Spatial Aggregation: Theory and Applications

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.Comment: See http://www.jair.org/ for any accompanying file

Form, science, and narrative in the anthropocene

A significant strand of contemporary fiction engages with scientific models that highlight a constitutive interdependency between humanity and material realities such as the climate or the geological history of our planet. This article looks at the ways in which narrative may capture this human-nonhuman interrelation, which occupies the foreground of debates on the so-called Anthropocene. I argue that the formal dimension of scientific knowledge-as manifested by diagrams or metaphors used by scientists-is central to this narrative remediation. I explore two analogical strategies through which narrative may pursue a formal dialogue with science: clusters of metaphorical language and the global structuring of the plot. Rivka Galchen's novel Atmospheric Disturbances (2008), for instance, builds on a visual representation of meteorological patterns in a storm (lifted from an actual scientific paper) to stage the narrator's mental illness. Two other contemporary works (Orfeo by Richard Powers and A Tale for the Time Being by Ruth Ozeki) integrate scientific models through the overall design of the plot. By offering close readings of these novels, I seek to expand work in the area of New Formalism and show how formal choices are crucial to bringing together the human-scale world and more-than-human phenomena

The mind-body problem; three equations and one solution represented by immaterial-material data

Human life occurs within a complex bio-psycho-social milieu, a heterogeneous system that is integrated by multiple bidirectional interrelations existing between the abstract-intangible ideas and physical-chemical support of environment. The mind is thus placed between the abstract ideas/ concepts and neurobiological brain that is further connected to environment. In other words, the mind acts as an interface between the immaterial (abstract/ intangible) data and material (biological) support. The science is unable to conceives and explains an interaction between the immaterial and material domains (to understand nature of the mind), this question generating in literature the mind-body problem. We have published in the past a succession of articles related to the mind-body problem, in order to demonstrate the fact that this question is actually a false issue. The phenomenon of immaterial-material interaction is impossible to be explained because it never occurs, which means that there is no need to explain the immaterial-material interaction. Our mind implies only a temporal association between the immaterial data and material support, this dynamic interrelation being presented and argued here as a solution to the mind-body problem. The limited psycho-biologic approach of the mind-body problem is expanded here to a more comprehensive and feasible bio-psycho-social perspective, generating thus three distinct (bio- psychological, bio-social, and psycho-social) equations. These three equations can be solved through a solution represented by a dynamic cerebral system (two distinct and interconnected subunits of the brain) which presumably could have the capability of receiving and processing abstract data through association (with no interaction) between immaterial and material data

Multiple representations in cognitive architectures

The widely demonstrated ability of humans to deal with multiple representations of information has a number of important implications for a proposed standard model of the mind (SMM). In this paper we outline four and argue that a SMM must incorporate (a) multiple representational formats and (b) meta-cognitive processes that operate on them. We then describe current approaches to extend cognitive architectures with visual-spatial representations, in part to illustrate the limitations of current architectures in relation to the implications we raise but also to identify the basis upon which a consensus about the nature of these additional representations can be agreed. We believe that addressing these implications and outlining a specification for multiple represen- tations should be a key goal for those seeking to develop a standard model of the mind

Algebraic symbolism as a conceptual barrier in learning mathematics

The use of symbolism in mathematics is probably the mostly quoted reason people use for explaining their lack of understanding and difficulties in learning mathematics. We will consider symbolism as a conceptual barrier drawing on some recent findings in historical epistemology and cognitive psychology. Instead of relying on the narrow psychological interpretation of epistemic obstacles we use the barrier for situating symbolism in the ‘ontogeny recapitulates phylogeny’-debate. Drawing on a recent study within historical epistemology we show how early symbolism functioned in a way similar to concrete operational schemes. Furthermore we will discuss several studies from cognitive psychology which come to the conclusion that symbolism is not as abstract and arbitrary as one considers but often relies on perceptually organized grouping and concrete spatial relations. We will use operations on fractions to show that the reliance on concrete spatial operations also provides opportunities for teaching. We will conclude arguing that a better conceptual understanding of symbolism by teachers will prepare them for possible difficulties that students will be confronted with in the classroom

Moveable worlds/digital scenographies

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ Intellect Ltd 2010.The mixed reality choreographic installation UKIYO explored in this article reflects an interest in scenographic practices that connect physical space to virtual worlds and explore how performers can move between material and immaterial spaces. The spatial design for UKIYO is inspired by Japanese hanamichi and western fashion runways, emphasizing the research production company's commitment to various creative crossovers between movement languages, innovative wearable design for interactive performance, acoustic and electronic sound processing and digital image objects that have a plastic as well as an immaterial/virtual dimension. The work integrates various forms of making art in order to visualize things that are not in themselves visual, or which connect visual and kinaesthetic/tactile/auditory experiences. The ‘Moveable Worlds’ in this essay are also reflections of the narrative spaces, subtexts and auditory relationships in the mutating matrix of an installation-space inviting the audience to move around and follow its sensorial experiences, drawn near to the bodies of the dancers.Brunel University, the British Council, and the Japan Foundation