2.1 The Nature of Modeling
2.2 Surprise-generating mechanism

4.1 The new semantics of urban modeling
4.2 The new syntax of urban modeling

John L. Casti, who is widely regarded as one of the most prolific mathematicians and science writers in the world, has discussed in several of his recent books the fundamental nature of modeling and the reasons why our models sometimes fail (Casti, 1991; 1994; 1997). According to Casti (1994), surprise occurs when the expected results of our models do not match the reality we are trying to predict. The science of modeling is actually a science of surprise. To understand modeling, we must understand the mechanisms that contribute to the generation of surprise and find out how to deal with them. Essentially, Casti's science of surprise consists of the following two components:

2.1. The nature of modeling:

According to Casti (1994), the essence of modeling is a two-way mapping process: to encode certain characterizations (observables) in a natural (real world) system (N) into symbols and strings (theorems) in a formal (either logical or mathematical) system (F), and then to decode the modeling results from the formal system into words meaningful to the observables in the real world system. Casti (1997) further argues that the key to understanding this process of formalization is to recognize that all notions of meaning (semantics) reside in the real world system N. In contrast, F consists of mere abstract symbols and the rules (syntax) for how these symbols can be manipulated to form new strings. The meaning of these symbols are extracted by decoding the strings back into N. The semantics of N is often rendered in induction and causation whereas the syntax of system F favors deduction and inferences. The goal of any modeling exercises is to find the most essential characterizations of system N first, and then to search for the most truthful representation of these characterizations in system F. Modeling is not successful if we fail to interpret the meaning of system F in the context of system N.

2.2 Surprise-generating mechanism:

Surprise occurs when the results of F do not match those observables in system N. Surprise is the gap between our assumptions and expectations about the world and the way those events actually turn out. In essence, surprises are the end result of predications that fail. In an attempt to answer the challenging question as to why models fail, Casti summarized five main reasons for surprises by synthesizing the latest development in a vast array of disciplines such as quantum physics, computer science, biology, and mathematics. Although they are not mutually exclusive, the following five reasons are what Casti called the surprise-generating mechanism in complex systems:

Unpredictability: We are living in a world of essentially inconsistent phenomena, and long term prediction is impossible for complex systems. Chance must be treated as an actual cause for many things occurring in the real world..

Instability (the butterfly effect): Small changes in a system may cause large and catastrophic effects. These small changes are also implied throughout the system.

Uncomputability: Certain system behaviors defy explanations by rules. There is no prior reason to believe that any of the processes of nature and humans are necessarily rule-based. We could never see these processes manifest themselves in these surrogate worlds.

Irreucitbility: System behaviors cannot be understood by decomposing it into parts. Reductionism and atomistic view will lead to further illusion about reality. We must understand real world system as an organic whole.

Emergence (Co-evolution): Interactions among system components generate unexpected global system properties not present in any of the subsystems taken individually. Microlevel interactions between individual agents and global aggregate level patterns and behaviors mutually reinforce each other. Self- organizing patterns must be treated as both structure and process.

By combining a large amount of new discoveries from numerous scientific frontiers, Casti (1991; 1997) presented convincing evidence to support these five pervasive characteristics exhibited in both human and physical systems. Casti (1997) further argues that the science of surprise is how to deal with these five surprise-generating mechanisms. Geographers have also reported empirical evidences that are consistent with these five surprise-generating mechanism in both human and environmental systems (Dentrinos, 1990; Nijkamp and Reggiani, 1992; Phillips, 1993; 1995).

3. Evolving Versions of Urban Modeling

Casti's idea on modeling can be used as an organizing framework to examine the evolving versions of urban modeling. Comprehensive reviews on previous urban modeling efforts have already been made by Harris (1985), Batty (1994), and Wegner (1994). My intention here is to highlight the fundamental shifts in urban modeling during the past 40 years. I would like to use 1973 (the publication of Douglas Lee's article in JAPA) as a watershed year to group the highly diversified urban models into two versions (Table 1):

The first generation of urban models (1957-1973) can broadly be called the Lowry modeling tradition. The semantics rely on the implicit assumption of cities as simple systems which usually involve a finite number of individual elements with relatively weak interactions between them. The entities in the models are aggregated to predefined spatial units. The syntax of the first generation of urban models is based upon traditional linear, deterministic mathematical/statistical techniques such as those manifested in spatial interaction modeling, econometric methods, and optimization techniques borrowed from operations research (OR). The Lowry modeling heritage did not die after 1973 and modeling work following the Lowry tradition continues today all over the world (Wegner, 1994). During the past ten years, various modified versions of the Lowry type of models have been revitalized through their integration with GIS (Landis, 1995), but the core concepts and theories were developed during the 1950s and the 1960s. I have argued elsewhere that without critically examining the assumptions and theories, the integration of traditional urban modeling with GIS may be problematic just as putting old wine in new bottles does not make the wine any better (Sui, 1996; 1997a).

Table 1. Evolving Versions of Urban Modeling

The second generation of urban models (1973-present) tries to break away from the Lowry modeling tradition, with their emphasis on syntax (innovative mathematical concepts) and less concern on the semantics (new urban theories and urban realities). Different from the first generation of urban models, the second generation models conceive cities as complex systems which involve a large but finite number of intelligent and adaptive agents. The behaviors of these agents are contingent on the availability of information and subject to modify their rules of action based upon new information. This continual dynamism in the change of the behavior of agents makes the prediction and measurement by the old rules of science impossible. Therefore, the syntax of the second generation of urban models is characterized by the new concepts and theories in the non-linear dynamics. Beginning with Allen's work which introduced self-organizing and dissapitive structure theory into urban modeling in the late 1970s (Allen and Sanglier, 1981), urban modellers have jumped onto almost every major mathematical bandwagon invented after WWII, as evidenced by the introduction of catastrophe/bifurcation theory (Wilson, 1981), non-linear dynamics (Crosby, 1983; Bertuglia et al., 1990), fuzzy logic (Leung, 1988), Q-analysis (Gould, 1980), neural computing (Gimblett et al., 1994), chaos theory (Cartwright, 1991; Dendrinos, 1992), fractals (Batty and Longley, 1994), and cellular automata (Itami, 1994) etc. Several theoretical physicists have also contributed to this growth in urban modeling based upon non-linear dynamics and chaos theory (Maskse et al., 1995; Nagel and Barrett, 1997). In fact, TRANSIMS developed by physicists at Los Almos is perhaps the most ambitious urban model ever built. Unlike the first version of urban models, most of the second generation urban models are confined to the academia. Few models of the second generation of the modeling are operationalized for practical applications in decision making or policy impact analysis.

Although we can roughly identify these two different versions of urban modeling, I must stress that the current urban modeling practice is characterized by a plethora of models in both versions. However, the philosophical shifts espoused by the second version of urban models are quite distinct and profound. I can detect at least the following two: 1). From a predominantly mechanistic view of cities based upon Newtonian physics to an organic view of cities based upon analogies in biology; 2). From a top-down approach to a bottom-up approach. The new approach emphasizes that cities are formed from more local actions without centralized planning or macro control. This may reflect a devolutionary trend in politics and a shift in planning ideology from instrumental rationality to communicative rationality.

4. Visions for Future Urban Modeling

Casti's framework not only enables us to gain a clear understanding of the evolving versions of urban modeling so far, but also, perhaps more importantly, stimulates our thinking on visions for future modeling efforts. I believe that our future modeling efforts should 1) focus on the new urban reality and develop new urban models and theories (semantics); 2) incorporate the paradigm of the non-linear science (syntax); and 3) embrace the latest computing paradigm for the efficient and effective implementation of urban modeling.

4.1 The new semantics of urban modeling

The first important element of the new urban modeling semantics is to recognize that we are living in fundamentally different kinds of cities than thirty years ago due to rapid technological advances after WWII. Accompanying each major revolution in transportation and communication technologies, American cities during the past two hundred years have been progressively transformed from the mercantile city (primarily influenced by wagon and sail technology in rivers and canals), to the early industrial city (relying on railways and sea-going vessels), and to the mature industrial city (dominated by automobile and air travel and long-distance communication). Since 1970, the post-industrial city - informational city resulting from the on-going revolution in telecommunications, computer, and media technologies - has emerged (Castells, 1989; Sui, 1997a). Cities have evolved from a mercantile city to a metropolis, to a megalopolis, and to a gigalopolis. Cities are experiencing not only a territorial expansion over geographic space, but also an increasing interaction and integration over cyberspace.

Although the urban forms and processes in information cities are still poorly understood, Graham and Marvin (1996) argued that the roles of space and time in urban life have been fundamentally altered as cities are being transformed from industrial cities to informational cities. Industrial cities tend to be spatially compact. Their goal is to overcome time with space, i.e. developed to make communications easier by minimizing space constraints to overcome time constraints. Whereas in the informational cities, telematic technology has completely destroyed the geocode key. Informational cities tend to be spatially diffuse. Their goal is to overcome space with time, i.e. developed to make communications easier by minimizing time constraints to overcome space constraints. The dramatic transformation of cities calls for a redefinition of the concept of a city. Inspired by Thrift and Olds (1996), I believe that cities nowadays can be conceptualized at least by the following four ways, each of which corresponds to a different physical and biological metaphor (Table 2). So far urban land use/transportation modeling has concentrated predominantly on the first two conceptions of cities. As cities are becoming more informational and further integrated with electronic spaces, we should give the last two conceptions of cities a higher priority. The first two conceptions of cities may be sufficient for industrial cities, but to completely understand information cities, we must combine all the four metaphors.

Table 2. Alternative Conceptualizations of Cities
[Modified after Thrift and Olds (1996)

This new urban reality poses many new challenges for urban land use modeling. I would like to mention only two here.

1). Telecommuting is one of the major trends in the U.S. now. According to a national survey, more 32 million Americans are working or running their businesses from home because of the increasing use of faxes, the Internet, cellular phones, etc. Obviously, what this entails is that residential land uses are increasingly blurred with commercial land uses. This means that we need to develop a new urban land use classification scheme for the information age rather than following the Anderson scheme. Telecommuting affects not only the traffic flows, but also the land use patterns in other parts of a city. My own study has shown that the increasing number of white- and pink collar workers working at home may be one of the main reasons for the high vacancy rate of downtown corporate office towers. In some cities, the vacancy rate of down town office towers is over 60%, and as a result, quite a few high-rise office buildings have been rented out for miscellaneous non-commercial purposes. It would be misleading to continue classify them as commercial land uses.

2). Traditionally, mapping the communication infrastructure and computer networks has not been treated very seriously in land use planning and monitoring. Even the new edition of Chapin's urban land use planning bible (Kaiser et al., 1995) makes no mention of it. But for information cities, computer and information infrastructures are crucial because of the changing nature of our cities. How cities are wired will be a very important factor influencing urban land use patterns. Because of the invisibility of information infrastructures and proprietary commercial interests, it is going to be a very challenging task to map the information infrastructures and make them an integral part of new urban models.

Obviously, we need a new semantics for urban land use modeling. This new semantic framework should unify land use structures (urban forms), land use functions (urban processes), and land use dynamics ( urban policies to guide changes in forms and functions). This will require us to conduct thorough research on informational cities and examine how the current telematic revolution will manifest itself on the land. Without grounding modeling efforts solidly in the new urban reality, our sophisticated techniques may have little meaningful to say about the critical issues facing today's cities.

4.2. The new syntax for urban modeling

The new semantics of urban modeling demands that we must have a new syntax to model the complexity of the information city. Although linear and deterministic techniques are still applicable in certain situations, we need to expand our efforts to develop a coherent syntax for urban modeling using concepts and theories in non-linear dynamics. Incorporating insights gained from non-linear dynamics is the best way to handle the surprises in our future modeling efforts. Table 1 summarizes major techniques to handle each of the five surprise-generating mechanism. Although incomplete and overlapping among the five possible solutions, these solutions listed in Table 3 are a good starting point for the development of a unified framework to integrate those fragmented urban modeling works based upon non-linear dynamics.

Table 3. Possible Methods and Techniques to Handle Surprises in modeling

I believe that chaos theory will play a central role in the new syntax for urban modeling. Chaos theory offers us a possibility of elegantly reconciling the simultaneous presence of complexity/irregularity and simplicity/regularity in a complex system. Chaos theory implies both apparent randomness out of order and order out of randomness. According to chaos theory, complex non-linear systems are inherently unpredictable, no matter how sophisticate or detailed the model may be. However, it is generally quite possible, even easier, to model the overall behavior of system. The way to express such an unpredictable system lies not in exact equations, but in representations of the behavior of the system -- in plots of strange attractors or in fractals. Pioneering works have already revealed that urban forms are essentially fractals in nature, and urban processes can be simulated as self-organizing cellular automata and neural networks (Batty and Longley, 1994; Clarke, 1997; Itami, 1994). We can expect that new developments in non-linear dynamics will play an increasingly important role as we switch our modeling focus from industrial cities as bounded regions and networks to information cities as space of flows and quantum states. In parallel to the unified semantic framework, we also need to develop a coherent syntactic framework integrating the concepts and theories listed in Table 3, just as what Alan Wilson did 30 years ago using the entropy maximization concept.

4.3 The new computing paradigm

The computational implementation of the new vision for urban modeling is inescapably tied to GIS. Rather than the stand-alone, layer-based approach, the emerging network-oriented feature-based GIS (FBGIS) through distributed computing and new protocols may represent the most ideal computing platform for the implementation of urban land use models.

Unlike the layer-based GIS in which we try to fit a map layer containing geographic entities into a Cartesian coordinate system (an absolute conceptualization of space and time), the FBGIS lends us a new conceptual framework to implement those alternative views of space and time and various new models depicting the physical and socio-economic processes in the real world (Tang et al. 1996). In a feature-based GIS, space, time and themes are defined as integral parts of a geographic feature instead of referencing all the entities into an arbitrary Cartesian grid. By providing direct access to spatial, temporal and thematic attributes, the FBGIS is not constrained to map and layered representations of geography and thus supports multiple dimensions of spatial/temporal events.

The other very important computing trend is to cultivate the interoperability of software products across distributed computing platforms (DCPs) according to the concept of the Open Geo-data Interoperatbility Specification (OGIS) (McKee 1996). The concept of OGIS has already stimulated new software development trends in the industry. Instead of developing a fully integrated GIS, more and more software vendors are engaging in developing a much leaner core module with numerous task specific, embeddable modules. These object-oriented, embeddable modules can not only be easily loaded into a core GIS package, but also can be seamlessly integrated with other application programs. In addition, with the explosive growth of both the Internet and the Intranet, the development of web-based software tools is necessary so that whoever has access to the Internet can run the program regardless of user's physical location. To implement new urban models using some of the web-based software development tools such as Java is definitely an area worth pursuing in the future. Those web-based modeling tools for urban development will enable citizen to more actively participate in the policy decision-making process. The development LUCAS is an exciting beginning for DCP-based land use modeling (Berry et al., 1996).

The prospects for urban modeling are obviously more than just another twist in the change of spatial or temporal scales or a jump onto mathematicians' new bandwagon. New urban reality and new theories in science demand us to embark a fundamental paradigm shift for urban modeling at both semantic and syntactic levels. At the semantic level, we must realize that we are dealing with fundamentally different kinds of cities - informational cities as a result of the telematic revolution. Many old concepts and theories we are accustomed to are no longer applicable and new theories to this new urban reality have yet to be developed. At the syntactic level, the new development of science and technology during the later half of 20th century has provided us with a new set of language to describe and model various facets of urban reality. These new theories and concepts, as reflected in chaos theory, cellular automata, fractal geography, self-organizing theory etc., are rapidly coalescing into a non-linear science that challenges our deterministic, linear thinking that has existed since the time of Newton. Insights gained from preliminary studies using these concepts have enabled us to better understand the complexity of cities and the dynamics of land use patterns.

It would be entirely impossible to meet the dual challenges of urban modeling at both the semantic and syntactic levels without computers. Indeed, computers not only provide us with the tools to understand urban reality, but also are becoming an integral part of our cities we are trying to model using the same computers. To what extent we can succeed in this endeavor is a profound issue for all of us to ponder on for the days to come. We may never be able to eliminate surprises from our models, yet we can still hold out the possibility of creating something approximating what Casti called a science of the surprising.

Allen P M, Sanglier M, 1981, "Urban evolution, self-organization, and decision making" Environment and Planning A 13 167-183

Batty M, Longley P 1994 Fractal Cities (London: Academic Press)

Batty M, 1994, "A chronicle of scientific planning: The Anglo-American modeling experience" Journal of the American Planning Association 60 7-16.

Berry M W, Flamm R O,. Hazen B C, and MacIntyre R L, 1996, "Lucas: A System for Modeling Land-Use Change" IEEE Computational Science and Engineering 3 24-35.

Bertuglia C S, Leonardi G, and Wilson AG (editors) 1990 Urban Dynamics (London: Routledge).

Cartwright T J, 1991, "Planning and chaos theory" Journal of the American Planning Association 57 44-56.

Castells M, 1989 The Informational City (Oxford: Blackwell).

Casti J L, 1991 Searching for Certainty: What scientists can know about the future (New York: William Morrow)

Casti J L, 1994 Complexification: Explaining a paradoxical world through the science of surprise (New York: HarperCollins).

Casti J L, 1997 Would-Be Worlds: How simulation is changing the frontiers of science (New York: John Wiley & Sons Inc.)

Clarke K C, 1997, "Long term urban growth prediction using a cellular automation model and GIS: Applications in San Francisco & Washington/Baltimore" Paper presented at the International Workshop on GIS in Spatial Population Analysis & Regional Economic Development, March 24-25, Hong Kong.

Crawford-Tilley J S, Acevedo W, Foresman T, and Prince Q, 1996, "Developing a temporal database of urban development for the Baltimore/Washington region" Proceedings of ACSM/ASPRS Annual Meeting, Washington D.C., 3 101-110

Crosby R W (ed.), 1993 Cities and Regions as Nonlinear Decision Systems (Boulder, CO: Westview Press).

Dendrinos D S 1990 Chaos and Socio-Spatial Dynamics (New York : Springer-Verlag).

Dendrinos D S 1992 The Dynamics of Cities : Ecological determinism, dualism and chaos (New York : Routledge).

Gimblett R H, and Ball, G L, and Guisse, A W, 1994, "Autonomous rule generation and assessment for complex spatial modeling" Landscape and Urban Planning 30 13-16.

Gould P G, 1980, "Q-analysis, or a language of structure: An introduction for social scientists, geographers and planners," International Journal of Man-Machine Studies 12 169-199

Graham S, Marvin S, 1996 Telecommunications and the City: Electronic spaces, urban places (London:
Routledge).

Harris B, 1985, "Urban simulation models in regional science" Journal of Regional science 25:545-568

Itami R M, 1994, "Simulating spatial dynamics: Cellular automata theory" Landscape and Urban Planning" 30 27-47.

Kaiser E J, Godschalk D R, and Chapin F S, Jr., 1995 Urban Land Use Planning (4th edition) (Urbana: University of Illinois Press)

Kirtland D, Gaydos L, Clarke K, De Cola L, Acevedo W, and Bell C 1994 "An analysis of transformations in the San Francisco Bay/Sacramento area" World Resource Review 6 206-217.

Landis J D, 1995, "Imagining land use futures: Applying the California urban futures model" Journal of the American Planning Association 61 438-457

Lee D B, 1973, "Requiem for large-scale models" Journal of the American Institute of Planners 39 163-178.

Leung Y, 1988 Spatial Analysis and Planning under Imprecision (Amsterdam: North Holland)

Makse H A, Havlin S, and Stanley H E, 1995, "Modeling urban growth patterns" Nature 377 608-612

McKee L, 1996, "OGIS spans distributed computing platforms" GIS World 9 56.

Nagel K, Barrett C L, 1997, "Using microsimulation feedback for trip adaptation for realistic traffic in Dallas" International Journal of Modern Physics (forthcoming), http://studguppy.tsasa.lanl.gov/research_team/papers/ [Website for TRANSIMS]

Nijkamp P, Reggiani A, 1992 "Interaction, Evolution, and Chaos in Space" (Berlin: Springer-Verlag).

Phillips J D, 1993, "Spatial domain chaos in landscapes" Geographical Analysis 25 101- 117.

Phillips J D, 1995, "Self-organization and landscape evolution" Progress in Physical Geography 19 309-321

Sui D Z, 1996, "Urban forms, urban processes, and urban policies: A research agenda for the metropolis in the 21st century" In Spatial Technologies, Geographic Information, and the City, compiled by H. Couclelis (Santa Barbara, CA.: NCGIA Technical Report 96-10), 210-213.

Sui D Z, 1997a, "Reconstructing urban reality: From GIS to electropolis" Urban Geography 18 74-89.

Sui D Z, 1997b, "GIS-based urban modeling: Practice, problems, and prospects" Paper presented at the International Workshop on GIS in Spatial Population Analysis & Regional Economic Development, March 24-25, Hong Kong (available from the author).

Tang A Y, Adams T M, and Usery E L, 1996, "A spatial data model design for feature-based geographic information systems" International Journal of Geographic Information Systems 10 643-659.

Thrift N., Olds K., 1996, "Reconfiguring the economic in economic geography. Progress in Human Geography 20 311-337.

Wegener M, 1994, "Operational urban models: State of the art. Journal of the American Planning Association 60 17-29.

Wilson A G, 1981 Catastrophe Theory and Bifurcation (Croom Helm, Beckenham, Kent)