A Topos Foundation for Theories of Physics: III. The Representation of Physical Quantities With Arrows

This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. In paper II, we studied the topos representations of the propositional language PL(S) for the case of quantum theory, and in the present paper we do the same thing for the, more extensive, local language L(S). One of the main achievements is to find a topos representation for self-adjoint operators. This involves showing that, for any physical quantity A, there is an arrow \breve{\delta}^o(A):\Sig\map\SR, where \SR is the quantity-value object for this theory. The construction of $\breve{\delta}^o(A)$ is an extension of the daseinisation of projection operators that was discussed in paper II. The object \SR is a monoid-object only in the topos, $\tau_\phi$, of the theory, and to enhance the applicability of the formalism, we apply to \SR a topos analogue of the Grothendieck extension of a monoid to a group. The resulting object, \kSR, is an abelian group-object in $\tau_\phi$. We also discuss another candidate, \PR{\mathR}, for the quantity-value object. In this presheaf, both inner and outer daseinisation are used in a symmetric way. Finally, there is a brief discussion of the role of unitary operators in the quantum topos scheme.Comment: 38 pages, no figure

Collaboration between Science and Religious Education teachers in Scottish Secondary schools

The article reports on quantitative research that examines: (1) the current practice in collaboration; and (2) potential for collaboration between Science and Religious Education teachers in a large sample of Scottish secondary schools. The authors adopt and adapt three models (conflict; concordat and consonance) to interrogate the relationship between science and religion (and the perceived relation between these two subjects in schools) (Astley and Francis 2010). The findings indicate that there is evidence of limited collaboration and, in a few cases, a dismissive attitude towards collaboration (conflict and concordat and very weak consonance). There is, however, evidence of a genuine aspiration for greater collaboration among many teachers (moving towards a more robust consonance model). The article concludes by discussing a number of key factors that must be realised for this greater collaboration to be enacted

Filling in the gaps:A grounded theory of the experiences and needs of healthcare staff following a colleague death by suicide in the UK

Health-workers are more likely to die by suicide than their counterparts in other occupational groups. The suicide of a staff member can be widely felt by colleagues, leading to complex emotional and cognitive responses. Exposure to suicide heightens the risk of dying by suicide. We investigated the impact of a colleague suicide on National Health Service (NHS) staff. Twenty-nine staff were interviewed; all participants were white British, and so not representative of the ethnic make-up of the NHS. Data were analyzed using grounded theory methods. A theory, “filling in the gaps” was developed. Staff experiences gave rise to needs that were not always met. Staff endeavoured to “fill in the gaps” in support; however, sometimes fell through those gaps. Organizational and professional contexts shaped their experiences and responses. Recommendations include skilled and targeted support and compassion for affected staff. Cultural change is needed to challenge suicide stigma and unhelpful narratives

Directed evolution study of temperature adaptation in a psychrophilic enzyme

We have used laboratory evolution methods to enhance the thermostability and activity of the psychrophilic protease subtilisin S41, with the goal of investigating the mechanisms by which this enzyme can adapt to different selection pressures. A combined strategy of random mutagenesis, saturation mutagenesis and in vitro recombination (DNA shuf¯ing) was used to generate mutant libraries, which were screened to identify enzymes that acquired greater thermostability without sacri®cing lowtemperature activity. The half-life of seven-amino acid substitution variant 3-2G7 at 60 C is $500 times that of wild-type and far surpasses those of homologous mesophilic subtilisins. The dependence of half-life on calcium concentration indicates that enhanced calcium binding is largely responsible for the increased stability. The temperature optimum of the activity of 3-2G7 is shifted upward by$10 C. Unlike natural thermophilic enzymes, however, the activity of 3-2G7 at low temperatures was not compromised. The catalytic ef®ciency, k cat /K M , was enhanced $threefold over a wide temperature range (10 to 60 C). The activation energy for catalysis, determined by the temperature dependence of k cat /K M in the range 15 to 35 C, is nearly identical to wild-type and close to half that of its highly similar mesophilic homolog, subtilisin SSII, indicating that the evolved S41 enzyme retained its psychrophilic character in spite of its dramatically increased thermostability. These results demonstrate that it is possible to increase activity at low temperatures and stability at high temperatures simultaneously. The fact that enzymes displaying both properties are not found in nature most likely re¯ects the effects of evolution, rather than any intrinsic physicalchemical limitations on proteins

Information and Communication Technology (ICT) and International Business Travel: Mobility Allies?

Like forecasts about the paperless office, technological solutions to the problem of international business travel continue to be deferred. As with the increased use of office paper, international business travel is defying predictions of its decline. There is growing evidence to suggest that business sectors which seem ideally placed to substitute information and communication technology (ICT) for travel, are actually generating more physical travel than other sectors. This paper develops a case study of the Irish software industry to exemplify why international travel is not diminishing in importance how and the ICT and business travel relationship is changing in this sector. The paper presents research findings that suggest that a cycle of substitution, generation and modification relationships have occurred as mobility interdependencies have developed.Peer Reviewe

Primordialists and Constructionists: a typology of theories of religion

This article adopts categories from nationalism theory to classify theories of religion. Primordialist explanations are grounded in evolutionary psychology and emphasize the innate human demand for religion. Primordialists predict that religion does not decline in the modern era but will endure in perpetuity. Constructionist theories argue that religious demand is a human construct. Modernity initially energizes religion, but subsequently undermines it. Unpacking these ideal types is necessary in order to describe actual theorists of religion. Three distinctions within primordialism and constructionism are relevant. Namely those distinguishing: a) materialist from symbolist forms of constructionism; b) theories of origins from those pertaining to the reproduction of religion; and c) within reproduction, between theories of religious persistence and secularization. This typology helps to make sense of theories of religion by classifying them on the basis of their causal mechanisms, chronology and effects. In so doing, it opens up new sightlines for theory and research

The Impact of Colleague Suicide and the Current State of Postvention Guidance for Affected Co-Workers: A Critical Integrative Review.

People bereaved by suicide are affected psychologically and physically and may be at greater risk of taking their own lives. Whilst researchers have explored the impact of suicide on family members and friends, the area of colleague suicide has been neglected and postvention guidance for supporting surviving colleagues is often poorly developed. This critical integrative review explored the impact of colleague suicide on surviving co-workers and reviewed postvention guidance for workplaces. Systematic searches found 17 articles that met the inclusion criteria. Articles were appraised for quality and extracted data were analysed using a thematic network method. Article quality was moderate. Two global themes were developed: impact of a colleague suicide comprised themes of 'suicide loss in the workplace'; 'professional identities and workplace roles'; 'perceptions of professional uniqueness'; and 'professional abandonment and silencing'. Postvention following a colleague suicide comprised 'individualised responses'; 'the dual function of stigma'; and 'complex pressure on managers'. A unifying global network 'after a colleague suicide' describes the relationships between all themes. A series of disconnects between existing postvention guidance and the needs of impacted workers are discussed. This review demonstrates the need for robust, systemic postvention for colleagues impacted by the complex issue of colleague suicide

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice

`What is a Thing?': Topos Theory in the Foundations of Physics

The goal of this paper is to summarise the first steps in developing a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. In doing so we provide a new answer to Heidegger's timeless question ``What is a thing?''. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics uses the topos of sets. Other theories involve a different topos. For the types of theory discussed in this paper, a key goal is to represent any physical quantity $A$ with an arrow \breve{A}_\phi:\Si_\phi\map\R_\phi where \Si_\phi and $\R_\phi$ are two special objects (the `state-object' and `quantity-value object') in the appropriate topos, $\tau_\phi$. We discuss two different types of language that can be attached to a system, $S$. The first, \PL{S}, is a propositional language; the second, \L{S}, is a higher-order, typed language. Both languages provide deductive systems with an intuitionistic logic. With the aid of \PL{S} we expand and develop some of the earlier work (By CJI and collaborators.) on topos theory and quantum physics. A key step is a process we term `daseinisation' by which a projection operator is mapped to a sub-object of the spectral presheaf \Sig--the topos quantum analogue of a classical state space. The topos concerned is \SetH{}: the category of contravariant set-valued functors on the category (partially ordered set) \V{} of commutative sub-algebras of the algebra of bounded operators on the quantum Hilbert space \Hi.Comment: To appear in ``New Structures in Physics'' ed R. Coeck