We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the (...) Hertz potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q. (shrink)

The papers in this volume reflect much of the current unease of a world that perceives itself once more at the edge of chaos. The authors present different vistas of that experience and their inherent dialectic, expressed in numerous and ceaseless conflicts between ordering and disordering processes. They can be read as comments on the ongoing processes that lead toward greater complexity.

This paper argues that we can see our lives as a snapshot happening now or as a moving picture extending across time. These dual ways of seeing our lives inform how we conceive of the problem of age group justice. A snapshot view sees age group justice as an interpersonal problem between distinct age groups. A moving picture view sees age group justice as a first-person problem of prudential choice. This paper explores these different ways of thinking about age (...) group justice and illustrates them using a principle of respect for human dignity, understood in terms of reasonable support for floor level central human capabilities at each stage of life. I argue that different frames are suitable for different kinds of decisions, and each provides a true, but partial, picture of aging and age group justice. (shrink)

In one of the most famous but equally obscure passages in the Timaeus, Plato describes the generation of time and the heavens. The “moving image of eternity” (37d5) is commonly read as Plato’s most general characterisation of time. Rémi Brague famously challenged the traditional interpretation on linguistic grounds by claiming that Plato actually did not conceive of time as an image (εἰκών) but rather as a number (ἀριθμός). In this paper, I shall claim that this controversy is (...) by no means a modern one. The traditional interpretation is mostly owed to Plato’s most prominent reader, Plotinus, who famously conceives of time in relation to eternity (Enn. III.7.13.24-25). Brague’s alternative reading, however, is anticipated by Simplicius’ attempt to refute the Plotinian interpretation, as I shall show. According to my reconstruction, Simplicius’ reading of the Timaeus not only shows why the traditional interpretation falls short, but it also offers a systematic argument that bolsters Brague’s alternative reading. Finally, I shall show that this is consistent with Plato’s text. It shall become clear that current interpretative problems are essentially prefigured in the late ancient debate. (shrink)

Nearly all listeners consider the subjective aspects of music, such as its emotional tone, to have primary importance. But contemporary philosophers often downplay, ignore, or even deny such aspects of experience. Moreover, traditional philosophies of music try to decontextualize it. Using music as an example, this paper explores the structure of qualitative experience, demonstrating that it is multi-layer emergent, non-compositional, enacted, and situation dependent, among other non-Cartesian properties. Our explanations draw on recent work in cognitive science, including blending, image schemas, (...) and sensory memory, as well as on phenomenology. A hierarchical structure transformation based complexity theory is applied to obtain a non-linear dynamical systems explanation of qualia and emotion that respects phenomenological insights about time, including retention and protention. The complexity measure provides both a metric structure and a potential function, on spaces of pieces that are constructed using given elements and transformations, with weights that reflect their cognitive difficulty. However, the approach is not reductionist; using improvisation and the evolution of musical notation as data, we argue that situatedness, especially enactment and social context, are key aspects of musical consciousness. (shrink)

In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (...) (3-modal) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames. (shrink)

The perception of time shifts as patients enter hospice care. As a complex, socially determined construct, time plays a significant role in end‐of‐life care. Drawing on Buddhist and Western perspectives, conceptualizations of linear and cyclical time are discussed alongside notions of time as interplay of embodied experience and concept. Buddhist understandings of self as patterns of relating and the theory of ‘dependent origination’ are introduced. Implications for understanding death, dying and end‐of‐life care within these differing perspectives (...) are considered. These explorations contribute to the growing dialogue in nursing between Buddhist and Western traditions. (shrink)

Theodore Sider has recently produced an argument which he takes to show that three-dimensionalism is incompatible with the possibility of time travel. I wish to argue that there is indeed a problem for the three-dimensionalist who wishes to countenance time travel, but that Sider has misdiagnosed it. I show why his putative challenge fails, and furthermore that if it were to succeed this would be as problematic for a wide class of four-dimensionalist positions, including Sider’s own, as it (...) would be for three-dimensionalism. Finally, I present the problem that the possibility of time travel genuinely poses for the three-dimensionalist. (shrink)

The problem of finite-time stability of switched genetic regulatory networks with time-varying delays via Wirtinger’s integral inequality is addressed in this study. A novel Lyapunov–Krasovskii functional is proposed to capture the dynamical characteristic of GRNs. Using Wirtinger’s integral inequality, reciprocally convex combination technique and the average dwell time method conditions in the form of linear matrix inequalities are established for finite-time stability of switched GRNs. The applicability of the developed finite-time stability conditions is validated by (...) numerical results. (shrink)

The conception of time, presented by St. Augustine, unites within itself the physical-philosophical views of Aristotle, and its own psychological view concerning the lived experience of the flow of sensory impressions from the past towards the future. H. Majkrzak underlines, in Augustine, the existential moment of time. The time of a human life is limited: it is situated within borders stretching from the day of birth to the day of death. This faithful and precise representation of the (...) Augustinian conception of time, nevertheless brings the reader up against a problem: What value does it have today? (shrink)

Definitions of time symmetry and examples of time-directed behaviour are discussed in the framework of discrete Markov processes. It is argued that typical examples of time-directed behaviour can be described using time-symmetric transition probabilities. Some current arguments in favour of a distinction between past and future on the basis of probabilistic considerations are thereby judged to be unjustified.

_Beauvoir in Time_ situates _The Second Sex_ in the historical contexts of its writing and later international receptions, showing the continued, though paradoxical, value of her views on sexuality, race, class, and politics for feminists today.

This chapter explores one theme that in the author judgment has not received as much sustained attention as it warrants: the distinction between historical and current time slice theories of epistemic justification. It devotes to the hermeneutical tasks of explicating and contextualizing the distinction between historical and current time slice theories. The chapter examines Goldman's longstanding claim that no current time slice theory can possibly do justice to the epistemic role of preservative memory. It argues that a (...) principle governing preservative memory proposed by Goldman. The author argues that a recent attempt by Earl Conee and Richard Feldman to meet Goldman's challenge by providing a current time slice reconstruction of the relevant epistemic phenomena is similarly unsuccessful. The chapter develops argument against current time slice theories, an argument that proceeds from the detailed consideration of certain cases involving temporally extended reasoning. (shrink)

The temporal structure of behavior contains a rich source of information about its dynamic organization, origins, and development. Today, advances in sensing and data storage allow researchers to collect multiple dimensions of behavioral data at a fine temporal scale both in and out of the laboratory, leading to the curation of massive multimodal corpora of behavior. However, along with these new opportunities come new challenges. Theories are often underspecified as to the exact nature of these unfolding interactions, and psychologists have (...) limited ready-to-use methods and training for quantifying structures and patterns in behavioral time series. In this paper, we will introduce four techniques to interpret and analyze high-density multi-modal behavior data, namely, to: (1) visualize the raw time series, (2) describe the overall distributional structure of temporal events (Burstiness calculation), (3) characterize the nonlinear dynamics over multiple timescales with Chromatic and Anisotropic Cross-Recurrence Quantification Analysis (CRQA), (4) and quantify the directional relations among a set of interdependent multimodal behavioral variables with Granger Causality. Each technique is introduced in a module with conceptual background, sample data drawn from empirical studies and ready-to-use Matlab scripts. The code modules showcase each technique’s application with detailed documentation to allow more advanced users to adapt them to their own datasets. Additionally, to make our modules more accessible to beginner programmers, we provide a “Programming Basics” module that introduces common functions for working with behavioral timeseries data in Matlab. Together, the materials provide a practical introduction to a range of analyses that psychologists can use to discover temporal structure in high-density behavioral data. (shrink)

The relationship between intelligent systems and their environment is at the forefront of research in cognitive science. The Unexplained Intellect: Complexity, Time, and the Metaphysics of Embodied Thought shows how computational complexity theory and analytic metaphysics can together illuminate long-standing questions about the importance of that relationship. It argues that the most basic facts about a mind cannot just be facts about mental states, but must include facts about the dynamic, interactive mental occurrences that take place when a creature (...) encounters its environment. In a discussion that is organised into four clear parts, Christopher Mole begins by examining the mathematics of computational complexity, arguing that the results from complexity theory create a puzzle about how human intelligence could possibly be explained. Mole then uses the tools of analytic metaphysics to draw a distinction between mental states and dynamic mental entities, and shows that, in order to answer the complexity-theoretic puzzle, dynamic entities must be understood to be among the most basic of mental phenomena. The picture of the mind that emerges has important implications for our understanding of intelligence, of action, and of the mind’s relationship to the passage of time. The Unexplained Intellect is the first book to bring insights from the mathematics of computational complexity to bear in an enquiry into the metaphysics of the mind. It will be essential reading for scholars and researchers in the philosophy of mind and psychology, for cognitive scientists, and for those interested in the philosophical importance of complexity. (shrink)