Purpose – The purpose of this paper is to explain how abstract space of the State – universally and specifically within the context of Middle Eastern cities – aims to homogenise the city and eliminate any anomaly that threatens its power structure. Design/methodology/approach – Through a historical and discourse analysis of these policies and processes in the two case studies, this paper presents a contextualised reading of Lefebvre’s concept of abstract space and process of abstraction in (...) relation to the alienation of political public spaces. Findings – The paper proposes that regardless of these homogenising strategies being applied universally, they fail to respond to contextual particularities and therefore they – in a contradictory manner – may themselves produce a space of resistance and difference. Originality/value – This paper focusses on Iran, the case of Tehran and Turkey, the case of Taksim Square and Gezi Park in Istanbul. Recent policies and strategies have been proposed and implemented to reduce, alienate and possibly neutralise the impacts of urban and political protests in these cities and socio-political contexts. (shrink)

In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching space-time models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract space-time structures based on the real numbers and the integers, considering three different accessibility (...) relations between spatio-temporal points. (shrink)

Deictic pointers allow the nervous system to exploit information in a frame that is centered on the object of interest. This processing may take place in visual or haptic space, but the information processing advantages of deictic pointing can also be applied in abstract spaces, providing the basis for analogical transfer. Simulation and behavioral results illustrating this progression from embodiment to abstraction are discussed.

L’objectif de cet article est de montrer que la réflexion engagée par Jules Vuillemin sur les structures algébriques dans les années 1960 lui permettra de dégager une conception structurale de l’abstraction, dont il tirera une compréhension nomologique de l’objectivité. Ces deux concepts seront alors convoqués bien des années plus tard pour proposer une construction de l’espace représentatif, que Vuillemin conçoit comme une réfutation de l’idéalisme matériel de Berkeley. La possibilité de retracer la genèse de nos notions spatiales et de leur (...) garantir une certaine objectivité serait ainsi rendue possible par un emprunt aux méthodes de l’algèbre moderne, conformément à l’esprit de La Philosophie de l’algèbre. (shrink)

Several modern accounts of explanation acknowledge the importance of abstraction and idealization for our explanatory practice. However, once we allow a role for abstraction, questions remain. I ask whether the relation between explanations at different theoretical levels should be thought of wholly in terms of abstraction, and argue that changes of the quantities in terms of which we describe a system can lead to novel explanations that are not merely abstractions of some more detailed picture. I use the example of (...) phase transitions as described by statistical mechanics and thermodynamics to illustrate this, and to demonstrate some details of the relationship between abstraction, idealization, and novel explanation. (shrink)

The present paper aims to contribute to the substantivalism versus relationalism debate and to defend general relativity (GR) against pseudoscientific attacks in a novel, especially inclusive way. This work was initially motivated by the desire to establish the incompatibility of any ether theories with accelerated cosmic expansion and inflation (motto: where would a hypothetical medium supposedly come from so fast?). The failure of this program is of interest for emergent GR concepts in high energy particle physics. However, it becomes increasingly (...) important to guard scientific results against their misrepresentation by fundamentally anti-scientific agendas. We therefore argue that although it is not known whether the perceived space-time is fundamental (rather than a condensed state or a particular membrane), in a fundamental theory, space-time must be abstract relational: fundamental space-time is the consistent spatial-temporal arrangement of events. To pursue its own goals, this work should be accessible to a wide audience: physicists, philosophers of science, those being tempted by anti-relativity theories, but also those who vigorously defend some orthodox relativity that is not actually supported by GR. It must thus be extensive in order to satisfy the different parties’ desire to have included and understood their respective positions. (shrink)

We study computability of the abstract linear Cauchy problem equation image)where A is a linear operator, possibly unbounded, on a Banach space X. We give necessary and sufficient conditions for A such that the solution operator K: x ↦ u of the problem is computable. For studying computability we use the representation approach to computable analysis developed by Weihrauch and others. This approach is consistent with the model used by Pour-El/Richards.

Coordinate formalism on Hilbert manifolds developed in \cite{Kryukov} is reviewed. The results of \cite{Kryukov} are applied to the simpliest case of a Hilbert manifold: the abstract Hilbert space. In particular, functional transformations preserving properties of various linear operators on Hilbert spaces are found. Any generalized solution of an arbitrary linear differential equation with constant coefficients is shown to be related to a regular solution by a (functional) coordinate transformation. The results also suggest a way of using generalized functions (...) to solve nonlinear problems on Hilbert spaces. (shrink)

Think of a number, any number, or properties like fragility and humanity. These and other abstract entities are radically different from concrete entities like electrons and elbows. While concrete entities are located in space and time, have causes and effects, and are known through empirical means, abstract entities like meanings and possibilities are remarkably different. They seem to be immutable and imperceptible and to exist "outside" of space and time. This book provides a comprehensive critical assessment (...) of the problems raised by abstract entities and the debates about existence, truth, and knowledge that surround them. It sets out the key issues that inform the metaphysical disagreement between platonists who accept abstract entities and nominalists who deny abstract entities exist. Beginning with the essentials of the platonist–nominalist debate, it explores the key arguments and issues informing the contemporary debate over abstract reality: arguments for platonism and their connections to semantics, science, and metaphysical explanation the abstract–concrete distinction and views about the nature of abstract reality epistemological puzzles surrounding our knowledge of mathematical entities and other abstract entities. arguments for nominalism premised upon concerns about paradox, parsimony, infinite regresses, underdetermination, and causal isolation nominalist options that seek to dispense with abstract entities. Including chapter summaries, annotated further reading, and a glossary, _Entities_ is essential reading for anyone seeking a clear and authoritative introduction to the problems raised by abstract entities. (shrink)

This book presents an innovative analysis of the role of imagination as a central concept in both literary and art criticism. Dee Reynolds brings this approach to bear on works by Rimbaud, Mallarme;, Kandinsky, and Mondrian. It allows her to redefine the relationship between Symbolism and abstract art, and to contribute new methodological perspectives to comparative studies of poetry and painting. The late nineteenth and early twentieth century was a crucial period in the emergence of new modes of representation, (...) and is currently at the forefront of critical enquiry. This is the first book to examine Symbolism and abstraction in this way, and the first to treat these poets and painters together. It is an original contribution to interdisciplinary scholarship in art history, literary history, and comparative aesthetics. (shrink)

concepts are defined as concepts that cannot be experienced directly through the sensorimotor modalities. Explaining our understanding of such concepts poses a challenge to neurocognitive models of knowledge. One account of how these concepts come to be represented is that sensorimotor representations of grounded experiences are reactivated in a way that is constitutive of the abstract concept. In the present experiment, we investigated how sensorimotor information might constitute GOD-related concepts, and whether a person’s self-reported religiosity modulated this grounding. To (...) do so, we manipulated both the state of the body and the state of stimuli in two tasks that required conceptual categorization of abstract words. Linear Mixed Effects model fitting procedures were used to determine which manipulated factors best predicted response latency and accuracy in both tasks. We successfully replicated previous research demonstrating faster categorization of GOD-related words when they were presented at the top of the screen. Importantly, results demonstrated that the kneeling posture manipulation enhanced this effect, as did religiosity, as participants who scored higher in religiosity showed a greater effect of the posture manipulation on the speed with which word categorization occurred when those words were presented in the higher visuospatial presentation condition. Overall, we interpreted our findings to suggest that directly manipulating sensorimotor information can facilitate the categorization of abstract concepts, supporting the notion that this information in part constitutes the representation of abstract concepts. (shrink)

Most research on metaphors that construe time as motion (motion metaphors of time) has focused on the question of whether it is the times or the person experiencing them (ego) that moves. This paper focuses on the equally important distinction between metaphors that locate times relative to ego (the ego-based metaphors Moving Ego and Moving Time) and a metaphor that locates times relative to other times (sequence is relative position on a path). Rather than a single abstract target domain (...) TIME, these two kinds of temporal metaphor metaphorize different kinds of temporal concept—perspective-specific vs. perspective-neutral temporal concepts. Recognition of this distinction enhances the explanatory potential of conceptual metaphor theory (Lakoff and Johnson 1980). An example involves the interaction of deixis and the temporal reference crosslinguistically of vocabulary with the spatial meanings in-front and behind. More generally, this approach refines our ability to describe the temporal concepts involved in motion metaphors of time. Such temporal concepts are present not only in the target domains, but also in the source domains of motion metaphors of time, where we find space-to-time metonymy, which may play a role in motivating the metaphors. In order to distinguish such metonymy from metaphor, we need to characterize metaphor as a mapping across frames rather than domains. (shrink)

The Abstract Conceptual Feature (ACF) framework predicts that word meaning is represented within a high‐dimensional semantic space bounded by weighted contributions of perceptual, affective, and encyclopedic information. The ACF, like latent semantic analysis, is amenable to distance metrics between any two words. We applied predictions of the ACF framework to abstract words using eyetracking via an adaptation of the classical “visual word paradigm” (VWP). Healthy adults (n = 20) selected the lexical item most related to a probe (...) word in a 4‐item written word array comprising the target and three distractors. The relation between the probe and each of the four words was determined using the semantic distance metrics derived from ACF ratings. Eye movement data indicated that the word that was most semantically related to the probe received more and longer fixations relative to distractors. Importantly, in sets where participants did not provide an overt behavioral response, the fixation rates were nonetheless significantly higher for targets than distractors, closely resembling trials where an expected response was given. Furthermore, ACF ratings which are based on individual words predicted eye fixation metrics of probe‐target similarity at least as well as latent semantic analysis ratings which are based on word co‐occurrence. The results provide further validation of Euclidean distance metrics derived from ACF ratings as a measure of one facet of the semantic relatedness of abstract words and suggest that they represent a reasonable approximation of the organization of abstract conceptual space. The data are also compatible with the broad notion that multiple sources of information (not restricted to sensorimotor and emotion information) shape the organization of abstract concepts. While the adapted “VWP” is potentially a more metacognitive task than the classical visual world paradigm, we argue that it offers potential utility for studying abstract word comprehension. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main (...) reason for producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

Coordinate form of tensor algebra on an abstract (infinite-dimensional) Hilbert space is presented. The developed formalism permits one to naturally include the improper states in the apparatus of quantum theory. In the formalism the observables are represented by the self-adjoint extensions of Hermitian operators. The unitary operators become linear isometries. The unitary evolution and the non-unitary collapse processes are interpreted as isometric functional transformations. Several experiments are analyzed in the new context.

The growing body of research on temporal and spatial experience lacks a comprehensive theoretical approach. Drawing on Giddens’ framework, we present time-space distanciation as a construct for theorizing the relations between culture, time, and space. TSD in a culture may be understood as the extent to which time and space are abstracted as separate dimensions and activities are extended and organized across time and space. After providing a historical account of its development, we outline a multi-level (...) conceptualization of TSD supported by research on cultural differences in the experience of time and space. We impact this conceptualization by examining two ethnographic case studies. We conclude by highlighting future research directions. TSD is an integrative, interdisciplinary, multi level construct with the potential to guide the burgeoning social science of time and space. (shrink)

Modern cosmology treats space and time, or rather space-time, as concrete particulars. The General Theory of Relativity combines the distribution of matter and energy with the curvature of space-time. Here space-time appears as a concrete entity which affects matter and energy and is affected by the things in it. I question the idea that space-time is a concrete existing entity which both substantivalism and reductive relationism maintain. Instead I propose an alternative view, which may be (...) called non-reductive relationism, by arguing that space and time are abstract entities based on extension and changes. (shrink)

When entering an environment, animals – including humans – tend to consult their memories to determine what they know about the place. This information is useful to determine: is this place safe? And what happens next? In this chapter, we argue on both empirical and conceptual grounds that memory is largely organized by space. Spatial relations determine what is recalled and which experiences are combined in generalizations. Time does not play an analogous role. We show that space and (...) time in memory are thus deeply asymmetrical. We conclude with a consequence of our view: spatial organization entails a basic form of abstraction in a way temporal organization does not, and so the spatial organization of memory reveals that memory involves generalization from the very beginning. (shrink)

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its (...) angles and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

PREFACE: - BY his theory of relativity Albert Einstein has provoked a revolution of thought in physical science. The achievement consists essentially in this Einstein has succeeded in separating far more completely than hitherto the share of the observer and the share of external nature in the things we see happen. The perception of an object by an observer depends on his own situation and circumstances for example, distance will make it appear smaller and dimmer. We make allowance for this (...) almost unconsciously in interpreting what we see. But it now appears that the allowance made for the motion of the observer has hitherto been too crude a fact overlooked because in practice all observers share nearly the same motion, that of the earth. Physical space and time are found to be closely bound up with this motion of the observer and only an amorphous combination of the two is left inherent in the external world. When space and time are relegated to their proper source the observer the world of nature which remains appears strangely unfamiliar but it is in reality simplified, and the underlying unity of the principal phenomena is now clearly revealed. The deductions from this new outlook have, with one doubtful exception, been confirmed when tested by experiment. It is my aim to give an account of this work without intro ducing anything very technical in the way of mathematics, physics, or philosophy. The new view of space and time, so opposed to our habits of thought, must in any case demand unusual mental exercise. The results appear strange and the incongruity is not without a humorous side. For the first nine chapters the task is one of interpreting a clear-cut theory, accepted in all its essentials by a large and growing school of physicists although perhaps not everyone would accept the authors views of its meaning. Chapters x and xi deal with very recent advances, with regard to which opinion is more fluid. As for the last chapter, containing the authors specula tions on the meaning of nature, since it touches on the rudiments of a philosophical system, it is perhaps too sanguine to hope that it can ever be other than controversial. A non-mathematical presentation has necessary limitations and the reader who wishes to learn how certain exact result follow from Einsteins, or even Newtons, law of gravitation m bound to seek the reasons in a mathematical treatise. But thj limitation of range is perhaps less serious than the limitation of intrinsic truth. There is a relativity of truth, as there is a relativity of space. For is and IS-NOT though with Rule and Line And UP-AND-DOWK without, I could define, Alas It is not so simple. We abstract from the phenomena that which is peculiar to the position and motion of the observer but can we abstract that which is peculiar to the limited imagina tion of the human brain We think we can, but only in the symbolism of mathematics. As the language of a poet rings with a truth that eludes the clumsy explanations of his commentators, so the geometry of relativity in its perfect harmony expresses a truth of form and type in nature, which my bowdlerised version misses. But the mind is not content to leave scientific Truth in a dry husk of mathematical symbols, and demands that it shall be alloyed with familiar images. The mathematician, who handles x so lightly, may fairly be asked to state, not indeed the in scrutable meaning of a in nature, but the meaning which x conveys to him. Although primarily designed for readers without technical knowledge of the subject, it is hoped that the book may also appeal to those who have gone into the subject more deeply. A few notes have been added in the Appendix mainly to bridge the gap between this and more mathematical treatises, and to indicate the points of contact between the argument in the text and the parallel analytical investigation. It is impossible adequately to express my debt to con temporary literature and discussion... (shrink)

Abstract:This article correlates the physical composition of the built environment with social interactions and human relationships. The resulting framework draws on an embodied cognitive position through interdisciplinary knowledge with priority given to architectural theory and cognitive linguistics. This approach does not address idiosyncratic, phenomenological descriptions of experiences of place but the potential relationship of human bodies through situated semantics suggested by spatial composition. In this article we ask how the physical arrangement of a space can provide information for (...) analyzing the probable social relations such as positions of hierarchy, power, and authority. We identify two theoretical models, namely latent embodied cognitive operations and space as a situated concept, which can be used to correlate physical arrangements with social meaning. (shrink)

Many metaphor theorists argue that our mental experience of time is grounded in our understanding of space, including motion through space. Results from recent experiments – in which people think about motion, which in turn influences their thinking about time – support this position. Still, many questions remain about the nature of the metaphorical connection between time and space. Can the mere suggestion of motion influence how people reason about time, and if so, when and how? Three (...) experiments investigated how thinking about “abstract” motion through sequences of numbers or letters would influence reasoning about time. Our results extend earlier psychological work on the link between time and space by showing that even motion in non-physical domains can influence temporal reasoning. The results provide further evidence that metaphorical understanding is grounded in our everyday physical and conceptual experience. (shrink)

Hume's discussion of the idea of space in his Treatise on Human Nature is fundamental to an understanding of his treatment of such central issues as the existence of external objects, the unity of the self, the relation between certainty and belief, and abstract ideas. Marina Frasca-Spada's rich and original study examines this difficult part of Hume's philosophical writings and connects it to eighteenth-century works in natural philosophy, mathematics and literature. Focusing on Hume's discussions of the infinite divisibility (...) of extension, the origin of the idea of space, geometry, and the notion of a vacuum, she shows that the central questions of Hume's 'science of human nature' - what does the 'science of human nature' reveal about the mind and its operations? what is experience? - underlie all of these discussions. Her analysis points the way to a reassessment of the central current interpretative problems in Hume studies. (shrink)

Abstract.Russell Stannard distinguishes between objective time as measured in theoretical physics and subjective time, or time as experienced by human beings in normal consciousness. Because objective time, or four‐dimensional space‐time for the physicist, does not change but exists all at once, Stannard argues that this is presumably how God views time from eternity which is beyond time. We human beings are limited to experiencing the moments of time successively and thus cannot know the future as already existing in (...) the same way that God does. I argue that Stannard is basically correct in his theological assumptions about God's understanding of time but that his explanation would be more persuasive within the context of a neo‐Whiteheadian metaphysics. The key points in that metaphysics are (1) that creation is contained within the structured field of activity proper to the three divine persons of the Christian doctrine of the Trinity and (2) that the spontaneous decisions of creatures are continually ordered and reordered into an ever‐expanding totality already known in its fullness by the divine persons. (shrink)

_Time, Space, and Phantasy_ examines the connections between time, space, phantasy and sexuality in clinical practice. It explores the subtleties of the encounter between patient and analyst, addressing how aspects of the patient’s unconscious past are actualised in the present, producing new meanings that can be re-translated to the past. Perelberg’s analysis of Freud’s Multi-dimensional model of temporality suggests that he always viewed the constitution of the individual as non-linear. In Freud’s formulations, the individual is decentred and ruled (...) by different temporalities, most of which escape their consciousness. Perelberg identifies the similarities between this and Einstein’s theory of relativity which states that rather than being absolute, time depends on the relative position and speed of the observing individual suggesting that rather than being a reality, time is an abstraction, connecting objects and events. Throughout this text, Perelberg draws together connections between time, mental space, and phantasy showing how time is constantly reshaped in the light of new events and experiences. This book will be of interest to psychoanalysts, psychotherapists, psychologists, and social workers. (shrink)

Russian abstract: В данном сборнике статей раскрывается формирование структурно-онтологического представления о таком явлении, как городское пространство. Наряду с соответствующей концептуализацией, также представлено и объяснено определение городского сообщества. Обоснована логика классификации городских сообществ. А также проанализированы факторы, обуславливающие их устойчивость. -/- English abstract: This collection of articles reveals the formation of a structural-ontological concept of such a phenomenon as urban space. Along with relevant conceptualization, the definition of an urban community is also presented and explained. The logic of (...) classification of urban communities is substantiated. And also analyzed the factors that determine their stability. (shrink)

TheConceptual Feature framework predicts that word meaning is represented within a high-dimensional semantic space bounded by weighted contributions of perceptual, affective, and encyclopedic information. The ACF, like latent semantic analysis, is amenable to distance metrics between any two words. We applied predictions of the ACF framework to abstract words using eyetracking via an adaptation of the classical “visual word paradigm”. Healthy adults selected the lexical item most related to a probe word in a 4-item written word array comprising (...) the target and three distractors. The relation between the probe and each of the four words was determined using the semantic distance metrics derived from ACF ratings. Eye movement data indicated that the word that was most semantically related to the probe received more and longer fixations relative to distractors. Importantly, in sets where participants did not provide an overt behavioral response, the fixation rates were nonetheless significantly higher for targets than distractors, closely resembling trials where an expected response was given. Furthermore, ACF ratings which are based on individual words predicted eye fixation metrics of probe-target similarity at least as well as latent semantic analysis ratings which are based on word co-occurrence. The results provide further validation of Euclidean distance metrics derived from ACF ratings as a measure of one facet of the semantic relatedness of abstract words and suggest that they represent a reasonable approximation of the organization of abstract conceptual space. The data are also compatible with the broad notion that multiple sources of information shape the organization of abstract concepts. While the adapted “VWP” is potentially a more metacognitive task than the classical visual world paradigm, we argue that it offers potential utility for studying abstract word comprehension. (shrink)

We care not just how things are but how they could have been otherwise – about possibility and necessity as well as actuality. Many philosophers regard such talk as beyond the reach of respectable science, since observation tells us how things are but not how they could have been otherwise. I argue that, on the contrary, such criticisms are ill-founded: possibility and necessity are studied in natural science, for example through phase spaces, abstract mathematical representations of the possible states (...) of a physical system. The possibility is objective, not merely epistemic, though it may be more restricted than pure metaphysical possibility. The elements of a phase space are very similar to Kripke's possible worlds, despite being time slices rather than total histories. The absence of explicit modal operators in the mathematical models used by scientists does not show science to be non-modal; rather, it manifests reliance on a mathematical framework for theorizing about objective possibility similar to the mathematical framework of possible worlds model theory. (shrink)

Many critics have pointed to the failures of modernist urban design, which include its obliteration of thriving neighborhoods, isolation of functions and production of alienating spaces hostile to the human form. Less focus has been placed on defining the source of the modernists’ errors. This essay argues that these errors were in part due to neglect of the nature of fully embodied experience, a neglect manifested in an overwhelmingly visual disposition in embodiment. The author argues that a visual disposition is (...) implicated in the occlusion of place by the modern concept of abstract space. This concept of space and the visual disposition that is implicated in it undergird the utopianism and veneration for abstract forms that characterized the project of modernist urban design. The author concludes by suggesting that the basis for a humanizing urbanism should be the solicitation of all the senses in synesthetic interaction. This phenomenological critique can help us to see precisely where modernist urban design went wrong; it can also help lead us out of the false dichotomy between alienating modernism and orthodox traditionalism by establishing a basis for successful urban environments in embodiment rather than in any rigidly determined formula for urban design. (shrink)

In finite type arithmetic, the real numbers are represented by rapidly converging Cauchy sequences of rational numbers. Ulrich Kohlenbach introduced abstract types for certain structures such as metric spaces, normed spaces, Hilbert spaces, etc. With these types, the elements of the spaces are given directly, not through the mediation of a representation. However, these abstract spaces presuppose the real numbers. In this paper, we show how to set up an abstract type for the real numbers. The appropriateness (...) of our construction works in tandem with the bounded functional interpretation. (shrink)

Philosophers have long been tempted by the idea that objects and properties are abstractions from the facts. But how is this abstraction supposed to go? If the objects and properties aren't 'already' there, how do the facts give rise to them? Jason Turner develops and defends a novel answer to this question: The facts are arranged in a quasi-geometric 'logical space', and objects and properties arise from different quasi-geometric structures in this space.

Penrose’s Spin Geometry Theorem is extended further, from SU(2) and E(3) (Euclidean) to E(1, 3) (Poincaré) invariant elementary quantum mechanical systems. The Lorentzian spatial distance between any two non-parallel timelike straight lines of Minkowski space, considered to be the centre-of-mass world lines of E(1, 3)-invariant elementary classical mechanical systems with positive rest mass, is expressed in terms of E(1, 3)-invariant basic observables, viz. the 4-momentum and the angular momentum of the systems. An analogous expression for E(1, 3)-invariant elementary quantum (...) mechanical systems in terms of the basic quantum observables in an abstract, algebraic formulation of quantum mechanics is given, and it is shown that, in the classical limit, it reproduces the Lorentzian spatial distance between the timelike straight lines of Minkowski space with asymptotically vanishing uncertainty. Thus, the metric structure of Minkowski space can be recovered from quantum mechanics in the classical limit using only the observables of abstract quantum mechanical systems. (shrink)

Questions concerning the epistemological status of computer science are, in this paper, answered from the point of view of the formal verification framework. State space reduction techniques adopted to simplify computational models in model checking are analysed in terms of Aristotelian abstractions and Galilean idealizations characterizing the inquiry of empirical systems. Methodological considerations drawn here are employed to argue in favour of the scientific understanding of computer science as a discipline. Specifically, reduced models gained by Dataion are acknowledged as (...) Aristotelian abstractions that include only data which are sufficient to examine the interested executions. The present study highlights how the need to maximize incompatible properties is at the basis of both Abstraction Refinement, the process of generating a cascade of computational models to achieve a balance between simplicity and informativeness, and the Multiple Model Idealization approach in biology. Finally, fairness constraints, imposed to computational models to allow fair behaviours only, are defined as ceteris paribus conditions under which temporal formulas, formalizing software requirements, acquire the status of law-like statements about the software systems executions. (shrink)

We develop the general theory of topometric spaces, i.e., topological spaces equipped with a well-behaved lower semi-continuous metric. Spaces of global and local types in continuous logic are the motivating examples for the study of such spaces. In particular, we develop Cantor-Bendixson analysis of topometric spaces, which can serve as a basis for the study of local stability (extending the ad hoc development in Ben Yaacov I and Usvyatsov A, Continuous first order logic and local stability. Trans Am Math Soc, (...) in press), as well as of global ${\aleph_0}$ -stability. We conclude with a study of perturbation systems (see Ben Yaacov I, On perturbations of continuous structures, submitted) in the formalism of topometric spaces. In particular, we show how the abstract development applies to ${\aleph_0}$ -stability up to perturbation. (shrink)

In this compendium of essays, some of the world's leading thinkers discuss their conceptions of space and time, as viewed through the lens of their own discipline. With an epilogue on the limits of human understanding, this volume hosts contributions from six or more diverse fields. It presumes only rudimentary background knowledge on the part of the reader. Time and again, through the prism of intellect, humans have tried to diffract reality into various distinct, yet seamless, atomic, yet holistic, (...) independent, yet interrelated disciplines and have attempted to study it contextually. Philosophers debate the paradoxes, or engage in meditations, dialogues and reflections on the content and nature of space and time. Physicists, too, have been trying to mold space and time to fit their notions concerning micro- and macro-worlds. Mathematicians focus on the abstract aspects of space, time and measurement. While cognitive scientists ponder over the perceptual and experiential facets of our consciousness of space and time, computer scientists theoretically and practically try to optimize the space-time complexities in storing and retrieving data/information. The list is never-ending. Linguists, logicians, artists, evolutionary biologists, geographers et cetera, all are trying to weave a web of understanding around the same duo. However, our endeavour into a world of such endless imagination is restrained by intellectual dilemmas such as: Can humans comprehend everything? Are there any limits? Can finite thought fathom infinity? We have sought far and wide among the best minds to furnish articles that provide an overview of the above topics. We hope that, through this journey, a symphony of patterns and tapestry of intuitions will emerge, providing the reader with insights into the questions: What is Space? What is Time? Chapter [15] of this book is available open access under a CC BY 4.0 license. (shrink)

Abstract.Since the earliest ages of humanity, the contemplation of the starry sky has invited the human being to ask: “Who am I? Where is my origin? What is my destiny?” The revolution introduced by modem astronomy has affected how humankind understands itself, and the development of aeronautical and then astronautical techniques introduced a new experiment for humanity—that of being citizen of the sky. By carrying out the dream of Icarus, has humanity realized the attempt of Prometheus? Would we take (...) the place of the gods or God? Do religions have to fear the conquest of space? Despite modern science and the knowledge we have accumulated, space still holds its share of mystery, nurtured by its vast dimensions and startling beauty. Space continues to raise the issue of meaning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Space, Place and Capitalism: The Literary Geographies of “The Unknown Industrial Prisoner” by Brett HeinoDavid McLaughlinSpace, Place and Capitalism: The Literary Geographies of “The Unknown Industrial Prisoner” BY BRETT HEINO Singapore: Palgrave Macmillan, 2021I would not be the first to describe Brett Heino’s new book as timely. Its publication in 2021 coincided with the fiftieth anniversary of the first publication of David Ireland’s The Unknown Industrial (...) Prisoner (1971). This experimental novel, centered on a “kaleidoscopic vision” of its characters and their lives, tells the story of a group of workers at the Puroil refinery in a fictionalized part of Sydney. In Heino’s own words, this project emerged from a desire to write about industrialization and representation in Australian fiction. Working primarily as a legal scholar and historian, this work represents his first foray into literary geography.At the heart of Heino’s argument is a question: What does literature know about space? In his pursuit of a spatially-directed reading of The Unknown Industrial Prisoner, Heino eschews work in literary geography that cultural geographers might recognize— particularly the writings of Sheila Hones, the doyenne of an emerging interdiscipline of literary geography, whose practitioners work at the interstices between literary studies and geography. Heino criticizes this interdisciplinary literary geography as being too focused on establishing the “sovereignty” or “imperialism” of fictional space at the expense of recognizing the [End Page 132] role of literature in the world. Arguably, such a stance is a misreading of the thinking within literary geography that “reading literature is essentially an experimental process in which the categorical distinction between the frames of ‘fact’ and ‘fiction’ become blurred,”1 and where the “ontological distinction between literary and non- literary spaces” is undermined.2 Neither of these statements supposes that reading literature is a practice by which the world falls away and nothing remains but the book. Instead, following Doreen Massey’s idea that space is a complicated process of events and happenings, literary geographers in this mold argue that fiction is a part of life as it happens, and reading is a constitutive practice in the co- production of space.In its place, Heino emphasizes a form of literary geographical thinking that understands literature’s role as being separate from, but intimately connected to, the actual world. His theoretical framework is multi-layered, borrowing from Marxist literary scholars, including Terry Eagleton and Fredric Jameson, and Marxist geographers, including Henri Lefebvre. In essence, however, it can be expressed neatly in the following quotation from geocritic Bertrand Westphal:Fiction does not reproduce the real, but actualises new virtualities that had remained unformulated, and then goes on to interact with the real according to the hypertextual logic of interfaces... fiction detects possibilities buried in the folds of the real, knowing that these folds have not been temporised.3I think that Heino’s rejection of what he characterizes as poststructural literary geography, of the kind represented in his analysis of Sheila Hones’s work, misses some opportunities. First, there are similarities between his conception of literary geography and those he leaves aside— not least, their shared acceptance of the productive tension that sits between literature as text and world as practical, non- representational, and exceeding narrative. Secondly, the shared aim of both approaches is to understand how “representation ‘takes place’ and precisely how texts are part of what happens.”4 This is particularly powerful in the light of Heino’s aim to understand the development and contents of literary texts in materialist terms. Despite these areas [End Page 133] of convergence, Heino’s argument that literary geography’s potential to analyze class and political structures remains untapped is well founded. This is where Heino’s contribution is at its strongest.Heino’s work is at its most convincing when he discusses the realities of “abstract space” that both permeate the spaces of The Unknown Industrial Prisoner and structure the very fabric of latter- twentieth century Australia. Running through both Heino’s critique and Ireland’s novel is an understanding “that the inherent drive of capital is towards the creation of a fragmented, homogenised and hierarchised space within which it can produce and... (shrink)