of memory and anticipation entail the conception of ‘real time’ in which prediction is genuinely impossible to the extent that the flow of events affects the agents’ knowledge and behavior rules. Three classes of system description were proposed based on the absence or presence of a fixed or evolving regulator or agent, and these were further elaborated as three generic types of data models for implementation in a temporal GIS. The significance of these qualitative differences in coupling together models specified at different levels was raised as a potentially important issue but was not further pursued in this paper.

The paper is just a first cut into these difficult problems. Future work along these lines should include:

1. Formalizing the conceptual model proposed here and developing a language for mapping actual environmental models and sub-models into each of the three types of system descriptions. The formal hierarchy of system specifications described in Zeigler at al. (2000) appears a very promising source of tools and insights for this task.

2. Implementing the model in some user-friendly model language and developing a graphic interface compatible with widely used GIS software to assist modelers in coupling together models with qualitatively different predictive properties.

3. Integrating space explicitly into the model. Indeed, geographers have proposed several conceptual models of space that could be interpreted as ‘real space’ in analogy with ‘real time’. In a model of real space locations would have different properties depending on the unique context of other locations with which each of them interacts. Geo-Algebra, a formal modeling language proposed by Takeyama and Couclelis (1997) appears capable of handling good approximations of a concept of real space as well as real time.

These are our objectives at this time. But the authors have no good model to predict in what specific directions future research – undoubtedly influenced by the events and interactions at the Banff conference- might actually evolve. The future will show: ‘Que sera, sera’.

Ackowledgements

References used

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Authors

Helen Couclelis, Professor, Department of Geography
University of California, Santa Barbara, CA 93106
Email:cook@geog.ucsb.edu, Tel: +1-805-893-2196, Fax: +1-805-893-3146.

XiaoHang Liu, Graduate Student Researcher, Department of Geography
University of California, Santa Barbara, CA 93106
Email: xhliu@geog.ucsb.edu, Tel: +1-805-893-8652, Fax: +1-805-893-8617.