We use the notion of polar duality from convex geometry and the theory of Lagrangian planes from symplectic geometry to construct a fiber bundle over ellipsoids that can be viewed as a quantum-mechanical substitute for the classical symplectic phase space. The total space of this fiber bundle consists of geometric quantum states, products of convex bodies carried by Lagrangian planes by their polar duals with respect to a second transversal Lagrangian plane. Using the theory of the John (...) ellipsoid we relate these geometric quantum states to the notion of “quantum blobs” introduced in previous work; quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle. We show that the set of equivalence classes of unitarily related geometric quantum states is in a one-to-one correspondence with the set of all Gaussian wavepackets. We emphasize that the uncertainty principle appears in this paper as geometric property of the states we define, and is not expressed in terms of variances and covariances, the use of which was criticized by Hilgevoord and Uffink. (shrink)

ArgumentTwo simultaneous episodes in late nineteenth-century mathematical research, one by Karl Hermann Brunn and another by Hermann Minkowski, have been described as the origin of the theory of convex bodies. This article aims to understand and explain how and why the concept of such bodies emerged in these two trajectories of mathematical research; and why Minkowski's – and not Brunn's – strand of thought led to the development of a theory of convexity. Concrete pieces of Brunn's and (...) Minkowski's mathematical work in the two episodes will, from the perspective of the above questions, be presented and analyzed with the use of the methodological framework of epistemic objects, techniques, and configurations as adapted from Hans-Jörg Rheinberger's work on empirical sciences to the historiography of mathematics by Moritz Epple. Based on detailed descriptions and a comparison of the objects and techniques that Brunn and Minkowski studied and used in these pieces it will be concluded that Brunn and Minkowski worked in different epistemic configurations, and it will be argued that this had a significant influence on the mathematics they developed for those bodies, which can provide answers to the two research questions listed above. (shrink)

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of Lukasiewicz. For the proof we only use Minkowski's convex body theorem and the rudiments of piecewise linear topology.

John Locke:When we set before our eyes a round globe of uniform colour, v.g. gold, alabaster or jet, it is certain that the idea thereby imprinted in our mind is of a flat circle, variously shadowed, with several degrees of light and brightness coming to our eyes. But we having, by use, been accustomed to perceive what kind of appearance convex bodies are wont to make in us, what alterations are made in the reflections of light by the (...) difference of the sensible figures of bodies: the judgment presently, by an habitual custom, alters the appearances into their causes.H.H. Price:…. a distant hillside which is full of protuberances, and slopes upwards at quite a gentle angle, will appear flat and vertical….. This means that the sense-datum, the colour expanse which we sense, actually is flat and vertical. (shrink)

John Locke:When we set before our eyes a round globe of uniform colour, v.g. gold, alabaster or jet, it is certain that the idea thereby imprinted in our mind is of a flat circle, variously shadowed, with several degrees of light and brightness coming to our eyes. But we having, by use, been accustomed to perceive what kind of appearance convex bodies are wont to make in us, what alterations are made in the reflections of light by the (...) difference of the sensible figures of bodies: the judgment presently, by an habitual custom, alters the appearances into their causes.H.H. Price:…. a distant hillside which is full of protuberances, and slopes upwards at quite a gentle angle, will appear flat and vertical….. This means that the sense-datum, the colour expanse which we sense, actually is flat and vertical. (shrink)

Body movement is a primary nonverbal communication channel in humans. Coordinated social behaviors, such as dancing together, encourage multifarious rhythmic and interpersonally coupled movements from which observers can extract socially and contextually relevant information. The investigation of relations between visual social perception and kinematic motor coupling is important for social cognition. Perceived coupling of dyads spontaneously dancing to pop music has been shown to be highly driven by the degree of frontal orientation between dancers. The perceptual salience of other aspects, (...) including postural congruence, movement frequencies, time‐delayed relations, and horizontal mirroring remains, however, uncertain. In a motion capture study, 90 participant dyads moved freely to 16 musical excerpts from eight musical genres, while their movements were recorded using optical motion capture. A total from 128 recordings from 8 dyads maximally facing each other were selected to generate silent 8‐s animations. Three kinematic features describing simultaneous and sequential full body coupling were extracted from the dyads. In an online experiment, the animations were presented to 432 observers, who were asked to rate perceived similarity and interaction between dancers. We found dyadic kinematic coupling estimates to be higher than those obtained from surrogate estimates, providing evidence for a social dimension of entrainment in dance. Further, we observed links between perceived similarity and coupling of both slower simultaneous horizontal gestures and posture bounding volumes. Perceived interaction, on the other hand, was more related to coupling of faster simultaneous gestures and to sequential coupling. Also, dyads who were perceived as more coupled tended to mirror their pair's movements. (shrink)

The fitness of any evolutionary unit can be understood in terms of its two basic components: fecundity (reproduction) and viability (survival). Trade-offs between these fitness components drive the evolution of life-history traits in extant multicellular organisms. We argue that these trade-offs gain special significance during the transition from unicellular to multicellular life. In particular, the evolution of germ–soma specialization and the emergence of individuality at the cell group (or organism) level are also consequences of trade-offs between the two basic fitness (...) components, or so we argue using a multilevel selection approach. During the origin of multicellularity, we study how the group trade-offs between viability and fecundity are initially determined by the cell level trade-offs, but as the transition proceeds, the fitness trade-offs at the group level depart from those at the cell level. We predict that these trade-offs begin with concave curvature in single-celled organisms but become increasingly convex as group size increases in multicellular organisms. We argue that the increasingly convex curvature of the trade-off function is driven by the cost of reproduction which increases as group size increases. We consider aspects of the biology of the volvocine green algae – which contain both unicellular and multicellular members – to illustrate the principles and conclusions discussed. (shrink)

Aberrations -- Absorption -- Accuracy and precision -- Alpha radiation -- Amplitude -- Angular forces -- Angular momentum -- Antenna -- Arago dot -- Aperture -- Archimedes's principle -- Band theory of solids -- Bernoulli's principle -- Beta radiation -- Blackbody radiation -- Bohr atom -- Bose condensation -- Bra-ket notation -- British thermal unit (BTU) -- Calculating system efficiency -- Circular motion -- Closed systems and isolated systems -- Concave and convex -- Conservation of charge -- Conservation of (...) energy -- Convection and conduction -- Cosmic radiation -- Crest and trough -- Density and specific gravity -- Diode -- Distance and area -- Distortion -- Doppler effect -- Dynamic systems theory -- Edison effect -- Eigenvectors -- Elastic and inelastic collisions -- Electric circuits: Parallel vs series, diagrams and components -- Electric potential -- Energy and power -- Enthalpy -- Entropy -- Euler's laws of motion -- Falling bodies and physics -- Faraday's law -- Feynman diagrams -- Flywheel -- Focal point -- Free body diagram -- Frequency -- Gamma radiation -- Gauss's law -- Gluon -- Gravitational potential energy -- Harmonic oscillator -- Harmonics -- Heisenberg uncertainty principle -- Higgs boson -- Horsepower -- Ideal gas law -- Joule --. (shrink)

Gil R, Arroyo-Anllo EM, Ingrand P, Gil M, Neau JP, Ornon C, Bonnaud V. Self-consciousness and Alzheimer’s disease. Acta Neurol Scand 2001: 104: 296–300. # Munksgaard 2001. Objectives – To propose a neuropsychological study of the various aspects of self-consciousness (SC) in Alzheimer’s disease. Methods – Forty-five patients with probable mild or moderate AD were included in the study. Severity of their dementia was assessed by the Mini Mental State (MMS). Fourteen questions were prepared to evaluate SC. Results – No (...) significant correlations were found between SC score and educational level, age, and duration of disease. A significant correlation was found between SC score and the severity of dementia, whereas frontal disturbances were just short of the significance threshold. The various aspects of SC were not impaired to the same degree. The most disturbed ones were awareness of cognitive deficiencies, moral judgements and prospective memory. The least disturbed aspects were awareness of identity and of mental representation of the body. Items relating to anosognosia and moral judgements were significantly correlated with the MMS score, whereas affective state, body representation disorders, prospective memory, and capacities for introspection were not related to the severity of the dementia. Consciousness of identity was sound, regardless of MMS score. Conclusions – AD clearly induces an heterogeneous impairment of SC. SC requires a convergence of many neural networks. In AD, neuronal alterations involve many cortical areas and information sent to the associative frontal cortex from memory, language and visuospatial areas is lacking or disturbed. Thus, the sequential order of successive stimuli cannot be maintained by the heteromodal associative cortex (dorsal convexity of the prefrontal cortex), and the supramodal associative cortex (located rostrally in the frontal lobes) is unable to provide reliable monitoring and assessment of simultaneous neural cognitive networks carrying insufficient and inadequate input. The core deficiency in AD patients might be impaired SC equated with the disability to maintain sequential and simultaneous ‘‘attention to life’’. The Self-Consciousness Questionnaire, a clinical scale providing multidimensional measurement, indicates that different aspects of consciousness are not correlated with overall cognitive deficiency as determined by the MMSE. (shrink)

Prospect theory emerged as one of the leading descriptive decision theories that can rationalize a large body of behavioral regularities. The methods for eliciting prospect theory parameters, such as its value function and probability weighting, are invaluable tools in decision analysis. This paper presents a new simple method for eliciting prospect theory’s value function without any auxiliary/simplifying parametric assumptions. The method is applicable both to choice under ambiguity (Knightian uncertainty) and risk (when events are characterized by objective probabilities). Our new (...) elicitation method is implemented in a simple paper-and-pencil experiment (via an iterative multiple price list format). This is one of the first experiments that elicits non-parametric prospect theory’s value function with salient rewards. The collected data generally confirm findings in the existing literature: the value function is S-shaped (concave in the gain domain and convex in the loss domain) though there is a weaker loss aversion on the aggregate level and a substantial heterogeneity in loss aversion on the individual level (41% loss averse, 6% loss neutral and 53% gain seeking). (shrink)

One of the theories defined in Baldwin's Dictionary of Philosophy and Psychology, published in 1901, is ‘The Double Aspect Theory’. It is ‘the theory of the relation of mind and body, which teaches that mental and bodily facts are parallel manifestations of a single underlying reality’. It ‘professes to overcome the onesidedness of materialism and idealism by regarding both series as only different aspects of the same reality, like the convex and the concave views of a curve; or, according (...) to another favourite metaphor, the bodily and the mental facts are really the same facts expressed in different language’. (shrink)

One of the theories defined in Baldwin's Dictionary of Philosophy and Psychology, published in 1901, is ‘The Double Aspect Theory’. It is ‘the theory of the relation of mind and body, which teaches that mental and bodily facts are parallel manifestations of a single underlying reality’. It ‘professes to overcome the onesidedness of materialism and idealism by regarding both series as only different aspects of the same reality, like the convex and the concave views of a curve; or, according (...) to another favourite metaphor, the bodily and the mental facts are really the same facts expressed in different language’. (shrink)

After describing the three European strategies focused on social control, this essay will first demonstrate that the first two strategies try less to protect societies than to enforce efficient tools of governance. Additionally, they reinforce stereotypes harming Muslim immigrants. I show that diverse approaches in policing can make a difference in the communities where police forces operate. The third strategy, that of prevention requiring the cooperation of the citizens, may be more sustainable in the long term as it facilitates communication (...) among local politicians and involved actors. Finally, I point out that the interplay of interests, ideas and institutions matter a great deal to the comparison. (shrink)

Inspired by locale theory, we propose “pointfree convex geometry”. We introduce the notion of convexity algebra as a pointfree convexity space. There are two notions of a point for convexity algebra: one is a chain-prime meet-complete filter and the other is a maximal meet-complete filter. In this paper we show the following: the former notion of a point induces a dual equivalence between the category of “spatial” convexity algebras and the category of “sober” convexity spaces as well as a (...) dual adjunction between the category of convexity algebras and the category of convexity spaces; the latter notion of point induces a dual equivalence between the category of “m-spatial” convexity algebras and the category of “m-sober” convexity spaces. We finally argue that the former notion of a point is more useful than the latter one from a category theoretic point of view and that the former notion of a point actually represents a polytope and the latter notion of a point properly represents a point. We also remark on the close relationships between pointfree convex geometry and domain theory. (shrink)

As study of knowledge, epistemology attempts at identifying its necessary and sufficient conditions and defining its sources, structure and limits. From this pointof view, until present, there are no applied approaches to the Romanian archaeology. Consequently, my present paper presents an attempt to explore the structural characteristics of the knowledge creation process through the analysis of the results of a series of interviews conducted on Romanian archaeologists. The interviews followed a qualitative approach built upon a semi-structured frame. Apparent data saturation (...) was reached after four interviews within initial target group (senior researchers with institutional authority). Under these conditions a decision was made to continue the interviews within a secondary control group (young doctoral or post-doc researchers guided by members of the initial target group) in order to both verify the observed data saturation and to assess the impact of the attitude of senior researchers towards scientific research on the younger generation. The preliminary results allow to assert that Romanian archaeology is still caught in a highly conservative and intradisciplinarian manner of knowledge production with a negative effect on both new knowledgeproduction and future specialists’ education. (shrink)

As part of a research conducted in the field of professional didactics for the design of video-based training for saddlers, we mobilize an iterative and collaborative analysis protocol with professionals. We compare the effects produced during a debate between experts mediated by the researcher, based sometimes on a confrontation with video traces of the activity, sometimes on the temporary diagrams of a conceptual structure of the situation. Using the argumentative trilogue analysis framework, we show how these methodologies are able to (...) foster the expression of a process of conceptualization depending on whether professionals are confronted with lived images or concep-tualizations produced by the researcher. (shrink)

IntroductionThe world pandemic of the virus SARS-CoV-2, which causes COVID-19 infection was announced by the World Health Organization on March 11, 2020. Due to the restrictions that were introduced in order to minimize the spread of the virus, people more often suffer from stress, depression, anxiety, and sleep disorders. The aim of this study was evaluation of the stress levels and sleep disorders among nursing students during the pandemic SARS-CoV-2.Materials and Study MethodsThis is a cross-sectional study conducted among 397 nursing (...) students on March 2020. The research tools used were original questionnaires, Perceived Stress Scale, and the Athenian Insomnia Scale, as well as Coping with Stress Inventory.ResultsRespondents felt a high level of stress, which occurred in 68.8% of interviewees regarding whether there was a danger of contracting COVID-19. Respondents experienced 84% stress levels when a family member suffered from COVID-19. Sleep disorders were determined mainly by the fear of infection and contact with someone who might be infected with the virus. Nursing students who felt a high level of stress often suffered from sleep disorders more frequently than students who felt a low or average stress level. The respondents decided to cope with stress by denial, taking psychoactive substances, ceasing action, or blaming themselves. The greater the intensity of stress experienced by students, the more often they undertook avoidance behaviors or showed helplessness.ConclusionDuring the pandemic, students experienced severe stress, which resulted in sleep disorders and avoidance behaviors. (shrink)

Children with innate variations of sex characteristics (also termed differences of sex development or intersex traits) are routinely subjected to medical interventions that aim to make their bodies appear or function more typically female or male. Many such interventions lack clear evidence of benefit, they have been challenged for thirty years, and they are now understood to violate children’s rights to bodily autonomy and bodily integrity. In this paper I argue that these persist in part due to epistemic injustices (...) and biomedical authority. Epistemic injustices include limited disclosure of current practices, the systemic marginalisation of community voices and psychosocial professionals, and attempts to discredit or misrepresent testimony. Bioethics has largely failed to change medical practice, and sometimes plays a role in perpetuating epistemic injustices. I find that the development of an intersex movement provides opportunities for epistemic justice and liberation by engaging with other disciplines and promoting oversight of medical decision-making. The paper draws particularly on Australian sources, including internationally influential ethical principles. (shrink)

Drawing from the lives of Ossie Davis, Frantz Fanon, Malcolm X, and W. E. B. Du Bois, as well as his own experience, and fully updated to account for what has transpired since the rise of the Black Lives Matter movement, Yancy provides an invaluable resource for students and teachers of courses in African American Studies, African American History, Philosophy of Race, and anyone else who wishes to examine what it means to be Black in America.

Descriptions of bodies within the literature of the enactive approach to cognitive science exhibit an interesting dialectical tension. On the one hand, a body is considered to be a unity which instantiates an identity, forming an intrinsic basis for value. On the other, a living body is in a reciprocally defining relationship with the environment, and is therefore immersed and entangled with, rather than distinct from, its environment. In this paper I examine this tension, and its implications for the (...) enactive approach, particularly the enactive conceptions of life and bodies. Following the lead of others, I argue that enactive cognitive science can benefit from a deeper reading and integration with extant work on the complexity and multiplicity of the living body within feminist philosophy and feminist science studies. (shrink)

How we understand Descartes’s physics rests on how we interpret his ontological commitment to individual bodies, and in particular on how we account for their individuation. However, Descartes’s contemporaries as well as contemporary philosophers have seen Descartes’s account of the individuation of bodies as deeply flawed. In the first part of this paper, I discuss how the various problems and puzzles involved in Descartes’s account of the individuation of bodies arise, and the relevance of these problems for (...) his physics. With an eye toward resolving these puzzles, I argue for an interpretation of the Cartesian ontology in which bodies are not individuated by motion but, instead, are mind-dependent. As part of this reading, I demonstrate the sense in which we can clearly and distinctly perceive bodies, and also the senses in which the real, conceptual, and modal distinctions apply to them. I conclude by explaining how this account of the mind-dependent individuation of bodies is consistent with Descartes’s definition of ‘motion’ and ‘a body’ in Principles, Part II, section 25—the very passage that prima facie entails the most troubling of the individuation puzzles. Finally, I show that this account is consistent with Descartes’s general goal in constructing his physics. (shrink)

Foucault proposes at the end of the first volume of The History of Sexuality to shift the focus of sexual studies from sex-desire to bodies and pleasures. This article seeks to establish what he means by this shift, how he proposes it be made, and what the consequences are for thinking about sexuality together with `sex'. Foucault's shift involves a historiographical claim about the superability of the recent past, and can be read as an effort to relegate the concerns (...) about sexual difference and kinship to the past, and to establish a contemporary field for sexuality that involves bodies without history, pleasures without sex. The article suggests a way around this questionable historiographical assumption and marks a different departure for a Foucauldian study of sexuality. It also seeks to highlight some of the contemporary tensions between feminist and lesbian and gay studies, especially queer studies, in light of this reading of Foucault. (shrink)

Globalization leads to cross-border business transactions between societies with very different norms and regulations regarding bribery. Bribery in international business transactions can be seen as a function of not only the demand for such bribes in different countries, but the supply, or willingness to provide bribes by multinational firms and their representatives. This study addresses the propensity of firms from 30 different countries to engage in international bribery. The study incorporates both domestic (economic development, culture, and domestic corruption in the (...) supplying country) and international factors (those countries’ patterns of trade and involvement in international accords) in explaining the willingness to bribe abroad. The propensity to provide bribes was the lowest when corruption was not tolerated in the multinational firms’ home countries, when the firms’ countries were signatories of the Organization for Economic Cooperation and Development (OECD) anti-bribery convention, and when those countries traded heavily with wealthier nations. Further, these findings are maintained when controlling for levels of economic development and cultural values in the supplying country. In terms of culture, firms from high power distance countries showed a somewhat greater propensity for providing bribes in transactions with less-developed nations. (shrink)

This article examines how the so-called disembodied criminal subject is given structure and form through the law of homicide and assault. By analysing how the body is materialised through the criminal law’s enactment of death and injury, this article suggests that the biological positioning of these harms of violence as uncontroversial, natural, and universal conditions of being ‘human’ cannot fully appreciate what makes violence wrongful for us, as embodied entities. Absent a theory of the body, and a consideration of corporeality, (...) the criminal law risks marginalising, or altogether eliding, experiences of violence that do not align with its paradigmatic vision of what bodies can and must do when suffering its effects. Here I consider how the bionic body disrupts the criminal law’s understanding of human violence by being a body that is both organic and inorganic, and capable of experiencing and performing violence in unexpected ways. I propose that a criminal law that is more receptive to the changing, technologically mediated conditions of human existence would be one that takes the corporeal dimensions of violence more seriously and, as an extension of this, adopts an embodied, embedded, and relational understanding of human vulnerability to violence. (shrink)

This introductory article provides a contextual and theoretical overview to this special issue of Body & Society. The special issue presents five selected case studies – focusing on the contexts of transplantation, psychiatry, amputation and war, and a transvalued media ecology of cancer – to offer meditations on a number of interlinked questions. The first of these is the entanglement of biomedical governance – political/economic as well as self-disciplinary – with the nexus of estrangement, which can denote both the distancing (...) of otherness and self-division. Second is the realm of feeling, of phantasmatic projection and of the ways in which the biopolitical becomes reciprocally, discursively, enmeshed in a wider cultural imaginary. Third is the shifting terrain of gender and feminist politics, a key dimension of which is the necessary reworking of feminist thought in the wake of a radically altered biomedical and biotechnological landscape. Under the rubric of Estranged Bodies, the collection considers themes of dissolution and the fragility of the body/subject read through bodily catastrophe, radical body modification and extreme medical intervention. Also considered is the notion of assemblage – the provisional coming together of disparate parts – which encourages a rethinking of questions of reconstituted, displaced and re-placed bodies. (shrink)