The contribution deals with some key problems of cognitive science, whose plurality transcends the boundaries of the disciplines drawn by classical epistemology. In particular, it addresses the issues of mental images, spaces of representation, and the architecture of cognitive processes in vision theory. The thesis presented is that a proper treatment of vision within psychophysics entails an analysis of a series of interconnected spaces, objects and methodologies, from psychophysics to the many virtual realities of representation.

Philosophical considerations as well as several recent studies from neurophysiology, neuropsychology, and psychophysics converged in showing that the peripersonal space is structured in a body-centred manner and represented through integrated sensory inputs. Multisensory representations may deserve the function of coding peripersonal space for avoiding or interacting with objects. Neuropsychological evidence is reviewed for dynamic interactions between space representations and action execution, as revealed by the behavioural effects that the use of a tool, as a physical extension of (...) the reachable space, produces on visual–tactile extinction. In particular, tool-use transiently modifies action space representation in a functionally effective way. The possibility is discussed that the investigation of multisensory space representations for action provides an empirical way to consider in its specificity pre-reflexive self-consciousness by considering the intertwining of self-relatedness and object-directness of spatial experience shaped by multisensory and sensorimotor integrations. (shrink)

Nowadays the issues of space and place pertain more than ever to the ongoing discussion about personal/regional/national identities. The worlds of private archives of memory often exist independently of political and administrative divisions, while dominant ideologies are often capable of re-defining national archives of memory through selective representation of the past. The way we remember our past and our heritage inscribes the space we live in: the places we remember and the places we wish to forget, the (...) monuments we pull down and erect and the museums we build are only some of the signposts on the landscape of our cultural memory. The essays collected in this volume examine the role of places and spaces in the formation of both cultural practices and the existential experience of modern individual. (shrink)

The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural (...) solution to the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented. (shrink)

When left-neglect patients are required to extend horizontal segments to double their original length, relative left overextension is frequently observed. Less frequently, relative left underextension may also be found. It was hypothesized that this contrast could depend on the degree of horizontal anisometry of the medium for the representation of spatial properties. The present paper reports an experiment conducted in order to test that hypothesis, on the basis of which left overextension should be larger with shorter than with longer (...) segments and with segments lying in the right rather than in the left hemispace. Although supportive, the results unveiled unexpected complications: the expected effect of line length was found only in neglect patients with frontal damage, while the expected effect of side of presentation was found only in neglect patients without frontal damage. (shrink)

Ninety-one right brain-damaged patients with left neglect and 43 right brain-damaged patients without neglect were asked to extend horizontal segments, either left- or rightward, starting from their right or left endpoints, respectively. Earlier experiments based on similar tasks had shown, in left neglect patients, a tendency to overextend segments toward the left side. This seemingly paradoxical phenomenon was held to undermine current explanations of unilateral neglect. The results of the present extensive research demonstrate that contralesional overextension is also evident in (...) most right brain-damaged patients without contralesional neglect. Furthermore, they show that in a minority of left neglect patients, the opposite behavior, i.e., right overextension can be found. The paper also reports the results of correlational analyses comprising the parameters of line-extension, line-bisection, and cancellation tasks, as well as the parameters relative to the Milner Landmark Task, by which a distinction is drawn between perceptual and response biases in unilateral neglect. A working hypothesis is then advanced about the brain dysfunction underlying neglect and an attempt is made at finding an explanation of neglect and the links between the mechanisms of space representation and consciousness through the study of the changes induced by unilateral brain lesions in the characteristics of space-coding neurons. Abbreviations: C, control group;GN+91,full group of neglect patients;GN+27,group of neglect patients with relative left overextension;GN+14,group of neglect patients with relative right overextension;GN-43,full group of non-neglect patients;GN-9,group of non-neglect patients with relative left overextension; H canc, H cancellation task; LE, left extension; LE/RE, ratio of left-right extension; N+, neglect patients; N-, non-neglect patients; PB Land-M, perceptual bias on Landmark motor task; PB Land-V, perceptual bias on Landmark verbal task; RB Land-M, response bias on Landmark motor task; RB Land-V, response bias on Landmark verbal task; RE, right extension. (shrink)

We apply the Galilean covariant formulation of quantum dynamics to derive the phase-space representation of the Pauli–Schrödinger equation for the density matrix of spin-1/2 particles in the presence of an electromagnetic field. The Liouville operator for the particle with spin follows from using the Wigner–Moyal transformation and a suitable Clifford algebra constructed on the phase space of a (4 + 1)-dimensional space–time with Galilean geometry. Connections with the algebraic formalism of thermofield dynamics are also investigated.

The quasiclassical representations of quantum theory, generalizing the concept of a phase-space representation of quantum mechanics, are studied with particular emphasis on some questions connected with the Jordan structure of the classical and quantum algebras of observables. A generalized version of the theorem of Gleason, Kahane, and Zelazko is used to establish some nonclassical features of these representations.

In this commentary, I propose that horizontal and vertical dimensions of space are represented together inside a common metrics mechanism located in the parietal cortex. Importantly, this network is also involved in the processing of number magnitudes and environment-directed actions. Altogether, the evidence suggests that different magnitude dimensions could be intertwined with the horizontality and verticality of our world representation.

During the last decades, many cognitive architectures (CAs) have been realized adopting different assumptions about the organization and the representation of their knowledge level. Some of them (e.g. SOAR [35]) adopt a classical symbolic approach, some (e.g. LEABRA[ 48]) are based on a purely connectionist model, while others (e.g. CLARION [59]) adopt a hybrid approach combining connectionist and symbolic representational levels. Additionally, some attempts (e.g. biSOAR) trying to extend the representational capacities of CAs by integrating diagrammatical representations and reasoning (...) are also available [34]. In this paper we propose a reflection on the role that Conceptual Spaces, a framework developed by Peter G¨ardenfors [24] more than fifteen years ago, can play in the current development of the Knowledge Level in Cognitive Systems and Architectures. In particular, we claim that Conceptual Spaces offer a lingua franca that allows to unify and generalize many aspects of the symbolic, sub-symbolic and diagrammatic approaches (by overcoming some of their typical problems) and to integrate them on a common ground. In doing so we extend and detail some of the arguments explored by G¨ardenfors [23] for defending the need of a conceptual, intermediate, representation level between the symbolic and the sub-symbolic one. In particular we focus on the advantages offered by Conceptual Spaces (w.r.t. symbolic and sub-symbolic approaches) in dealing with the problem of compositionality of representations based on typicality traits. Additionally, we argue that Conceptual Spaces could offer a unifying framework for interpreting many kinds of diagrammatic and analogical representations. As a consequence, their adoption could also favor the integration of diagrammatical representation and reasoning in CAs. (shrink)

Life, but not as we know it -- Still life in nearly present time -- Driving and the city -- Movement-space -- Afterwords -- From born to made -- Spatialities of feeling -- But malice aforethought -- Turbulent passions.

Visual space can be distinguished from physical space. The first is found in visual experience, while the second is defined independently of perception. Theorists have wondered about the relation between the two. Some investigators have concluded that visual space is non-Euclidean, and that it does not have a single metric structure. Here it is argued that visual space exhibits contraction in all three dimensions with increasing distance from the observer, that experienced features of this contraction are (...) not the same as would be the experience of a perspective projection onto a fronto-parallel plane, and that such contraction is consistent with size constancy. These properties of visual space are different from those that would be predicted if spatial perception resulted from the successful solution of the inverse problem. They are consistent with the notion that optical constraints have been internalized. More generally, they are also consistent with the notion that visual spatial structures bear a resemblance relation to physical spatial structures. This notion supports a type of representational relation that is distinct from mere causal correspondence. The reticence of some philosophers and psychologists to discuss the structure of phenomenal space is diagnosed in terms of the simple materialism and the functionalism of the 1970s and 1980s. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” Type-1 (...) problems, by contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

The dominating models of information processes have been based on symbolic representations of information and knowledge. During the last decades, a variety of non-symbolic models have been proposed as superior. The prime examples of models within the non-symbolic approach are neural networks. However, to a large extent they lack a higher-level theory of representation. In this paper, conceptual spaces are suggested as an appropriate framework for non- symbolic models. Conceptual spaces consist of a number of 'quality dimensions' that often (...) are derived from perceptual mechanisms. It will be outlined how conceptual spaces can represent various kind of information and how they can be used to describe concept learning. The connections to prototype theory will also be presented. (shrink)

The posterior parietal cortex (PPC) is the most likely site where egocentric spatial relationships are represented in the brain. PPC cells receive visual, auditory, somaesthetic, and vestibular sensory inputs; oculomotor, head, limb, and body motor signals; and strong motivational projections from the limbic system. Their discharge increases not only when an animal moves towards a sensory target, but also when it directs its attention to it. PPC lesions have the opposite effect: sensory inattention and neglect. The PPC does not seem (...) to contain a “map” of the location of objects in space but a distributed neural network for transforming one set of sensory vectors into other sensory reference frames or into various motor coordinate systems. Which set of transformation rules is used probably depends on attention, which selectively enhances the synapses needed for making a particular sensory comparison or aiming a particular movement. (shrink)

What is the role of language in constructing knowledge? In this article, we ask whether learning new relational language can create new ways of thinking. In Experiment 1, we taught English speakers to talk about time using new vertical linguistic metaphors, saying things like “breakfast is above dinner” or “breakfast is below dinner”. In Experiment 2, rather than teaching people new metaphors, we relied on the left–right representations of time that our American college student participants have already internalized through a (...) lifetime of visuospatial experience reading and writing text from left to right. In both experiments, we asked whether the representations are susceptible to verbal interference. We found that learning new metaphors created new space–time associations that could be detected in a nonlinguistic implicit association task; these newly learned representations were not susceptible to verbal interference; and with respect to both verbal and visual interference, representations newly learned from linguistic metaphor behaved just like those on the left–right axis that our participants had acquired through years of visuospatial experience. Taken together, these results suggest that learning new relational language can be a powerful tool in constructing new representations and expanding our cognitive repertoire. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large type-2 problems. they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of (...) recoding biases so as to reduce specific type-2 problems to (tractable) type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general (not task-specific) strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy representational redescription language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Religious Representation in Place brings together an interdisciplinary group of scholars from the Humanities and Sciences to broaden the understanding of how religious symbols and spatial studies interact. The essays consider the relevance of religion in the experience of space, a fundamental dimension of culture and human life.

This article illustrates the ways in which visual representations construct the meanings of norms governing the spaces we commonly inhabit. I argue that norms regulating public spaces such as streets, parks, plazas, and beaches arise within the process of conceiving tourist representations of space that benefit hegemonic groups in society. My argument is empirically grounded on evidence from a case study on public space regulation in Acapulco, Mexico. By means of a semiotic analysis of tourist materials such as (...) maps and postcards, I show that images related to tourism represent urban space in a way that includes some elements and excludes others. By doing so, they portray a very specific image of the city and its public spaces. Because representations of space are performed upon the entire society, the imagery reproduced by tourist materials is part of the expectations that surround social actors’ actions. This is one of the mechanisms through which the tourism industry influences the regulation of public spaces. (shrink)

We illustrate the application of the conceptual analysis (CA) method outlined in Part I by the example of quantum mechanics. In the present part the Hilbert space structure of conventional quantum mechanics is deduced as a consequence of postulates specifying further idealized concepts. A critical discussion of the idealizations of quantum mechanics is proposed. Quantum mechanics is characterized as a “statistically complete” theory and a simple and elegant formal recipe for the construction of the fundamental mathematical apparatus of quantum (...) mechanics is formulated. Our analysis may also lead to a criticism of quantum mechanics as a “strongly idealized” theory. A critical analysis of the fundamental structure of quantum mechanics seems an indispensable and natural starting point for the construction of new theories. A major technical problem in a more general application of the CA method is the lack of mathematical representation theorems for more general algebraic structures. (shrink)

A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An application of this result provides a (...) characterization of the projection lattices in operator algebras. (shrink)

This article analyses the multimodal representations of public space in Chilean broadcast news reports on the figure of the hooded rioter and its alleged connections with the student movement. We seek to identify how space is constructed as a legitimation strategy in relation to the actors involved and the actions taking place across four different news broadcast pieces in the light of Multimodal Critical Discourse Analysis and Systemic Functional Linguistics. Results show that the multimodal representations of space (...) are crucial to identify and functionalize hooded rioters as belonging to the student movement. Actions are dependent on the spaces in which actors operate, restricting the occupation of certain spaces to specific actors. Thus, transgressive protest actions are to be contained to educational spaces and represented as naturalized vandalism, ignoring the students’/demonstrators’ motivations to recuperate/vindicate the public space. (shrink)

b>: The problem of how physical systems, such as brains, come to represent themselves as subjects in an objective world is addressed. I develop an account of the requirements for this ability that draws on and refines work in a philosophical tradition that runs from Kant through Peter Strawson to Gareth Evans. The basic idea is that the ability to represent oneself as a subject in a world whose existence is independent of oneself involves the ability to represent space, (...) and in particular, to represent oneself as one object among others in an objective spatial realm. In parallel, I provide an account of how this ability, and the mechanisms that support it, are realized neurobiologically. This aspect of the article draws on, and refines, work done in the neurobiology and psychology of egocentric and allocentric spatial representation. (shrink)

We introduce and study several nonstandard representations of Banach-valued operators defined on the space of Bochner integrable functions. They will be less restrictive than the usual standard representation. In particular, without any hypothesis, we shall find a representation whose kernel belongs to a space of “extended Bochner integrable functions”, introduced by Zimmer by using Loeb measures.

We show that metric spaces and continuous functions between them are domain representable using the category of Scott-Ershov domains. A notion of effectivity for metric spaces is thereby inherited from effective domain theory. It is shown that a separable metric space with an effective metric can be represented by an effective domain. For a class of spaces, including the Euclidean spaces, the usual notions of effectivity are obtained. The Banach fixed point theorem is a consequence of the least fixed (...) point theorem for domains. A notion of semieffective domains is introduced and used to give a new proof of Ceitin's theorem. (shrink)

We investigate ideals of the form {A⊆ω: Σn∈Axnis unconditionally convergent} where n∈ωis a sequence in a Polish group or in a Banach space. If an ideal onωcan be seen in this form for some sequence inX, then we say that it is representable inX.After numerous examples we show the following theorems: An ideal is representable in a Polish Abelian group iff it is an analytic P-ideal. An ideal is representable in a Banach space iff it is a nonpathological (...) analytic P-ideal.We focus on the family of ideals representable inc0. We characterize this property via the defining sequence of measures. We prove that the trace of the null ideal, Farah’s ideal, and Tsirelson ideals are not representable inc0, and that a tallFσP-ideal is representable inc0iff it is a summable ideal. Also, we provide an example of a peculiar ideal which is representable inℓ1but not in ℝ.Finally, we summarize some open problems of this topic. (shrink)

We look at bimodal logics interpreted by cartesian products of topological spaces and discuss the validity of certain bimodal formulae in products of so-called cardinal spaces. This solves an open problem of van Benthem et al.

Social interaction and the constitution of mediated and nested space in the court of appeal -- Conclusion -- Concluding remarks: On becoming juridical -- Ways of spacing law and politics -- Becoming juridical -- Towards hybrid juridical spaces -- References -- Index.

Most historians of science eagerly acknowledge that the early modern period witnessed a shift from a prevailing Aristotelian, spherical, centered conception of space to a prevailing Cartesian, rectilinear, oriented spatial framework. Indeed, this shift underlay many of the important advances for which the period is celebrated. However, historians have failed to engage the general conceptual shift, focusing instead on the particular explanatory developments that resulted. This historical lacuna can be attributed to a historiographical problem: the lack of an adequate (...) unit of analysis by which to investigate the conceptual change. Here, a philosophical argument is made for representations of space as an appropriate category of historical investigation, and methods of textual interrogation are suggested to this end. Finally, two examples, taken from Aristotle and Newton, demonstrate the feasibility and importance of this project. (shrink)

We investigate the use of coalgebra to represent quantum systems, thus providing a basis for the use of coalgebraic methods in quantum information and computation. Coalgebras allow the dynamics of repeated measurement to be captured, and provide mathematical tools such as final coalgebras, bisimulation and coalgebraic logic. However, the standard coalgebraic framework does not accommodate contravariance, and is too rigid to allow physical symmetries to be represented. We introduce a fibrational structure on coalgebras in which contravariance is represented by indexing. (...) We use this structure to give a universal semantics for quantum systems based on a final coalgebra construction. We characterize equality in this semantics as projective equivalence. We also define an analogous indexed structure for Chu spaces, and use this to obtain a novel categorical description of the category of Chu spaces. We use the indexed structures of Chu spaces and coalgebras over a common base to define a truncation functor from coalgebras to Chu spaces. This truncation functor is used to lift the full and faithful representation of the groupoid of physical symmetries on Hilbert spaces into Chu spaces, obtained in our previous work, to the coalgebraic semantics. (shrink)

Kant argued that the perceptual representations of space and time were templates for the perceived spatiotemporal ordering of objects, and common to all modalities. His idea is that these perceptual representations were specific to no modality, but prior to all—they are pre-modal, so to speak. In this paper, it is argued that active perception—purposeful interactive exploration of the environment by the senses—demands premodal representations of time and space.

The libidinal economy could be exploited by both political movements and advertising campaigns in a pictorial space that is related to the social space at any historical moment. The arrangement of desires in a propaganda poster of the Chinese Cultural Revolution is, in light of political semiotics, the same as in a campaign poster in a consumer society today. The same libidinal economy is rooted in our political unconsciousness and remains to be the deep structure of our political (...) performance. A critical image analysis or a political semiotic critique of this libidinal economy that rules us in the Chinese Cultural Revolution and in consumer society today is necessary and urgent. (shrink)

Abstract:Unable to produce scales of one-to-one in places or spaces, people interact as they develop common representations, actions, and objects. In places, they can point to connect representations and objects. Places may be small spaces, but spaces can contain places and even more variations. Unable to name each variation, actors and analysts create abstractions. They might use a part to represent the whole, with miles of track for railroads, kilowatt-hours for electric power, and barrels of oil for energy. Some treat (...) their representations as hegemonic, even true. However, dealing with social and material variations, actors and analysts represent, build, maintain, and repair combinations of cultures, economies, governments, and materials. Thus, railroads and power systems, like other technologies and infrastructures, do not design, build, or repair themselves. To resolve problems, people with relevant skillsets interact in places to create common representations, actions, and objects tying themselves and others together in spaces. (shrink)