1. Introduction

Cities coordinate activities among a large number of human beings. To do this requires complex patterns of cooperation. Furthermore, this task must be accomplished under conditions in which the activities are changing continuously. There is a competition between opposing goals. One goal is to optimize the efficiency of exchange patterns best suited to the present situation, by making the infrastructure and information paths permanent. Another goal is to leave everything suboptimal but highly adaptive, so as to be able to change with unexpected variations in conditions. Still another is to impose hardware (i.e. buildings and roads) onto a city that achieves neither of the previous goals.

As an example that compares specialized versus adaptive cities in the long term, Jane Jacobs [1] contrasts a static city such as 19th century Manchester with a dynamic city such as Birmingham (England). Manchester was very successful in the cotton industry, but declined in the face of external competition. On the other hand, it has never been possible to point to one industry by which Birmingham earns its living; rather its capability has been the creation of new industries in response to changed conditions.

A specialized city that works well can be compared to a real-time electronic system, in that its functionality is decided beforehand and is specified in complete detail. Any functional change in an electronic system must be designed with all possible consequences in mind. This requires extensive testing before implementation in order to avoid undesirable side effects. For systems such as cities and biological brains, however, change is to a considerable degree heuristic (i.e. learned by the system itself in response to experience). Many other natural and artificial systems work by coordinating a complex combination of changing functions.

This paper talks about urban nodes and connections, and their interrelationship. It is a follow-up of an earlier paper [2]. Our work is part of recent attempts to understand cities as complex systems, including those by Peter Allen [3], Juval Portugali [4], and their collaborators. Jane Jacobs [1], Richard Meier [5], and Christopher Alexander [6] pioneered the understanding of complex city structure, studying and describing urban form in more realistic ways than the simplistic spatial geometry of the CIAM (Congrès Internationaux d'Architecture Moderne) model [7]. We are looking for the processes whereby a living city develops, and a pathological city decays.

City form is dynamic, and it evolves heuristically. Planners need to implement a process of diagnosis and repair of the urban fabric, much as biological tissue calls upon mechanisms to repair itself. While our discussion here is going to be very general, a broad picture emerges of what a city is, and how to best help it do what it does. Some recommendations arise out of our conception of a city as a complex, organized system. We cannot deny that those proposals represent the opposite of the postwar CIAM approach to planning, which has prevented their implementation up until now. We hope that our conclusions will now give a needed boost to older insights we believe to be both correct and prescient.

2. Understanding the city as a system

Adaptivity, or the need to change functionality, forces a complex system to be modular at many levels of scale [8]. Following the example of electronic systems, "modules" are defined as clumps of activity that have larger information exchange within the module than with other modules [9, 10]. In a city, a functional module at the smallest level of scale could identify a person with the buildings and spaces in which most of his or her time is spent. At a somewhat higher level, modules could include small groups of people who interact strongly on a daily basis with various urban nodes. At a yet higher level, modules correspond approximately with institutions, individual businesses, educational and political organizations, etc.

Modularization is only approximate, because a city function may be partly in an identifiable module, but some elements of it will certainly reside within other modules. It is important to point out that our use of the term "module" is more akin to "network" than to a spatially compact object or region. This paper is liable to be misunderstood if the reader incorrectly envisions a functional module as a spatial module -- i.e. some physical built cube. Our modules enclose distributed patterns of interactivity, where actions occurring in different places communicate. They are really groups of structured links, so their visualization must avoid the misleading twentieth-century urban image of non-interacting spatial entities placed rigidly on some regular grid.

The networks of a city -- the paths, roads, telecommunications, etc. -- are the mechanisms that support information exchange. Nevertheless, a city processes information rather than merely moving it around. A complex pattern of information exchange coordinates city functions, drives a city's dynamics, and determines its evolving structure [5]. Information exchange at the smallest level of scale includes conversation, observation, and display by individuals. At a higher level, people or groups of people move from one function to another. Goods are moved, consumed, changed, combined, and created in a city. Exchanging information is much cheaper than moving people and goods, so a city has to efficiently coordinate different exchanges of different cost.

A system needs to minimize the overall cost of information exchange. Analyzing a city as a system therefore begins by identifying groups of people who exchange more information within the group than external to that group. Modules on any level cannot be identified cognitively in advance, and certainly not via any particular spatial distribution. City modules in general do not correspond with simple city functions. Urban structure needs to be assessed by abandoning strict visual ordering based on aerial views, and following the information flow. Concentrating on the evolving information and movement networks, intervention would then try to enhance city functionality by making information exchange more efficient (by means that include altering the physical structure). We are going to try and understand a city based on its networks of information exchange rather than its appearance on plan.

Before even defining urban modules, one method of improving city functionality is to make sure each of its channels carries multiple information exchanges. By that we mean that an information transfer or physical movement does more than a single thing -- more connections can then fit into the city because its paths help people carry out many different tasks simultaneously. People moving along such paths for the purpose of higher level information exchange can thus carry out lower level information exchange (e.g. observing). The time required for higher level exchange is therefore used more effectively.

Technically speaking, we are proposing fractal loading, which implies the coexistence of different but related things at different levels of scale. Fractal loading means that each high-level exchange also carries with it simultaneous exchanges on many smaller levels. This opposes maximizing the capacity of uniform communications channels dedicated to a single type of exchange. Thus, an ensemble of exchanges on different scales should be supported by a physical infrastructure that permits mixed information exchanges, and which does not let other competing exchanges squeeze out the weaker or lower-level exchanges. The opposite case of monofunctional planning forces many separate and competing exchanges of the same type into a single communications channel. An example of the latter is a choked highway, or the overloading of subway cars at rush hour. Not only is this inefficient, but it excludes other types of exchange.

We confirm one instance of fractal loading [11]. The use of urban space is linked to the information field generated by surrounding surfaces, and to how easily the information can be received by pedestrians. A primary information exchange is a pedestrian going from one point to another. He or she observes things that are unrelated to the primary reason for movement. This information is functional; it can recommend secondary behaviors to the observer who is executing a primary information exchange. A successful city is one in which even simple movements are a rich and rewarding experience. Urban space therefore works by violating the "functional" rule of twentieth-century planning. Successful urban geometry serves a multitude of needs on distinct scales; some strictly functional and others pleasurable.

Walking to an appointment in a European capital (indeed, in most of the world's cities) can be more pleasant than a drive to achieve the same end in a North American metropolitan area. In the former case, one sees other people, some of whom one might wish to talk to; observing others may provide clues on social currents and interactions; window displays provide information on available products and services, etc. Of course, we are discounting negative factors which would interfere with effective information exchange such as crime, inclement weather, or overcrowding. Drivers are subjected to unwanted information from billboards, while they choose aural information from music, news/talk radio, or chatting on their cellphone. Again, the primary exchange is loaded with secondary (wanted or unwanted) information.

Fractal loading has the crucial feature that removing the largest level of scale leaves all the other smaller levels of scale intact. Not having to execute a definite errand, undirected wandering in informationally-rich cities allows the visitor to accept recommendations offered by different visual environments, and to discover the results of such movement. It is thus possible to learn the rich and complex "visual language" of an unfamiliar city that has only changed gradually over hundreds of years. By contrast, in a non-fractal deterministic environment lacking all lower levels of scale, if you don't need to go somewhere, you will most certainly avoid doing so -- every movement is a chore, with nothing new to learn. This discussion re-affirms the importance of having a variety of information exchanges that can be achieved by physical movement.

3. Cities should optimize information exchange

Optimization makes possible the exchange of a maximum of information with a minimum of effort. The cost of information exchange in most urban activities is woefully underestimated. A half hour trip has a cost and a value. How much valuable information exchange occurs? Do you see a wide range of behaviors? Are you exposed to people you want to influence? Would a city be more effective if people saw more directly what was going on? True costs are frequently disguised, because they are computed only for the "useful" portion of the trip. Note the tradeoff with shopping malls -- while those minimize information exchange costs for shopping, they result in excessive costs for transportation.

Informational networks do not possess a localized spatial geometry, hence do not fit neatly into a spatial module. They are and will always be at odds with a city that is forced into a simplistic visual plan. And yet, informational networks are what make up a living city. It is certainly impractical to design the informational networks of a major city in advance, and in any case, as the functions of the city evolve, it is vital that the city have the capability to evolve heuristically so as to optimize information exchange. No leadership will be able to anticipate and manage this at all levels of detail [7].

Consider, for example, the process by which decisions are made to invest in a new business. Such decisions require coordination between future technology directions, market needs, financial resources, and business resources. This knowledge will be distributed across many city networks. A city with efficient information exchange of the required type will be more effective in creating new business than one without. There is always a conflict, however, between the information exchange needs of different city functions. Ideally, the result will be a compromise that allows all functions to operate effectively. There must also exist mechanisms for adjusting this compromise as functional needs change. We propose a drastic change in the optimization processes used in planning: instead of optimizing single-channel connective links among monofunctional spatial nodes, we instead argue for optimizing the overall information exchange in a city.

The functions of an intermediate level module such as a restaurant include preparing meals from raw food; distributing prepared food for take-out; providing a node of social life where people go to see how others dress and behave; providing a center of social communication; hosting meetings between people to discuss business or politics, etc. This module is contained within the building that houses the restaurant, which is itself contained in a larger network module. Some restaurants become focal points for information exchange in a city -- often identified with a particular business in a large metropolitan area, or the restaurant is an important node in a small town's social and government networks. A larger module encompassing spatial patterns of activity in the neighborhood includes the restaurant as a submodule.

Nodes that do not form part of a larger module are often parasitic to the city, since they use its infrastructure without contributing to an overall functional coherence. Nevertheless, that is how most restaurants, stores, supermarkets, and office buildings are built nowadays. Entirely surrounded by an isolating parking lot, they are designed to be built in the middle of a wilderness, yet they are forced right into the urban fabric, tearing it in the process. Restaurants designed to work as highway truck stops are routinely erected inside the city, and of course they don't belong to it. People working in a nearby office building, which could provide clientele at lunchtime, have to drive their cars around a busy road to get to a restaurant that is literally next door.

Planners have in recent decades mostly adopted urban typologies that are essentially anti-urban. Every building ignores its local context and tries to be independent of ANY context. This is really an attempt to lower the complexity overhead due to local adaptation, a strategy that superficially appears to cut costs, but which in reality increases long-term costs. The cost-cutting corporate approach of "one size fits all" is prompted by the desire to connect a node to the entire city without giving preferential treatment to the adjoining urban fabric. Not only are local connections not given any consideration; they are explicitly excluded, making it impossible to connect to neighboring buildings. It is naively expected that a new building will connect instantly to the entire city, while totally ignoring the prohibitive transportation costs of doing so. This approach, however, merely reflects the modernist planning philosophy -- no concession to the surroundings, which means no local connectivity.

Naively separating housing areas from shopping areas creates serious problems. First, any information exchange between these functions will be at high cost. Second, there is little scope for network modules with necessary functions but no physical structure/location to contain them (in contrast to, say, a restaurant). We emphasize that the network has a separate importance for the city than spatial urban form. It is not sufficient to simply erect apartments next to office buildings. Functional modules must either be designed beforehand, or the connective geometry must be such as to allow their spontaneous emergence (impossible with today's modernist zoning laws). The footpaths, parking arrangements, and proximity to other locations all affect the effectiveness of information exchange within any emergent module. A particular urban unit must fit into the global whole; not only in spatial terms, but in terms of the information exchange with its neighbors and the rest of the city.

4. Different types of complexity

A wide range of systems are called complex, and it is important to recognize major differences between distinct types of complexity. We identify two broad categories of complexity, using the computer analogies of HARDWARE and SOFTWARE. A physically simple system in general contains a small number of component types, and all components of one type are identical. Physical simplicity results from the fact that components are interchangeable among themselves. Complexity arises only when those components interact. The interaction between any two components depends primarily on the types of the components and the distance between them. Complexity in this case derives from the very large number of latent connections of exactly the same type among many identical components. The combinatorics of having to connect every identical unit to each other generates an enormous number of connections. Since every system works according to its connections, using the above analogy labels this type of system as akin to complex software.

In a system where the hardware in complex, on the other hand, while there could still be a small number of different component types, different components of the same type are similar but not identical. The interaction between any pair of components is in general unique to that particular pair. We thus have a large number of connections, but each one is identifiable and distinct. Here, the components are encouraged to form markedly different connections among themselves. Since all components are unique, only those connections are necessary that are needed for the system to function. The total number of connections is drastically reduced from the previous system, which had to provide all theoretically possible connections among identical components, precisely because its components were neither unique nor identifiable.

The starting states in a physical or economic system are the initial conditions under which a dynamic process begins. In an urban context, a starting state is the state of a city at some given time in the past, and we are interested to see if the city remains healthy, or develops insoluble problems as it evolves in the future. The two different types of complexity imply drastically different system properties and behaviors. In a complex system that works in a manner more analogous to complex software, very slightly different starting states can give rise to radically different end points. This is called "chaotic" behavior. (Chaotic behavior is observed in a large number of systems in physics, biology, economics, etc., and is a key reason for the difficulty of weather prediction. Readers of popular science recognize the extremely sensitive dependence on initial conditions as the "Butterfly Effect", in which a butterfly in Brazil causes an infinitesimally small disturbance that can nevertheless affect weather patterns in Europe much later [12]).

In a complex system that is more analogous to complex hardware, slightly different starting points will tend to give rise to similar end points (i.e. similar input conditions should generate similar behaviors). Partial insensitivity to input variability guarantees stability -- called "homeostasis" in living systems, which are structurally complex by virtue of morphogenetic mechanisms that generate uniquely individual organisms within the same typology. Convergence on appropriate end points is achieved by controlling the variability at the system level.

Living cities combine both types of complex structure and functionality. A crucial realization is that a living city surpasses a certain "complexity threshold", below which it is dead and sterile. Incredibly, modernist planners deliberately created such dead cities, either on green sites, or out of previously living urban fabric. Analogies based on physical complexity that rely on identical components and interactions can be misleading. A stable complex system is characterized by uniquely individual components interacting in distinct ways. It does, however, give the misleading appearance of physical disorder as seen diagrammatically. Thinking of the traditional city as undesirably complex in its physical form mistakenly led planners to think that cleaning up visual complexity would solve urban problems. That idea is based on a serious misunderstanding of system architecture. The modernist city -- consisting of identical units interacting in the same way -- is problematic. Unmanageable complexity in the sense of software complexity is unavoidable for systemic reasons, despite the visual appearance of "order" imposed by the regular geometry.

Examples of this misunderstanding in action are described by Jane Jacobs [1]. City planners looking at aerial photos of living urban fabric found them to be visually complex, and decided to replace them with high-rise apartment blocks, which look neat on a plan. They thus killed the urban life in that region -- and never even acknowledged their mistake. The same misunderstanding led to such acts of violence to urban systems as cutting expressways through historical city cores. It seemed a visually simple and direct way to connect roads efficiently, but it totally ignored the fundamental complexity of the city. The automobile network must adapt itself into -- rather than disrupt or replace -- the network of information exchange that powers a compact, living city. We should expect that even a rudimentary understanding of system complexity be a prerequisite for any future urban planning decisions.

5. Systems and modular decomposition

Complex systems are coherent working wholes that cannot be completely separated into fully independent modules. A structure that can be easily separated into non-interacting constituents is not a complex system, but rather an aggregation of units (called a "heap" in systems theory). A conceptual separation into modules with some degree of interaction is widely used both for the design of artificial systems, and for the understanding of natural systems. Modules are defined as clumps of activity that interact more strongly within the module than external to it. Herbert Simon [13] has argued that there could be a small number of inequivalent separations of a system into components, all of which might make some sense because they identify different subsystems [7].

Systems driven by information exchange, whether natural or artificial, distribute their complexity between their hardware and software. Any functionally complex system is forced into a hierarchy of functional modules for two reasons [8, 14]. The first reason is that there are always advantages in minimizing the volume of information (design or genetic) required to build the system. As a result, such systems tend to contain a relatively small number of fundamentally different types of components. The system will be constructed from large numbers of a few basic types, with relatively slight variations within one type.

The second reason for a hierarchical structure is that any system needs to fix problems, and to make functional changes that do not disrupt existing functionality. Knowledge of a problem to be fixed, or a functional change to be made generally exists at a fairly high level in the system (e.g. a feature of the entire system does not work properly; an area of the city is declining). The necessary actions, however, must be taken on a much lower level in the hierarchy (e.g. replace a specific group of transistors; implement investment and regulatory actions). One has to find and follow logical paths that link high level conditions with detailed actions that are generating those symptoms. Connections linking the higher with the lower levels in a system help to define a hierarchy. These are the forces that lead to modularization; we now proceed to examine how modules are defined.

External information exchange among different modules must be minimized as far as possible, and activity largely (but not entirely) contained within the modules themselves. All modules on one level of scale must be roughly equal in terms of the number of primary component operations each module contains. If one module were much larger than the others, then most logical paths would pass through that one module, which would result in centralization instead of the distribution of functions. Most cities do have a central region, which is characterized by a peak in occupancy and traffic density, but larger cities are also polycentric.

An important lesson from computer systems is the hardware/software separation. Modular decomposition in software, such as occurs with "objects" and "patterns", works entirely in the abstract space where the program executes. This is entirely independent from the physical structure of the computer's hardware. In exactly the same way, a city works in two distinct spaces: the information exchange network, and the separate space of physical structures. We are applying modular decomposition to the former, not the latter.

Very large information exchange between two modules precludes their effective separation for the purpose of tracing logical paths. Modules are separated so that information exchange is minimized, corresponding with Courtois' [9] point that the join between modules -- the interface -- will be successful only if it occurs along a region that is weaker than any individual module's internal connections. No preconception, such as neat spatial ordering, can ever determine the partition into functional modules [7]. Defining modules by this process of "finding a compromise among different paths of information exchange" implies that such modules may have a very complex geometry. Using the above general rules for module formation gives guidelines for generating healthy urban fabric.

The geographical separation of residences from workplaces (enforced by postwar monofunctional zoning) is a case in point. Because these two urban regions -- apartment blocks or groups of suburban houses on the one hand, and office towers on the other -- interact so strongly with each other as a whole, they do NOT define separate functional modules, despite the simplistic expectations due to spatial clustering. Instead, the geometry forces functional module formation of the most inconvenient kind, with information exchange that is very expensive to maintain because of long links [2, 7]. The modules that do form are too weak, and suffer from overextended transport connections and a lack of internal coherence.

Another problem with this example is that there is simply no way to form modules of intermediate size. A stable hierarchy of different modules that fit within larger modules can never evolve in a monofunctional urban region; yet we know this to be a crucial feature of any working complex system. The nuclear household and its immediate connections defines the smallest module containing work, school, office, and supermarket. In the majority of cases, there is no successively larger module that contains this elementary module -- one immediately jumps from the nuclear household to the entire city. This lack of hierarchy is pathological from a systems point of view. From a social point of view, the decline of contemporary urban geometry is reflected in the fact that today's individual does not belong to any particular neighborhood or region.

High-rise office buildings and horizontal "office parks" are not functional modules. Typically, there is very little to no interaction between different offices in the same building or "park", compared to the exchange between each individual office and its headquarters, branch locations, customers, suppliers, bankers, etc. This elementary analysis invalidates both the office building and the "office park" as useful urban typologies, despite their recent proliferation. For similar reasons a region of suburban houses is not a functional module [7]. Creating office blocks and suburban house groups makes all genuine functional exchange high cost (or imposes systemic isolation). This is the system force behind Jane Jacobs' [1] observation that successful city neighborhoods are always mixed usage.

6. Plug-and-play strategies are misleading

Module reusability gives planners a false understanding of systems. Plug-and-play strategies in modular design offer the possibility of replacing a module that fails, or is superseded by an improved module. This also allows a module to be added to a system without rearranging the entire system. Conversely, a module can be removed when not needed, without requiring a complete reorganization. Plug-in complex modules became popular during World War II in military hardware. Savings in time resulting from the ability to quickly service a complex mechanism overrode the higher cost of replacing a module instead of diagnosing and fixing one of the module's internal components. The same mentality has been inherited by the computer industry, with throwaway modules as today's hardware standard. All of this depends on an interface that permits modules to connect easily to the system.

A successful application of this strategy is the development of a standard interface for connecting computer components, such as external hard disks, keyboards, monitors, etc. These standard connectors permit the rapid transmission of a large amount of data between hardware modules. Standardization is achieved by placing restrictions on the permitted interfaces, which leads to the simplification of protocols for information exchange. This in turn permits the interchangeability of modules.

Such plug-and-play capabilities can be misleading, however. In many instances of the forced modularization of complex computer systems, the net gain has been minimal or zero, because the modularization has been achieved by shifting the system complexity from the hardware to the software. In contrast to the above successful example, which is made possible by a simplification of protocols for information exchange, oftentimes simplifying the hardware makes the software carry the burden of complexity. That is, functionally simplifying the hardware moves most of the functional complexity into software. In those cases, the interface between modules becomes more complex rather than less complex. The system therefore becomes more difficult to maintain, even though its physical design looks simpler. So far, we are discussing physical (hardware) modules. As noted earlier, we need to consider the separate question of the modular decomposition of software.

It is extremely difficult to achieve plug-and-play with software modules in a complex real time system, unless the functions performed by different modules have very little interaction [15]. Object-oriented programming uses standard, simplified interfaces to stick software modules together, so as to enable different components to communicate inside a large complex program. Some complex software has been designed for plug-and-play modularity; for example, many large commercial programs possess modular features that a user may turn on or off. Nevertheless, cases are known of complex evolved software, such as that used for the air traffic control system, where one module cannot be removed without crashing the system (even though it is not supposed to affect the other modules).

Buildings, spaces, and infrastructure provide a rubric in which people exchange information through communication and movement. Planners picked up the idea of a spatial module as a result of thinking about visual complexity, and missed the fact that cities instead form functional modules. This misunderstanding has led to major typological and planning errors. A new residential subdivision, office tower, or shopping center is approved, with the misguided expectation that it will neatly plug into the existing city. As soon as one of these (non)modules is plugged in, urban forces spontaneously generate functional modules that do not look like anything envisioned by planners. Those functional modules stretch across a city, adding to its traffic congestion and utility wastage. The genuine modules that evolve are usually forced to be extremely weak by the wrong infrastructure and zoning, which are geared to support the integrity of the urbanistically irrelevant spatial (non)modules.

In fact, contemporary planning is heavily reliant on generating new spatial (non)modules, and plugging them into the city. Ostensibly designed as perfectly independent of the city, they are nothing of the sort. A suburban house cluster, office tower, or office park plugs into the city transportation network via a single road. This method falsely appears to follow the computer industry practice of using a restricted interface that permits module interchangeability -- but it is based on a misconception. Since such (non)modules contain a large number of interchangeable components, the latent connections with the rest of the city are enormous, and all have to go through the single available channel. This overloading certainly doesn't comply with the criterion of a simplified interface suitable for limited inter-modular interactivity. Paradoxically, when the interface works as it ought to -- by restricting interchange -- then the module dies off.

We know that early twentieth century urbanists adopted mass-production techniques from manufacturing, and applied them to cities. One of these was the extreme visual simplification of a city's hardware components, in the misguided attempt to implement the idea that urban units ought to look like reusable spatial modules. We should not be surprised, therefore, at the system consequences of this action. Physical separation and segregation of functions removes functional complexity from the city's built structure, and overburdens people's daily movement. The simplistic visual ordering of modernist planning, therefore, has as its unintended consequence an extreme functional complication (hence overloading) of the transportation network.

Going back to the city/computer analogy, much of today's urban activity and costs are due to the shifting of data. This is not a useful activity in a computer, but something that occurs only when there is a bug. Shifting data around and around serves no useful function -- it is not a part of software, and does not compute or process anything. Useful computing time is spent in processing information. The urban analogy of useless information shuffling is forcing people to move around a city unnecessarily to accomplish their daily tasks, consequently wasting time and energy. Planners using plug-in spatial (non)modules maximize this wasteful shifting around by means of an inappropriate urban geometry.

7. A city works like a brain, not a computer

Different system architectures characterize complex systems that work in a different manner, as for example a digital computer versus a mammalian brain. The functionality of an electronic system is expressed as a series of commands in software. The use of unambiguous contexts results in the familiar memory/processing separation of the von Neumann system architecture upon which most computers are based [8]. Information exchanged between two modules must have an unambiguous meaning to the recipient module in terms of its own functionality. Modules can then use their input information to generate outputs that are commands for the system.

Maintaining unambiguous contexts is impractical in a complex system such as a city, however, which has to heuristically modify its own functionality, or learn. In a system that learns, modules must heuristically determine their own inputs and outputs (i.e. learn by trial and error). Nevertheless, if a module changes its outputs, it is difficult for other modules which have previously received inputs from that module to readjust. The receiving modules cannot assign an unambiguous meaning to the new output. Therefore, outputs from modules can only change gradually, in ways that minimize the loss of meaning to other modules. In a city, this means that healthy urban fabric is generated by a slow evolution, and also a city must be allowed to evolve over time. On the other hand, radical redevelopment of healthy urban fabric destroys meaningful information exchanged within the city. The result is city dysfunction until enough time has passed to rebuild information contexts.

There are two possible information architectures for a complex system. One is the von Neumann architecture with a memory/processing separation supporting unambiguous information exchange, in which functionality is explicitly controlled. The other is the recommendation architecture with a clustering/competition separation supporting meaningful yet slightly ambiguous information exchange, in which functionality is defined heuristically [8, 14]. A competition subsystem interprets the outputs of submodules as a range of alternative behaviors, and quickly selects one of the alternatives. This process depends critically on consequence feedback to determine appropriate system behavior.

When it is necessary for functionality to change heuristically, or without central direction, a system adopts the recommendation architecture. Biological brains have evolved a recommendation architecture [8, 14, 16]. In the mammalian brain the clustering/competition separation corresponds with the anatomical separation between cortex and subcortical structures [8]. Commercial electronic systems, on the other hand, invariably use the von Neumann architecture. In the most complex electronic systems it is extremely difficult to evolve functionality in a controlled fashion. When a change is made, extensive testing and error correction is required, with the testing covering not just the modified functionality, but examples of all different system functions.

A von Neumann system architecture is not scaleable. Thus, a city that is finely tuned to work at a certain size cannot handle changes in its size very effectively. Since the recommendation architecture uses more resources than the von Neumann architecture to perform the same functionality, if there is no need for functional change, operational forces push the system towards the von Neumann architecture. Information exchange then tends to become unambiguous because the action required in every condition is well understood. However, if conditions begin to change, such a system will find it very hard to adapt. The system can no longer find an effective compromise between module equality and information exchange, which reveals itself in a steadily decreasing ability to make changes. The failure of 19th century Manchester is one urban example. The city became extremely efficient for the cotton industry, but could not adapt when circumstances changed.

Resolution of conflicting recommendations must occur in an institutionally separate function which does not require complex coordination. Electoral and legal institutions perform this role in a city. There are interesting similarities between the competitive subsystem as defined here, and legal and political mechanisms. In a physiological brain the competitive function will in general choose one or another option rather than try to find a compromise, because it is impossible to know whether a compromise will not make things worse. Thus the legal and government regulation process for resolving conflict in general selects a winner from amongst existing alternatives rather than generating novel behavior.

8. The role of telecommunications

Information and communications technologies need to be incorporated into traditional city functions [17, 18]. The dynamics of the rapidly evolving electronic city are as yet little understood, while the twentieth-century model of a city based on simplistic spatial ordering is irrelevant for modeling a communications network. Blocks of functionally segregated buildings, strictly aligned to a rectangular grid, do not reveal the various overlapping networks that actually drive a city to function [19, 20]. As a complex system whose output is commercial wealth and culture, a city has a functional architecture based on information exchange [5]. Information and communications technologies should fit neatly into the hierarchy of information exchange functions at different levels of scale.

As has been well documented [21, 22], the advent of telecommunications ever since the introduction of the telephone dramatically altered urban systems. Information exchange intensified to a degree that was previously unimaginable. Telecommunications is low cost in the sense that it requires very little physical movement of people. One of the principal reasons for the initial aggregation of people into cities was in order to communicate with each other at a low cost, and this is still the driving force behind, say, the Diamond districts of New York City and Antwerp. It could be argued that the need for persons in the same trade to cluster is in part replaced by telecommunications. However, this is only true if the type of information exchanged by telecommunications is exactly the same as that exchanged by personal contact.

Some authors predicted that telecommunications would replace commuting. The reasons this prediction failed are not hard to see when analyzed from the perspective of information architecture. Information exchanged through personal contact and people movement has a much richer content, including information derived from a combination of voice tone, expression, and body language [23]. In addition, a visit allows the visitor to observe a quantity of otherwise unavailable information, and allows the visited person to observe the reaction of the visitor to this information. The multiplicity of sources of environmental information cannot be duplicated by a restricted number of communications channels.

The developing field of "Knowledge Management" addresses some of the crucial issues that have long been ignored by architects and urbanists [24]. For example, what is the optimal physical working environment that is conducive to creative output? Surely this is a trillion-dollar question, considering that our civilization is based on an economic engine driven by human creativity inside buildings, rather than by subsistence farming. Going beyond the strictly spatial aspects of the surrounding information field [11], researchers in knowledge management identify every informational aspect of the environment, including office decoration and artifacts, human interactions, and social dynamics, as crucial to either supporting or hindering creative work [24].

Large corporations have generally found that introducing new communications mechanisms such as e-mail or videoconferencing does not in fact reduce the amount of physical travel. The effect of the new communication capability is to increase the complexity of projects which can then be undertaken, rather than to replace existing communications (again, we see the optimization tendency towards fractal loading). The exception is that if a new communication mechanism results in the same information exchange at lower cost in resources or time, the new one will replace the old. Examples are the replacement of telegraph by fax, and the replacement in North America of interstate train travel by air travel.

Working from home via an electronic link is now feasible, and there are several instances of successful applications. First, individuals constrained to remain at home can now link to informational nodes that would otherwise be too costly (in terms of time and arrangements) to interact with physically. Second, powerful and wealthy individuals can set up residence in some fancy resort, and conduct their business via electronic links. This is made possible because their financial resources enable them to have all necessary information available, and any personal level of information exchange is taken care of by a quick trip. The module here is an informationally stimulating environment for those who can afford it.

Someone stuck in an informationally-starved environment may not be altogether happy to work exclusively from home, however. He or she normally prefers to fight rush-hour traffic because an outing at least gives some informational stimulation, and enables face-to-face information exchange with coworkers. Suburbanites feel informationally deprived, spending hours on the telephone and in front of the television or computer monitor in an effort to remedy this. The workplace has for many people replaced the home as the primary social node. People don't want just to eliminate the ordeal of a lengthy daily commute by car, bus, or train; they want to get their daily information exchange at a lesser cost. Today we pay an inordinately high price in automobile traffic for very little meaningful information.

The same remarks also hold true for teleshopping. Certainly, the ability to order a product from a computer screen at home has revolutionized commercial interactivity, and will probably lead to further major changes in consumer habits. Nevertheless, key components of the shopping experience are social, sensory, and public. These include the trip to the shop; interacting with other customers; touching and feeling the product before making a decision; combining a shopping trip with something else, etc. This social dimension drives "shopping for entertainment", a past-time for a large number of people, and an emotionally-satisfying method of information exchange for everyone, including the busiest individuals on this planet.

Jennifer Light has examined the interactions between the physical city and the electronic city [25]. She does not share the pessimism of other authors about the latter replacing the former. We agree with her when she says that: "The decline of cities, then, cannot be explained simply as a physical phenomenon attributed to the growth of electronic media" [25]. This coincides with our own observations of new urban activity patterns, which use electronic connectivity to reinforce and regenerate the pedestrian urban fabric. Light even defends the shopping mall, which expresses information exchange needs that have been suppressed elsewhere in the city [25]. In our opinion, the decline of cities is a consequence of misunderstanding urban forces and networks, and urban typologies such as the shopping mall are reactions to rather than the causes of this decline.

The last examples demonstrate the need for functional module formation in a connected hierarchy. A nuclear module of one person working from home requires that it be contained in a larger functional module. If that is impossible, then the smaller module breaks down. This is the reason for people not being motivated to work from home, and this lack of a hierarchy of modules has prevented the realization of the much-hyped "telecity". In contrast to this, the wealthy businessperson who can work with a laptop computer from a high-class coffee shop, or next to the swimming pool of a resort hotel, has become embedded in a very pleasant and stimulating environmental module.

9. Networks and evolving city form

Unless adequate meaning can be conveyed by telecommunications, information exchange will involve the movement of people. An effective transportation network will allow a high proportion of required information exchange to take place via short walks (say < 10 minutes each way) with secondary information exchange; an intermediate proportion to take place by moderate overhead mechanical transport (say < 30 minutes each way); and only a small proportion requiring high overhead mechanical transport (say from 30 minutes to 1 hour each way). Journeys that occupy in total much of a working day will in general be ruled out. The distribution of both pathlengths and journey times should follow an inverse-power scaling law favoring the small scale -- where the number of paths is inversely proportional to their length [7].

Creating an effective network depends on the functional partitioning of the city, and will always require a compromise. The decision to reduce the overhead for one type of trip may increase the overhead for another type of trip. For example, widening a road and increasing vehicular traffic may make many pedestrian trips across the new road much longer, or make them altogether impractical, thus destroying many working functional modules that depended on those paths. It is therefore essential to investigate whether an apparent demand for a new high level network connection such as a major road could be addressed by a different module partitioning, which might reduce the need for trips in the direction of the proposed road.

Change in a city is ubiquitous. The goal of urbanism is to help a city evolve and redefine its modules so they can modify their functionality. It is not easy to determine the appropriate module and network changes so as to respond to changes in the city's needs and environment. Urban change must be a natural built-in function of the system, driven by a complex pattern of information exchange. As discussed earlier, centrally-directed changes typically introduce large numbers of unanticipated and undesirable side effects. Any attempt at total central direction of modules and networks on every level will result in steadily increasing dysfunctionality. In spite of this, planning now focuses on large-scale interventions, and does not tolerate spontaneous evolution driven by input at different levels.

The different modules on every level of scale will need to generate alternative recommendations for module and network change. A simple competitive process must select the most appropriate change. Consequence feedback then has to adjust the competitive subsystem to evolve its selections towards those that optimize the network. Knowledge relevant to one change may exist on a number of levels. There must therefore be mechanisms by which modules at many different levels of scale recommend change, which can then be received, interpreted, and integrated into a decision that optimizes overall city effectiveness. Less successful cities can copy explicitly from more successful cities, provided that the functional relationships are copied, and not just physical structures and individual institutions.

Here is precisely where the electronic city can help the real city. There are many ideas being generated on how to involve people in their own environment; promote both education on urban issues and feedback from residents; simulate and coordinate urban interventions; many things that were extremely difficult to do before the internet and the World-Wide Web [25]. If we proceed about this task in an intelligent fashion, then a new understanding of urban systems can be applied to revitalize urban life in many regions, and also to prevent the extinction of existing life in regions threatened by blind "modernization".

10. Conclusion

We made steps towards identifying the system architecture of cities by comparing them to complex information systems such as digital computers, biological organisms, and the human brain. A city works according to an information architecture that recommends, but does not demand an action. Functionality on all levels of scale is driven by the need to optimize information exchange, from a face-to-face meeting between two persons, to the movement of individuals, up to the daily movement of many people between urban nodes.

Functional modules should develop in a way such that more information is exchanged within a module than between different modules. Cities, like human brains but unlike electronic systems, must modify their functionality without explicit intellectual control over every detail of the change. Our model allows us to help a living city repair itself much as a living organism does, and to guide its evolution under changing conditions. Rather than using models based on visually regular aerial geometries, this approach makes it possible to evaluate changes to city plans, zoning codes, transportation, and communication networks in terms of their impact on overall city effectiveness.