Representations of Space and Time
-Donna J. Peuquet

Introduction to Part II: New Tools, New Opportunities
(Uncorrected Proof)

So far in this book, I have examined human cognition of geographic space and time from the perspective of what has been derived through observation of human behavior and examination of traditional external knowledge representations. In Part II, I will examine the formal representation of spatial and temporal knowledge. The intent here is not to review what can be called "traditional" formal representations as known in mathematics, for example. This is something that is not directly related to the main focus of his book. Rather, I will focus upon how cognitively-informed representations can be advanced within a computing context.

The underlying purpose of a more human-centered approach to representation than is currently practiced in a computing environment is threefold: The first is to gain a better understanding of the implications of human cognition within the context of GIS as a means of indirect experience; of "exploring virtual worlds." The second is to gain a better understanding of how computers, as tools, can aid people in complex problem-solving tasks related to the environment. The third is to gain insight into how what we know about how people represent space, learn and solve ill-defined problems can be used to improve the autonomous problem-solving capabilities of computer-based technologies in today's data-rich environment.

Exploring Virtual Worlds

There are a number of issues related to the use of GIS for learning through indirect experience. A desktop computer connected to a network has provided almost instant access to a tremendous wealth of information available throughout the world in digital form, and indeed can convey whole virtual worlds. Information is portrayed on the computer screen in deceivingly familiar forms: as text, pictures, diagrams and cartographic images. Nevertheless, there are some obvious and some not so obvious differences in these computer displays that can affect the way that information is interpreted.

As discussed in Chapter 7, paper maps and other forms of traditional external knowledge representation are specifically designed by one person, or group of people, to convey a specific message. The representation utilized is selected by the designer(s) to aid in the conveyance of that message. In drawing a map and writing instructions for directing guests to a party at one's house, for example, this is often done intuitively, and it usually works effectively. In the case of a published map, it is designed by a professional who is either trained in the semiotics and other conventions of cartography or a graphic designer who is trained in the use of various graphic devices.

Now, with the widespread use of GIS and other forms of computer-based software systems with mapping capability, the end user-or reader of the map-is no longer a passive recipient. The user himself becomes the map designer. Although the results of a GIS query (e.g., "Show me the spatial distribution of people over 100 years old in the United States," or " Show me all state-owned parcels of land within the county.") can often be displayed in a variety of forms (e.g., a table, graph or a map), a map is often the user's preferred form of response. Such maps are usually drawn using colors, symbology, and other cartographic design elements that are set as defaults within the software. Since these are general defaults, with no way of knowing in advance what type of data or what type of application the maps will be used to display, the software defaults can at best only account for aesthetics in, for example, providing pleasing color combinations and standardized progressions for monochromatic color schemes to represent a sequence of values. Even worse, the mapping software is often designed and implemented by individuals with no background in cartography or graphic design. The user has the capability of changing these defaults, but most often, the end user is also not a trained cartographer. As the possible result of an inadvertently inappropriate use of color or other symbology, the user may misinterpret the information displayed on the map. The symbology may actually mask important patterns or other features in the data.

The other complexity of the use of cartography and other graphic forms in a modern, interactive computing environment is that much of the use of GIS and online geographic databases is exploratory in nature. The map designer/user has no "message" they are trying to portray in a static and single display. Rather, they are using the tool in a highly interactive fashion, without a preconceived hypothesis, exploring the data and applying general domain knowledge in looking for associations and patterns. The user may change the colors in the original display to accentuate certain values, and then others. The user may then choose to display other data for the same area, or the same type of data for a different geographic area, compare a map with the same data for the same area displayed in a histogram, etc. This means that cognitive principles about how people learn, and how people use maps, images and other forms of graphics, as well as text, to gain knowledge from indirect experience needs to be considered within a basic theoretical representational framework for dealing with space-time information. In this way, computing technology can be used to facilitate and enhance the discovery and learning process, and to enable people to better deal with what would otherwise be overwhelming volumes of observational data.

It is these issues, and others that derive from the differing nature of computers as a representational medium and tool for spatial exploration, as compared to traditional approaches. Other central issues include: How should traditional cartographic and other forms of external knowledge representation be rethought for this highly interactive, user-as-designer environment? What aspects of graphic symbology can be considered "natural" or intuitive for untrained users? Which aspects of current methods should be made available only to experienced users? How can the untrained user be guided through the process of discovering information within graphical displays?

Computers as Geographic Problem-Solving Tools

Strongly linked with how people learn and explore is the issue of how computers can most effectively be used to assist in geographic problem-solving. The basic challenge in this is how to capitalize upon the unique capabilities of computing technology in order to complement the unique capabilities of human cognition; to utilize the speed and tireless computational accuracy of computers to aid the imagination of people and the ability to see visual patterns, using each to best advantage in helping people in solving complex problems.

How the data are represented within the database is as important as any visual representation for solving problems, since how the data are represented is central to how a problem can be solved, and the ease or difficulty of arriving at a solution. Indeed, in an automated context, the database representation drives the visual representation. Geographic, or any other type of locational data, can be formatted digitally either in an array of grid cells where the grid cells represent contiguous small areas of space (also often called raster format), or as vectors of x-y coordinates. A series of coordinate vectors can delineate the boundary of some polygonal object, such as a lake or political district, or the spatial configuration of a linear object, such as a road or a river.

Similarly, data or information can be represented in either temporal order along a time-line (according to temporal location), or as distinct events (temporal objects). Time lines can either be open-ended, representing the linear and experiential view of time, or cyclical. Both temporal location and temporal object representations can also utilize either absolute (May 2, 2000, Tuesday, spring, etc.) or relative (before, after, during, etc.) temporal locations.

Attributes are associated with individual locations or individual geographic entities. From a cognitive perspective, the grid format corresponds to a survey view. In a mathematical sense, this is in a general sense equivalent to a field-based view. A vector format that represents boundaries around individual objects or for individual linear objects corresponds to a discrete view. This discrete view of objects can thus also be called an object-based view. At the same time, coordinates in either gridded or vector format can be expressed in either absolute or relative coordinates. Specifically, a vector format, emphasizing how objects are related to are related to each other, corresponds in cognitive terms to a route-based view. These objects can include the links themselves as "edges" and their endpoints as "nodes." In mathematical terms, a representation of multiple interconnections, or routes, is a network.

Thus, there are a variety of types of spatially based and temporally based database representations developed over the past thirty years that correspond to the various general types of cognitive representations. These were developed with a focus on efficiency and other technical issues in an evolutionary and frequently ad hoc manner. Representational approaches were borrowed and translated from mathematics, cartography and other fields. It is interesting to note that what in retrospect is a seemingly comprehensive array of spatial database representations, corresponding to the basic types of cognitive representations, these developed without any underlying theoretical framework. The real answer of "all of the above" in the very active raster versus vector debate of the 1970s and 1980s came mostly as a result of accumulated experience with computer-based systems for geographic data handling and display. Placing these also within a cognitive context is coming very belatedly, almost as hindsight. Already having these digital representations, however, it is the development of a comprehensive framework based upon human cognition that will allow better understanding of how these should be best employed in helping people learn via virtual worlds and in helping people to solve problems.

Just as people may shift their cognitive knowledge representation to suit a particular task at hand, each of these various types of computer representations is advantageous for solving various types of problems. Figuring out the shortest route from one place to another, for example, is most easily achieved using a vector type of representation, while looking for overall spatial pattern is best accomplished using a grid format, or survey view. Changing from one view to another is something that is automatic and fairly effortless for people to do cognitively, but is nonautomatic and time-consuming to do in a computer.

There has also been a significant amount of research within the realm of what we now call Geographic Information Science into the development of a formalized language for use in GIS and related computer-based systems. At the core of this effort has been the identification of a set of spatial relationships and how these interrelate. There have historically been three distinct paths taken in this research. One utilizes algebraic and geometric principles directly, as perhaps best exemplified by Dana Tomlin's Map Algebra (Tomlin 1983; Tomlin 1990). A second path has focused upon how to extend SQL, the standardized query language that has been used for Database Management Systems (DBMS), traditionally used for nonspatial applications, into the spatial and spatio-temporal domains. SQL is itself built upon principles of Set Theory from mathematics. This latter path is exemplified in work by Herring (1988) and by Egenhofer (1989). A third path within the GIS research community has focused on natural language in the context of spatial expressions, but little has yet resulted in any spatial query language being implemented. Another path that has arisen more recently is the application of Human-Computer Interaction principles (HCI). This shifts the focus from formalized language and relationships toward a form of interaction that relies more on the use of the senses (vision, touch, sound, etc.) in a way that is more related to how we interact with the real world (Nyerges, Mark et al. 1995).

All of this leads to additional questions: How much do these current representations coincide, at least on a conceptual level, with cognitive knowledge representations? Can new types of representations be developed for DBMS and GIS that better reflect human cognition? Can a robust and universal spatial query language be built based upon a finite and elemental set of cognitive relationships? Need there be a mixture of textual and pictorial protocols for optimal human/machine interaction? If so, for what kinds of tasks is each best suited?

Autonomous Problem Solving; Machines that "Think"

The idea of creating a machine that can think has been around since Charles Babbage (1792-1871) invented his "Analytical Engine." This was his follow-on to the "Difference Engine," which was successfully built and demonstrated as a numerical calculating machine. Although never built, the "Analytical Engine" was envisioned as having a "store" (memory), a "mill" (calculating and decision-making unit), and a control. This control was to dictate the sequence of operations, which was to be input by means of Jaquard loom punched cards. While this is commonly cited as the first computer since all of the basic components of modern programmable computers were anticipated in Babbage's design, Babbage and others at the time also recognized the potential for mechanized intelligence. It was the first design for a machine that was capable of performing something other than a fixed set of operations. Babbage himself described his Analytical Engine as capable of "eating its own tail," i.e., altering its own program (Hofstadter 1979).

The field of Artificial Intelligence (AI) came into being in concert with the advent of modern computers in the 1940s and 1950s. The focus of AI is the development of computer systems that exhibit behaviors that we would normally associate with intelligence in human behavior (Barr and Feigenbaum 1981). Winston (1992) has defined AI as "The study of the computations that make it possible to perceive, reason, and act" (p. 5). The field of AI incorporates study in four distinct areas.

The first is robotics, which is concerned with programs that are capable of manipulating mechanical devices in complex ways. This area has in large part been driven by the practical requirements of industry for machines that can perform tasks with greater speed and repetitive accuracy than humans can perform, or in environments that would be too hazardous for people. Perhaps the best known application of robotic technology is the mechanical welding arms used in auto manufacturing.

A second area, Computer vision, is closely associated with robotics in that the utility of such devices is greatly increased if they can be equipped with sensory inputs; particularly the ability to "see." Computer vision is also important in a number of specific application areas, which have historically included medical and military uses. Computer vision is also of increasing importance in interpreting the massive amounts of imagery data-from satellites, areal photography and a variety of other sources-that are currently being collected. The main goal is image understanding. This means to have computers identify objects within a scene, interpret a scene as a whole and react accordingly, and to detect new information from images.

A third area of AI is expert systems, where the focus is upon the encoding of knowledge within a specific domain of expertise. Applications are almost infinite; from medical diagnoses, to playing chess, to computer system design, to wine selection. The basic idea is to imitate how a human expert would reason about a particular, potentially unanticipated, problem and come up with a solution, as well as learning new knowledge that in turn can be used to increase decision-making abilities. Key issues in expert systems are how to represent domain knowledge, how that knowledge is used in deriving conclusions, and how new knowledge is acquired and integrated into the knowledge base.

A fourth area of AI is language. Here, the emphasis is to understand statements in either spoken or textual natural language form for the purpose of either interpreting statements as computer commands or translating into another natural language. The nuances of accurate translation relies upon a vast amount of highly interrelated contextual knowledge, as in expert systems. So again, a main issue in automated natural language understanding involves how to represent and utilize stored contextual knowledge.

Certainly, one motivation historically for work in AI has been to realize the full potential of computers-to make them more flexible independent of human intervention by imitating human decision-making and learning. The other motivation has been to better understand the nature of intelligence and the thinking process. The former is the domain primarily of computer scientists and engineers, while the latter is the domain of psychologists, linguists and philosophers. In using computers to better understand intelligence, the hope is that by constructing models of how people (or animals) represent information and use that information to think, we may learn more about the inner workings of the thinking process. The computer can in this way be used to both verify (or cast doubt upon) results from human experiments, and to derive new insights that in turn can be verified via human experiments. Ultimately, the hope is that AI can provide insight into what the mind is, in relation to the body and the environment (Wagman 1991).

Although the idea of "machines that think" has inspired an entire genre of science fiction stories dealing with both the technological possibilities and the sociological implications, the current state-of-the-art is still far away from replicating human capabilities. Robots that can navigate through natural (i.e., nonconstrained) environmental space are still mostly blind, relying on simple turning algorithms when something is bumped into. Recognizing groupings and patterns, matching patterns and identifying objects within an image by computer is still a relatively time-consuming process that often requires human intervention.

Perhaps the biggest success story to date is in the area of expert systems. Computer programs to play chess are well-known examples, as well as programs for such things as medical diagnosis. There are numerous commercially available expert systems software packages available today. These programs have improved over time and are increasingly used for instruction, but they still can't outperform a human expert. These programs, and their associated knowledge bases, are also always limited to a specific domain. For example, a chess-playing program cannot be used to make medical diagnoses.

One obvious element that is missing is the ability to imitate the human ability to derive and use metaphor and other forms of imaginative thought for connecting different knowledge domains. Because of the necessary reliance on much contextual information in generating correct interpretations of natural language that are very often nonliteral, again relying on imaginative thought, the interpretation of natural language has been recognized as a problem compounded. Voice recognition and text recognition programs, as well as translation programs have, however, become available recently that are useable for practical applications and are also modest in cost. These still tend to be somewhat limited in what they can do in that they have the ability to recognize the correct word from the surrounding words, but the voice and text recognition programs commonly available at present have no ability to place phrases within a larger cultural or situational context.

Thus, many questions relating to AI remain. The classic question here is; can a machine be built that replicates human capabilities? Many of the questions of the previous section arise again: How is knowledge represented? How is information processed? How is new information acquired and integrated into the preexisting knowledge base?

Knowledge Discovery in Data-Rich Environments

Data relating to human and natural processes in the environment is now being collected in digital form from diverse sources and from very local (e.g., a single farm or urban property) to global scales. Collection is occurring at a rate that is far beyond what can be looked at and interpreted manually, either in graphical or textual form, in the sense of "exploring virtual worlds" without significant assistance from computers. This problem is made more acute by the accumulation of data through time regarding what are inherently dynamic processes. In the interest of observing change, data are not replaced as "obsolete," but rather added to in an ever increasing and complex data store. As in the case of human cognition and learning, the raw data needs to first be filtered, selecting only what is relevant and ignoring the rest. Then the relevant, or "interesting," elements need to be identified, interpreted, and then either discarded as redundant, stored for future reference, or used to modify the appropriate knowledge structure. This multistep process has become known as Knowledge Discovery in Databases (KDD). Within a computing context, these steps have been defined in various ways, but in general terms includes; (Fayyad, Piatetsky-Shapiro, et al. 1996)

  • selecting and compiling the data set,
  • cleaning the data, including recoding elements in a consistent form and dealing with missing and erroneous elements
  • analyzing the data to find patterns and associations
  • interpreting and evaluating the derived information
  • verifying the derived information through subsequent KDD as well as other methodologies.
Data mining is the term used to refer to the actual discovery portion of the process. Although these steps imply a linear process, as in human cognition, it is very much iterative in nature. As such, MacEachren, Wachowicz, Haug, Edsall, and Masters (1999) have noted that the name Knowledge Discovery is somewhat of a misnomer and would more appropriately be called knowledge construction, The steps involved in the process of KDD conform also to the observation, analysis, theory development, prediction-observation cycle institutionalized as the methodology of science.

KDD developed as a collection of various techniques developed in the fields of database management systems, statistics, visualization, and not surprisingly, AI. Although KDD and data mining are viewed as highly interactive processes, the sheer volume of data makes adaptation and autonomous learning within the machine a much needed element. Techniques for the analysis, or data mining component include Baysian classification, maps and scatterplot displays, decision trees, association rules, neural networks and genetic algorithms.

The basic idea in KDD, as discussed by Adriaans(1996), is to reduce individual observations to points within a multidimensional data space. This makes the use of visualization techniques particularly important and useful in KDD when dealing with geographic data. A number of authors have recently discussed this and how visualization can and should be used as an important tool at each step in the process (Derthick, Kolojejchick et al. 1997; Lee, Ong et al. 1995; MacEachren, Wachowicz et al. 1999).

These authors have demonstrated how specific visual tools, such as maps and scatterplots, can be used to derive insights concerning patterns and interrelationships, but how do these relate to the cognitive process of perceiving and learning? How can what is already known about the role of vision and other sensory perception be used to improve the KDD process?

Toward a New Perspective

Unlike the real-world environment, which has always acted as an individual's extended knowledge store with the individual reacting to environmental inputs and potentially changing the environment, the computer can become more. The computer can act as an active participant in the thinking and problem-solving process, both performing tasks that are components of a larger process, and communicating these results back and forth. This also means that the of ease of translation back and forth between internal and external representation becomes a consideration. The more that internal and external forms correspond to each other, the easier and thereby more efficient translation between these forms becomes. This, however, can be viewed purely as a technical issue. The more important issue is that the more that both of these correspond to cognitive representations, the easier it is for efficient-and effective-man-machine communication. This is the central thesis of this book. As explored in Part I, sensory perceptions lead to cognitive information, as interpreted observations that have been imbued with meaning. An accumulation of information in turn leads to knowledge via linkages, as integrated understanding, that may also be applied to varying contexts. Data are observations collected via direct perception or via mechanical or electronic sensing devices, which are then externally recorded. This can be viewed as part of the same process-of gaining information, and eventually, of attaining knowledge.

The correspondences between the cycle of knowledge acquisition in the cognitive and scientific contexts are shown in the figure below. In the scientific context, theories are formulated via filtering of the data to select those observations that are considered relevant or "interesting." This selection tends to reveal patterns or consistencies in the observed phenomenon. Theories represent formulations of apparent generalized characteristics, relationships or underlying rules of behavior for specific types of entities or phenomena. This equates to the formulation of information, as generalized characteristics and contextualized rules. The key difference between the cognitive and scientific perspectives is that data are externally recorded, and as such, they are not subject to the fading of human memory. Data can be reexamined repeatedly without loss of detail, and perhaps more importantly, can be shared with others. Data are the raw material of formal and scientific analysis.

The similarities between the cognitive and scientific perspectives on learning is thus readily apparent. The scientific perspective, as a formalization of this cognitive process, has in large extent already been translated into the computing context. Computers and computing technology, after all, began as a scientific tool, and they remain an essential tool for scientific learning and discovery.

So, what can be said about computer representation of data and information? A fundamental tenet of representation, whether cognitively or computer-based, is that any representation is more effective for performing some tasks than for other tasks. This is why our cognitive knowledge representation is a multirepresentational and highly dynamic system. This is also why any computing system intended for any range of uses, including modern database management systems (DBMS) and GIS, incorporates multiple representations. Computer representations are also devised by humans, so it follows that computer representations must at least to some degree reflect human representation of spatial information.

This gives rise to subsequent questions. In particular, if cognitive knowledge representation is a highly interrelated, multirepresentational and dynamic system, then what are the practical implications concerning the difficulty of implementing such complex representations in a computing context, if these are much more than current computer representations? Would these also entail a major compromise in machine efficiency for performing various tasks and translating information from one form into another more suitable for a specific task?

These questions and the others mentioned in the preceding sections of this introduction are among the issues that will be explored in Part II.

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