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)

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.

This article reviews experimental evidence for a specific sensorimotor function which can be dissociated from higher level representations of space. It attempts to delineate this function on the basis of results obtained by psychophysical experiments performed with brain damaged and healthy subjects. Eye and hand movement control exhibit automatic features, such that they are incompatible with conscious control. In addition, they rely on a reference frame different from the one used by conscious perception. Neuropsychological cases provide a strong support (...) for this specific motor representation of space, which can be spared in patients with lesions of primary sensory systems who have lost conscious perception of visual, tactile or proprioceptive stimuli. Observation of these patients also showed that their motor behavior can be ''attracted'' by a goal only under specific conditions, that is, when the response is immediate and when no cognitive representation of this goal is elaborated at the same time. Beyond the issue of the dissociation between an implicit motor representation and more cognitive processing of spatial information, the issue of the interaction between these two systems is thus a matter of interest. It is suggested that the conscious, cognitive representation of a stimulus can contaminate or override the short-lived motor representation, but no reciprocal influence seem to occur. The interaction observed in patients can also be investigated in normals. The literature provides examples of interaction between sensorimotor and cognitive framing of space, which confirm that immediate action is not mediated by the same system as delayed action, and that elaborating a categorial representation of the action goal prevents the expression of the short-lived sensorimotor representation. It is concluded that action can be controlled by a sensory system which is specialized for on-line processing of relevant goal characteristics. The temporal constraints of this system are such that it can affect the action before a full sensory analysis of this goal has been completed. The performance obtained on the basis of this spatial sensory processing suggests that short-lived motor representations may rather be considered as real ''presentation'' of the action world, which share its metric properties. (shrink)

:Space is not an empirical concept that has been drawn from outer experiences. For in order for certain sensations to be related to something outside me , thus in order for me to represent them as outside and next to one another, thus not merely different but as in different places, the representation of space must already be their ground. Thus the representation of space cannot be obtained from the relations of outer appearance through experience, (...) but this outer experience is itself first possible only through this representation. 1Abstract:Der Raum is kein empirischer Begriff, der von äußeren Erfahrungen abgezogen worden. Denn damit gewisse Empfindungen auf etwas außer mir bezogen werden, imgleichen damit ich sie als außer und neben einander, mithin nicht bloß verschieden, sondern als in verschiedenen Orten vorstellen können, dazu muß die Vorstellung des Raumes schon zum Grunde liegen. (shrink)

Functional imaging techniques, such as positron emission tomography and functional magnetic resonance imaging, present a unique opportunity to examine, in humans, the cerebral representation of space in vivo. Space is ubiquitous and not a unitary phenomenon, and the brain uses visual, vestibular and proprioceptive inputs to produce multiple representations of space subserving spatial cognition, ranging from gaze control to remembering multiple complex large-scale environments. Functional imaging studies have shown the importance of the parietal cortex in perceptual, (...) motor, attention and working memory aspects of body-centred human spatial cognition. Functional imaging has also revealed pathways in humans homologous to those found in monkeys for the separate processing of spatial location and object identity. There are further suggestions of similar differentiation in working memory. The importance of the medial temporal region in the recall of spatial location has been confirmed also and novel virtual reality paradigms are now providing insights into the cerebral representation of spatially-extended large-scale environments. We still have much to learn about the cerebral representation of space in the human brain and functional brain imaging, in concert with patient studies and animal models, will allow us to continue investigating. (shrink)

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)

In this commentary, we highlight a difficulty for metric navigation arising from recent data with grid and place cells: the integration of piecemeal representations of space in environments with repeated boundaries. Put simply, it is unclear how place and grid cells might provide a global representation of distance when their fields appear to represent repeated boundaries within an environment. One implication of this is that the capacity for spatial inferences may be limited.

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)

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)

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)

Two thousand five hundred years ago, in 507–506 B.C.E., the institutions of Athen were rocked by the reforms of Cleisthenes. Although the word did not yet exist, here was the foundation of democracy. First published in French in 1964, Cleisthenes the Athenian has become the classic study of the philosophical, political, and aesthetic background and significance of these reforms. The book has influenced a generation of scholars in anthropology, sociology, urban planning, political science, philosophy, and classical studies. This English translation (...) contains the complete text of the original essay and is supplemented by a discussion among Vidal-Naquet, Leveque, and the philosopher Cornelius Castoriadis on the invention of democracy, as well as a new authors' introduction. (shrink)

Two thousand five hundred years ago, in 507–506 B.C.E., the institutions of Athen were rocked by the reforms of Cleisthenes. Although the word did not yet exist, here was the foundation of democracy. First published in French in 1964, Cleisthenes the Athenian has become the classic study of the philosophical, political, and aesthetic background and significance of these reforms. The book has influenced a generation of scholars in anthropology, sociology, urban planning, political science, philosophy, and classical studies. This English translation (...) contains the complete text of the original essay and is supplemented by a discussion among Vidal-Naquet, Leveque, and the philosopher Cornelius Castoriadis on the invention of democracy, as well as a new authors' introduction. (shrink)

Psychophysical experiments have demonstrated large and highly systematic perceptual distortions of tactile space. Such a space can be referred to our experience of the spatial organisation of objects, at representational level, through touch, in analogy with the familiar concept of visual space. We investigated the neural basis of tactile space by analysing activity patterns induced by tactile stimulation of nine points on a 3 × 3 square grid on the hand dorsum using functional magnetic resonance imaging. (...) We used a searchlight approach within pre-defined regions of interests to compute the pairwise Euclidean distances between the activity patterns elicited by tactile stimulation. Then, we used multidimensional scaling to reconstruct tactile space at the neural level and compare it with skin space at the perceptual level. Our reconstructions of the shape of skin space in contralateral primary somatosensory and motor cortices reveal that it is distorted in a way that matches the perceptual shape of skin space. This suggests that early sensorimotor areas critically contribute to the distorted internal representation of tactile space on the hand dorsum. (shrink)

Articulating a non-representational perspective on knowledge production and artistic practices, combined with an analysis of space, this book offers a new performative and relational re-turn to representation in contemporary technospaces. The radically materialist, posthumanist and performative position from which this situated aesthetics of technospaces is elaborated, aligns this book not only with non-representational theory, but also with the theories of material feminism, feminist geography, situated epistemologies, science and technology studies, actor-network theory, performance studies and new media studies.

In some recent papers (G. ‘t Hooft and others), it has been argued that quantum mechanics can arise from classical cellular automata. Nonetheless, G. Shpenkov has proved that the classical wave equation makes it possible to derive a periodic table of elements, which is very close to Mendeleyev’s one, and describe also other phenomena related to the structure of molecules. Hence the classical wave equation complements Schrödinger’s equation, which implies the appearance of a cellular automaton molecular model starting from classical (...) wave equation. The other studies show that the microworld is constituted as a tessellation of primary topological balls. The tessellattice becomes the origin of a submicrospic mechanics in which a quantum system is subdivided to two subsystems: the particle and its inerton cloud, which appears due to the interaction of the moving particle with oncoming cells of the tessellattice. The particle and its inerton cloud periodically change the momentum and hence move like a wave. The new approach allows us to correlate the Klein-Gordon equation with the deformation coat that is formed in the tessellatice around the particle. The submicroscopic approach shows that the source of any type of wave movements including the Klein-Gordon, Schrödinger, and classical wave equations is hidden in the tessellattice and its basic exciations – inertons, carriers of mass and inert properies of matter. We also discuss possible correspondence with Konrad Zuse’s calculating space. (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)

The grand duchy of Luxembourg is a showcase example for the constructed nature of national identities. This book explores this construction process from the nineteenth to the twenty-first century, focusing on representations of the past, space and language.

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.

The category of Scott-domains gives a computability theory for possibly uncountable topological spaces, via representations. In particular, every separable Banach-space is representable over a separable domain. A large class of topological spaces, including all Banach-spaces, is representable by domains, and in domain theory, there is a well-understood notion of parametrizations over a domain. We explore the link with parameter-dependent collections of spaces in e. g. functional analysis through a case study of "Lp" -spaces. We show that a well-known domain (...) representation of "Lp" as a metric space can be made uniform in the sense of parametrizations of domains. The uniform representations admit lifting of continuous functions and are effective in p. Dependent type constructions apply, and through the study of the sum and product spaces, we clarify the notions of uniformity and uniform computability. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim). (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.

D′ ⊆ D is a normal totality on a Scott domain D if it is upward closed and x ⊓ y ∈ D′ is an equivalence relation on D′. We prove that every topological space can be represented by a domain with norma totality.

We examined the neural basis of tactile distance perception by analyzing activity patterns induced by tactile stimulation of nine points on a 3 x 3 square grid on the hand dorsum using functional magnetic resonance (fMRI). We used a searchlight approach within pre-defined regions of interests (ROIs) to compute the pairwise Euclidean distances between the activity patterns elicited by tactile stimulation. Then, we used multidimensional scaling (MDS) to reconstruct skin space at the neural level and compare it with skin (...) space at the perceptual level. Our reconstructions of the shape of skin space in contralateral primary somatosensory (SI) and motor (M1) cortices reveal that it is distorted in a way that matches the perceptual shape of skin space. This suggests that early sensorimotor areas are critical to processing tactile distance perception. (shrink)

The visual system captures a unique contrast between implicit and explicit representation where the same event (location of a visible object) is coded in both ways in parallel. A method of differentiating the two representations is described using an illusion that affects only the explicit representation. Consistent with predictions, implicit information is available only from targets presently visible, but, surprisingly, a two-alternative decision does not disturb the implicit representation.

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)