On Information, Meaning, Space and Geometry

On Information, Meaning, Space and Geometry

Sándor Darányi (University of Gothenburg, Sweden & University College Borås, Sweden) and Péter Wittek (National University of Singapore, Singapore)
DOI: 10.4018/978-1-60566-020-2.ch016
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Current methods of automatic indexing, automatic classification, and information retrieval treat index and query terms, that is, vocabulary units in any language, as locations in a geometry. With spatial sense relations among such units identified, and syntax added, the making of a geometric equivalent of language for advanced communication is an opportunity to be explored.
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In what follows, we offer a few general considerations, with theoretical overtones, working toward the definition and generation of a geometric language for practical purposes, prominently for information retrieval (IR). This chapter is a nonmathematical introduction to the mathematical modelling of meaning of both words and sentences, outlining already existing components of such an endeavour, and hinting at directions of synthesis. Technical aspects of realization will be discussed in forthcoming articles.

A mathematical treatise of the dependence of information visualization on structures being visualized, first and foremost, the interdependencies between language and space, has been long overdue. Elements of such a systematic treatise are emerging in the interacting fields of information retrieval and language technology, whenever the structure of concept space is discussed by addressing subject classifications inhabiting such spaces and influencing the efficiency of information retrieval. Fine recent examples on the topic include van Rijsbergen (2004) and Widdows (2004). In a general sense, questions about the nature of information and meaning, in the form of word and sentence semantics, are pertinent to the outcome of the modelling effort: the better the mathematical description of linguistic information (and the behaviour of linguistic and nonlinguistic information per se), the higher hopes one may have for constructing more efficient IR models and systems. On the other hand, the number of observations pointing in the same direction, the feasibility of such a general model, is on the increase, a fact hopefully justifying our attempt at listing some of them.

To start with an immediate difficulty, meaning is both perceived and processed; therefore, it can be assigned both to percept and concept spaces. This distinction goes back to Karl Pearsson (1911, pp. 191-208, reprinted in Kockelmans, 1999, pp. 191-205), for whom perceptual spaces are, strictly speaking subjective, whereas concept spaces as a means of scientific description are objective. Further, “[S]pace is not a thing but an order of things. To say that a thing exists in space is to assert that our perceptive faculty has distinguished this thing as a group of sense perceptions from other groups of sense perceptions which actually (or possibly) coexist. In other words, space is not a real thing in the sense on an immediately given phenomenon, but merely our mode of perceiving phenomena, in short a mode of our perceptive faculty” (Kockelmans, 1999, p. 190). On the other hand, if the space of perception is like this, the question arises: “What is conceptual space – the space with which we deal in the science of geometry? We have seen that our perceptive faculty presents sense-impressions to us as separated into groups, and further that though this separation is most serviceable for practical purposes, it is not very exactly and clearly defined “at the limits.” How do we represent in thought, in conception, this separation into groups that results from our mode of perception? The answer is, „we conceive sense-impressions to be bound by surfaces, to be limited by straight or curved lines. Thus our consideration of conceptual space leads us at once to a discussion of surfaces and lines – to a study, in fact, of Geometry” (Pearson, 1911, p. 191). Likewise, for Wittgenstein, geometry is the grammar of space (Baker, 2003, p. 521)1 and of spatial relations (Hacker, 1996, p. 50), that is Pearson’s distinction prevails. This raises the question whether such phrases as “perceptual space” and “concept space” have a geometric reality; that is, if kinds of geometry can model percept and concept agglomerations to a reasonable extent; and in particular, whether meaning in language, regardless of being considered a percept or a concept, can be adequately reproduced by means of geometry.

Complete Chapter List

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Table of Contents
Chapter 1
Alan Dix
Map, mazes, myths, magic, and mathematics, computation, cognition, community, and the constructed environment, all reveal something of our internal... Sample PDF
Paths and Patches: Patterns of Geognosy and Gnosis
Chapter 2
Jon Kerridge
This chapter concerns the question of how people navigate through a space in which other people are also present. Issues addressed include how the... Sample PDF
Let's Meander Through a Measured Space
Chapter 3
Matthew Leach
The Speckled Computing project is a large multisite research project based in Scotland, UK. The aim of the project is to investigate, prototype, and... Sample PDF
Navigating a Speckled World: Interacting with Wireless Sensor Networks
Chapter 4
John Willy Bakke
Workplaces are key loci for expressing and studying organizational identity, even in distributed work. In organization studies, there is a growing... Sample PDF
Contested Terrain: Place, Work, and Organizational Identities
Chapter 5
Anne Sofie Laegran
The chapter is based on a study of Internet cafés in Norway, and interrogates the way space and place is produced in interconnections between people... Sample PDF
Technosocial Space: Connecting People and Places
Chapter 6
Lynne Hall
This chapter discusses artists’ use of virtual space to collaboratively create a digital stained-glass rose window. It explores the use of virtual... Sample PDF
Reconfiguring the Rose: An Exploration of the Use of Virtual Space by Artists Collaboratively Creating Digital Stained Glass
Chapter 7
Elin K. Jacob
In distinguishing between space and place, one approach is to contrast the physicality of space with the sociality of place: space directs attention... Sample PDF
Context, Boundedness, and Structure: The Apprehension of Place in the Development of Information Environments
Chapter 8
Richard Coyne
The widespread use of mobile telephony prompts a reevaluation of the role of the aural sense in spatial understanding. There are clear correlations... Sample PDF
Voice and Space: Agency of the Acousmêtre in Spatial Design
Chapter 9
Susan Turner
This chapter considers the role of sound, and more specifically, listening, in creating a sense of presence (of “being there”) in “places” recreated... Sample PDF
Listening, Corporeality, Place and Presence
Chapter 10
Stephen Boyd Davis
The chapter is concerned with the relationship between the planar space of graphic representations and the world space that they represent. To... Sample PDF
Representing Space: The Pictorial Imperative
Chapter 11
Fiona Carroll
The art of the visual-narrative is not a new phenomenon. Artists and designers have been using images to tell stories for thousands of years. From... Sample PDF
The Spatial Development of the Visual-Narrative from Prehistoric Cave Paintings to Computer Games
Chapter 12
Shaleph O’Neill
The Situationists defined the increasingly spectacularized society (The Society of the Spectacle ) as the alienation of the individual by an... Sample PDF
The Interactive Spectacle and the Digital Situationist
Chapter 13
Shaun Lawson
People use spatial language in everyday face-to-face conversation, and we also now use such language during everyday computer-mediated interactions.... Sample PDF
Spatial Language in Computer Mediated Communication
Chapter 14
Phil Turner
Recent years have witnessed a number of initiatives to develop technology (“memory prosthetics”) to enhance and extend human memory. Typical of... Sample PDF
Space, Place, and Memory Prosthetics
Chapter 15
Julian Warner
This chapter is concerned with exposing the material basis for the concepts of the syntagm and paradigm from linguistics, and the message and... Sample PDF
Materializing Communication Concepts: Linearity and Surface in Linguistics and Information Theory
Chapter 16
Sándor Darányi, Péter Wittek
Current methods of automatic indexing, automatic classification, and information retrieval treat index and query terms, that is, vocabulary units in... Sample PDF
On Information, Meaning, Space and Geometry
About the Contributors