Ordinarily, what we experience does not jump from one place or time to another—we have to pass through all the intermediate times and places. But in films, what we experience can jump in both dimensions, both separately and together. This phenomenon has been memorably described in film criticism by Rudolph Arnheim and it has been deployed philosophically by Suzanne Langer and Colin McGinn. But discussion of space-time discontinuity remains hampered by the lack of attunement between film critical (...) and philosophical investigations. Without philosophy, the valuable insights of film criticism lack rigour and have been blunted by conceptual imprecision and confusion; without film criticism, the provocative claims of philosophy lack support, floating free of the evidence that a suitably sharp awareness of the details of particular films alone provides. This paper brings philosophy and film criticism to bear on each other so that we stand to make headway on the issue of film and space-time discontinuity. (shrink)

Franz Brentano is recognised as one of the most important philosophers of the late nineteenth and early twentieth centuries. This work, first published in English in 1988, besides being an important contribution to metaphysics in its own right, has considerable historical importance through its influence on Husserl’s views on internal time consciousness. The work is preceded by a long introduction by Stephan Körner in collaboration with Brentano’s literary executor Roderick Chisholm. It is translated by Barry Smith.

This book is a study of the categoriality presumed by a coherent account of nature. It is a "speculative" philosophy of nature in the Hegelian sense. Harris argues that the standpoint of "mechanism," an empirical realism which "regards the objective world as a system of external relations", is both incoherent and pernicious. Mechanism is incoherent because its attempts to conceptualize the order of nature have the characteristic of Kantian antinomies: they constantly pass over into counterpositions. It is pernicious because it (...) suggests that we are related to nature as to a force hostile to our freedom. (shrink)

INTRODUCTION In Einstein's theory of gravitation matter and its dynamical interaction are based on the notion of an intrinsic geometric structure of the space -time continuum. The ideal aspiration, the ultimate aim, of the theory is not more and ...

_ Source: _Volume 5, Issue 2, pp 290 - 322 Einstein's special theory, as interpreted by Herman Minkowski, suggests that an understanding of space and time requires the replacement of three-dimensional space and one dimensional time with a four-dimensional spacetime continuum, as a natural kind of thing with a characteristic, geometrical, structure. Issues of space and time in general, and of special relativity in particular, are not addressed in Bhaskar's _A Realist Theory of (...) Science_, and their treatment in subsequent realist writings has been patchy and indecisive. Some of Bhaskar's observations in later writings, including his defence of fundamental ontological asymmetries between space and time, and between present, past and future, appear incompatible with a relativistic perspective. Equally problematic, from a critical realist perspective, is the apparent ontological prioritisation of events, and causation as action-by-contact, within the Minkowski interpretation of special relativity. This paper argues that the four-dimensional spacetime continuum of special relativity occupies its own level at the base of the ontological hierarchy of natural kinds, providing lower-order components and laws for higher-order physical, chemical, biological and social structures. While providing no definitive reconciliation of relativistic and realist perspectives, this paper does suggest that A. N. Whitehead's idea of atomic events, or ‘actual occasions’, could pave the way for some possible future reconciliation. (shrink)

In earlier articles an account has been given of some of the chief notions in the Organic Philosophy, namely Creativity, Actual Entities, Eternal Objects, God. In the present article the writer will endeavour to present Whitehead's doctrine concerning the space-time continuum and the nature of enduring objects implicated therein.

Mathematically, the fusion of space and time may be explained as follows. In pre-relativity physics, space was envisaged as a three-dimensional Euclidean continuum. Such a continuum is homogeneous and isotropic, and its metrical character can be specified by the definition of the distance between any two points in the continuum: s2 = 2 + 2 + 2. Now, while it is possible to speak of a four-dimensional continuum in pre-relativity physics by adding the (...) time-coordinate to the three space-coordinates, there is no way, corresponding to the definition of s, to define the spatio-temporal "separation" or "interval" between any two points in this new four-dimensional continuum. Thus, while it makes sense from the classical point of view to ask for the distance between two points in space, it does not make sense to ask for the spatio-temporal interval between two events occurring in different places at different times. The spatio-temporal interval between non-simultaneous, spatially separated events is simply not defined in pre-relativity physics. Another way of putting it is that in classical physics space and time are measured in entirely disparate units and no method is provided for making these units comparable with one another. In relativity physics, on the other hand, light--or rather the velocity of light--provides the means for making the results of spatial and temporal measurement comparable quantities: one simply multiplies the time-like intervals by c, the fixed velocity of light, in order to obtain space-like intervals. The interval between any two events is defined as: s2 = 2 + 2 + 2 - c22. Interval, so defined, is an invariant, whereas spatial and temporal "separation" are now relative to the state of motion of the observer. The geometry of the four-dimensional continuum characterized by this formula is called "semi-Euclidean". (shrink)

The symplectic quantization scheme proposed for matter scalar fields in the companion paper (Gradenigo and Livi, arXiv:2101.02125, 2021) is generalized here to the case of space–time quantum fluctuations. That is, we present a new formalism to frame the quantum gravity problem. Inspired by the stochastic quantization approach to gravity, symplectic quantization considers an explicit dependence of the metric tensor gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} on an additional time variable, named intrinsic (...) time at variance with the coordinate time of relativity, from which it is different. The physical meaning of intrinsic time, which is truly a parameter and not a coordinate, is to label the sequence of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} quantum fluctuations at a given point of the four-dimensional space–time continuum. For this reason symplectic quantization necessarily incorporates a new degree of freedom, the derivative g˙μν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{g}}_{\mu \nu }$$\end{document} of the metric field with respect to intrinsic time, corresponding to the conjugated momentum πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document}. Our proposal is to describe the quantum fluctuations of gravity by means of a symplectic dynamics generated by a generalized action functional A[gμν,πμν]=K[gμν,πμν]-S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }] = {\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }] - S[g_{\mu \nu }]$$\end{document}, playing formally the role of a Hamilton function, where S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} is the standard Einstein–Hilbert action while K[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} is a new term including the kinetic degrees of freedom of the field. Such an action allows us to define an ensemble for the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document} analogous to the microcanonical one in statistical mechanics, with the only difference that in the present case one has conservation of the generalized action A[gμν,πμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {A}}[g_{\mu \nu },\pi _{\mu \nu }]$$\end{document} and not of energy. Since the Einstein–Hilbert action S[gμν]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S[g_{\mu \nu }]$$\end{document} plays the role of a potential term in the new pseudo-Hamiltonian formalism, it can fluctuate along the symplectic action-preserving dynamics. These fluctuations are the quantum fluctuations of gμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g_{\mu \nu }$$\end{document}. Finally, we show how the standard path-integral approach to gravity can be obtained as an approximation of the symplectic quantization approach. By doing so we explain how the integration over the conjugated momentum field πμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi _{\mu \nu }$$\end{document} gives rise to a cosmological constant term in the path-integral approach. (shrink)

In the spirit of philosophy as the synthesis of wisdom, David Farrell Krell offers a novel bridge between the proper disciplines of philosophy and architecture. His result examines the term “architecture” as one which finds its basis in the Greek root “tic,” which broadens the use of the root tec to suggest not merely a making or producing, but a reproducing or procreating. Krell employs a spectrum of philosophers from Plato to Derrida to position architecture as more than just an (...) enterprise of design, aesthetic planning, and space allocation. He develops the art of archeticture as paying heed to the lived body’s extension into its environment, with a sensitivity for architecture’s role in orchestrating the locus of life. Just as a mother extends herself for her progeny, she first lovingly extends herself into her progeny. In much the same manner, Krell exhorts design specialists to beget their space planning as much as they would craft it. The text calls for a rethinking of lived space from merely considering it as a three-dimensional continuum to conceiving it as an inscrutable receptacle into which we move, produce, and confront our cares and concerns. Krell suggests that architects sensitize themselves to the dynamism of the human body as it interacts with and navigates its environment. (shrink)

The Oxford University Studies in the Enlightenment series, previously known as SVEC, has published over 500 peer-reviewed scholarly volumes since 1955 as part of the Voltaire Foundation at the University of Oxford. International in focus, Oxford University Studies in the Enlightenment volumes cover wide-ranging aspects of the eighteenth century and the Enlightenment, from gender studies to political theory, and from economics to visual arts and music, and are published in English or French.

Arina Orekhova’s interview with Professor Serhii Secundant, devoted to Leibniz’s concept of time and space, the peculiarities of Michael Fatch’s interpretation of this concept, and various historico-philosophical approaches to understanding Leibniz’s philosophy as a whole.

In view of the primacy assigned to the 'present' in traditional metaphysics, in terms of the ways in which questions about existence are expressed, the following discussion takes the question of the temporalizing of the present as its theme. This involves unravelling the historical traces of the thought of the present as a finite, closed, objective point of a successive continuum of discrete moments (a real oscillation between the now and the not-now) by returning to the phenomenological sense of (...) the present as the stretching out of an opening – the 'living Present' (lebendige Gegenwart) – which bears its continuity of presence and non-presence within itself (without restriction to linearity). The transition itself suggests something like a quantum-leap and, in another sense, it also extends beyond the bounds of this simile (and the discontinuity that is implied) by evoking the image of a 'twist' or a 'turn.’ In order to grasp the significance of this turn we shall first examine – re turn to – its main obstacle: the concept of time as a linear and corpuscular continuum. The traditional model of time as a succession of 'now-points' (a notion that 1 still infects discourse on temporality) has always undermined our understanding of 'presence' as that which maintains itself (abides) through succession. In effect, presence must be 'maintained' [maintenant] within the 'now.' Yet, if the 'now' is constantly shifting into non-being through its replacement by a new 'now' then presence must be infused with its own negation and a certain discontinuity. How is it possible, then, to speak of the 'persistence' of 'identity' as something unitary (simultaneous with itself) existing through plurality and successive fragmentation into non-being? Furthermore, in reference to motion, what is entailed in the possibility of experiencing the transition of a selfsame (particular) object from one spatial location to another: how is it that the object 'endures' through its spatial and temporal transition? Since antiquity the question of simultaneity has been taken for granted – generally being consigned to mere spatial models.. (shrink)

Hume’s discussion of space, time, and mathematics at T 1.2 appeared to many earlier commentators as one of the weakest parts of his philosophy. From the point of view of pure mathematics, for example, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum and infinite divisibility. I shall argue, on the contrary, that Hume’s views on this topic are deeply connected with his radically empiricist reliance on phenomenologically given sensory images. He insightfully shows (...) that, working within this epistemological model, we cannot attain complete certainty about the continuum but only at most about discrete quantity. Geometry, in contrast to arithmetic, cannot be a fully exact science. A number of more recent commentators have offered sympathetic interpretations of Hume’s discussion aiming to correct the older tendency to dismiss this part of the Treatise as weak and confused. Most of these commentators interpret Hume as anticipating the contemporary idea of a finite or discrete geometry. They view Hume’s conception that space is composed of simple indivisible minima as a forerunner of the conception that space is a discretely (rather than continuously) ordered set. This approach, in my view, is helpful as far as it goes, but there are several important features of Hume’s discussion that are not sufficiently appreciated. I go beyond these recent commentators by emphasizing three of Hume’s most original contributions. First, Hume’s epistemological model invokes the “confounding” of indivisible minima to explain the appearance of spatial continuity. Second, Hume’s sharp contrast between the perfect exactitude of arithmetic and the irremediable inexactitude of geometry reverses the more familiar conception of the early modern tradition in pure mathematics, according to which geometry (the science of continuous quantity) has its own standard of equality that is independent from and more exact than any corresponding standard supplied by algebra and arithmetic (the sciences of discrete quantity). Third, Hume has a developed explanation of how geometry (traditional Euclidean geometry) is nonetheless possible as an axiomatic demonstrative science possessing considerably more exactitude and certainty that the “loose judgements” of the vulgar. (shrink)

In 1922, Albert Einstein rejected Bergson’s concept of time. He even declared that Bergson’s duration did not exist, something that Bergson never quite came to terms with. On the other hand, some of Bergson’s reflections indicated that in a certain respect he was close to the spirit of modern physics, especially quantum theory. The author, therefore, asks whether it is possible to equate Bergson’s duration with the quantum space-time continuum and thus rehabilitate Bergson’s concept. The first (...) part of the article, in addition to the definition of duration, focuses on the connection of the subject, time, and matter in Bergson, which represents one of the points of contact with quantum theory. The second part describes the role of the subject in quantum theory. The third part presents the definition of the mentioned space-time continuum. The final section compares the two concepts and answers the research question. (shrink)

This is of course the relational, as opposed to the Newtonian absolutist, theory of space and time. The trouble is, as Clarke indicated several times during the correspondence, and as Russell pointed out in his early study of Leibniz: if continua such as space and time are relations, then it must be shown how a relation can behave as we recognize a continuum to do. How, for example, can a relation be divided or measured as (...) we think space and time can? Russell says. (shrink)

In his Poetics, Aristotle articulated certain ideas on the structure of drama that dominated both dramatic literature and theatre practices for the centuries to come. In this article I show how the thorough analysis of his statements leads us to believe that he endorses causality, narrativity, and temporal linearity as primary factors in the organization of dramatic and stage texts. Tracing various modifications of causality throughout theatre history, I use the work of the two prominent contemporary directors, Eimuntas Nekrosius and (...) Anatoly Vasilyev, to demonstrate how postmodernist theatre has arrived at non-Aristotelian theatrical model based on the unity of a time–space continuum rather than temporal development. (shrink)

In 1905 Albert Einstein, in a paper entitled “On the Electrodynamics of Moving Bodies”, as a solution to the disagreement between classical mechanics and the results of the Michelson's experiment, who showed the invariance of the speed of light in vacuum measured in different inertial reference systems, developed the theory of special relativity. In this essay Einstein expounded a theory that, instead of introducing a privileged system, required the revision of the concepts of space and time of classical (...) physics. Combining the principle of Galilean relativity, according to which the laws of physics are invariant in all inertial reference systems, with the physics of electromagnetism, according to which the speed of light in a vacuum is constant, Einstein concluded that time is no more than a relative measure, namely that whenever we have to do with speed equal to or close to that of light, time is no longer a variable absolute and independent of the reference system adopted, but depends on the variable position. This is what Einstein shows through the critical examination of the concept of simultaneity. The abandonment of the traditional conception of space and time based on the idea of a spatial continuum flowing through a temporal continuum coherently leads to the assumption of a space-time continuum in which distances and time intervals vary with the changing the reference system, and together vary, of course, all other sizes to those connected. (shrink)

Cyberspace, a term popularized in the 1984 novel Neuromancer, was used by William Gibson to describe the ‘consensual hallucination’ and interstitial online world that lies between the reality of our world and that of the surreal terrain of dreamscapes. While many attempts have been made to describe this intangible, yet seemingly perceptible space, the digital domain as a metaphor mirrors in many ways our own inadequate understanding of consciousness. Conversely, the physicist Michio Kaku explains that our reality is bounded (...) by hyperspace – a multi-dimensioned space beyond our quotidian 3D existence that runs parallel, or tangential, to us along with the phenomenon of time. Indeed, if space and time (here considered as space–time) are a consolidated whole in the physical sense, perhaps our consciousness, as a structure manifest within this continuum may itself be thought of as a sensorial projection of this amalgam that attempts to observe and make sense, or meaning, of this condition. In truth, what if our need and delight in storytelling is driven by the evolution of our biology, as well as our impulse to locate our place in the universe? This article will attempt to examine and delimit the narrative confines of space–time as an appeal to, and an endeavour at, uncovering the alterity of storytelling as a function of consciousness. It will visit the realms of the holograph, quantum mechanics, virtual and augmented realities, as well as other scientific and philosophical tracts as a means to investigate and explore the physiology of space and our imperative desire to share stories. (shrink)

It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum (...) view is fallacious on the ground that the microscopic details of a physical system are not necessarily decoupled from continuum models. We show how temperature discontinuities are present in both data (experiments and simulations) and phenomena (theory and models) and how discontinuum models of temperature variation may have greater empirical adequacy and explanatory power. The conclusions of our paper are: a) continuum idealisations are not indispensable to modelling physical phenomena and both continuous and discontinuous representations of phenomena work depending on the context; b) temperature is not necessarily a continuously defined function in our best scientific representations of the world; and c) that its continuity, where applicable, is a contingent matter. We also raise a question as to whether discontinuous representations should be considered truly de-idealised descriptions of physical phenomena. (shrink)

Our article is an overview of a selection of findings in physics relating to the issue of time—we do not present in it any “time theory” of our own. After making some general remarks on the issue of time, we present historical outline and a brief description of the current state of time interval measurements. Subsequently, we go on to discuss certain (relating to the concept of time) consequences of both theories of relativity: special and (...) general. Here, time is a geometrical component of space-time continuum. Following section is dedicated to time in the so-called Hamiltonian formulations of the theory of particles, where it appears as a parameter of evolution. The last section contains remarks referring to certain attempts of going beyond the recognized physical theories relating to the question of time. (shrink)

Our article is an overview of a selection of findings in physics relating to the issue of time—we do not present in it any “time theory” of our own. After making some general remarks on the issue of time, we present historical outline and a brief description of the current state of time interval measurements. Subsequently, we go on to discuss certain (relating to the concept of time) consequences of both theories of relativity: special and (...) general. Here, time is a geometrical component of space-time continuum. Following section is dedicated to time in the so-called Hamiltonian formulations of the theory of particles, where it appears as a parameter of evolution. The last section contains remarks referring to certain attempts of going beyond the recognized physical theories relating to the question of time. (shrink)

The plane of the present is a concept that is useful for discussing the various paradigms of time. Here by ‘plane of the present’ we mean the temporal interface that represents the present instant and that forms the boundary between the past and the future. We use the geometrical term ‘plane’ to indicate an extended surface in the space-time continuum, as opposed to a ‘point’ on some time axis. This point/plane dichotomy is intended to raise (...) issues of extension and simultaneity and to examine the degree to which these are meaningful concepts from various physical viewpoints. We will show by example in the present work that the plane of the present is a pivotal concept that offers considerable power in differentiating between various views of the nature of time. The concept of time within the main stream of physics thinking has followed a rather convoluted path over the past three millennia. Anticipating the modern motion picture, Zeno of Elea (c.490-c.430 B.C) questioned whether time should appropriately be viewed as a continuously flowing river, or should more properly be considered as a rapid sequence of stop-motion ‘freeze-frames’, in effect rendering geometrical each instant as a separate infinitesimal point on the line of time. Adopting this view, he asked how physical motion could occur. He argued paradoxically that motion is not possible, since it appears to happen only between the frozen frames of time instants.1 From the viewpoint of Zeno, the plane of the present would be simply the last and most recent in this sequence of freeze-frames. It would be that frozen instant, spanning the universe, which changes progressively as the instant we call ‘now’ becomes the frozen past and future possibility freezes into the ‘now’ of present reality. We note that the plane of the present as a concept does not resolve the arrow paradox that Zeno raised. It only provides a way of thinking about it. (shrink)

This book gathers together for the first time an important body of texts written between 1672 and 1686 by the great German philosopher and polymath Gottfried Leibniz. These writings, most of them previously untranslated, represent Leibniz's sustained attempt on a problem whose solution was crucial to the development of his thought, that of the composition of the continuum. The volume begins with excerpts from Leibniz's Paris writings, in which he tackles such problems as whether the infinite division of (...) matter entails perfect points, whether matter and space can be regarded as true wholes, whether motion is truly continuous, and the nature of body and substance. Comprising the second section is Pacidius Philalethi, Leibniz's brilliant dialogue of late 1676 on the problem of the continuity of motion. In the selections of the final section, from his Hanover writings of 1677-1686, Leibniz abandons his earlier transcreationism and atomism in favor of the theory of corporeal substance, where the reality of body and motion is founded in substantial form or force.Leibniz's texts (one in French, the rest in Latin) are presented with facing-page English translations, together with an introduction, notes, appendixes containing related excerpts from earlier works by Leibniz and his predecessors, and a valuable glossary detailing important terms and their translations. (shrink)

It is a commonplace in the analytic geometry of physical space-time that an extended straight line segment, having positive length, is treated as “consisting of” unextended points, each of which has zero length. Analogously, time intervals of positive duration are resolved into instants, each of which has zero duration.

Since the emergence of computing as a mode of investigation in the sciences, computational approaches have revolutionised many fields of inquiry. Recently in philosophy, the question has begun rendering bit by bit—could computation be considered a deeper fundamental building block to all of reality? This paper proposes a continuum computing construct, predicated on a set of core computational principles: computability, discretisation, stability and optimisation. The construct is applied to the set of most fundamental physical laws, in the form of (...) non-relativistic conservation equations which underpin our governing physics. The discretisation approach divides all of space into a mesh of discrete computational cells, and evolution of data in those cells must obey pre-defined stability conditions from established continuum computing theory, namely, the Courant–Friedrichs–Lewy condition. Evolving cell-state data in a manner which logically optimises computational efficiency, combined with the defined stability condition, the construct derives a central coupling of space, time, and the fastest speed of information propagation. This coupling formed at the lowest level by the computing construct, naturally and inherently produces aspects of special relativity and general relativity at the macroscale. This paper therefore proposes a new explanation of why the nature of space and time may be fused, and explores simple emergent congruities with relativity. The theory invites us to reverse the philosophical premise of the original Simulation Argument. This argument currently leads us to consider: how might all of the observed physics of our reality be reproduced computationally in a simulation of our existence? This work asks instead: could foundations of the physics of our universe—namely spacetime coupling—emerge inherently, and necessarily, from fundamental principles of computation? (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture (...) Kant’s theory of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

The relativistic theory of unconstrained p-dimensional membranes (p-branes) is further developed and then applied to the embedding model of induced gravity. Space-time is considered as a 4-dimensional unconstrained membrane evolving in an N-dimensional embedding space. The parameter of evolution or the evolution time τ is a distinct concept from the coordinate time t=x0. Quantization of the theory is also discussed. A covariant functional Schrödinger equation has a solution for the wave functional such that it is (...) sharply localized in a certain subspace P of space-time, and much less sharply localized (though still localized) outside P. With the passage of evolution the region P moves forward in space-time. Such a solution we interpret as incorporating two seemingly contradictory observations: (i) experiments clearly indicate that space-time is a continuum in which events are existing; (ii) not the whole 4-dimensional space-time, but only a 3-dimensional section which moves forward in time, is accessible to our immediate experience. The notorious problem of time is thus resolved in our approach to quantum gravity. Finally we include sources into our unconstrained embedding model. (shrink)

Space, Time, and Stuff is an attempt to show that physics is geometry: that the fundamental structure of the physical world is purely geometrical structure. Along the way, he examines some non-standard views about the structure of spacetime and its inhabitants, including the idea that space and time are pointless, the idea that quantum mechanics is a completely local theory, the idea that antiparticles are just particles travelling back in time, and the idea that (...) class='Hi'>time has no structure whatsoever. The main thrust of the book, however, is that there are good reasons to believe that spaces other than spacetime exist, and that it is the existence of these additional spaces that allows one to reduce all of physics to geometry. Philosophy, and metaphysics in particular, plays an important role here: the assumption that the fundamental laws of physics are simple in terms of the fundamental physical properties and relations is pivotal."--P. [4] of cover. (shrink)

In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples. For the first time, non-commutative linguistic topological spaces (...) are introduced. The notion of a linguistic special subset of doubly non-commutative topological spaces of linguistic topological spaces is introduced in this book. (shrink)

Branching space-time is a simple blend of relativity and indeterminism. Postulates and definitions rigorously describe the causal order relation between possible point events. The key postulate is a version of everything has a causal origin; key defined terms include history and choice point. Some elementary but helpful facts are proved. Application is made to the status of causal contemporaries of indeterministic events, to how splitting of histories happens, to indeterminism without choice, and to Einstein-Podolsky-Rosen distant correlations.

The time of vegetal life itself—denoted as plant-time in this article, following the work of Michael Marder—is essential to human-plant relations. Conceptualized as a multi-dimensional plexity, vegetal temporality embodies the endemic land-based seasons, rhythms, cycles, and timescales of flora in conjunction with human patterns. The contemporary poet Judith Wright invoked a time-space continuum throughout her writing as a means to convey the primordial character of Australian plants while resisting the imposition of a colonialist schema of (...) time. Wright’s bold textualization of vegetal temporality embodies her commitment to fostering botanical ethics and locally-grounded activism on behalf of Aboriginal people and the Australian environment. (shrink)

The time of vegetal life itself—denoted as plant-time in this article, following the work of Michael Marder—is essential to human-plant relations. Conceptualized as a multi-dimensional plexity, vegetal temporality embodies the endemic land-based seasons, rhythms, cycles, and timescales of flora in conjunction with human patterns. The contemporary poet Judith Wright invoked a time-space continuum throughout her writing as a means to convey the primordial character of Australian plants while resisting the imposition of a colonialist schema of (...) time. Wright’s bold textualization of vegetal temporality embodies her commitment to fostering botanical ethics and locally-grounded activism on behalf of Aboriginal people and the Australian environment. (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)

Presenting the history of space-time physics, from Newton to Einstein, as a philosophical development DiSalle reflects our increasing understanding of the connections between ideas of space and time and our physical knowledge. He suggests that philosophy's greatest impact on physics has come about, less by the influence of philosophical hypotheses, than by the philosophical analysis of concepts of space, time and motion, and the roles they play in our assumptions about physical objects and physical (...) measurements. This way of thinking leads to interpretations of the work of Newton and Einstein and the connections between them. It also offers ways of looking at old questions about a priori knowledge, the physical interpretation of mathematics, and the nature of conceptual change. Understanding Space-Time will interest readers in philosophy, history and philosophy of science, and physics, as well as readers interested in the relations between physics and philosophy. (shrink)

When it was first released in 1962, The Shape of Time presented a radically new approach to the study of art history. Drawing upon new insights in fields such as anthropology and linguistics, George Kubler replaced the notion of style as the basis for histories of art with the concept of historical sequence and continuous change across time. Kubler’s classic work is now made available in a freshly designed edition. “ The Shape of Time is as relevant (...) now as it was in 1962. This book, a sober, deeply introspective, and quietly thrilling meditation on the flow of time and space and the place of objects within a larger continuum, adumbrates so many of the critical and theoretical concerns of the late twentieth and early twenty-first century. It is both appropriate and necessary that it re-appear in our consciousness at this time.”—Edward J. Sullivan, New York University. (shrink)

It is true that there were some important dissenting voices among physicists as well as among philosophers. Paul Langevin was one of the first who protested against calling time "the fourth dimension of space. Einstein himself admitted that the asymmetry of time is preserved even in its relativistic fusion with space when he recognized that "we cannot send wire-messages into the past." When Meyerson in the session of the French Philosophical Society of April 6, 1922 insisted (...) on the distinction of space and time even in the theory of relativity, Einstein, who attended the session, explicitly agreed. Meyerson's argument was fully developed in his book, La Déduction Relativiste, and Einstein in his highly favorable comment about it again praised Meyerson's criticism of the spatialization of time. According to Einstein, the spatialization of time is a misinterpretation of the theory of relativity, a misinterpretation committed not only by popularizers, but even by many scientists, though it is often present in their minds only implicitly. Hermann Weyl, when he was in a less Kantian mood of thought, warned against a facile confusion of space and time when he claimed that it is more accurate to speak about the 3 + 1-dimensional continuum instead of the four-dimensional entity. In the same decade, Eddington among the physicists and Whitehead, Bergson and Reichenbach among the philosophers issued similar warnings. (shrink)

When it was first released in 1962, The Shape of Time presented a radically new approach to the study of art history. Drawing upon new insights in fields such as anthropology and linguistics, George Kubler replaced the notion of style as the basis for histories of art with the concept of historical sequence and continuous change across time. Kubler’s classic work is now made available in a freshly designed edition. “ The Shape of Time is as relevant (...) now as it was in 1962. This book, a sober, deeply introspective, and quietly thrilling meditation on the flow of time and space and the place of objects within a larger continuum, adumbrates so many of the critical and theoretical concerns of the late twentieth and early twenty-first century. It is both appropriate and necessary that it re-appear in our consciousness at this time.”—Edward J. Sullivan, New York University. (shrink)