A general framework for the explanation of perceptual phenomena as internalizations of external regularities was developed by R. N. Shepard. A particular example of this framework is his account of perceived curvilinear apparent motions. This paper contains a brief summary of the relevant psychophysical data, some basic kinematical considerations and examples, and several criticisms of Shepard's account. The criticisms concern the feasibility of internalization of critical motion types, the roles of simplicity and uniqueness, the contrast between classical physics and (...) class='Hi'>kinematic geometry, the import of perceived path curvilinearity, and the relation of perceptual and scientific knowledge. Key Words: internalization of regularities; kinematic geometry; simplicity. (shrink)

The Kubovy-Epstein proposal for the formalization of the relation between kinematic geometry and perception of motion has formal problems in itself. Motion phenomena are inadequately captured by the relational structures and the notion of isomorphism taken over from measurement theory. [Kubovy & Epstein].

After having reformulated optics, Ibn al-Haytham conceived of an analogous project for astronomy. This has just been revealed by an important book by the mathematician which has never been studied until now. Ibn al-Haytham's reform consists in excluding all cosmology, and in developing a systematic study of a celestial kinematics that has been completely geometrized. In turn, the realization of such a reform demanded innovative research in infinitesimal geometry. In this article, an attempt is made to present this new (...) geometry, as well as the mathematical means invented to elaborate it. (shrink)

We study the space geometry of a rotating disk both from a theoretical and operational approach; in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an extended 3-space, which we call “relative space:” it is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the “physical space of the rotating platform.” (...) Then, the geometry of the space of the disk turns out to be non Euclidean, according to the early Einstein's intuition; in particular the Born metric is recovered, in a clear and self consistent context. Furthermore, the relativistic kinematics reveals to be self consistent, and able to solve the Ehrenfest's paradox without any need of dynamical considerations or ad hoc assumptions. (shrink)

This paper examines explanations that turn on non-local geometrical facts about the space of possible configurations a system can occupy. I argue that it makes sense to contrast such explanations from "geometry of motion" with causal explanations. I also explore how my analysis of these explanations cuts across the distinction between kinematics and dynamics.

In this review article we discuss some of the applications of noncommutative geometry in physics that are of recent interest, such as noncommutative many-body systems, noncommutative extension of Special Theory of Relativity kinematics, twisted gauge theories and noncommutative gravity.

This paper examines explanations that turn on non-local geometrical facts about the space of possible configurations a system can occupy. I argue that it makes sense to contrast such explanations from “geometry of motion” with causal explanations. I also explore how my analysis of these explanations cuts across the distinction between kinematics and dynamics.

The evidence for a kinematics of the mind is confounded by uncontrolled properties of pictures. Effects of illumination and of picture-plane geometry may underlie some evidence given for a process of mental rotation. Pictured rotation is confounded by picture similarity, gauged by gray -level correlations. An example is given involving the depicted rotation of Shepard-Metzler solids in depth. [Hecht; Kubovy & Epstein; Shepard; Todorovic].

Shepard has supposed that the mind is stocked with innate knowledge of the world and that this knowledge figures prominently in the way we see the world. According to him, this internal knowledge is the legacy of a process of internalization; a process of natural selection over the evolutionary history of the species. Shepard has developed his proposal most fully in his analysis of the relation between kinematic geometry and the shape of the motion path in apparent motion (...) displays. We argue that Shepard has made a case for applying the principles of kinematic geometry to the perception of motion, but that he has not made the case for injecting these principles into the mind of the percipient. We offer a more modest interpretation of his important findings: that kinematic geometry may be a model of apparent motion. Inasmuch as our recommended interpretation does not lodge geometry in the mind of the percipient, the motivation of positing internalization, a process that moves kinematic geometry into the mind, is obviated. In our conclusion, we suggest that cognitive psychologists, in their embrace of internal mental universals and internalization may have been seduced by the siren call of metaphor. Key Words: apparent motion; imagery; internalization; inverse projection problem; kinematic geometry; measurement; metaphors of mind. (shrink)

The electronic and muonic hydrogen energy levels are calculated very accurately [1] in Quantum Electrodynamics (QED) by coupling the Dirac Equation four vector (c ,mc2) current covariantly with the external electromagnetic (EM) field four vector in QED’s Interactive Representation (IR). The c -Non Exclusion Principle(c -NEP) states that, if one accepts c as the electron/muon velocity operator because of the very accurate hydrogen energy levels calculated, the one must also accept the resulting electron/muon internal spatial and time coordinate operators (ISaTCO) (...) derived directly from c without any assumptions. This paper does not change any of the accurate QED calculations of hydrogen’s energy levels, given the simplistic model of the proton used in these calculations [1]. The Proton Radius Puzzle [2, 3] may indicate that new physics is necessary beyond the Standard Model (SM), and this paper describes the bizarre, and very different, situation when the electron and muon are located “inside” the spatially extended proton with their Centers of Charge (CoCs) orbiting the proton at the speed of light in S energy states. The electron/muon center of charge (CoC) is a structureless point that vibrates rapidly in its inseparable, non-random vacuum whose geometry and time structure are defined by the electron/muon ISaTCO discrete geometry. The electron/muon self mass becomes finite in a natural way due to the ISaTCOs cutting off high virtual photon energies in the photon propagator. The Dirac-Maxwell-Wilson (DMW) Equations are derived from the ISaTCO for the EM fields of an electron/muon, and the electron/muon “look” like point particles in far field scattering experiments in the same way the electric field from a sphere with evenly distributed charge “e” “looks” like a point with the same charge in the far field (Gauss Law). The electron’s/muon’s three fluctuating CoC internal spatial coordinate operators have eight possible eigenvalues [4, 5, 6] that fall on a spherical shell centered on the electron’s CoM with radius in the rest frame. The electron/muon internal time operator is discrete, describes the rapid virtual electron/positron pair production and annihilation. The ISaTCO together create a current that produce spin and magnetic moment operators, and the electron and muon no longer have “intrinsic” properties since the ISaTCO kinematics define spin and magnetic moment properties. (shrink)

Statistical regularities of the environment are important for learning, memory, intelligence, inductive inference, and in fact, for any area of cognitive science where an information-processing brain promotes survival by exploiting them. This has been recognised by many of those interested in cognitive function, starting with Helmholtz, Mach, and Pearson, and continuing through Craik, Tolman, Attneave, and Brunswik. In the current era, many of us have begun to show how neural mechanisms exploit the regular statistical properties of natural images. Shepard proposed (...) that the apparent trajectory of an object when seen successively at two positions results from internalising the rules of kinematic geometry, and although kinematic geometry is not statistical in nature, this is clearly a related idea. Here it is argued that Shepard's term, “internalisation,” is insufficient because it is also necessary to derive an advantage from the process. Having mechanisms selectively sensitive to the spatio-temporal patterns of excitation commonly experienced when viewing moving objects would facilitate the detection, interpolation, and extrapolation of such motions, and might explain the twisting motions that are experienced. Although Shepard's explanation in terms of Chasles' rule seems doubtful, his theory and experiments illustrate that local twisting motions are needed for the analysis of moving objects and provoke thoughts about how they might be detected. Key Words: Chasles' rule; evolution; geometry; perception; redundancy; statistics; twisting. (shrink)

Roger Shepard's proposals and supporting experiments concerning evolutionary internalized regularities have been very influential in the study of vision and in other areas of psychology and cognitive science. This paper examines issues concerning the need, nature, explanatory role, and justification for postulating such internalized constraints. In particular, I seek further clarification from Shepard on how best to understand his claim that principles of kinematic geometry underlie phenomena of motion perception. My primary focus is on the ecological validity of (...) Shepard's kinematic constraint in the context of ordinary motion perception. First, I explore the analogy Shepard draws between internalized circadian rhythms and the supposed internalization of kinematic geometry. Next, questions are raised about how to interpret and justify applying results from his own and others' experimental studies of apparent motion to more everyday cases of motion perception in richer environments. Finally, some difficulties with Shepard's account of the evolutionary development of his kinematic constraint are considered. Key Words: apparent motion; circadian rhythms; constraints; ecological validity; evolution; internalizated regularities; kinematic principle. (shrink)

Kubovy and Epstein distinguish between systems that follow rules, and those that merely instantiate them. They regard compliance with the principles of kinematic geometry in apparent motion as a case of instantiation. There is, however, some reason to believe that the human visual system internalizes the principles of kinematic geometry, even if it does not explicitly represent them. We offer functional resemblance as a criterion for internal representation. [Kubovy & Epstein].

The limitations of the concept of internalised kinematic geometry have been recognised by Barlow, Hecht, Kubovy & Epstein, and Todorovic. I am in agreement but I still find the perception of curvature in two frames of apparent motion fascinating and I suggest some new directions. [Barlow; Hecht; Kubovy & Epstein; Shepard; Todorovic].

Shepard's (1994) choice of kinematic geometry to support his theory is questioned by Todorovic, Schwartz, and Hecht. His theoretical framework, however, can be applied to another domain that may be less susceptible to some of their concerns. The domain is the representation of spatial layout. [Hecht; Schwartz; Shepard; Todorovic].

Shepard's internalization concept is defended against Hecht's criticisms. By ignoring both Shepard's evolutionary perspective and the fact that internalization does not preclude modularization, Hecht advances inconclusive evidence. Developmental research supports Shepard's conclusion that kinematic geometry may be more deeply internalized than physical dynamics. This research also suggests that the internalization concept should be broadened to include representations acquired during ontogeny. [Hecht; Shepard].

We present the unification of Riemann–Cartan–Weyl (RCW) space-time geometries and random generalized Brownian motions. These are metric compatible connections (albeit the metric can be trivially euclidean) which have a propagating trace-torsion 1-form, whose metric conjugate describes the average motion interaction term. Thus, the universality of torsion fields is proved through the universality of Brownian motions. We extend this approach to give a random symplectic theory on phase-space. We present as a case study of this approach, the invariant Navier–Stokes equations for (...) viscous fluids, and the kinematic dynamo equation of magnetohydrodynamics. We give analytical random representations for these equations. We discuss briefly the relation between them and the Reynolds approach to turbulence. We discuss the role of the Cartan classical development method and the random extension of it as the method to generate these generalized Brownian motions, as well as the key to construct finite-dimensional almost everywhere smooth approximations of the random representations of these equations, the random symplectic theory, and the random Poincaré–Cartan invariants associated to it. We discuss the role of autoparallels of the RCW connections as providing polygonal smooth almost everywhere realizations of the random representations. (shrink)

The generative and governing "idea" of radical modernity is spawned by the technique of mathematical construction deployed and interpreted by the major early-modern thinkers and their legatees. ;Chapter I is a survey of this legacy as it appears in Vico, Kant, Fichte, Marx and Nietzsche and in the post-Nietzschean inheritance of contemporary philosophy, hyperbolic in the case of Derrida et al., elliptical, in the case of Carnap and Goodman. ;In Chapter II I try to show how the pre-modern mathematical tradition, (...) represented by Euclid, aimed at keeping the enticements of technical facility in check by means of didactic phronesis and how the post-Kantian interpretation of "existence" in Euclid as constructibility betrays his usage and self-understanding. I suggest that his focus in the postulates and elsewhere is on the undistorted iterability of graphic evocations of the items already intelligible thanks to the definitions or to the pre-understanding shared by the teacher and student. ;In Chapter III, devoted to Descartes the principal claims of modern constructivism are brought to sight. After examining Descartes' fabulous autobiography and its emphasis on self-origination, I turn to the style, contents and under-pinnings of the Geometry in an effort to extract from that text what he once referred to as "the metaphysics of geometry." The latter yields the conditions of successful problem-solving, i.e., dimensional homogeneity and kinematic continuity. These conditions, in turn, find their justification in Descartes' theses in the Rules concerning order, measure and the uniformity of "mental" activity. In the final section I apply the lessons learned from the Geometry and the Rules to one critical issue in the later Meditations, the transition from essence to existence. Descartes' "solution" generates a sequence of perplexities with Hobbes, Leibniz, Kant and other radical moderns continue to wrestle. (shrink)

We present a new metaphysical framework for physics that is conceptually clear, ontologically parsimonious, and empirically adequate. This framework relies on the notion of self-subsisting structure, that is, a set of fundamental physical elements whose individuation and behavior are described in purely relational terms, without any need for a background spacetime. Although the specification of the fundamental elements of the ontology depends on the particular physical domain considered---and is thus susceptible to scientific progress---, the empirically successful structural features of the (...) framework are preserved through theory change. The kinematics and dynamics of these self-subsisting structures are technically implemented using the theoretical framework of Pure Shape Dynamics, which provides a completely relational physical description of a system in terms of the intrinsic geometry of a suitably defined space called shape space. (shrink)

The numerical representations of measurement, geometry and kinematics are here subsumed under a general theory of representation. The standard theories of meaningfulness of representational propositions in these three areas are shown to be special cases of two theories of meaningfulness for arbitrary representational propositions: the theories based on unstructured and on structured representation respectively. The foundations of the standard theories of meaningfulness are critically analyzed and two basic assumptions are isolated which do not seem to have received adequate justification: (...) the assumption that a proposition invariant under the appropriate group is therefore meaningful, and the assumption that representations should be unique up to a transformation of the appropriate group. A general theory of representational meaningfulness is offered, based on a semantic and syntactic analysis of representational propositions. Two neglected features of representational propositions are formalized and made use of: (a) that such propositions are induced by more general propositions defined for other structures than the one being represented, and (b) that the true purpose of representation is the application of the theory of the representing system to the represented system. On the basis of these developments, justifications are offered for the two problematic assumptions made by the existing theories. (shrink)

After introductory surveys of Poincaré’s role in the Dreyfus case and of his “Fourth Geometry,” I turn to the main question. The problem confronting both Poincaré and Einstein was how to reconcile the phenomena of electrodynamics, notably the optical principle of relativity, with the principles of Newtonian mechanics. I show that, on such questions as the existence and role of the ether and the relation between kinematics and dynamics, Poincaré and Einstein held diametrically opposed views. Poincaré did everything to (...) preserve the old viewpoint, while Einstein abandoned the absolute time and proposed a new mechanics. (shrink)

In this article, we assess the heuristic power of Greek geometrical analysis by trying to reconstruct some analyses of extant propositions of which only the demonstration is found in the text. We have reconstructed the analysis of the trisection of an angle, the property of the tangent to the parabola, to the hyperbola/ellipse, and to the spiral line. In all of these cases, the results and the demonstrations can be found by the analysis alone, without arguments by analogy with other (...) figures or kinematic considerations. We have thus concluded that analysis is a much more powerful tool than is usually assumed to be. We have also examined a part of Apollonius’ Cutting off of a ratio and confirmed that the number of possible cases to be distinguished in analysis tended to increase because the geometric objects and the magnitudes related to them were always considered in the geometric arrangement in which they appear. We suggest that the absence of an algebraic approach that would have detached the magnitudes from their geometrical context may have been one of the major obstacles to further development of Greek geometry. (shrink)

In this paper non-Hausdorff manifolds as potential basic objects of General Relativity are investigated. One can distinguish four stages of identifying an appropriate mathematical structure to describe physical systems: kinematic, dynamical, physical reasonability, and empirical. The thesis of this paper is that in the context of General Relativity, non-Hausdorff manifolds pass the first two stages, as they enable one to define the basic notions of differential geometry needed to pose the problem of the evolution-distribution of matter and are (...) not in conflict with the Einstein equations. With regard to the third stage, various potential conflicts with physical reasonability conditions are considered with a tentative conclusion that non-Hausdorff manifolds are more likely to pass this stage than is typically assumed. When dealing with some of these problems, the modal interpretation of non-Hausdorff manifolds is invoked, according to which they represent bundles of alternative possible spacetimes rather than single spacetimes. (shrink)

The existence of White Hole (WH) has been suggested by Schwarzschild solution to the Einstein field equation as a time-reversed Black Hole (BH), besides there has not been observational evidence for their existence yet. Our idea of the “inverse universe”, in which we introduce the time-reversed kinematics as another geometric state, can explain that WH should appear in such a geometry after a matter falls into a BH. In this work, we present a new operation for WH conversion from (...) BH, and by using it the nearly infinity point on the universe, for instance the inside of BH, is geometrically connected to the inside of WH on the inverse universe. Such a conversion is useful to provide the simple solution to the problem of “information loss” in BH. Furthermore, we find another conversion point as the prior geometric state to the Big Bang, and we propose a new cosmology of cyclic universe. (shrink)

Epitome V (1621), and consisted of matching an element of area to an element of time, where each was mathematically determined. His treatment of the area depended solely on the geometry of Euclid's Elements, involving only straight-line and circle propositions – so we have to account for his deliberate avoidance of the sophisticated conic-geometry associated with Apollonius. We show also how his proof could have been made watertight according to modern standards, using methods that lay entirely within his (...) power. The greatest innovation, however, occurred in Kepler's fresh formulation of the measure of time. We trace this concept in relation to early astronomy and conclude that Kepler's treatment unexpectedly entailed the assumption that time varied nonuniformly; meanwhile, a geometrical measure provided the independent variable. Even more surprisingly, this approach turns out to be entirely sound when assessed in present-day terms. Kepler himself attributed the cause of the motion of a single planet around the Sun to a set of `physical' suppositions which represented his religious as well as his Copernican convictions; and we have pared to a minimum – down to four – the number he actually required to achieve this. In the Appendix we use modern mathematics to emphasize the simplicity, both geometrical and kinematical, that objectively characterizes the Sun-focused ellipse as an orbit. Meanwhile we highlight the subjective simplicity of Kepler's own techniques (most of them extremely traditional, some newly created). These two approaches complement each other to account for his success. (shrink)

This book describes Carmeli's cosmological general and special relativity theory, along with Einstein's general and special relativity. These theories are discussed in the context of Moshe Carmeli's original research, in which velocity is introduced as an additional independent dimension. Four- and five-dimensional spaces are considered, and the five-dimensional braneworld theory is presented. The Tully-Fisher law is obtained directly from the theory, and thus it is found that there is no necessity to assume the existence of dark matter in the halo (...) of galaxies, nor in galaxy clusters.The book gives the derivation of the Lorentz transformation, which is used in both Einstein's special relativity and Carmeli's cosmological special relativity theory. The text also provides the mathematical theory of curved space?time geometry, which is necessary to describe both Einstein's general relativity and Carmeli's cosmological general relativity. A comparison between the dynamical and kinematic aspects of the expansion of the universe is made. Comparison is also made between the Friedmann-Robertson-Walker theory and the Carmeli theory. And neither is it necessary to assume the existence of dark matter to correctly describe the expansion of the cosmos. (shrink)

This paper has three goals: (i) to show that the foundational program begun in the Begriffsschroft, and carried forward in the Grundlagen, represented Frege's attempt to establish the autonomy of arithmetic from geometry and kinematics; the cogency and coherence of 'intuitive' reasoning were not in question. (ii) To place Frege's logicism in the context of the nineteenth century tradition in mathematical analysis, and, in particular, to show how the modern concept of a function made it possible for Frege to (...) pursue the goal of autonomy within the framework of the system of second-order logic of the Begriffsschrift. (iii) To address certain criticisms of Frege by Parsons and Boolos, and thereby to clarify what was and was not achieved by the development, in Part III of the Begriffsschrift, of a fragment of the theory of relations. (shrink)

In the covariant Hamiltonian mechanics with action-at-a-distance, we compare the proper time and dynamical time representations of the coordinate space world line using the differential geometry of nongeodesic curves in 3+1 Minkowski spacetime. The covariant generalization of the Serret-Frenet equations for the point particle with interaction are derived using the arc length representation. A set of invariant point particle kinematical properties are derived which are equivalent to the solutions of the equations of motion in coordinate space and which are (...) functions of either the proper time or the dynamical time. Expressions for the quantities are given for the example of the covariant harmonic oscillator and comments are offered regarding the measurability of the dynamical time. (shrink)

Kepler’s laws provided sufficient geometry and kinematics to strengthen astronomers’ preference for heliocentrism. While Kepler outlined some dynamic arguments, they were not rigorous enough to turn his laws into kinematic tools. As a result, some astronomers found ways to reconcile Kepler’s findings with geo-heliocentrism. One of these was the Jesuit astronomer Giovanni Battista Riccioli, who proposed a method known as the “epic-epicycle” (Riccioli, Almagestum novum, 1651). This paper will explore how Riccioli received and interpreted Kepler’s first and second (...) laws within his own astronomical framework. This analysis will include a discussion of how Riccioli understood the concept of “physics” in his work, beginning with a study of the Sun’s motion (Riccioli, Astronomia reformata, 1665). (shrink)

This paper focuses on the mathematisation of mechanics in the seventeenth century, specifically on how the representation of compounded rectilinear motions presented in the ancient Greek Mechanica found its way into Newton’s Principia almost two thousand years later. I aim to show that the path from the former to the latter was optical: the conceptualisation of geometrical lines as paths of reflection created a physical interpretation of dia­grammatic principles of geometrical point-motion, involving the kinematics and dynamics of light reflection. Upon (...) the atomistic conception of light, the optical interpretation of such geometrical principles entailed their mechanical generalisation to local motion; rectilinear motion via the physico-mathemat­ics of reflection and the Mechanica’s parallelogram rule; circular motion via the physico-mathematics of reflection, the Archimedean squaring of the circle and the Mechanica’s extension of the parallelogram rule to centripetal motion. This appeal to the physico-mathematics of reflection forged a realist founda­tion for the mathematisation of motion. Whereas Aristotle’s physics rested on motions which had their source in the nature of the elements, early modern thinkers such as Harriot, Descartes, and Newton based their new principles of mechanical motion upon selected elements of the mechanics of light motion, projected upon the geometry of the parallelogram rule for rectilinear and, ultimately, circular motion. (shrink)

The structure of the Lorentz transformation depends intimately on the conventional operations for measurement of lengths (L) and time intervals (T). The prescription for length measurement leads to justifiable utilization of Euclidean geometry over finite values of the coordinates. Then T-values can be regarded as ratios of length measurements within a suitably defined clock. In certain cases the synchronization process should be supplemented by measurements providing position certification. The Lorentz transformation emerges from three specific symmetry statements, assured by the (...) nature of the L and T operations: (1) one-one correspondence of finite values of the coordinates of two inertial frames, (2) frame reciprocity, and (3) spatial isotropy. (Light signaling is not needed in this derivation. Afterward, it is assumed that light is indeed an agent moving with the common speed revealed by the transformation.) When rest masses have been determined in the conventional fashion, the conservation of momentum and of energy follow from the kinematics—a result due to Einstein. (shrink)

Evolution produced many species whose members are pre-programmed with almost all the competences and knowledge they will ever need. Others appear to start with very little and learn what they need, but appearances can deceive. I conjecture that evolution produced powerful innate meta-knowledge about a class of environments containing 3- D structures and processes involving materials of many kinds. In humans and several other species these innate learning mechanisms seem initially to use exploration techniques to capture a variety of useful (...) generalisations after which there is a "phase transition" in which learnt generalisations are displaced by a new generative architecture that allows novel situations and problems to be dealt with by reasoning -- a pre-cursor to explicit mathematical theorem proving in topology, geometry, arithmetic, and kinematics. This process seems to occur in some non-human animals and in preverbal human toddlers, but is clearest in the switch from pattern-based to syntax-based language use. The discovery of non-linguistic toddler theorems has largely gone unnoticed, though Piaget investigated some of the phenomena, and creative problem solving in some other animals also provides clues. A later evolutionary development seems to have enabled humans to cope with domains that involve both regularities and exceptions, explaining "U-shaped" language learning. Only humans appear to be able to develop meta-meta-competences needed for teaching learnt "theorems" and their proofs. I'll sketch a speculative theory, present examples, and propose a research programme, reducing the 'G' in AGI, while promising increased power in return. (shrink)

RésuméChaque science, c'est‐à‐dire chaque système, est formée d'un modèle et d'une théorie de la mesure permettant de la vérifier expérimentalement. Les modèles contemporains sont — pour la plupart — des théories déductives. Il existe toute une hiérarchie de systèmes de plus en plus larges: logique, arithmétique, théorie des probabilités , géométrie, cinématique, dynamique.Each science is formed by a model and a measure theory . Nearly all to‐day models are deductive theories. There exists a hierarchy of systems more and more extensive: (...) logics, arithmetics, theory of probability , geometry, kinematics, dynamics. (shrink)

In the course of his work on optics and electrodynamics in systems moving through the ether, the 19th-century medium for light waves and electric and magnetic fields, Lorentz discovered and exploited the invariance of the free-field Maxwell equations under what Poincaré later proposed to call Lorentz transformations. To account for the negative results of optical experiments aimed at detecting the earth’s motion through the ether, Lorentz, in effect, assumed that the laws governing matter interacting with light waves are Lorentz invariant (...) as well. Like Lorentz, Einstein first encountered the Lorentz transformations in electrodynamics. Unlike Lorentz, for whom the transformation merely provided convenient mathematical substitutions, but like Poincaré, Einstein recognized that the Lorentz-transformed quantities are the measured quantities for the moving observer. More importantly, Einstein recognized that the Lorentz invariance of all physical laws had nothing to do with electrodynamics per se, but reflected the kinematics in a new relativistic space-time, to be named after Minkowski who worked out its geometry a few years later. (shrink)

Richard Jeffrey regarded the version of Bayesian decision theory he floated in ‘The Logic of Decision’ and the idea of a probability kinematics—a generalisation of Bayesian conditioning to contexts in which the evidence is ‘uncertain’—as his two most important contributions to philosophy. This paper aims to connect them by developing kinematical models for the study of preference change and practical deliberation. Preference change is treated in a manner analogous to Jeffrey’s handling of belief change: not as mechanical outputs of combinations (...) of intrinsic desires plus information, but as a matter of judgement and of making up one’s mind. In the first section Jeffrey’s probability kinematics is motivated and extended to the treatment of changes in conditional belief. In the second, analogous kinematical models are developed for preference change and in particular belief-induced change that depends on an invariance condition for conditional preference. The two are the brought together in the last section in a tentative model of pratical deliberation. (shrink)

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant Λ is discussed by using Inönü–Wigner contractions of the de Sitter groups and spaces. When Λ→∞, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c→∞ is further considered, the kinematical group in this case being a modified Galilei (...) group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology. (shrink)

Every physical theory has two different forms of mathematical equations to represent its target systems: the dynamical and the kinematical. Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory (...) treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. (shrink)

Les architectures molles, sculptées, transparentes, immatérielles prétendent se libérer des contraintes géométriques, comme si la géométrie ne revendiquait que la droite et la forme orthogonale ou le cercle! Certains architectes s'abandonnent aux " hasards " informatiques et construisent des édifices à la géométrie chahutée par un logiciel. Des urbanistes opposent encore le plan radioconcentrique au plan en damier en ce qui concerne l'expansion des villes et, refusant d'imaginer d'autres morphologies, laissent faire la promotion immobilière, les opportunités foncières et le chacun (...) pour soi. La géométrie, dans notre culture marquée par la philosophie grecque, est constitutive et de l'architecture et de l'urbanisme. Elle est mise en débat par le jeu extraordinairement varié des formes et de leurs agencements, aussi bien que par des régulations qui donnent une mesure au monde et suscitent des questionnements quant à ce qui est à la mesure de l'existence. Depuis le simple pas jusqu'aux théories les plus sophistiquées, la géométrie - qui n'a jamais cessé de se complexifier depuis Pythagore ou Euclide jusqu'aux géométries algébrique, infinitésimale et variable - se rappelle à nous. C'est ce rappel qu'il nous faut entendre, comme une invitation à penser aussi bien notre corps que le paysage, aussi bien la maison que la ville et la cité. Cet ouvrage collectif veut questionner géométriquement et philosophiquement l'urbain contemporain et les architectures qu'il provoque. En d'autres termes, il espère saisir à partir de la confrontation entre mathématiciens, géomètres, historiens, architectes, urbanistes, paysagistes et philosophes l'expérience existentielle de l'espace-temps des lieux. (shrink)

Quantum geometry on a discrete set means a directed graph with a weight associated to each arrow defining the quantum metric. However, these ‘lattice spacing’ weights do not have to be independent of the direction of the arrow. We use this greater freedom to give a quantum geometric interpretation of discrete Markov processes with transition probabilities as arrow weights, namely taking the diffusion form ∂+f = f for the graph Laplacian Δθ, potential functions q, p built from the probabilities, (...) and finite difference ∂+ in the time direction. Motivated by this new point of view, we introduce a ‘discrete Schrödinger process’ as ∂+ψ = ıψ for the Laplacian associated to a bimodule connection such that the discrete evolution is unitary. We solve this explicitly for the 2-state graph, finding a 1-parameter family of such connections and an induced ‘generalised Markov process’ for f = |ψ|2 in which there is an additional source current built from ψ. We also mention our recent work on the quantum geometry of logic in ‘digital’ form over the field F2 = {0, 1}, including de Morgan duality and its possible generalisations. (shrink)

Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of “spherically symmetric” line (...) elements that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the “real” coordinate transformations from the Lorentz transformations. (shrink)

We try to find a possible origin of the holographic principle in the Lorentz-covariant Yang’s quantized space-time algebra (YSTA). YSTA, which is intrinsically equipped with short- and long-scale parameters, λ and R, gives a finite number of spatial degrees of freedom for any bounded spatial region, providing a basis for divergence-free quantum field theory. Furthermore, it gives a definite kinematical reduction of spatial degrees of freedom, compared with the ordinary lattice space. On account of the latter fact, we find a (...) certain kind of kinematical holographic relation in YSTA, which may be regarded as a primordial form of the holographic principle suggested so far in the framework of the present quantum theory that appears now in the contraction limit of YSTA, λ→0 and R→∞. (shrink)

Contextualism is the view that knowledge ascriptions – utterances of sentences containing the word “knows” - express different propositions in different contexts of utterance. But what features of context determine the propositions expressed by knowledge ascriptions? According to a version of contextualism I call conversational contextualism, the conversational dynamics or kinematics determine the propositions expressed by knowledge ascriptions. In this paper I argue that the most sophisticated version of conversational contextualism, which is the view defended by Michael Blome-Tillmann (2009; 2014), (...) faces serious problems. My (very) tentative conclusion will be that conversational contextualism should be abandoned because of these problems. (shrink)