This is a pdf of a Mathematica calculation that supplements the paper "Presentist Fragmentalism and Quantum Mechanics" forthcoming in Foundations of Physics. In that paper the Born rule (or at least a progenitor) is derived from experimental conditions on the mutual observations of two fragments. In this pdf the experimental conditions are applied to Hilbert space dimensions 3, 4, and 5. It turns out each of these have a 1-dimensional solution space which, it is hoped, can be interpretated (...) as the phase. (shrink)

Social consciousness is the most comprehensive historically differentiated and dynamic relatively independent spiritual system. It performs its function both with regard to social being and to the life and consciousness of the individual members of society. As a many-sided, heterogeneous and complex system social consciousness should be analyzed from various points of view. Varied approaches and methods are employed in its study, heterogeneous criteria, close-ups and cross sections are used in investigating its content.

The Dimensions of Difference examines space, time, and bodies in the works of three contemporary women directors and four continental philosophers, leading to a new approach to the question of sexual difference and its place within film criticism.

This book explores the evolution of space and time from the apeiron — the spaceless, timeless chaos of primordial nature. Here Western culture’s efforts to deny apeiron are examined, and we see the critical need now to lift the repression of the apeiron for the sake of human individuation.

This article engages critically with Bourdieu’s notion of field. It questions the emphasis that Bourdieu places on what he terms ‘objective relations’ at the expense of the actual relations of those within a field. This not only involves relations between human actors but the interactions of humans with the non-human such as inanimate objects that over time, and in particular spaces, engender certain forms of embodiment. The intention of the article is to think through these phenomenological dimensions of field. It (...) does this by firstly examining these issues as theoretical questions before siting them within an empirical context, revisiting data from an earlier study into the differential achievement of students of Chinese-, Pacific Islander- and Anglo-Australian backgrounds to ascertain the ways in which various micropractices performed within the home promote different dispositions to learning, some more and some less of value at school. (shrink)

Space and time are the most fundamental features of our experience of the world, and yet they are also the most perplexing. Does time really flow, or is that simply an illusion? Did time have a beginning? What does it mean to say that time has a direction? Does space have boundaries, or is it infinite? Is change really possible? Could space and time exist in the absence of any objects or events? What, in the end, are (...) space and time? Do they really exist, or are they simply the constructions of our minds? Robin Le Poidevin provides a clear, witty, and stimulating introduction to these deep questions and many other mind-boggling puzzles and paradoxes. He gives a vivid sense of the difficulties raised by our ordinary ideas about space and time, but he also gives us the basis to think about these problems independently, avoiding large amounts of jargon and technicality. His book is an invitation to think philosophically rather than a sustained argument for particular conclusions, but Le Poidevin does advance and defend a number of controversial views. He argues, for example, that time does not actually flow, that it is possible for space and time to be both finite and yet be without boundaries, and that causation is the key to an understanding of one of the deepest mysteries of time: its direction. Drawing on a variety of vivid examples from science, history, and literature, Travels in Four Dimensions brings to life some of the most profound questions imaginable. (shrink)

This book, which is the fruit of papers presented at the seventh Cambridge French Graduate Conference, offers innovative analyses of how space can provide metaphors for human thoughts, utterances and experiences. The authors cross-fertilise different approaches to the significance of space as a thematic and structuring principle in French and Francophone poetry, prose, philosophy and film. They are interested in three broad areas of enquiry: how spaces can be suffused with explorations of identity; how the dividing work done (...) by maps marks and makes spaces; and how particular questions are thrown up by urban spaces. Throughout, the book examines the symbiotic relationship between internal and external, between delimitation and difference. (shrink)

It is taken for granted that the explanation of the Universe’s space-time dimension belongs to the host of the arguments that exhibit the superiority of modern (inflationary) cosmology over the standard model. In the present paper some doubts are expressed . They are based upon the fact superstring theory is too formal to represent genuine unification of general relativity and quantum field theory. Neveretheless, the fact cannot exclude the opportunity that in future the superstring theory can become more (...) physical. Hence this paper does not aim to query neither string cosmology, nor superstring theory; it asks for “tolerance in the matters cosmological”. It advices the researchers not to dwell on the common way of unification and to take into consideration the other ways as well. (shrink)

If is a Polish metric space of dimension 0, then by Wadge’s lemma, no more than two Borel subsets of X are incomparable with respect to continuous reducibility. In contrast, our main result shows that for any metric space of positive dimension, there are uncountably many Borel subsets of that are pairwise incomparable with respect to continuous reducibility. In general, the reducibility that is given by the collection of continuous functions on a topological space \\) (...) is called the Wadge quasi-order for \\). As an application of the main result, we show that this quasi-order, restricted to the Borel subsets of a Polish space \\), is a well-quasiorder if and only if \\) has dimension 0. Moreover, we give further examples of applications of the construction of graph colorings that is used in the proofs. (shrink)

INTRODUCTION Our universe is an amazing and humbling place. The planet we live on is filled with wondrous things, yet it is only an unimaginably tiny part ...

And the first step of the Peripatetick argument is that, where Aristotle proveth the integrity and perfection of the World, telling us, that it is not a simple line, nor a bare superficies, but a body adorned with Longitude, Latitude and Profundity; and because there are no more dimensions but these three; the World having them, hath all, and having all, is to be concluded perfect. And again, that by simple length, that magnitude is constituted, which is called a line, (...) to which adding breadth, there is formed a Superficies, and yet further adding the altitude or profundity, there results the Body, and after these three the dimensions there is no passing farther, so that in these three the integrity, and to so speak, totality is terminated, which I might but with justice have required Aristotle to have proved to me by necessary consequences, the rather in regard he was able to do it very plainly and speedily. *Received 9. iii. 54. (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)

(2008). Book Review: “Dimensions of Apeiron: A Topological Phenomenology of Space, Time, and Individuation”. World Futures: Vol. 64, No. 8, pp. 631-633.

This paper reviews the present status of the material dualist theory of brain-consciousness relations. I cover first the history of its development by Priestly, Broad, Price, Carr, Jourdan, and myself. The theory is then described with its basis in higher-dimensional geometry, the phenomenology of consciousness, the neurological concept of the body image, and the application of Leibniz's Law to the current dominant identity theory of brain-consciousness relations. A model based on Flatland is developed to illustrate the theory followed by a (...) discussion of its application to recent findings in NDE cases together with the use by Jourdan and Brumblay of higherdimensional geometry to account for the remarkable phenomenology revealed. Finally I discuss possible ways to test the theory by experiment. (shrink)

In this paper, we investigate non-homogeneous wave equations in fractional space-time domains of space dimension _D_, \(0 and time dimension \(\beta\), \(0. We write the wave equations in terms of potential functions and non-zero source terms. For scalar source terms, the potential functions are also scalar functions, and for vector source terms, the potential functions are vector functions. We derived an expression for the wave to propagate from the source point to the observation point. The study (...) shows that the time for a wave to propagate from the source point to the observation point in a fractional space-time domain could be different from that in an integer order space-time domain. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:This essay considers hagiography as a spatial-theological genre emerging, so to speak, from the crypts of Christian martyrs where liturgical celebrations commemorate their paradoxical witness to the Paschal mystery, whereby the faithful gain eternal life through temporal death. Later the virtues and miracles of holy men and women, such as ascetics, bishops, mystics and founders of religious communities, are recounted in vitae intended for liturgical offices and contemplative reflection. (...) The relics of these saints are a site for the construction of religious identity and a locus of pilgrimage, as the faithful gather in the churches where the bodily remains are located. Often miracle accounts, collected soon after the death of the saint, are accompanied by miracles at the tomb thereby initiating or furthering the process of veneration and canonization, whence the relics are subsequently transferred to a prominent place within the church, such as the area near the altar. Miracle stories are a constant in liturgical legends, and the vitae of Saint Francis are no exception.In the case of Francis of Assisi, canonization and construction are contemporaneous, since Thomas of Celano's official legend, the Life of Saint Francis, is presented during the initial building phase of the sepulcher basilica. The Paschal paradox of the miraculous, evident in the spatial localization of transcendent power, informs Celano's hagiographical account of miracles in his first text, as well as in the later Legend for Use in the Choir, the Remembrance of the Desire of the Soul, and the Treatise on Miracles. Bonaventure's subsequent conceptualization of Francis's dream body in the Journey of the Soul into God and literary reorganization of the miracle stories in the Major Life, and the absence of Francis's reliquary remains in the Minor Life, dislodges the miraculous from sepulchral stone and regional locales into textual space, which is located in a narrative history but freed from the spatial constraints of ecclesial edifices and geographical locations. As a result, the thaumaturgical founder of Celano's narratives, whose wonders in life and death find a spatial locus in Italy and, particularly, at the basilica tomb, is replaced by the stigmatized Francis. He is the central miracle of Bonaventure's narratives, and readily present anywhere – albeit mediated by the General Minister's own memory – in prayer. This essay posits that this "transitus" of Francis from miracle worker to abiding miracle, especially noticeable in Celano's Legend for Use in the Choir and Bonaventure's Minor Life, is best understood when the performative nature of liturgical legends in sacred space is recognized.1. Choir Legends, Sacred Space and Performative IdentityChoir legends are primarily conceived, composed, and received as spatial texts, ritually performed in a designated sacred space and season. Their ritual context is the Liturgy of the Hours, where believers enter into a dialogical exchange with the divine, grounded in the paradox of the Paschal mystery. Choir legends are unique witnesses to a particular communal image of a saint, whose life of virtue and miraculous deeds is recounted within the dynamics of liturgical prayer and the dominant cultic-cultural identity. Given their essential status within worship, these biographical texts assume a level of iconicity not shared by non-liturgical documents. Specifically intended for communal contemplation and not the promulgation of the saint's cult throughout the universal church, choir legends are similar to opaque windows opening inward on a secluded courtyard of those gathered to recount their family story. While the narrative is accessible to all those who gaze through the aperture and listen attentively, the locus of intent is within the religious community. When the community members – or at least influential leaders – no longer espouse this "prayed" likeness of their father or mother figure, a new image may be constructed, and the previous choir legend is supplanted or even suppressed by another legend that reflects the revised cultural-theological identity. Evidence of this process is found among second.. (shrink)

The relationship between space (absolute space) and matters (relative space) is similar to that between a stage and performers, where they both exist independently and are interconnected. This work first explores the hypothesis that the Essential space of the Universe is absolute and is zero-dimensional. The second part of the hypothesis discusses that the three-dimensional Universe is a relative space occupied by matters and a representation of its relative positions. The hypothesis in this work will (...) be explored and discussed using reference from the correspondence between Clarke and Leibniz. This work tentatively concludes that the space is absolute and zero-dimensional. (shrink)

Facial information is a powerful channel for human-to-human communication. Characteristically, faces can be defined as biological objects that are four-dimensional (4D) patterns, whereby they have concurrently a spatial structure as well as temporal dynamics. The spatial characteristics of facial objects possess three dimensions (3D), namely breadth, height and importantly, depth. The temporal properties of facial objects are defined by how a 3D facial structure evolves dynamically over time; where time is referred to as the fourth dimension (4D). Our entire (...) perspective of another’s face, whether it be social, affective or cognitive perceptions, is therefore built on a combination of 3D and 4D visual cues. Counterintuitively, over the past few decades of experimental research in psychology, facial stimuli have largely been presented to participants as a spatial pattern that has been flattened into two dimensions (2D), while remaining largely static. The following review aims to advance and update facial researchers, on the recent revolution in computer-generated, realistic 4D facial models produced from real-life human subjects. We delve in-depth to summarize recent studies which have utilized facial stimuli that possess 3D structural cues (geometry and depth) and 4D temporal cues (3D structure + dynamic viewpoint and movement). In sum, we have found that higher-order perceptions such as identity, gender, ethnicity, emotion and personality, are critically influenced by the 4D characteristics embedded within natural human faces. In future, it is recommended that facial stimuli incorporate the 4D space-time perspective with the proposed time-resolved methods. (shrink)

A meta-analysis and an experiment show that the degree of compression of the in-depth dimension of visual space relative to the frontal dimension increases quickly as a function of the distance between the stimulus and the observer at first, but the rate of change slows beyond 7 m from the observer, reaching an apparent asymptote of about 50 %. In addition, the compression of visual space is greater for monocular and reduced cue conditions. The pattern of (...) compression of the in-depth dimension as a function of distance is similar to the ratio of in-depth to frontal visual angles of stimuli, but is not as extreme as this ratio would suggest, implying that observers are incapable of fully ignoring size information provided by cues to depth. Size and distance judgments may be described by an Affine transformation of physical space; however, the compression parameter in this model changes as a function of distance from the observer and other experimental conditions. (shrink)

A deep investigation of proprioceptive processes is necessary to understand the relationship between sensory afferent inputs and motor outcomes. In this work, we investigate whether and how perception of wrist position is influenced by the direction along which the movement occurs. Most previous studies have tested Joint Position Sense through 1 degree of freedom wrist movements, such as flexion/extension or radial/ulnar deviation. However, the wrist joint has 3-DoF and many activities of daily living produce combined movements, requiring at least 2-DoF (...) wrist coordination. For this reason, in this study, target positions involved movement directions that combined wrist flexion or extension with radial or ulnar deviation. The chosen task was a robot-aided Joint Position Matching, in which blindfolded participants actively reproduced a previously passively assumed target joint configuration. The JPM performance of 20 healthy participants was quantified through measures of accuracy and precision, in terms of both perceived target direction and distance along each direction of movement. Twelve different directions of movement were selected and both hands tested. The left and right hand led to comparable results, both target extents and directions were differently perceived according to the target direction on the FE/RUD space. Moreover, during 2-DoF combined movements, subjects’ perception of directions was impaired when compared to 1-DoF target movements. In summary, our results showed that human perception of wrist position on the FE/RUD space is symmetric between hands but not isotropic among movement directions. (shrink)

The introduction of electron microscopy profoundly altered biomedical research, providing a tool for a more detailed but at the same time a spatially and temporally more restricted visual analysis. Examining the case study of Golgi apparatus research in the 1950s and 1960s, it will be shown how microscopists handled these challenges, and how these confrontations modified the general concept of cellular organization. This will also shed light on the artifact debate and on the question of scientific realism in the field (...) of microscopy. (shrink)

Several reaction time (RT) studies report faster responses when responses to temporal information are arranged in a spatially congruent manner than when this arrangement is incongruent. The resulting space–time congruency effect is commonly attributed to a culturally salient localization of temporal information along a mental timeline (e.g., a mental timeline that runs from left to right). The present study aims to provide a compilation of the published RT studies on this time–space association in order to estimate the size (...) of its effect and the extent of potential publication bias in this field of research. In this meta-analysis, three types of task are distinguished due to hitherto existing empirical findings. These findings suggest that the extent to which time is made relevant to the experimental task has a systematic impact on whether or not the mental timeline is activated. The results of this meta-analysis corroborate these considerations: First, experiments that make time a task-relevant dimension have a mean effect size of d = 0.46. Second, in experiments in which time is task irrelevant, the effect size does not significantly deviate from zero. Third, temporal priming studies have a surprisingly high mean effect size of d = 0.47, which, however, should be adjusted to d = 0.36 due to publication bias. (shrink)

In Decision Space: Multidimensional Utility Analysis, first published in 2001, Paul Weirich increases the power and versatility of utility analysis and in the process advances decision theory. Combining traditional and novel methods of option evaluation into one systematic method of analysis, multidimensional utility analysis is a valuable tool. It provides formulations of important decision principles, such as the principle to maximize expected utility; enriches decision theory in solving recalcitrant decision problems; and provides in particular for the cases in which (...) an expert must make a decision for a group of people. The multiple dimensions of this analysis create a decision space broad enough to accommodate all factors affecting an option's utility. The book will be of interest to advanced students and professionals working in the subject of decision theory, as well as to economists and other social scientists. (shrink)

In this paper, we continue the study of the Killing symmetries of a N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the translations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\widetilde M_4 $$ (...) \end{document}. (shrink)

Bridging the gap between the world of science and the realm of the spiritual, B. Alan Wallace introduces a natural theory of human consciousness that has its roots in contemporary physics and Buddhism. Wallace's "special theory of ontological relativity" suggests that mental phenomena are _conditioned_ by the brain, but do not _emerge_ from it. Rather, the entire natural world of mind and matter, subjects and objects, arises from a unitary dimension of reality that is more fundamental than these dualities, (...) as proposed by Wolfgang Pauli and Carl Jung. To test his hypothesis, Wallace employs the Buddhist meditative practice of _samatha_, refining one's attention and metacognition, to create a kind of telescope to examine the space of the mind. Drawing on the work of the physicist John Wheeler, he then proposes a more general theory in which the participatory nature of reality is envisioned as a self-excited circuit. In comparing these ideas to the Buddhist theory known as the Middle Way philosophy, Wallace explores further aspects of his "general theory of ontological relativity," which can be investigated by means of _vipasyana_, or insight, meditation. Wallace then focuses on the theme of symmetry in reference to quantum cosmology and the "problem of frozen time," relating these issues to the theory and practices of the Great Perfection school of Tibetan Buddhism. He concludes with a discussion of the general theme of complementarity as it relates to science and religion. The theories of relativity and quantum mechanics were major achievements in the physical sciences, and the theory of evolution has had an equally deep impact on the life sciences. However, rigorous scientific methods do not yet exist to observe mental phenomena, and naturalism has its limits for shedding light on the workings of the mind. A pioneer of modern consciousness research, Wallace offers a practical and revolutionary method for exploring the mind that combines the keenest insights of contemporary physicists and philosophers with the time-honored meditative traditions of Buddhism. (shrink)

Spaces in the brain can refer either to psychological spaces, which are derived from similarity judgments, or to neurocognitive spaces, which are based on the activities of neural structures. We want to show how psychological spaces naturally emerge from the underlying neural spaces by dimension reductions that preserve similarity structures and the relevant categorizations. Some neuronal representational formats that may generate the psychological spaces are presented, compared and discussed in relation to the mathematical principles of monotonicity, continuity and convexity. (...) In particular, we discuss the spatial structures involved in the connections between perception and action, for example eye-hand coordination, and argue that spatial organization of information makes such mappings more efficient. (shrink)

In this paper, we continue the study of the Killing symmetries of an N-dimensional generalized Minkowski space, i.e., a space endowed with a metric tensor, whose coefficients do depend on a set of non-metrical coordinates. We discuss here the finite structure of the space–time rotations in such spaces, by confining ourselves to the four-dimensional case. In particular, the results obtained are specialized to the case of a “deformed” Minkowski space M_4, for which we derive the explicit (...) general form of the finite rotations and boosts in different parametric bases. (shrink)

Is there a space of the sensory modalities? Such a space would be one in which we can represent all the actual, and at least some of the possible, sensory modalities. The relative position of the senses in this space would indicate how similar and how different the senses were from each other. The construction of such a space might reveal unconsidered features of the actual and possible senses, help us to define what a sense is, (...) and provide grounds that we might use to decide what is one token sense rather than multiple token senses. -/- In this paper, I explore, refine, and defend the idea that we can construct such a space—an idea that I briefly proposed in earlier work (Macpherson 2011a and 2011b). In doing so, I defend the idea from an objection that Richard Gray (2012) has voiced. Gray claims that the dimensions of the space of sensory modalities must generate a non-­‐arbitrary ordering of the senses. He argues that we cannot find dimensions that do so. I disagree. I identify different ways in which a space could be arbitrary but I argue that we can define a space of the sensory modalities in a non-arbitrary manner. I give examples of what the dimensions might be. (shrink)

This book addresses the social, functional and symbolic dimensions of urban space in today’s world. The twelve essays range from a conceptual framing of the issues to case descriptions, rich with illustrations. Together they provide a thorough exploration of the nature and significance of social space and particular aspects of its distribution in today’s urban spaces and the various factors that are competing for it. -/- The book addresses a topic that is intrinsically interdisciplinary. Questions of space (...) are examined from a rich variety of perspectives from urban planning to political philosophy, shedding some light on this shadowy process. Some of the issues addressed include the dichotomies of public and private space, rights and duties regarding the use of space, and conflicts over its allocation. Well-reasoned and lively discussions are offered from the perspective of basic values and rights. The recognition of the specifics of (minority community) identity as an institutional policy is raised in opposition to “abstract distributive accounts of justice” – economic pressures by developers and would-be gentrifiers. (shrink)