W. de Sitter, „On the relativity of inertia. Remarks concerning Einstein’s latest hypothesis”, Proceedings of the Section of Sciences. Koninklijke Akademie van Wetenschappen te Amsterdam, Vol. XIX, No. 9 i 10, Johannes Müller, Amsterdam, September 1917, pp. 1217–1225. Translated to Polish by Robert Janusz.

A fiber bundle constructed over spacetime is used as the basic underlying framework for a differential geometric description of extended hadrons. The bundle has a Cartan connection and possesses the de Sitter groupSO(4, 1) as structural group, operating as a group of motion in a locally defined space of constant curvature (the fiber) characterized by a radius of curvatureR≈10−13 cm related to the strong interactions. A hadronic matter field ω(x, ζ) is defined on the bundle space, withx the spacetime (...) coordinate and ζ varying in the local fiber. The components of a generalized tensor current ℑ μab (M) (x) are introduced, involving a bilinear expression in the fields ω(x, ζ) and ωΔ(x, ζ) integrated over the local fiber at the pointx. This hadronic matter current is considered as a source current for the underlying fiber geometry by coupling it in a gauge-invariant manner to the curvature expressions derived from the bundle connection coefficients, which are associated here with strong interaction effects, i.e., play the role of meson fields induced in the geometry. Studying discrete symmetry transformations between the 16 differently soldered Cartan bundles, a generalized matter-antimatter conjugation Ĉ is established which leaves the basic current-curvature equations Ĉ-invariant. The discrete symmetry transformation Ĉ turns out to be the direct product of an ordinary charge conjugation for the Dirac point-spinor part of ω(x, ζ) and an internal $\hat P\hat T$ transformation applied globally on the bundle to the fiber (i.e., de Sitter) part of ω(x, ζ). (shrink)

To represent extension of objects in particle physics, a modified Weyl theory is used by gauging the curvature radius of the local fibers in a soldered bundle over space-time possessing a homogeneous space G/H of the (4, 1)-de Sitter group G as fiber. Objects with extension determined by a fundamental length parameter R0 appear as islands D(i) in space-time characterized by a geometry of the Cartan-Weyl type (i.e., involving torsion and modified Weyl degrees of freedom). Farther away from the (...) domains D(i), space-time is identified with the pseudo-Riemannian space of general relativity. Extension and symmetry breaking are described by a set of additional fields ( $(\tilde \xi ^a (x),R(x)) \in {G \mathord{\left/ {\vphantom {G H}} \right. \kern-0em} H}x R^ +$ , given as a section on an associated bundle $\tilde E(B,{G \mathord{\left/ {\vphantom {G H}} \right. \kern-0em} H}x R^ + ,\tilde G)$ over space-time B with structural group $\tilde G$ = G ⊗ D(1), where D(1) is the dilation group. Field equations for the quantities defining the underlying bundle geometry and for the fields $\tilde \xi ^a (x)$ are established involving matter source currents derived from a generalized spinor wave function. Einstein's equations for the metric are regarded as the part of the $\tilde G$ -gauge theory related to the Lorentz subgroup H of G exhibiting thereby the broken nature of the $\tilde G$ -symmetry for regions outside the domains D(i). (shrink)

The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ $_{\bar \eta }^{(\rho )} $ , being a resolution kernel Hilbert space (with resolution generator $\tilde \eta $ and generalized coherent state basis) carrying a spin-zero phase space representation of G=SO(4, 1) belonging (...) to the principal series of unitary irreducible representations determined by the parameter ρ. The bundle ℋ, associated to the de Sitter frame bundle P(B, G), provides a geometric arena with built-in fundamental length parameter R (taken to be of the order of 10−13 cm characterizing hadron physics) yielding, in the presence of gravitation, a quantum kinematical framework for the geometro-stochastic description of spinless matter described in terms of generalized quantum mechanical wave functions, Ψ x ρ (ξ, ζ), defined on #x210B;. By going over to a nonlinear realization of the de Sitter group with the help of a section ξ(x) on the soldered bundle E, associated to P, with homogeneous fiber V′4⋍G/H, one is able to recover gravitation in a de Sitter gauge invariant manner as a gauge theory related to the Lorentz subgroup H of G. ξ(x) plays the dual role of a symmetry-reducing and an extension field. After introducing covariant bilinear source currents in the fields Ψ x ρ (ξ, ζ) and their adjoints determined by G-invariant integration over the local fibers in ℋ, a quantum fiber dynamical (QFD) framework is set up for the dynamics at small distances in B determining the geometric quantities beyond the classical metric of Einstein's theory through a set of current-curvature field equations representing the source equations for axial vector torsion and the de Sitter boost contributions to the bundle connection (the latter defining the soldering forms of the Cartan connection in P(B, G) in the nonlinear gauge). The presented bundle framework yields a theory for quantized material objects in interaction with gravitation, the long-range metrical part of which remains classical. (shrink)

The Unruh-Wald scenario for mining quantum black holes is applied to de Sitter space. The following questions are addressed: Will the generalized second law of thermodynamics be maintained for de Sitter horizons? Does the mining process allow the recovery of unlimited energy from the cosmological gravitational field? The evaporation of a black hole in de Sitter space is also investigated in the context of the second law.

According to Whitehead, nature is disclosed to mind by an ensemble of events characterized by unobservable hidden intrinsic factors (e.g., mass, gravitation) and observable extrinsic factors (e.g., motion, density). Mass is not the substratum of dynamics. It implies spatial extension and temporal duration, which are both necessary conditions of observable natural phenomena. Therefore, an instant, deprived of duration, is immeasurable. Whitehead’s claims on mass, space, and time corroborate Verlinde’s alternative conception of quantum gravitation. Within the de Sitter space-time, this (...) conception starts from the competition of the short distance degrees of freedom of the Ryn-Takanayagi tensor with long-distance thermalized excitations. This enables the creation of a baryonic mass and a decrease in de Sitter entropy. The memory effect of the original baryon creation leads to gravitation and the production of extensive thermodynamic entropy. However, the baryon production shrinks, and the dissipating space-time transforms into a space-timeless cold sink with an accompanying strong contracting memory effect. This is equivalent to the alternate motion of a giant Carnot engine, where the heat source and sink energy exchange produce the eternal periodic dynamics of the Universe. This suggests that the Universe did not start from Big Bang but oscillated eternally as a Big Bounce Universe. (shrink)

The majority of healthcare professionals regularly witness fragility, suffering, pain and death in their professional lives. Such experiences may increase the risk of burnout and compassion fatigue, especially if they are without self-awareness and a healthy work environment. Acquiring a deeper understanding of vulnerability inherent to their professional work will be of crucial importance to face these risks. From a relational ethics perspective, the role of the team is critical in the development of professional values which can help to cope (...) with the inherent vulnerability of healthcare professionals. The focus of this paper is the role of Communities of Practice as a source of resilience, since they can create a reflective space for recognising and sharing their experiences of vulnerability that arises as part of their work. This shared knowledge can be a source of strength while simultaneously increasing the confidence and resilience of the healthcare team. (shrink)

We argue that, under certain plausible assumptions, de Sitter space settles into a quiescent vacuum in which there are no dynamical quantum fluctuations. Such fluctuations require either an evolving microstate, or time-dependent histories of out-of-equilibrium recording devices, which we argue are absent in stationary states. For a massive scalar field in a fixed de Sitter background, the cosmic no-hair theorem implies that the state of the patch approaches the vacuum, where there are no fluctuations. We argue that an (...) analogous conclusion holds whenever a patch of de Sitter is embedded in a larger theory with an infinite-dimensional Hilbert space, including semiclassical quantum gravity with false vacua or complementarity in theories with at least one Minkowski vacuum. This reasoning provides an escape from the Boltzmann brain problem in such theories. It also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere while slow-roll inflation occurs, suggesting that eternal inflation is much less common than often supposed. On the other hand, if a de Sitter patch is a closed system with a finite-dimensional Hilbert space, there will be Poincaré recurrences and dynamical Boltzmann fluctuations into lower-entropy states. Our analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation, since reheating naturally generates a high-entropy environment and leads to decoherence, nor does it affect the existence of non-dynamical vacuum fluctuations such as those that give rise to the Casimir effect. (shrink)

BackgroundFor many decades, the debate on children’s competence to give informed consent in medical settings concentrated on ethical and legal aspects, with little empirical underpinnings. Recently, data from empirical research became available to advance the discussion. It was shown that children’s competence to consent to clinical research could be accurately assessed by the modified MacArthur Competence Assessment Tool for Clinical Research. Age limits for children to be deemed competent to decide on research participation have been studied: generally children of 11.2 (...) years and above were decision-making competent, while children of 9.6 years and younger were not. Age was pointed out to be the key determining factor in children’s competence. In this article we reflect on policy implications of these findings, considering legal, ethical, developmental and clinical perspectives.DiscussionAlthough assessment of children’s competence has a normative character, ethics, law and clinical practice can benefit from research data. The findings may help to do justice to the capacities children possess and challenges they may face when deciding about treatment and research options. We discuss advantages and drawbacks of standardized competence assessment in children on a case-by-case basis compared to application of a fixed age limit, and conclude that a selective implementation of case-by-case competence assessment in specific populations is preferable. We recommend the implementation of age limits based on empirical evidence. Furthermore, we elaborate on a suitable model for informed consent involving children and parents that would do justice to developmental aspects of children and the specific characteristics of the parent-child dyad.SummaryPrevious research outcomes showed that children’s medical decision-making capacities could be operationalized into a standardized assessment instrument. Recommendations for policies include a dual consent procedure, including both child as well as parents, for children from the age of 12 until they reach majority. For children between 10 and 12 years of age, and in case of children older than 12 years in special research populations of mentally compromised patients, we suggest a case-by-case assessment of children’s competence to consent. Since such a dual consent procedure is fundamentally different from a procedure of parental permission and child assent, and would imply a considerable shift regarding some current legislations, practical implications are elaborated. (shrink)

BackgroundThere is a lack of empirical research regarding the outcomes of such clinical ethics support methods as moral case deliberation (MCD). Empirical research in how healthcare professionals perceive potential outcomes is needed in order to evaluate the value and effectiveness of ethics support; and help to design future outcomes research. The aim was to use the European Moral Case Deliberation Outcome Instrument (Euro-MCD) instrument to examine the importance of various MCD outcomes, according to healthcare professionals, prior to participation.MethodsA North European (...) field survey among healthcare professionals drawn from 73 workplaces in a variety of healthcare settings in the Netherlands, Norway and Sweden. The Euro-MCD instrument was used.ResultsAll outcomes regarding the domains of moral reflexivity, moral attitude, emotional support, collaboration, impact at organisational level and concrete results, were perceived as very or quite important by 76%–97% of the 703 respondents. Outcomes regarding collaboration and concrete results were perceived as most important. Outcomes assessed as least important were mostly about moral attitude. ‘Better interactions with patient/family’ emerged as a new domain from the qualitative analysis. Dutch respondents perceived most of the outcomes as significantly less important than the Scandinavians, especially regarding emotional support. Furthermore, men, those who were younger, and physician-respondents scored most of the outcomes as statistically significantly less important compared with the other respondents.ConclusionsThe findings indicate a need for a broad instrument such as the Euro-MCD. Outcomes related to better interactions between professionals and patients must also be included in the future. The empirical findings raise the normative question of whether outcomes that were perceived as less important, such asmoralreflexivity andmoralattitude outcomes, should still be included. In the future, a combination of empirical findings (practice) and normative reflection (theories) will contribute to the revision of the instrument. (shrink)

The advent of new genetic and genomic technologies may cause friction with the principle of respect for autonomy and demands a rethinking of traditional interpretations of the concept of informed consent. Technologies such as whole‐genome sequencing and micro‐array based analysis enable genome‐wide testing for many heterogeneous abnormalities and predispositions simultaneously. This may challenge the feasibility of providing adequate pre‐test information and achieving autonomous decision‐making. At a symposium held at the 11th World Congress of Bioethics in June 2012 (Rotterdam), organized by (...) the International Association of Bioethics, these challenges were presented for three different areas in which these so‐called ‘new genetics’ technologies are increasingly being applied: newborn screening, prenatal screening strategies and commercial personal genome testing. In this article, we build upon the existing ethical framework for a responsible set‐up of testing and screening offers and reinterpret some of its criteria in the light of the new genetics. As we will argue, the scope of a responsible testing or screening offer should align with the purpose(s) of testing and with the principle of respect for autonomy for all stakeholders involved, including (future) children. Informed consent is a prerequisite but requires a new approach. We present preliminary and general directions for an individualized or differentiated set‐up of the testing offer and for the informed consent process. With this article we wish to contribute to the formation of new ideas on how to tackle the issues of autonomy and informed consent for (public) healthcare and direct‐to‐consumer applications of the new genetics. (shrink)

The Poincaré group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincaré as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant Λ is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of Λ (...) and to explain the cosmic coincidence. When applied to the propagation of ultra-high energy photons, it gives a good estimate of the time delay observed in extragalactic gamma-ray flares. It can, for this reason, be considered a new paradigm to approach the quantum gravity problem. (shrink)

Reductionism, in the sense of the doctrine that theories on different levels of reality should exhibit strict and general relations of deducibility, faces well-known difficulties. Nevertheless, the idea that deeper layers of reality are responsible for what happens at higher levels is well-entrenched in scientific practice. We argue that the intuition behind this idea is adequately captured by the notion of supervenience: the physical state of the fundamental physical layers fixes the states of the higher levels. Supervenience is weaker than (...) traditional reductionism, but it is not a metaphysical doctrine: one can empirically support the existence of a supervenience relation by exhibiting concrete relations between the levels. Much actual scientific research is directed towards finding such inter-level relations. It seems to be quite generally held that the importance of such relations between different levels is that they are explanatory and give understanding: deeper levels provide deeper understanding, and this justifies the search for ever deeper levels. We shall argue, however, that although achieving understanding is an important aim of science, its correct analysis is not in terms of relations between higher and lower levels. Connections with deeper layers of reality do not generally provide for deeper understanding. Accordingly, the motivation for seeking deeper levels of reality does not come from the desire to find deeper understanding of phenomena, but should be seen as a consequence of the goal to formulate ever better, in the sense of more accurate and more-encompassing, empirical theories. (shrink)

Artifacts are probably our most obvious everyday encounter with technology. Therefore, a good understanding of the nature of technical artifacts is a relevant part of technological literacy. In this article we draw from the philosophy of technology to develop a conceptualization of technical artifacts that can be used for educational purposes. Furthermore we report a small exploratory empirical study to see to what extent teachers’ intuitive ideas about artifacts match with the way philosophers write about the nature of artifacts. Finally, (...) we suggest a teaching and learning strategy for improving teachers’ concepts of technical artifacts through practical activities. (shrink)

Spoken language consists of a linear sequence of units, from which the existence of particular underlying hierarchical processing mechanisms is inferred. Uddén et al. use graph theory to provide a framework for describing the possible structural relationships that may underlie a linear output sequence. Being more explicit in defining different structures can help identifying and testing for such structures in AGL experiments, as well as help showing how behavioral and neuroimaging data reveals signatures of hierarchical processing in humans.

The validity of the conclusion to the nonlocality of quantum mechanics, accepted widely today as the only reasonable solution to the EPR and Bell issues, is questioned and criticized. Arguments are presented which remove the compelling character of this conclusion and make clear that it is not the most obvious solution. Alternative solutions are developed which are free of the contradictions related with the nonlocality conclusion. Firstly, the dependence on the adopted interpretation is shown, with the conclusion that the alleged (...) nonlocality property of the quantum formalism may have been reached on the basis of an interpretation that is unnecessarily restrictive. Secondly, by extending the conventional quantum formalism along the lines of Ludwig and Davies it is shown that the Bell problem may be related to complementarity rather than to nonlocality. Finally, the dependence on counterfactual reasoning is critically examined. It appears that locality on the quantum level may still be retained provided one accepts a newly proposed principle of nonreproducibility at the individual quantum level as an alternative of quantum nonlocality. It is concluded that the locality principle can retain its general validity, in full conformity with all experimental data. (shrink)

DURING THE SECOND DECADE of the twentieth century at least three different hypotheses involving the radial velocities of spiral nebulae appeared in astronomical journals, marking the introduction of a new field of study for astronomers. Willem de Sitter argued that a velocity-distance relation would exist if space were curved.' W. W. Campbell speculated on a possible link between radial velocities and evolutionary stages of nebulae.2 And V. M. Slipher announced his belief that the radial velocities of spiral nebulae were (...) a reflection of our galaxy's motion relative to the nebulae. 3 The hypotheses were similar in that each created a theoretical framework within which the measurement of radial velocities of spiral nebulae was viewed as important. The origins of the hypotheses and their consequences for developments n astronomy were, however, dissimilar. (shrink)

Translating ethical theories into clinical practice presents a perennial challenge to educators. While many suggestions have been put forth to bridge the theory-practice gap, none have sufficiently remedied the problem. We believe the ascendance of hospital medicine, as a dominant new force in medical education and patient care, presents a unique opportunity that could redefine the way clinical ethics is taught. The field of hospital medicine in the United States is comprised of more than 50,000 hospitalists—specialists in inpatient medicine—representing the (...) fastest growing subspecialty in the history of medicine, and its members have emerged as a dominant new force around which medical education and patient care pivot. This evolution in medical education presents a unique opportunity for the clinical ethics community. Through their proximity to patients and trainees, hospitalists have the potential to teach medical ethics in real time on the wards, but most hospitalists have not received formal training in clinical ethics. We believe it is time to strengthen the ties between hospital medicine and medical ethics, and in this article we outline how clinical ethicists might collaborate with hospitalists to identify routine issues that do not rise to the level of an “ethics consult,” but nonetheless require an intellectual grounding in normative reasoning. We use a clinical vignette to explore how this approach might enhance and broaden the scope of medical education that occurs in the inpatient setting: A patient with an intra-abdominal abscess is admitted to the academic hospitalist teaching service for drainage of the fluid, hemodynamic support, and antimicrobial therapy. During the initial encounter with the hospitalist and his team of medical students and residents, the patient reports night sweats and asks if this symptom could be due to the abscess. How should the hospitalist approach this question? (shrink)

ABSTRACTThis is the first study to investigate multiple cognitive biases in adolescence simultaneously, to examine whether anxiety and depression are associated with biases in attention and interpretation, and whether these biases are able to predict unique variance in self-reported levels of anxiety and depression. A total of 681 adolescents performed a Dot Probe Task, an Emotional Visual Search Task, and an Interpretation Recognition Task. Attention and interpretation biases were significantly correlated with anxiety. Mixed results were reported with regard to depression: (...) evidence was found for an interpretation bias, and for an attention bias as measured with the EVST but not with the DPT. Furthermore, interpretation and attention biases predicted unique variance in anxiety and depression scores. These results indicate that attention and interpretation biases are unique processes in anxiety and depression. They also suggest that anxiety and depression are partly based on similar underlying... (shrink)

This chapter contains sections titled: Types of Knowledge in Technology A Neglected Topic Empirical Studies Philosophical Explorations References and Further Reading.

Apart from the scientific unknowns and technological barriers that complicate the development of medical neuroimaging applications, various relevant actors might have different ideas on what is considered advancement or progress in this field. We address the challenge of identifying societal actors and their different points of view concerning neuroimaging technologies in an early phase of neuroimaging development. To this end, we conducted 16 semistructured interviews with societal actors, including governmental policy makers, health professionals, and patient representatives, in the Netherlands. We (...) show how the contextual aspects of applications and underlying features of the ideal health system determine the desirability. Neuroimaging developments are perceived as innovations that will optimize the current health system or as opportunities to change existing structures and practices of the current health system more radically. Insights into and understanding of these visions show incongruence between visions regarding desirable medical neuroimaging use and potential conflicting visions regarding the embedding of neuroimaging applications. We conclude that it is possible to prospectively identify incongruent visions and analyze when these visions will most likely come into conflict with each other. Such an analysis might provide a reflective space, beyond personal and political interest, suitable as a starting point for joint reflection and mutual learning in order to manage medical neuroimaging innovations towards more responsible applications. (shrink)

Large language models (LLMs) structure the linguistic landscape by reflecting certain beliefs and assumptions. In this paper, we address the risk of people unthinkingly adopting and being determined by the values or worldviews embedded in LLMs. We provide a Nietzschean critique of LLMs and, based on the concept of will to power, consider LLMs as will-to-power organisations. This allows us to conceptualise the interaction between self and LLMs as power struggles, which we understand as negotiation. Currently, the invisibility and incomprehensibility (...) of LLMs make it difficult, if not impossible, to engage in such negotiations. This bears the danger that LLMs make reality increasingly homogeneous by recycling beliefs and creating feedback loops that ultimately freeze power struggles and thus consolidate the status quo. In view of this, LLMs constrain self-formation. Based on our critique, we provide some recommendations on how to develop interactions with LLMs that enable negotiations that allow for different ways of being. (shrink)

Decisions related to animal welfare standards depend on farmer’s multiple goals and values and are constrained by a wide range of external and internal forces. The aim of this paper is twofold, i.e., to develop a theoretical framework for farmers’ AW decisions that incorporates farmers’ goals, use and non-use values and to present an approach to empirically implement the theoretical framework. The farmer as a head of the farm household makes choices regarding production to maximize the utility of the household. (...) The overall utility of the farmer is determined by his multiple objectives. For the analysis of multi-objective problems, the multiple criteria decision - making paradigm provides an appropriate theoretical framework. However, theories from the field of social-psychology are needed to facilitate the identification of all relevant aspects in the decision making. The practical use of the conceptual framework is demonstrated using a simple numerical application of a multi-objective programming model. Two workshops were devoted to examining the scientific consistency and the practical usefulness of the approach. Implementing this approach will increase knowledge of the main factors and barriers that determine farmers’ decisions with regard to AW standards. This knowledge is relevant during the development of new AW concepts that aims to supply products that comply with above-legal AW standards for middle-market segments. (shrink)

Mole's (2008 [this issue]) argument that consciousness is a necessary concomitant of attention rests on the question of what is being attended in spatial attention. His answer is space. Some authors, including ourselves, claim that the fact that the processing of unseen objects can be modulated by spatial attention (e.g. Kentridge et al., 1999; 2004; 2008; Marzouki et al., 2007; Sumner et al., 2006) demonstrates that visual attention is not a sufficient precondition for visual awareness. Mole, however, contends that as (...) space, rather than any object that might occupy that space, is what is being attended, these experiments do not constitute evidence for a dissociation between attention and consciousness. We disagree. To understand the source of this disagreement we need to understand the various processes encompassed by the term 'attention' and to consider experimental evidence illustrating how these processes operate. We review evidence that spatial attention can be deployed with the specific goal of determining the properties of objects occupying the attended region of space. One might, for example, attend to a location with the goal of determining the colour of objects occupying that space as efficiently as possible. Mole's assumption that all that is attended in spatial attention is space is not consistent with this evidence. We conclude that attention can be directed at objects by mechanisms of so- called 'spatial attention' without those objects necessarily eliciting conscious visual experience and hence that attention is not a sufficient precondition for visual awareness. (shrink)

This article is part of a For-Discussion-Section of Methods of Information in Medicine about the paper "Biomedical Informatics: We Are What We Publish", written by Peter L. Elkin, Steven H. Brown, and Graham Wright. It is introduced by an editorial. This article contains the combined commentaries invited to independently comment on the Elkin et al. paper. In subsequent issues the discussion can continue through letters to the editor.

Prison work creates ethical challenges for which a training program was initiated for Dutch prison staff to foster their Moral Craftsmanship (MCS). The concept of MCS is not yet defined and operationalized in literature. This explorative study aims to 1) define MCS, 2) identify conceptual elements of MCS, and 3) develop a measurement tool for MCS. A document and literature study provided input for the definition and selection of conceptual elements related within DCIA policy documents, identifying three conceptual levels of (...) MCS: individual (cognition, attitude, and actions), team, and leadership. This first MCSQ consists of seventy-one items distributed across the domains: values and norms, judgment and reasoning, consultation, implementation, looking back, interactions, and leadership. We tested its usability via ‘think-aloud interviews.’ Validation of the current version of the MCS-Questionnaire and consensus among experts about what to include or exclude in the concept of MCS are needed for further development. (shrink)