SPATIAL COGNITION AND COMPUTATION, vol(issue), start–end Copyright © YYYY, Lawrence Erlbaum Associates, Inc An Analysis of the "Navigation" Metaphor − and Why it Works for the World Wide Web Hartwig H. Hochmair* and Klaus Lüttich** *St. Cloud State University, Department of Geography **University of Bremen, Faculty 3: Mathematics/Computer Science Abstract. People use spatial metaphors when they talk about activities on the World Wide Web, such as navigating the Web, reaching one’s goal, visiting a Web site, or moving back to a previous Web page. These expressions are mappings from the physical world to an application domain. We analyze why Web users conceptualize clicking on a sequence of Web links as navigation. The semantics of an object or an activity in its source domain can be defined over its behavior with a set of axioms. We propose that these axioms must also be satisfied in the target domain for an object or activity to yield a sound metaphor. We use a first-order algebraic specification language to define the semantics of “navigation” in the real world as a set of axioms, specify a Web navigating agent as algebra, and demonstrate that there exists a morphism between both specifications, which means that the Web agent behaves according to the set of wayfinding axioms. This suggested method is another step towards a formally grounded explanation of metaphorical mappings. Keywords: Metaphor, Web navigation, algebraic specification, agent model Correspondence concerning this article should be addressed to Hartwig H. Hochmair, St. Cloud State University, Department of Geography, 720 Fourth Ave South, St. Cloud, MN-56301, USA; email: [email protected] 2 HOCHMAIR, LÜTTICH 1 Introduction Metaphors have become a key idea especially in human-computer interaction (Carroll et al. 1988; Kuhn 1995). This holds specifically for spatial metaphors (Dieberger 1994; Sorrows & Hirtle 1999; Fabrikant 2000). Metaphors map features of the physical space to an abstract computational domain and allow the user to apply previously experienced concepts in the target domain. Maglio & Matlock (1998) found that Web users think of the Web as a kind of physical space in which they move, although the Web is not physical and Web users do not locomote. This result can be concluded from an extensive use of spatial metaphors when people talk about the Web. Physical navigation is often used as a metaphor for traversing hypertext documents or electronic databases (Marchionini 1995). Navigation as a goal-directed movement is a versatile concept and applicable in many domains, including many that are not literally spatial (Montello 2005). The same holds for wayfinding, which is similar to navigation in many respects. So, we can speak of "navigating through a math problem", "making one's way through one's studies", "finding one's way back to the stage", or "navigating the World Wide Web". However, like all metaphors, the navigation metaphor has some limitations and sounds strange when mapped to inappropriate activities, e.g. "navigating through a tournament" or "navigating through a book". This work tries to explain why examples such as the first four mentioned are good metaphors, whereas the latter two examples cause problems in their use. A Geographic Information System (GIS) is one of several application areas where metaphors will play an important role in the future − once remaining challenges are overcome. Through the increasing influence of the successful Macintosh user interface, advanced considerations about Human Computer Interface (HCI) for GISs have been discussed (Kuhn & Frank 1991), including object oriented approaches and graphical user interface (GUI) design. Since then, the GUI functions have been extended through direct manipulation from pure display of data to processing and analysis of geographic data, as tested for overlay functions in (Richards & Egenhofer 1995; Tsou & Buttenfield 1997). However, in GIS a comprehensive approach as found with the Star User Interface (Smith et al. 1983) is still a challenge, and GIS designers have not yet found generic user interfaces that support widely varying tasks of treating spatially referenced data. A problem is that metaphors don't scale very well. A metaphor that works well for a simple process in a simple program will often fail to work well as that process grows in size or complexity (Kuhn 1995). In general, the abstract nature of information technology creates a need for metaphors in GUIs so that users can conceptualize and understand software without having to master its technical workings. Moreover, various applications show the usability of graphical metaphors for data exploration tools, such as the clock or coil metaphor (MacEachren et al. 1999), or transparencies, folders, and push-pins (Elvins & Jain 1998). AN ANALYSIS OF THE “NAVIGATION” METAPHOR 3 1.1 Research Objective Metaphors, such as “chatroom” or “internet library”, map a familiar source concept to a more abstract target domain (Kuhn 1995). The research objective of this paper is to apply a new approach − describing why metaphors work, and how metaphors can be formalized. This approach is demonstrated for the navigation metaphor in particular. That is we try to give an explanation of why the metaphor of information seekers that navigate an information space (Nielsen 1990) is widely used and so easy to understand, and why moving the mouse pointer on hyperlinks and clicking the mouse button is referred to as navigation. We hypothesize that the semantics of a concept in the source domain can be defined through a set of axioms. Such concept would only then be comprehended as metaphor if these axioms are also satisfied in the target domain for that term, i.e., if the concept "behaves" in a similar way to how it does in the source domain. The constraints imposed on the behavior of the concept are widely independent of physical attributes. We claim that the navigation axioms are satisfied by all types of navigation in both the physical world and the Web, and we furthermore demonstrate this for one strategy in the physical world and another one in the Web space. It should be noted that these two strategies serve only as showcases, any other strategies could be chosen. Therefore, we do neither claim that the two presented strategies are similar in each respect, nor that they represent the most similar pair of strategies between the Web and the physical world. We restrict the description of mappings to behavioral patterns that are necessary to classify the described strategies and processes as navigation. All other mappings, if they exist, are irrelevant for the purpose of this work. 1.2 Research Method The approach to achieving the research objective is sketched in Figure 1. We derive the semantics for navigation in the physical world, and define a set of axioms that capture those semantics. These axioms are formalized as algebraic specification in first-order logic, shown in the left part of the dashed area in Figure 1. In a next step we describe an arbitrary Web navigation strategy in the target domain, i.e., the Web space, and abstract this behavior as executable algebraic specification, namely as a formal model. This is indicated in the right part of the dashed area. With the help of a formal language (CASL) and some software tools (HETS and Isabelle) for this language we will try to prove that the set of formalized navigation axioms, and the formal model of the Web navigation strategy, exhibit a specification morphism. 4 HOCHMAIR, LÜTTICH Figure 1. Formal approach to explain the “navigation” metaphor Besides this, we implement a real world navigation instance as a formal model. Although this is not required for the formal explanation of the metaphor, it demonstrates that the navigation axioms are also satisfied in the formal model describing navigation in the physical world. It will also help to clarify the commonalities and differences between navigating the Web space and the physical world. 1.3 Navigation Scenarios and Strategies for Both Environments The formal specification of the navigation agents with their strategies is motivated by two wayfinding scenarios, one in the Web space and one in the real world respectively. The two scenarios have been used in previous work and have been slightly adopted for the task of this paper. The first scenario (Hochmair & Frank 2001; Hochmair 2002) describes a Web navigating agent that moves in an internet directory to a Web page with a desired content, whereas the second scenario describes a navigating agent that acts in an unknown street network and uses the vector based least-angle strategy to reach its destination (Hochmair & Frank 2002; Hochmair 2005). Again, we point out here that for the purpose of this paper, namely to prove that both real world navigation and Web navigation behavior satisfy the set of navigation axioms, it is irrelevant which strategies are used in both environments, because all variations of navigation tasks and behaviors (e.g., using a map, commuting, following signs, etc.) would satisfy these axioms. A metaphor maps only analogies from its source to its target, but not all features. As a consequence, we will not attempt to map all features from the least-angle strategy to the Web strategy or the other way round. For example, it is irrelevant for the navigation process, whether the agent knows landmarks in its environment or not. Some strategies, such as piloting, may require such knowledge, where other strategies, such as following route instructions given by a GPS device, can cope without that knowledge. Inclusion of specific concepts in the comparison of strategies may be of interest when discussing the analogies between strategies, which is, however, not the focus of this paper. The strategies described in this paper are strong simplifications of real navigation behavior, but they serve the purpose of the paper.