A certain generalization of the mathematical formalism of quantum mechanics beyond operator algebras is considered. The approach is based on the concept of conditional probability and the interpretation of the Lüders-von Neumann quantum measurement as a probability conditionalization rule. A major result shows that the operator algebras must be replaced by order-unit spaces with some specific properties in the generalized approach, and it is analyzed under which conditions these order-unit spaces become Jordan algebras. An (...) application of this result provides a characterization of the projection lattices in operator algebras. (shrink)

Objective. Conceptualization of the definition of space as a semantic unit of language consciousness. -/- Materials & Methods. A structural-ontological approach is used in the work, the methodology of which has been tested and applied in order to analyze the subject matter area of psychology, psycholinguistics and other social sciences, as well as in interdisciplinary studies of complex systems. Mathematical representations of space as a set of parallel series of events (Alexandrov) were used as the initial theoretical basis (...) of the structural-ontological analysis. In this case, understanding of an event was considered in the context of the definition adopted in computer science – a change in the object properties registered by the observer. -/- Results. The negative nature of space realizes itself in the subject-object structure, the components interaction of which is characterized by a change – a key property of the system under study. Observer’s registration of changes is accompanied by spatial focusing (situational concretization of the field of changes) and relating of its results with the field of potentially distinguishable changes (subjective knowledge about «changing world»). The indicated correlation performs the function of space identification in terms of recognizing its properties and their subjective significance, depending on the features of the observer`s motivational sphere. As a result, the correction of the actual affective dynamics of the observer is carried out, which structures the current perception of space according to principle of the semantic fractal. Fractalization is a formation of such a subjective perception of space, which supposes the establishment of semantic accordance between the situational field of changes, on the one hand, and the worldview, as well as the motivational characteristics of the observer, on the other. -/- Conclusions. Performed structural-ontological analysis of the system formed by the interaction of the perceptual function of the psyche and the semantic field of the language made it possible to conceptualize the space as a field of changes potentially distinguishable by the observer, structurally organized according to the principle of the semantic fractal. The compositional features of the fractalization process consist in fact that the semantic fractal of space is relevant to the product of the difference between the situational field of changes and the field of potentially distinguishable changes, adjusted by the current configuration of the observer`s value-needs hierarchy and reduced by his actual affective dynamics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Walking the Bodhisattva Path/Walking the Christ PathU.S. Conference of Catholic BishopsCatholics and Buddhists brought together by Dharma Realm Buddhist Association, the San Francisco Zen Center, and the United States Conference of Catholic Bishops (USCCB) met 20-23 March 2003 in the first of an anticipated series of four annual dialogues. Abbot Heng Lyu, the monks and nuns, and members of the Dharma Realm Buddhist Association hosted the dialogue at the (...) City of Ten Thousand Buddhas in Talmage, California. The community had transformed their Confucius Hall into a chapel, with a large, newly constructed wooden cross on a wall above an altar facing out from a raised platform, so the Catholic delegation would have a space for worship. A special poster announcing the theme of the conference, "Walking the Bodhisattva Path/Walking the Christ Path," showing a Buddhist dharma wheel at one foot of a bridge and a Celtic cross at the other foot, had been created by the hosting community.The daily schedule for the dialogue did not interfere with the monastic routine at the City of Ten Thousand Buddhas, which included early morning chanting (4:00-5:00 am), daily rituals in the Buddha Hall, and the single large meal for monastics before noon to which all participants were invited. Catholics and Buddhists meeting in the dialogue began each day with an optional forty-five minutes of quiet sitting together in the monastery meditation hall, each following their own form of meditation and prayer. There was a Eucharist on Friday and Saturday evenings for the Catholics and to which the Buddhists were invited, and additional meals of breakfast and supper throughout the meeting at the City's Jyun Kang Restaurant.Fourteen Buddhists and fourteen Catholics participated in the formal discussions. Each participant spoke on what it means to them to follow Christ or the way of the Bodhisattvas or enlightened beings. In addition to speaking, each participant distributed a short passage, usually from a traditional text, on this topic. Several passages from Master Dogen's Shobogenzo and the Gospel of John were among those shared by the group. Other passages shared were taken from the Avatamsaka Sutra and the Shurangama Sutra and from the other gospels and the writings of Zen master HakuinZenji, the Dalai Lama, Korean Zen Master I-sahn Hye-yeon, the teachings of Master [End Page 247] Hsuan Hua, Shantideva, Origen, St. Ignatius, St. Benedict, the author of The Cloud of Unknowing, St. John of the Cross, and Chiara Lubich. A minute of silence separated the fifteen-minute segments for each presentation. With so large a group, most of the time in the formal sessions involved listening to series of presentations; however, during discussion periods the participants asked several challenging questions of one another.Some participants noted the tension they felt between belonging to a particular religious group and the need to let go of any consequential narrowness. The goal of the discussion was to promote understanding of the differences and similarities between Christianity and Buddhism. At one point, the participants noted several concerns about mutual enrichment: whether Buddhist methods can be separated from Buddhism and Christian methods from Christianity, and what specific aspects of Christian practice truly enrich Buddhists and which Buddhist practices likewise enrich Christians. Several times participants discussed their understanding of terms such as transformation, grace, the incarnation and the passion of Jesus, discernment of spirits, prayer, Buddha-nature, and related terms. There was consensus that Buddhists and Catholics can practically help one another regarding mental cultivation and religious precepts. They expressed this consensus in their choice of the topic forthe next dialogue, "Transformation of Hearts and Minds: Chan/Zen-Catholic Approaches to Precepts."The group agreed to reconvene in 2004 to respond to six presentations, three from each side, on different aspects of this topic.Chairing the sessions were Rev. Heng Sure for the Dharma Realm Buddhist Association, Rev. Taigen Dan Leighton for the San Francisco Zen Center, and Bishop John Webster for the United States Conference of Catholic Bishops. Their three organizations are the sponsors of the Northern California Chan/Zen-Catholic Dialogue. Chan and Zen are respectively the Chinese and Japanese terms for the meditation school... (shrink)

The 2016 United Nations’ Resolution 2325 “Non-proliferation of Weapons of Mass Destruction” manifests one of the greatest challenges for humankind in relation to preventing a global catastrophe, where it reaffirms that the proliferation of nuclear, chemical and biological weapons, as well as their means of delivery, constitutes a threat to international peace and security. However, regarding the continuous technological developments of terrestrial-based WMD aimed at orbiting space objects in near-Earth orbit, it is crucial to analyze whether, and if so, how (...) 2325 prevents their proliferation and utilization. Another relevant argument addresses the terminological factuality that, while treaty and customary law do provide some guidance on the legality of weaponization, the concept of a “space weapon” is still not clearly defined. Moreover, even though the Outer Space Treaty prohibits the placement of nuclear weapons and WMD in near-Earth orbit, installing them on the Moon or any other celestial body, or to otherwise station them in outer space, it simultaneously excludes terrestrial-based anti-satellite weapons, thus creating a legal loophole. National representatives of superpowers, particularly of space-faring nations, are aware of the existing issue and often express their concerns toward comprehensive ASAT development and utilization. Nevertheless, the potential weaponization of outer space will not be actively recognized and accepted as an official occurrence within the international community until our current space systems are eventually utilized in order to destroy or damage another State’s space object. (shrink)

We prove that the category of Nachbin’s compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of at most countable arity. Furthermore, we observe that the countable bound on the arity is the best possible: the category of compact ordered spaces is not dually equivalent to any variety of finitary algebras. Indeed, the following stronger results hold: the category of compact ordered spaces is not dually equivalent (...) to any finitely accessible category, any first-order definable class of structures, and any class of finitary algebras closed under products and subalgebras. An explicit equational axiomatisation of the dual of the category of compact ordered spaces is obtained; in fact, we provide a finite one, meaning that our description uses only finitely many function symbols and finitely many equational axioms. In preparation for the latter result, we establish a generalisation of a celebrated theorem by Mundici: our result—whose proof is independent of Mundici’s theorem—asserts that the category of unital commutative distributive lattice-ordered monoids is equivalent to the category of what we call MV-monoidal algebras.Abstract taken directly from the thesis.E-mail: [email protected]: https://air.unimi.it/retrieve/handle/2434/812809/1698986/phd_unimi_R11882.pdf. (shrink)

Is synaesthesia cognitively useful? Individuals with time–space synaesthesia experience time units as idiosyncratic spatial forms, and report that these forms aid them in mentally organising their time. In the present study, we hypothesised that time–space synaesthesia would facilitate performance on a time-related cognitive task. Synaesthetes were not specifically recruited for participation; instead, likelihood of time–space synaesthesia was assessed on a continuous scale based on participants’ responses during a semi-structured interview. Participants performed a month-manipulation task, which involved naming every second month (...) or every third month in reverse-chronological order, beginning and ending with a target month. Using hierarchical multiple regression, we found that time–space synaesthesia corresponded with faster performance on both versions of the task. We propose that time–space synaesthesia may expedite the cognitive manipulation of time-based information. Our results also indicate that synaesthesia is far less unusual than widely believed. (shrink)

The ArgumentEmergency medicine, a new medical specialty in the United States, is an ethical practice that has developed through its interaction with the spaces in which it is situated. We discuss this claim in two steps followed by a demonstration. First we examine the historical evolution of the hospital, to provide the background for a lengthier account of the historical transformation of the emergency room. We then introduce Foucault's approach to ethics, to explain the sense in which emergency medicine (...) is an ethical practice constituted, in part, by its space of operation. The preliminaries of the application of our historico-ethical framework to emergency medicine, are presented, focusing on cardiopulmonary resuscitation. Our intention is to provide a framework for the newest clinical specialty as an ethical practice in order to understand how to individuate its emerging ethical problems. The emphasis on space throughout enables us to integrate the historical development of emergency medicine with its present concrete setting, and to establish a basis for analyzing emergency medicine that does not rely uncritically on either a preferred ethical perspective or the perspective of its practitioners. (shrink)

Urban cities in the sub-Saharan Africa have witnessed unprecedented transformation because of the proliferation of religious orders within the social landscape. From Nigeria, Ghana and Cameroon to Uganda, religious practitioners are actively involved in the spatial transformation through the construction of sacred spaces or prayer camps. The Redeemed Christian Church of God (RCCG) typifies one of the several examples of African Pentecostal denominations with transnational status in 200 countries across the world with the hub of its international office situated (...) at the Redemption Camp, Mowe, Nigeria. The sacralisation of forest areas spanning 1600 ha of land has redefined religious institutions such as RCCG as perhaps one of the largest owners of private estate in Nigeria. However, there seems to be an intentional replication of the Redemption Camp, Mowe across Nigeria as well as across the Atlantic as part of the RCCG missionary enterprise. This study aims to utilise the ethnography of the Redemption Camps in Nigeria and Floyd, Texas, United States. The theoretical framework of social worlds is employed to examine the dynamics of religious creativity, innovations, contextual challenges of place-making involved in creating Redemption Camps across borders by the leadership of RCCG through the appropriation of religious capital of its community of sentiments. (shrink)

In this paper we prove the space of unital qubit channels is a Scott domain. In the process we provide a simple protocol to achieve Holevo capacity for these channels.

Starting from an abstract setting for the Lüders-von Neumann quantum measurement process and its interpretation as a probability conditionalization rule in a non-Boolean event structure, the author derived a certain generalization of operator algebras in a preceding paper. This is an order-unit space with some specific properties. It becomes a Jordan operator algebra under a certain set of additional conditions, but does not own a multiplication operation in the most general case. A major objective of the present paper (...) is the search for such examples of the structure mentioned above that do not stem from Jordan operator algebras; first natural candidates are matrix algebras over the octonions and other nonassociative rings. Therefore, the case when a nonassociative commutative multiplication exists is studied without assuming that it satisfies the Jordan condition. The characteristics of the resulting algebra are analyzed. This includes the uniqueness of the spectral resolution as well as a criterion for its existence, subalgebras that are Jordan algebras, associative subalgebras, and more different levels of compatibility than occurring in standard quantum mechanics. However, the paper cannot provide the desired example, but contribute to the search by the identification of some typical differences between the potential examples and the Jordan operator algebras and by negative results concerning some first natural candidates. The possibility that no such example exists cannot be ruled out. However, this would result in an unexpected new characterization of Jordan operator algebras, which would have a significant impact on quantum axiomatics since some customary axioms (e.g., power-associativity or the sum postulate for observables) might turn out to be redundant then. (shrink)

A simple recurrent artificial neural network is used to classify situations as permissible or impermissible. The trained ANN can be understood as having set up a similarity space of cases at the level of its internal or hidden units. An analysis of the network’s internal representations is undertaken using a new visualization technique for state space approaches to understanding similarity. Insights from the literature on moral philosophy pertaining to contributory standards will be used to interpret the state space set up (...) by the ANN as being structured by implicit reasons. The ANN, on its own, is not capable of explicitly representing or offering reasons to itself or others. That said, the low level similarity space set up by the network could be made available to higher order processes that exploit it for case-based reasoning. It is argued that for normative purposes, similarity could be seen as a contributor to procedural coherence in case-based reasoning and local forms of substantive coherence, but not to global forms of coherence given the computational complexity of managing those more ambitious forms of coherence. (shrink)

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

Under the leadership of Joshua Lederberg, some American biologists and chemists proposed exobiology as the most legitimate program for space research. These scientists used the fear of contamination—of earth and other planets—as a central argument for funding “nonpolitical,” “scientifically valid” experiments in extraterrestrial life detection. Exobiology's resemblance to popular science fiction narratives presented a significant challenge to its advocates' scientific authority. Its most practical applications, moreover, bore an unseemly resemblance to the United States Army's research on biological weapons. At the (...) same time that exobiologists wanted to use the media to attract support for their program, they had to monitor their statements carefully in order to maintain their view of exobiology as a peaceful, scientifically valid research program. In examining how exobiology's creators positioned their work in comparison to other space sciences as well as science fiction, this case study highlights how cultural and political imperatives entered science through practice and narrative during the Cold War. Since there are still so many unanswered scientific questions and problems all around us on earth, why should we start asking new questions and seeking out new problems in space? How can the results justify the costs?—“Introduction to Outer Space” (1958). (shrink)

The synthetic Maxwell equation, uniting all Maxwell equations within the framework of a Clifford algebra, can be treated as a first-order wave equation. A Hilbert space of its solutions describing classical free electromagnetic fields is introduced. This Hilbert space can be called “classical,” which means that the Planck constant is absent. The scalar square of an element of this space is the total energy of the field. The time independence of the scalar product is demonstrated. The time and space (...) translation generators are found; they are shown to not coincide with the energy and momentum operators. (shrink)

We study theorems from Functional Analysis with regard to their relationship with various weak choice principles and prove several results about them: “Every infinite‐dimensional Banach space has a well‐orderable Hamel basis” is equivalent to ; “ can be well‐ordered” implies “no infinite‐dimensional Banach space has a Hamel basis of cardinality ”, thus the latter statement is true in every Fraenkel‐Mostowski model of ; “No infinite‐dimensional Banach space has a Hamel basis of cardinality ” is not provable in ; “No infinite‐dimensional (...) Banach space has a well‐orderable Hamel basis of cardinality ” is provable in ; (the Axiom of Choice for denumerable families of non‐empty finite sets) is equivalent to “no infinite‐dimensional Banach space has a Hamel basis which can be written as a denumerable union of finite sets”; Mazur's Lemma (“If X is an infinite‐dimensional Banach space, Y is a finite‐dimensional vector subspace of X, and, then there is a unit vector such that for all and all scalars α”) is provable in ; “A real normed vector space X is finite‐dimensional if and only if its closed unit ball is compact” is provable in ; (Principle of Dependent Choices) + “ can be well‐ordered” does not imply the Hahn‐Banach Theorem () in ; and “no infinite‐dimensional Banach space has a Hamel basis of cardinality ” are independent from each other in ; “No infinite‐dimensional Banach space can be written as a denumerable union of finite‐dimensional subspaces” lies in strength between (the Axiom of Countable Choice) and ; implies “No infinite‐dimensional Banach space can be written as a denumerable union of closed proper subspaces” which in turn implies ; “Every infinite‐dimensional Banach space has a denumerable linearly independent subset” is a theorem of, but not a theorem of ; and “Every infinite‐dimensional Banach space has a linearly independent subset of cardinality ” implies “every Dedekind‐finite set is finite”. (shrink)

Intelligible speakers achieve specific vocal tract constrictions in rapid sequence. These constrictions are associated in theory with speech motor goals. Adult-focused models of speech production assume that discrete phonological representations, sequenced into word-length plans for output, define these goals. This assumption introduces a serial order problem for speech. It is also at odds with children's speech. In particular, child phonology and timing control suggest holistic speech plans, and so the hypothesis of whole word production. This hypothesis solves the serial (...) order problem by avoiding it. When the same solution is applied to adult speech the problem becomes how to explain the development of highly intelligible speech. This is the problem addressed here. A modeling approach is used to demonstrate how perceptual-motor units of production emerge over developmental time with the perceptual-motor integration of holistic speech plans that are also phonological representations; the specific argument is that perceptual-motor units are a product of trajectories (nearly) crossing in motor space. The model, which focuses on the integration process, defines the perceptual-motor map as a set of linked pairs of experienced perceptual and motor trajectories. The trajectories are time-based excursions through speaker-defined perceptual and motor spaces. By hypothesis, junctures appear where motor trajectories near or overlap one another in motor space when the shared (or extremely similar) articulatory configurations in these regions are exploited to combine perceptually-linked motor paths along different trajectories. Junctures form in clusters in motor space. These clusters, along with their corresponding (linked) perceptual points, represent perceptual-motor units of production, albeit at the level of speech motor control only. The units serve as pivots in motor space during speaking; they are points of transition from one motor trajectory to another along perceptually-linked paths that are selected to produce best approximations of whole word targets. (shrink)

The work broadens – to a considerable extent – Z. Pawlak’s original method (1982, 1992) of approximation of sets. The approximation of sets included in a universum U goes on in the contextual approximation space CAS which consists of: 1) a sequence of Pawlak’s approximation spaces (U,Ci), where indexes i from set I are linearly ordered degrees of contexts (I, <), and Ci is the universum partition U, 2) a sequence of binary relations on sets included in U, relations (...) called context relations indexed with degrees of contexts. The introduction of relations of contexts of sets was inspired by the work of W. Ziarnko (1993). Intuitively, set X is the context of set Y to the degree i, when on the basis of knowledge of the elements of set X we can obtain knowledge about the belonging of these elements to set Y to the degree i which is a degree of uncertainty or ambiguity, or inaccuracy. The operations of approximation of sets Ci-, BNi, Ci+, called lower approximation of the degree i, boundary of the degree i, upper approximation of the degree i, are formulated in a way which is analogous with the systems of Pawlak’s approximation, by expanding their formulas accordingly. In the next part of the work, it is shown (in an analogous way to Bryniarski’s work (1989)) that one can define the following operations on contextual rough sets: the union of contextual rough sets, the intersection of contextual rough sets and the complement of contextual rough set. It is proved that the algebra of contextual rough sets is a ditributive lattice with a unit and with a zero. On the basis of the results presented above the problem of defining operations on contextual rough sets by membership relations (Bryniarski 1989) may be formulated analogously to the classical operations on sets. (shrink)

I reinterpret the experiences and perceptions of child migrants through the lens of racialization and White Supremacy by advancing work by Cheryl Harris (1993) and Lisa Guenther (2019) on the critical phenomenology of “Whiteness as Property” (WaP) and the protection of “White Space.” WaP is “the collective investment in state violence” to protect the economic, territorial, and legal privileges of Whiteness, while White Space describes its two dimensions: “enclosure and territorial expansion” (Guenther 2019, 202). I build on this foundation by (...) examining the way WaP regulates sociogenic3 and emotive states in order to protect its accrued resources, resulting in an “economy” of racial identity where ownership produces and is produced by particular societal structures and relationships. I use these concepts to understand the framework that willfully misinterprets racialized children. I establish “the Child” as a sociogenic concept and symbol of national futurity and universalism, and therefore of the futurity and universalism of Whiteness; reiterating and interrogating the inconsistency that many immigration and child activists point to, that there is no such thing as an “illegal” or racialized child. Thus, the ICM either loses the privileges and protections afforded to children or must don the White Mask through a performance of victimhood. Through this framework, I undertake an examination of the ICMs as portrayed in the legal process using tools from legal sensorial studies and critical phenomenology, demonstrating the sociogenic shifts that occur for the ICM and how these shifts work to protect WaP. (shrink)

We present an adaptation of continuous first order logic to unbounded metric structures. This has the advantage of being closer in spirit to C. Ward Henson's logic for Banach space structures than the unit ball approach, as well as of applying in situations where the unit ball approach does not apply. We also introduce the process of single point emph{emboundment}, allowing to bring unbounded structures back into the setting of bounded continuous first order logic. Together with (...) results from cite{BenYaacov:Perturbations} regarding perturbations of bounded metric structures, we prove a Ryll-Nardzewski style characterisation of theories of Banach spaces which are separably categorical up to small perturbation of the norm. This last result is motivated by an unpublished result of Henson. (shrink)

Boundaries have gained analytical prominence in sociology of science. Notably, there have been studies on how academics differentiate themselves from outsiders in order to secure their legitimacy. In university departments, scholars engage in boundary work to defend their intellectual communities and institutional resources. While boundary struggles are characteristic of academia, they rarely result in departmental restructuring. This article examines a case where a theoretical divide between social and cultural anthropologists and biological anthropologists led to a departmental split. The study (...) reveals a shift from peaceful coexistence to a full-blown conflict between two intellectual communities and asks, what circumstances gave rise to the activation of a latent intellectual boundary? Drawing on interview data, I demonstrate how changes in the distribution of faculty and the alignment of intellectual, seniority, and gender differences activated the latent boundary. After its activation, scholars engaged in boundary work and expressed their intellectual differences in faculty meetings and interactions with colleagues, which led to arguments about the department’s identity that hampered the unit’s operation. The study shows how boundary work among scholars can pull apart the fabric of a department, causing intellectual identities to diverge and the organization to split. (shrink)

Ample sociological evidence demonstrates that binary gender ideologies are an intractable part of formal organizations and that transgender issues tend to be marginalized by a wide range of social institutions. Yet, in the last 15 years, more than 200 colleges and universities have attempted to ameliorate such realities by adopting gender-inclusive facilities in which students of any gender can share residential and restroom spaces. What cultural logics motivate these transformations? How can their emergence be reconciled with the difficulty of (...) altering the gender order? Using an original sample of 2,036 campus newspaper articles, I find that support for inclusive facilities frames such spaces as a resource through which an institution can claim improved standing in the field of higher education. This process of engendering reputation allows traditional gender separation in residential arrangements to be overcome, but it also situates institutional responsiveness to transgender issues as a means of enhancing a college or university’s public prestige. This, in turn, produces novel status systems in the field of higher education—albeit ones that perpetuate familiar forms of institutional and cultural exclusion. (shrink)

Race and Pedagogy identifies persistent, institutional racism as the cause of the lower rates of high school graduation among African Americans, Hispanics, and Native Americans in the United States. Adams and Buffington-Adams provide a retrospective look at their own and other teachers’ efforts to acknowledge the limitations of their own cultural lenses in order to identify, examine, and fix the failings of the current educational system.

In spatial sequence synaesthesia ordinal stimuli are perceived as arranged in peripersonal space. Using fMRI, we examined the neural bases of SSS and colour synaesthesia for spoken words in a late-blind synaesthete, JF. He reported days of the week and months of the year as both coloured and spatially ordered in peripersonal space; parts of the days and festivities of the year were spatially ordered but uncoloured. Words that denote time-units and triggered no concurrents were used in a control condition. (...) Both conditions inducing SSS activated the occipito-parietal, infero-frontal and insular cortex. The colour area hOC4v was engaged when the synaesthetic experience included colour. These results confirm the continued recruitment of visual colour cortex in this late-blind synaesthetes. Synaesthesia also involved activation in inferior frontal cortex, which may be related to spatial memory and detection, and in the insula, which might contribute to audiovisual integration related to the processing of inducers and concurrents. (shrink)

ABSTRACT In this article the Irish harp tradition is re-configured as a space consisting of visual and sonic dimensions. The visual dimension of the Irish harp space incorporates the employment of the instrument in contemporary iconography; the sonic dimension includes the employment of the instrument as a metaphor in contemporary literature and songs. By employing Bloch’s concept of surplus and tracing the path of the Irish harp from its earliest employment in Christian iconography, its prominence as an icon of colonial (...) and Ascendancy rule, and finally its utilisation as an utopian tool to inspire members of the Volunteer and United Irish movements in the late eighteenth century, I identify how the accumulation of centuries of utopian surplus resulted in the creation of an utopian icon that had the capacity to inspire a generation of Irish men and women to critique the prevailing social and political order in the eighteenth century. (shrink)

Despite the proliferation of specialised agencies designed to reduce the prevalence of refugees worldwide, the number of individuals fleeing persecution is increasing year on year as endemic violence in countries such as Iraq, Somalia and the Syrian Arab Republic continues. As a result, media broadcasts and political dialogues are saturated with discussions about these “persons of concern”. Fundamental questions nonetheless remain unanswered about what meaning these actors attribute to the label ‘refugee’ and what intent, other than paucity of knowledge, might (...) be driving the term’s use or manipulation. Though this is evidently important in the public arena, where incorrect conflations fuel mistrust and misunderstandings, the ramifications of these divergent understandings at the level of multi-lateral politics have yet to be critically explored. This article applies Barthes’ theory of the multiple orders of the sign to address this. Using the case study of the negotiations preceding the invocation of the Cessation Clause for Rwandan refugees, it illustrates how the word refugee is susceptible to numerous, simultaneous understandings, and discusses the implications of these manifold interpretations for how durable solutions are envisaged and negotiated in the refugee regime. In the case of Rwandan refugees in Uganda, this has meant that over a decade of stalemated discussions between the Governments of Uganda and Rwanda and the United Nations High Commissioner for Refugees over their future have been broken by a series of bilateral concessions that, whilst diminishing the political significance attached to this protracted caseload, have failed to address the continuing precarity of their situation. By conceptualising the word refugee as a sign according to the Saussurean model of semiotics, this paper therefore argues that despite the term’s established legal-normative definition, its inherent malleability makes it susceptible to processes of political instrumentalisation. This elevates the refugee as a rhetorical figure above the refugee as a physical-legal body entitled to certain forms of assistance. (shrink)

One of the foremost goals of research in physics is to find the most basic and universal theories that describe our universe. Many theories assume the presence of absolute space and time in which the physical objects are located and physical processes take place. However, it is more fundamental to understand time as relative to the motion of another object, e.g., the number of swings of a pendulum, and the position of an object primarily relative to other objects. This paper (...) aims to explain how using the principle of relationalism, classical mechanics can be formulated on a most elementary space, which is freed from absolute entities: shape space. In shape space, only the relative orientation and length of subsystems are taken into account. A sufficient requirement for the validity of the principle of relationalism is that by changing a system’s scale variable, all the theory’s parameters that depend on the length, get changed accordingly. In particular, a direct implementation of the principle of relationalism introduces a proper transformation of the coupling constants of the interaction potentials in classical physics. This change leads consequently to a transformation in Planck’s measuring units, which enables us to derive a metric on shape space in a unique way. In order to find out the classical equations of motion on shape space, the method of “symplectic reduction of Hamiltonian systems” is extended to include scale transformations. In particular, we will give the derivation of the reduced Hamiltonian and symplectic form on shape space, and in this way, the reduction of a classical system with respect to the entire similarity group is achieved. (shrink)

Recent setbacks to international institutions and projects of global governance have been viewed as marking a resurgence of nation-state sovereignty. In fact, however, many of the major controversies and developments in contemporary international law and geopolitics concern the administration, autonomy, and internal hierarchy not of states, but of supra-state regions. The spatial logic of a world divided into such regions is best articulated in Carl Schmitt’s theory of the Großraum, which in various respects describes and explains key features of modern (...) world order. Taking regional systems as self-constituting political units characterized by internal forms of dominance and legitimation aids in identifying the operation of hegemony in contemporary international law and institutions. It also makes possible a reinterpretation of global constitutionalist discourse as a democratizing project that finds its most important expressions in counter-hegemonic movements within the various “great spaces” constituting today’s world. (shrink)

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture (...) for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Religio-Political Narratives in the United States: From Martin Luther King Jr. to Jeremiah Wright by Angela D. Sims, F. Douglas Powe Jr., Johnny Bernard HillOluwatomisin OredeinReligio-Political Narratives in the United States: From Martin Luther King Jr. to Jeremiah Wright Angela D. Sims, F. Douglas Powe Jr., and Johnny Bernard Hill New York: Palgrave, 2014. 216PP. $90.00In a world where racial identity can serve as a means to power (...) or disempowerment, privilege or disadvantage, Christian prophetic speech can offer a corrective to subjugative realities. In Religio-Political Narratives in the United States: From Martin Luther King Jr. to Jeremiah Wright, Angela Sims, F. Douglas Powe Jr., and Johnny Bernard Hill attend to prophetic speech and its direct impact on the political through examining the politico-spiritual discourse and work of three storied black figureheads with roots in the black church: Martin Luther King Jr., Jeremiah Wright, and Barack Obama.It is not surprising that black ecclesial rhetoric is found within the orations of these prominent leaders, but what this work reveals is the relationship between social location, religious constitution, and political alignment. Black identity connected to the prophetic expressive tradition directly confronts any model of relationality that constructs injurious sociality. The prophetic, expressed through particular bodies, makes impossible the separation of church and state. As black identity was historically discoursed through deformation, devaluation, and dehumanization, black prophetic speech sought religious premise to speak back to and refute these ill-constructed social and political “realities.” Religiosity and sociality are affixed, adjoined in, on, and through the tongues of these three black influential figureheads of justice. The voices of King, Wright, and Obama move discursively between the religious and the political, using prophetic speech toward active political policy and toward recognizing those who are invisible in the United States and in the world. Employing the language and ideology of citizenry and community, their work and words ultimately move to emphasize human interconnectedness.Religio-Political Narratives in the United States reaches far and wide within academic discourse. A seminal work for black church studies, politics courses, ethics studies, courses in racial discourse, and Christian theological studies, it traces how the prophetic-political “verse” of these black leaders speaks back to the sinister forces that directly shape the experiences of many in the United States and the world. Blackness, an “invisibilized” identity, is ironically the space from which visibility and justice can materialize. Black identity, then, is prophetic in itself; it teaches audacious sight and visionary speech. [End Page 207]The brilliance of Religio-Political Narratives in the United States is in its characterization under one of its series headings, “Womanist Thought.” This identification is its most subtle yet forceful claim. Arguably grounded in the prophetic, womanist thought seeks to engage in “speaking back” to modes of oppressive practices within the black community and Christian context as a whole. Strangely, though, black women are absent from the text. Sims, Powe, and Hill honor womanist thought through recognizing its prophetic tone but overlook its advocates. Its womanist commitment is thus only partially seen, and questions emerge, such as: How did black women influence King, Wright, and Obama, and how can this be accounted for? How did black women historically influence other black women across time? Cannot voices such as those of Ida B. Wells and Pauli Murray be connected to the cadence of Loretta Lynch or Michelle Obama?The presence of black women’s voices is especially important in order to grant stability to the narration of political influence in the United States from within the black community. What must be avoided is the potential alignment of some sort of messianic imagery (and imagination) onto black male figures—and further, and arguably most importantly—aligning political and social change primarily with black males. Messianic mediation must be distinguished from prophetic illumination. Religio-Political Narratives in the United States wisely illumines the connections between body and policy; now we are prompted to ask: whose bodies are storied as legendary, influential, and worth giving account of?Oluwatomisin OredeinDuke Divinity SchoolCopyright © 2016 The Society of Christian Ethics... (shrink)

The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but in all the examples considered there it remains symmetric. Here we present a class of binary models where the transition probability is not symmetric, using the extreme points of the unit interval in an order unit space as quantum logic. We show that their state spaces (...) are strictly convex smooth compact convex sets and that each such set _K_ gives rise to a quantum logic of this class with the state space _K_. The transition probabilities are symmetric iff _K_ is the unit ball in a Hilbert space. In this case, the quantum logic becomes identical with the projection lattice in a spin factor which is a special type of formally real Jordan algebra. (shrink)

An axiomatic theory is formulated which describes a class of “yes-no” experiments, involving a fixed basic source, a fixed basic detector, and various filters. It is assumed that all filters considered can be constructed from a setP of primitive filters by composition and stochastic selection. Two physically plausible axioms are formulated which allow us to define the concept of asystem in the present context (cf. Definition2.4). To each system we can attach anorder unit module ( $^\circ \hat V, ^\circ (...) \hat V_ + , |1\rangle , \langle 1|$ ) (cf. Definition5.1) whereby ( $^\circ \hat V, ^\circ \hat V_ + , |1\rangle ,$ ) is acomplete, separable order unit space. Two additional axioms are proposed which have the effect that the space ( $^\circ \hat V, ^\circ \hat V_ + , |1\rangle ,$ ) becomes isomorphic to the order unit space underlying a JB-algebra, at least in the case where $^\circ \hat V$ isfinite dimensional (cf. Corollary7.9). (shrink)

The main result established in this paper is the following: If the base normed spaceV of completely additive weights is a norm-determining subspace of the space of finitely additive weights V acting on the order unit space spanning the operational logic, thenV has the ε-Jordan-Hahn property iff V has the approximate Jordan-Hahn property. Several examples illustrating the theory are given.

We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two.

The present paper is the first part of a work which follows up on H. Kummer: “A constructive approach to the foundations of quantum mechanics,”Found. Phys. 17, 1–63 (1987). In that paper we deduced the JB-algebra structure of the space of observables (=detector space) of quantum mechanics within an axiomatic theory which uses the concept of a filter as primitive under the restrictive assumption that the detector space is finite-dimensional. This additional hypothesis will be dropped in the present paper.It turns (...) out that the relevant mathematics for our approach to a quantum mechanical system with infinite-dimensional detector space is the noncommutative spectral theory of Alfsen and Shultz.We start off with the same situation as in the previous paper (cf. Sects. 1 and 2 of the present paper). By postulating four axioms (Axioms S, DP, R, and SP of Sec. 3), we arrive in a natural way at the mathematical setting of Alfsen and Shultz, which consists of a dual pair of real ordered linear spaces 〈Y, M〉: A base norm space, called the strong source space (which, however, in slight contrast to the setting of Alfsen and Shultz, is not 1-additive) and an order unit space, called the weak detector space, which is the norm and order dual space of Y. The last section of part I contains the guiding example suggested by orthodox quantum mechanics. We observe that our axioms are satisfied in this example. In the second part of this work (which will appear in the next issue of this journal) we shall postulate three further axioms and derive the JB-algebra structure of quantum mechanics. (shrink)

In this paper, I first examine the classification of mental derangements contained in Kant’s "Anthropology from a Pragmatic Point of View", in order to highlight the role played by imagination in their pathogenesis. Later, on the basis of this examination, I reflect on the origins of critical philosophy, which can be seen as an attempt to construct a control device for the imagination structured as a systematic, organic space.

§1. Introduction.The motivation of this work comes from two different directions: infinite abelian groups, and ordered algebraic structures. A challenging problem in both cases is that of classification. In the first case, it is known for example (cf. [KA]) that the classification of abelian torsion groups amounts to that of reducedp-groups by numerical invariants called theUlm invariants(given by Ulm in [U]). Ulm's theorem was later generalized by P. Hill to the class of totally projective groups. As to the second case, (...) let us consider for instance the class of divisible ordered abelian groups. These may be viewed as ordered ℚ-vector spaces. Their theory being unstable, we cannot hope to classify them by numerical invariants. On the other hand, being o-minimal, the theory enjoys several good model theoretic properties (cf. [P-S]), so the search for some reasonable invariants is well motivated. The common denominator of the two cases, as well as of many others, is valuation theory. Indeed given an ordered vector space, one can consider it as a valued vector space, endowed with the natural valuation. Also, the socleG[p] of a reduced abelianp-groupG, endowed with the height functionhG, is a valued vector space over(the prime field of characteristicp) with values in the ordinals (cf. [F]). (shrink)

This book offers geographical perspectives on the condition of the United States at the outset of the twenty-first century. It compares the American ideals of liberty, equality, individual opportunity, and social improvement with the contemporary condition of the regions, states and localities - the ideal American space with its reality as a place. It uses the public standard provided by the official ideology of the United States to see how well things are really going. The authors consider the contrast between (...) ideal and reality at local, state, and national levels in education, health, and welfare, in community, race, gender, and class relations, in economic and industrial development, and in the use and exploitation of America's landscape. Each chapter addresses the issues through evidence of long-term and recent trends, and grounds its arguments in information. American Space/American Place provides a series of compelling insights into the current condition of American society, its natural environment, and its place within the world. (shrink)

We study the class of Sperner spaces, a generalized version of affine spaces, as defined in the language of pointline incidence and line parallelity. We show that, although the class of Sperner spaces is a pseudo-elementary class, it is not elementary nor even ℒ∞ω-axiomatizable. We also axiomatize the first-order theory of this class.

We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies (...) and extends Sikora’s [28] investigation of orders on groups in topology and Solomon’s [31] investigation of these orders in computable algebra. Furthermore, we establish that a computable free group Fn of rank n>1 has a bi-order in every Turing degree. (shrink)

Mental state reasoning or theory-of-mind has been the subject of a rich body of imaging research. Although such investigations routinely tap a common set of regions, the precise function of each area remains a contentious matter. With the help of functional magnetic resonance imaging (fMRI), we sought to determine which areas are involved when processing mental state or intentional metarepresentations by focusing on the relational aspect of such representations. Using non-intentional relational representations such as spatial relations between persons and between (...) objects as a contrast, the results ascertained the involvement of the precuneus, the temporal poles, and the medial prefrontal cortex in the processing of intentional representations. In contrast, the anterior superior temporal sulcus and the left temporo-parietal junction were implicated when processing representations that refer to the presence of persons in relational contexts in general. The right temporo-parietal junction, however, was specifically activated for persons entering spatial relations. The level of representational complexity, a previously unexplored factor, was also found to modulate the neural response in some brain regions, such as the medial prefrontal cortex and the right temporo-parietal junction. These findings highlight the need to take into account the critical roles played by an extensive network of neural regions during mental state reasoning. (shrink)

Meehan finds fault with a number of my arguments, and proposes that better solutions to the problems I was addressing are available if we adopt a higher-order theory of consciousness. I start with some general remarks on theories of this sort. I connect what I had to say about the A-thesis with different forms of higher-order sense theories, and explain why I ignored higher-order thought theories altogether: there are compelling grounds for thinking they cannot provide a viable (...) account of phenomenal unity in phenomenal terms. Meehan. (shrink)

In his logical papers, Leo Esakia studied corresponding ordered topological spaces and order-preserving mappings. Similar spaces and mappings appear in many other application areas such the analysis of causality in space-time. It is known that under reasonable conditions, both the topology and the original order relation $${\preccurlyeq}$$ can be uniquely reconstructed if we know the “interior” $${\prec}$$ of the order relation. It is also known that in some cases, we can uniquely reconstruct $${\prec}$$ (and hence, (...) topology) from $${\preccurlyeq}$$. In this paper, we show that, in general, under reasonable conditions, the open order $${\prec}$$ (and hence, the corresponding topology) can be uniquely determined from its closure $${\preccurlyeq}$$. (shrink)

This chapter discusses the ordering of color percepts, and starts by presenting an overview of the critical issues surrounding the topic and by examining the relationship between stimuli and percepts. Certain types of variability were found by experimental psychology in the relationship between stimulus and response as a result of observation conditions. In the twentieth century, the view that the normal human color-vision system has a standard implementation and that all perceptual data are appropriately treated with normal statistical distribution methodology (...) became the standard paradigm. However, the idea that the large number of color percepts humans can experience must fit into some kind of ordering system is an old one, going as far back to Aristotle and his proposed color categories based on a scale of chromatic colors between white and black. The strengths and limitations of the more recently developed kinds of color order systems are also touched upon here. (shrink)

Closure spaces are generalizations of topological spaces, in which the Intersection of two open sets need not be open. The considered logic is related to closure spaces just as the standard logic S4 to topological ones. After describing basic properties of the logic we consider problems of representation of Lindenbaum algebras with some uncountable sets of infinite joins and meets, a notion of equality and a meaning of quantifiers. Results are extended onto the standard logic S4 and (...) they are valid also for some other standard modal logics. (shrink)