Constructing a concept of number

Numbers are concepts whose content, structure, and organization are influenced by the material forms used to represent and manipulate them. Indeed, as argued here, it is the inclusion of multiple forms (distributed objects, fingers, single- and two-dimensional forms like pebbles and abaci, and written notations) that is the mechanism of numerical elaboration. Further, variety in employed forms explains at least part of the synchronic and diachronic variability that exists between and within cultural number systems. Material forms also impart characteristics like linearity that may persist in the form of knowledge and behaviors, ultimately yielding numerical concepts that are irreducible to and functionally independent of any particular form. Material devices used to represent and manipulate numbers also interact with language in ways that reinforce or contrast different aspects of numerical cognition. Not only does this interaction potentially explain some of the unique aspects of numerical language, it suggests that the two are complementary but ultimately distinct means of accessing numerical intuitions and insights. The potential inclusion of materiality in contemporary research in numerical cognition is advocated, both for its explanatory power, as well as its influence on psychological, behavioral, and linguistic aspects of numerical cognition

A Formal Model of Metaphor in Frame Semantics

A formal model of metaphor is introduced. It models metaphor, first, as an interaction of “frames” according to the frame semantics, and then, as a wave function in Hilbert space. The practical way for a probability distribution and a corresponding wave function to be assigned to a given metaphor in a given language is considered. A series of formal definitions is deduced from this for: “representation”, “reality”, “language”, “ontology”, etc. All are based on Hilbert space. A few statements about a quantum computer are implied: The sodefined reality is inherent and internal to it. It can report a result only “metaphorically”. It will demolish transmitting the result “literally”, i.e. absolutely exactly. A new and different formal definition of metaphor is introduced as a few entangled wave functions corresponding to different “signs” in different language formally defined as above. The change of frames as the change from the one to the other formal definition of metaphor is interpreted as a formal definition of thought. Four areas of cognition are unified as different but isomorphic interpretations of the mathematical model based on Hilbert space. These are: quantum mechanics, frame semantics, formal semantics by means of quantum computer, and the theory of metaphor in linguistics

Reinventing discovery learning: a field-wide research program

© 2017, Springer Science+Business Media B.V., part of Springer Nature. Whereas some educational designers believe that students should learn new concepts through explorative problem solving within dedicated environments that constrain key parameters of their search and then support their progressive appropriation of empowering disciplinary forms, others are critical of the ultimate efficacy of this discovery-based pedagogical philosophy, citing an inherent structural challenge of students constructing historically achieved conceptual structures from their ingenuous notions. This special issue presents six educational research projects that, while adhering to principles of discovery-based learning, are motivated by complementary philosophical stances and theoretical constructs. The editorial introduction frames the set of projects as collectively exemplifying the viability and breadth of discovery-based learning, even as these projects: (a) put to work a span of design heuristics, such as productive failure, surfacing implicit know-how, playing epistemic games, problem posing, or participatory simulation activities; (b) vary in their target content and skills, including building electric circuits, solving algebra problems, driving safely in traffic jams, and performing martial-arts maneuvers; and (c) employ different media, such as interactive computer-based modules for constructing models of scientific phenomena or mathematical problem situations, networked classroom collective “video games,” and intercorporeal master–student training practices. The authors of these papers consider the potential generativity of their design heuristics across domains and contexts

Complexity as Process: Complexity Inspired Approaches to Composition

This article examines the use of Complexity Theory as an inspiration for the creation of new musical works, and highlights problems and possible solutions associated with its application as a compositional tool. In particular it explores how the philosophy behind Complexity Theory affects notions of process-based composition, indeterminacy in music and the performer/listener/environment relationship, culminating in providing a basis for the understanding of music creation as an active process within a context. The author presents one of his own sound installations, Cross-Pollination, as an example of a composition inspired and best understood from the philosophical position as described in Complexity Theory

Interactional Structure Applied to the Identification and Generation of Visual Interactive Behavior: Robots that (Usually) Follow the Rules

Peer reviewe

Cyberspace As/And Space

The appropriate role of place- and space-based metaphors for the Internet and its constituent nodes and networks is hotly contested. This essay seeks to provoke critical reflection on the implications of place- and space-based theories of cyberspace for the ongoing production of networked space more generally. It argues, first, that adherents of the cyberspace metaphor have been insufficiently sensitive to the ways in which theories of cyberspace as space themselves function as acts of social construction. Specifically, the leading theories all have deployed the metaphoric construct of cyberspace to situate cyberspace, explicitly or implicitly, as separate space. This denies all of the ways in which cyberspace operates as both extension and evolution of everyday spatial practice. Next, it argues that critics of the cyberspace metaphor have confused two senses of space and two senses of metaphor. The cyberspace metaphor does not refer to abstract, Cartesian space, but instead expresses an experienced spatiality mediated by embodied human cognition. Cyberspace in this sense is relative, mutable, and constituted via the interactions among practice, conceptualization, and representation. The insights drawn from this exercise suggest a very different way of understanding both the spatiality of cyberspace and its architectural and regulatory challenges. In particular, they suggest closer attention to three ongoing shifts: the emergence of a new sense of social space, which the author calls networked space; the interpenetration of embodied, formerly bounded space by networked space; and the ways in which these developments alter, instantiate, and disrupt geographies of power

Towards a Theory Grounded Theory of Language

In this paper, we build upon the idea of theory grounding and propose one specific form of theory grounding, a theory of language. Theory grounding is the idea that we can imbue our embodied artificially intelligent systems with theories by modeling the way humans, and specifically young children, develop skills with theories. Modeling theory development promises to increase the conceptual and behavioral flexibility of these systems. An example of theory development in children is the social understanding referred to as “theory of mind.” Language is a natural task for theory grounding because it is vital in symbolic skills and apparently necessary in developing theories. Word learning, and specifically developing a concept of words, is proposed as the first step in a theory grounded theory of language

A qualitative enquiry into OpenStreetMap making

Based on a case study on the OpenStreetMap community, this paper provides a contextual and embodied understanding of the user-led, user-participatory and user-generated produsage phenomenon. It employs Grounded Theory, Social Worlds Theory, and qualitative methods to illuminate and explores the produsage processes of OpenStreetMap making, and how knowledge artefacts such as maps can be collectively and collaboratively produced by a community of people, who are situated in different places around the world but engaged with the same repertoire of mapping practices. The empirical data illustrate that OpenStreetMap itself acts as a boundary object that enables actors from different social worlds to co-produce the Map through interacting with each other and negotiating the meanings of mapping, the mapping data and the Map itself. The discourses also show that unlike traditional maps that black-box cartographic knowledge and offer a single dominant perspective of cities or places, OpenStreetMap is an embodied epistemic object that embraces different world views. The paper also explores how contributors build their identities as an OpenStreetMaper alongside some other identities they have. Understanding the identity-building process helps to understand mapping as an embodied activity with emotional, cognitive and social repertoires

Tangible user interfaces : past, present and future directions

In the last two decades, Tangible User Interfaces (TUIs) have emerged as a new interface type that interlinks the digital and physical worlds. Drawing upon users' knowledge and skills of interaction with the real non-digital world, TUIs show a potential to enhance the way in which people interact with and leverage digital information. However, TUI research is still in its infancy and extensive research is required in or- der to fully understand the implications of tangible user interfaces, to develop technologies that further bridge the digital and the physical, and to guide TUI design with empirical knowledge. This paper examines the existing body of work on Tangible User In- terfaces. We start by sketching the history of tangible user interfaces, examining the intellectual origins of this field. We then present TUIs in a broader context, survey application domains, and review frame- works and taxonomies. We also discuss conceptual foundations of TUIs including perspectives from cognitive sciences, phycology, and philoso- phy. Methods and technologies for designing, building, and evaluating TUIs are also addressed. Finally, we discuss the strengths and limita- tions of TUIs and chart directions for future research