Mature representations of number are built on a core system of numerical representation that connects to spatial representations in the form of a ‘mental number line’. The core number system is functional in early infancy, but little is known about the origins of the mapping of numbers onto space. Here we show that preverbal infants transfer the discrimination of an ordered series of numerosities to the discrimination of an ordered series of line lengths. Moreover, infants (...) construct relationships between individual numbers and line lengths that vary positively, but not between numbers and lengths that vary inversely. These findings provide evidence for an early developing predisposition to relate representations of numerical magnitude and spatial length. A central foundation of mathematics, science and technology therefore emerges prior to experience with language, symbol systems, or measurement devices. (shrink)

Des branches entières des mathématiques sont fondées sur des liens posés entre les nombres et l’espace : mesure de longueurs, définition de repères et de coordonnées, projection des nombres complexes sur le plan… Si les nombres complexes, comme l’utilisation de repères, sont apparus relativement récemment (vers le XVIIe siècle), la mesure des longueurs est en revanche un procédé très ancien, qui remonte au moins au 3e ou 4e millénaire av. J-C. Loin d’être fortuits, ces liens entre les nombres et l’espace (...) reflèteraient une intuition fondamentale, universelle, façonnée au cours des millénaires par la sélection naturelle, et qui aurait servi de guide et d’inspiration aux mathématiciens au fil des siècles. (shrink)

The mapping of numbers onto space is fundamental to measurement and to mathematics. Is this mapping a cultural invention or a universal intuition shared by all humans regardless of culture and education? We probed number-space mappings in the Mundurucu, an Amazonian indigene group with a reduced numerical lexicon and little or no formal education. At all ages, the Mundurucu mapped symbolic and nonsymbolic numbers onto a logarithmic scale, whereas Western adults used linear mapping with (...) small or symbolic numbers and logarithmic mapping when numbers were presented nonsymbolically under conditions that discouraged counting. This indicates that the mapping of numbers onto space is a universal intuition and that this initial intuition of number is logarithmic. The concept of a linear number line appears to be a cultural invention that fails to develop in the absence of formal education. (shrink)

The performance of the Mundurucu on the number-space task may exemplify a general competence for drawing analogies between space and other linear dimensions, but Mundurucu participants spontaneously chose number when other dimensions were available. Response placement may not reflect the subjective scale for numbers, but Cantlon et al.'s proposal of a linear scale with scalar variability requires additional hypotheses that are problematic.

We assessed the automaticity of spatial-numerical and spatial-musical associations by testing their intentionality and load sensitivity in a dual-task paradigm. In separate sessions, 16 healthy adults performed magnitude and pitch comparisons on sung numbers with variable pitch. Stimuli and response alternatives were identical, but the relevant stimulus attribute (pitch or number) differed between tasks. Concomitant tasks required retention of either color or location information. Results show that spatial associations of both magnitude and pitch are load sensitive and that the (...) spatial association for pitch is more powerful than that for magnitude. These findings argue against the automaticity of spatial mappings in either stimulus dimension. (shrink)

Jerry Fodor and Ernest Lepore [(1992) Holism: a shopper's guide, Oxford: Blackwell; (1996) in R. McCauley (Ed.) The Churchlands and their critics , Cambridge: Blackwell] have launched a powerful attack against Paul Churchland's connectionist theory of semantics--also known as state space semantics. In one part of their attack, Fodor and Lepore argue that the architectural and functional idiosyncrasies of connectionist networks preclude us from articulating a notion of conceptual similarity applicable to state space semantics. Aarre Laakso and Gary (...) Cottrell [(1998) in M. A. Gernsbacher & S. Derry (Eds) Proceedings of the 20th Annual Conference of the Cognitive Science Society, Mahway, NJ: Erlbaum; Philosophical Psychology ] 13, 47-76 have recently run a number of simulations on simple feedforward networks and applied a mathematical technique for measuring conceptual similarity in the representational spaces of those networks. Laakso and Cottrell contend that their results decisively refute Fodor and Lepore's criticisms. Paul Churchland [(1998) Journal of Philosophy, 95, 5-32 ] goes further. He uses Laakso and Cottrell's neurosimulations to argue that connectionism does furnish us with all we need to construct a robust theory of semantics and a robust theory of translation. In this paper I shall argue that whereas Laakso and Cottrell's neurocomputational results may provide us with a rebuttal of Fodor and Lepore's argument, Churchland's conclusion is far too optimistic. In particular, I shall try to show that connectionist modelling does not provide any objective criterion for achieving a one-to-one accurate translational mapping across networks. (shrink)

The attention being paid to ethics education in accounting has been increasing, especially after the corporate accounting scandals at the turn of the century. This paper provides a comprehensive overview of the existing research in the field of ethics education in accounting. To synthesize past research, a bibliometric analysis that references 134 primary studies is performed and three bibliometric methods are applied. First, we visualize the historical evolution of ethics education in accounting research through historiography. Second, we use bibliographic coupling (...) to identify clusters of ethics education in accounting research before, during, and after major corporate scandals. Third, we perform a co-word analysis to connect the identified patterns into a map of a contextual space. The results reveal, in each decade, not only an increasing academic focus on this field of research, but also an increasing number of different research clusters. While the clusters Factors affecting moral judgement, Perception of ethics, and Lack of ethics topics in the last research period develop further from the respective clusters in the previous periods, Accounting beyond technical skills, Integration of ethics in accounting education, Use of developed ethics frameworks, and Professional values on the contrary develop anew in the last decade, as a consequence of a growing demand for teaching ethics. Overall, the paper presents the development patterns of ethics education in accounting research and sets up a research agenda that encourages future research. (shrink)

Exponential mappings into an imaginary space or number field for the axioms of a theory, which are in the form of propositional constants and variables, make possible: (a) an understanding of the meaning and differences between the Lorentz transformation constants, such that their product is still equal to one, but the axioms at each end of the transformations are logically inverse and separately consistent; (b) an interpretation of the psi function phase factor which is part of the axiomE=hf; (...) (c) the unification of the quantum-mechanical psi function and the electromagnetic wave function. Thus, those statements whose mechanisms are unknown (the axioms of the theory) are to be assigned the axiom propositional number symbol ϑ and are to be associated with the complex probability eiϑ, which is a uniform factor of the energy equations expressing the physical state. Such probabilistic axiom functions can be associated with both the special theory of relativity and the quantum-electromagnetic theory. (shrink)

The attempt to provide a faithful mapping from distal shape space to proximal state space in terms of a higher order relationship defined over proximal similarity space stumbles on the context sensitivity of higher order relationships. Proportional analogy problems using quadruples of figures illustrate that for a number of interesting perceptual problems, the number of relevant dimensions cannot be reduced.

Actions can be physically executed, observed, imagined, or simply thought about. Unifying mental processes, such as simulation, emulation, or predictive processing, are thought to underlie different action types, whether they are mental states, as in the case of motor imagery and action observation, or involve physical execution. While overlapping brain activity is typically observed across different actions which indicates commonalities, research interest is also concerned with investigating the distinct functional components of these action types. Unfortunately, untangling subtleties associated with the (...) neurocognitive bases of different action types is a complex endeavour due to the high dimensional nature of their neural substrate (e.g., any action process is likely to activate multiple brain regions thereby having multiple dimensions to consider when comparing across them). This has impeded progress in action-related theorising and application. The present study addresses this challenge by using the novel approach of multidimensional modeling to reduce the high-dimensional neural substrate of four action-related behaviours (motor imagery, action observation, action-related language, and action execution), find the least number of dimensions that distinguish or relate these action types, and characterise their neurocognitive relational links. Data for the model comprised brain activations for action types from whole-brain analyses reported in 53 published articles. Eighty-two dimensions (i.e., 82 brain regions) for the action types were reduced to a three-dimensional model, that mapped action types in ordination space where the greater the distance between the action types, the more dissimilar they are. A series of one-way ANOVAs and post-hoc comparisons performed on the mean coordinates for each action type in the model showed that across all action types, action execution and concurrent action observation (AO)-motor imagery (MI) were most neurocognitively similar, while action execution and AO were most dissimilar. Most action types were similar on at least one neurocognitive dimension, the exception to this being action-related language. The import of the findings are discussed in terms of future research and implications for application. (shrink)

On June 26, 2000, President Clinton, together with Francis Collins and Craig Venter, solemnly announced, from the East Room of the White House, that the grand effort to sequence the human genome, the Human Genome Project (HGP), was rapidly nearing its completion. Symbolism abounded. The event was framed as a crucial marker in the history of both humanity and knowledge by explicitly connecting the completion of the HGP with a number of already acknowledged and established scientific highlights. Tensions abounded (...) as well, however, notably between competing metaphors. In the course of the HGP, metaphors had become crucially important in framing and conveying what the HGP was really about. They had proved themselves to be of key importance when it came to defining and explaining the project’s significance for both science and society. Powerful images and metaphors had been deployed in order to secure unprecedented amounts of funding, on the one hand by comparing the HGP to other big technoscientific projects such as space travel, high energy physics, the atomic bomb and a territorial mapping exercise, and on the other hand through the suggestion that, once we have our “blueprint”, “code of codes”, “parts list”, etc. available, cancer genes will no longer have a place to hide. This article sets out to analyze this clash of metaphors, firmly embedded within the HGP but culminating at the press conference, arguing that the June 2000 event is even reminiscent of a somewhat similar event, depicted by a famous altarpiece, ‘The adoration of the Lamb’, on display in Ghent Cathedral and finished more than five centuries before. (shrink)

The number-line estimation task has become one of the most important methods in numerical cognition research. Originally applied as a direct measure of spatial number representation, it became also informative regarding various other aspects of number processing and associated strategies. However, most of this work and associated conclusions concerns processing numbers in a symbolic format, by school children and older subjects. Symbolic number system is formally taught and trained at school, and its basic mathematical properties can (...) easily be transferred into a spatial format of an oriented number line. This triggers the question on basic characteristics of number line estimation before children get fully familiar with the symbolic number system, i.e., when they mostly rely on approximate system for non-symbolic quantities. In our three studies, we examine therefore how preschool children estimate position of non-symbolic quantities on a line, and how this estimation is related to the developing symbolic number knowledge and cultural directionality. The children were tested with the Give-a-number task, then they performed a computerized number-line task. In Experiment 1, lines bounded with sets of 1 and 20 elements going left-to-right or right-to-left were used. Even in the least numerically competent group, the linear model better fit the estimates than the logarithmic or cyclic power models. The line direction was irrelevant. In Experiment 2, a 1–9 left-to-right oriented line was used. Advantage of linear model was found at group level, and variance of estimates correlated with tested numerosities. In Experiment 3, a position-to-number procedure again revealed the advantage of the linear model, although the strategy of selecting an option more similar to the closer end of the line was prevalent. The precision of estimation increased with the mastery of counting principles in all three experiments. These results contradict the hypothesis of the log-to-linear shift in development of basic numerical representation, rather supporting the linear model with scalar variance. However, the important question remains whether the number-line task captures the nature of the basic numerical representation, or rather the strategies of mapping that representation to an external space. (shrink)

According to classical theories of language and cognition, human cognition is characterized by strong universal commonalities built around notions such as object, space, agency, number, time, and event (Clark, 1973; Miller & Johnson‐Laird, 1976). Languages select from this prelinguistic conceptual repertoire the concepts that become encoded in their lexical and grammatical stock. Language acquisition, on this view, is a mapping process in which the learner needs to figure out which sounds in the language spoken in the environment (...) correspond to which concepts from the ones already in the mind (Fodor, 1975; Gleitman, 1990; Pinker, 1994). (shrink)

A compact complex space X is viewed as a 1-st order structure by taking predicates for analytic subsets of X, X \times X, … as basic relations. Let f: X→ Y be a proper surjective holomorphic map between complex spaces and set Xy:=f-1(y). We show that the set Ak,d:={y∈ Y: the number of d-dimensional components of Xy is (...) is a holomorphic map. The analogous result in the context of algebraic geometry gives rise to the definability of Morley degree. (shrink)

Núñez and Fias raised concerns on whether our results demonstrate a linear number-space mapping. Patro and Nuerk urge caution on the use of animal models to understand the origin of the orientation of spatial–numerical association. Here, we discuss why both objections are unfounded.

The semantic fluency task is a widely used clinical tool in the diagnostic process of Alzheimer's disease. The task requires efficient mapping of the semantic space to produce as many items as possible within a semantic category. We examined whether healthy volunteers and patients with early Alzheimer's disease take advantage of and travel in the semantic space differently. With focus on the animal fluency task, we sought to emulate the detailed structure of the multidimensional semantic space (...) by utilizing word2vec-method from the natural language processing domain. To render the resulting multidimensional semantic space visually comprehensible, we applied a dimensionality reduction algorithm, which enabled a straightforward division of the semantic space into sub-categories. Moving in semantic space was quantified with the number of items created, sub-categories visited, and switches and returns to these sub-categories. Multinomial logistic regression models were used to predict the diagnostic group with these independent variables. We found that returning to a sub-category provided additional information, besides the number of words produced in the task, to differentiate patients with Alzheimer's dementia from both amnestic Mild Cognitive Impairment patients and healthy controls. The results suggest that the frequency of returning to a sub-category may serve as an additional aid for clinicians in diagnosing early Alzheimer's disease. Moreover, our results imply that the combination of word2vec and subsequent t-SNE-visualization may offer a valuable tool for examining the semantic space and its sub-categories. (shrink)

Memory for numbers improves with age. One source of this improvement may be learning linear spatial-numeric associations, but previous evidence for this hypothesis likely confounded memory span with quality of numerical magnitude representations and failed to distinguish spatial-numeric mappings from other numeric abilities, such as counting or number word-cardinality mapping. To obviate the influence of memory span on numerical memory, we examined 39 3- to 5-year-olds’ ability to recall one spontaneously produced number (1-20) after a delay, and (...) the relation between numeric recall (controlling for non-numeric recall) and quality of mapping between symbolic and non-symbolic quantities using number-line estimation, give-a-number estimation, and counting tasks. Consistent with previous reports, mapping of numerals to space, to discrete quantities, and to numbers in memory displayed a logarithmic-to-linear shift. Also, linearity of spatial-numeric mapping correlated strongly with multiple measures of numeric recall (percent correct and percent absolute error), even when controlling for age and non-numeric memory. Results suggest that linear spatial-numeric mappings may aid memory for number over and above children’s other numeric skills. (shrink)

In seventeenth- and eighteenth-century London and Paris, growing numbers of poor alarmed notables and city officials who would come to view a policy of confinement as an appropriate social, economic, religious, and political solution. This work examines the motivations of patrons to support these institutions (called hospitals). In particular, this study looks at their support for the construction (or renovations) of chapels (e.g. chapel at La Salpêtrière and the chapel at the Lock Hospital) and their visitations to these hospitals. Vagrants, (...) beggars, prostitutes, and idlers of other sorts healthy or not were confined not necessarily for theirhealth but for their souls and for the social order of the city. The locations of these hospitals indicate a geographical isolation not only in their “placement” outside the city walls but even in the Christian charitable rhetoric or visitations by benefactors that emphasized their separateness. “Unclean livers” or destitute beggars were put on view so that the morally upright who patronized these institutions could view for instructional purposes and could be viewed for purposes of salvation, but remained as separate nonetheless. Great masses and grand sermons were heard in the chapels that adorned these institutions, but a clear policy of segregation existed that kept the godly patrons separate from the “polluted.”. (shrink)

We study the preservation of selective covering properties, including classic ones introduced by Menger, Hurewicz, Rothberger, Gerlits and Nagy, and others, under products with some major families of concentrated sets of reals.Our methods include the projection method introduced by the authors in an earlier work, as well as several new methods. Some special consequences of our main results are : Every product of a concentrated space with a Hurewicz S1S1 space satisfies S1S1. On the other hand, assuming the (...) Continuum Hypothesis, for each Sierpiński set S there is a Luzin set L such that L×SL×S can be mapped onto the real line by a Borel function. Assuming Semifilter Trichotomy, every concentrated space is productively Menger and productively Rothberger. Every scale set is productively Hurewicz, productively Menger, productively Scheepers, and productively Gerlits–Nagy. Assuming d=ℵ1d=ℵ1, every productively Lindelöf space is productively Hurewicz, productively Menger, and productively Scheepers.A notorious open problem asks whether the additivity of Rothberger's property may be strictly greater than addadd, the additivity of the ideal of Lebesgue-null sets of reals. We obtain a positive answer, modulo the consistency of Semifilter Trichotomy >ℵ1.Our results improve upon and unify a number of results, established earlier by many authors. (shrink)

Oral communication often takes place in noisy environments, which challenge spoken-word recognition. Previous research has suggested that the presence of background noise extends the number of candidate words competing with the target word for recognition and that this extension affects the time course and accuracy of spoken-word recognition. In this study, we further investigated the temporal dynamics of competition processes in the presence of background noise, and how these vary in listeners with different language proficiency (i.e., native and non-native) (...) using computational modeling. We developed ListenIN (Listen-In-Noise), a neural-network model based on an autoencoder architecture, which learns to map phonological forms onto meanings in two languages and simulates native and non-native spoken-word comprehension. We also examined the model's activation states during online spoken-word recognition. These analyses demonstrated that the presence of background noise increases the number of competitor words, which are engaged in phonological competition and that this happens in similar ways intra and interlinguistically and in native and non-native listening. Taken together, our results support accounts positing a “many-additional-competitors scenario” for the effects of noise on spoken-word recognition. (shrink)

The use of collaborative online social media applications as tools of communication is increasing in contemporary society. Correspondingly, a number of contemporary artists are exploring online interaction in their material public art practice, as a new form of documentation, promotion and creative collaboration. Mapping and analysing these new forms of interaction provide a method to determine the scope of their contribution to new artistic knowledge. This paper argues that contemporary public art practice can be cognisant of both physical (...) and virtual contributions as equally active participants in collaboration. It also identifies the convergence between artist and audience in virtual and physical space, and examines how this is affected by certain conditions and models of behaviour, which influence how a new collaborative creative discourse in public art can be constructed. (shrink)

continent. 1.4 (2011): 253—278. A Sense of French Politics Politics itself is not the exercise of power or struggle for power. Politics is first of all the configuration of a space as political, the framing of a specific sphere of experience, the setting of objects posed as "common" and of subjects to whom the capacity is recognized to designate these objects and discuss about them.(1) On April 14, 2011, France implemented its controversial ban of the niqab and burqa , (...) commonly referred to as the Islamic veil, in public places. On the coattails of the 2004 prohibition of religious artifacts, including the less concealing hijab or Islamic headscarves, in schools, the veil ban sparked equal outrage across both political and theological spectra, and many on both sides of the debate were quick to inquire about enforcement. As Steven Erlanger reports, “The police do not have the authority under the law to remove full veils, only to fine or require citizenship lessons for those who violate the new law.”(2) While the legal and social implications of this interdiction are ripe for study, the reprisals for breaking the law, notably compulsory citizenship classes, illuminate the strategic governmentality underlying the French government's targeting of the Muslim community, particularly those elements it considers affiliated with fundamentalist factions and/or terrorist organizations, if only through fashion—an integral component of French citizenship. Indeed, in allowing the (fashion) police to mandate instructional courses in citizenship for offenders, France implies that any Muslim choosing to wear the niqab or burqa , perhaps even for those who are already citizens, must not be aware of the subtle nuances of dress indicative of the French citizenry within public space. Furthermore, the degree of instruction requisite to citizenship, which clearly can and must be updated as the state sees fit, cements the imagined relation between citizens and states within the discourses on the veil ban. As Sharma contends, “Concepts of citizenship are the ideological glue that bonds the nation to the state. Citizenship provides the legal framework through which the state performs its role as ruler for the nation.”(3) Speaking for/as the state, French President Nicolas Sarkozy declared in a 2009 presentation before members of the government and other citizens that the burqa “is not welcome on the territory of France.”(4) Although there is nothing unique, especially recently, about a nation-state taking extreme measures to guard itself against what it deems to be threats to its sovereignty, the way in which the ongoing discourses on hijab have (d)evolved, which coincide with recent pronouncements by governmental leaders in Germany, Britain, and France that policies of multiculturalism have “failed,”(5) points toward nationalist reterritorializations, which is also to say physical and ideological re-appropriations, of public space within democratic milieux, which remain predicated upon the mediation of spaces. As Panagia deduces from Rancière, “Democracy […] is not an institutional form of government […], but an appearance whose visibilities and audibilites arise out of the dissonant blur of the everyday.”(6) Ultimately, the veil ban represents a calculated move to regulate the every day, which is to say the micropolitics of, that which is visible and invisible within French society, which makes it nothing short of a struggle to manage (the sensation of) bodies. Re-situating the political within the context of sense, Rancière argues that the fundamental essence of politics lies within the distinction between consensus and dissensus , and whereas most consider politics proper as fundamentally concerned with the fluid operations of the state— consensus , Rancière actually locates the political within events that disrupt the normative sensory order of things— dissensus . He explains, “Politics revolves around what is seen and what can be said about it, around who has the ability to see and the talent to speak, around the properties of spaces and the possibilities of time.”(7) This reformulation of politics centers on agency and, albeit perhaps unintended, representationality and offers a useful formulation for spatializing the discourses surrounding the Islamic veil, which are mired within seemingly senseless policies and practices of objectification. Instituting a normative “regime of visibility,” the French veil ban encapsulates the political economy of agency, now both mediated and representational, under the rule of nationalist governmentalities in increasingly transnational contexts.(8) Adjudicating presence within public space signals a concern with the sensory aspects of agency itself—what Rancière terms the “distribution of the sensible,” which is “a matrix that defines a set of relations between sense and sense: that is, between a form of sensory experience and an interpretation which makes sense of it.”(9) To be concerned with sense is to focus upon the body, and this somatic repositioning of the (fashionable) citizen within the territory of the state augurs the resurgence of nationalist bio-politics within Europe, since, as Hage explicates, “Nationalism, before being an explicit practice or a mode of classification, is a state of the body. It is a way of imagining one's position within the nation and what one can aspire to as a national.”(10) The French government's attempt to make (bodily) sense of public space for its citizens by and through policies aimed against a burqa-clad Muslim minority, which might only apply to “less then 400 to fewer than 2,000” women(11), reveals the necessary, yet mercurial, transmutation of public space into national space through bio-political strategies of sense-making, which, as Hage observes, denotes that “nationalists perceive themselves as spatial managers.”(12) At the center of this concern over public space is the equally contentious dimension of governing female Islamic identity, which has become one of the main critiques levied against Islam from outsiders who view the veil in its various forms as a clear sign of the religion's actual and symbolic violence against women, even if such critiques remain ensconced within nationalist discourses. As Halim and Meyers argue, “Although Western news media may focus their coverage of Muslim women on the debate over whether and the extent to which the veil may by oppressive to the women who wear it, they have exhibited little interest in the physical oppression of violence against women in Islamic countries.”(13) While it falls outside of the scope of this analysis to arbitrate all of the dimensions of this debate, understanding some of the issues related to female identity and hijab within public space are crucial to this study. As these topics are extraordinarily complex, even and perhaps especially within the Muslim community, it is necessary to provide some context concerning the value, purpose, and meaning of the Islamic veil, which has a rich and arduous history. The Art of the Veil At present, there are only two countries, Iran and Saudi Arabia, that require women to wear hijab , which is a decidedly problematic term and concept whose locus is itself caught within a struggle of sensation. Noting the strategic reterritorialization of the term, Berger explains: The choice of the name, hijab , now widely adopted to designate the “Islamic veil,” it itself interesting, although the semantic shift it operates is not directly commented upon by its users. Although the design (both the cut and the symbolic function) of the hijab and the Iranian chador are indeed the same, as opposed, for instance, to the traditional Algerian haik , the word hijab has come to replace the term chador popularized by the Iranian revolution, as a properly Arabic (hence Koranic) designation. This discursive shift points to the successful reclaiming of the national revolution in Iran by a transnational pan-Islamic movement, whose language of reference can only be Koranic Arabic.(14) While the hijab is certainly a point of contention within various countries dealing with immigrant Islamic populations (of which France has the largest in Europe as part of its colonial legacy in Algeria), it is clear that the veil is a historically contextualized artifact of Muslim identity with a variety of manifestations, even as forces outside of and within Islam seek to codify its actual and symbolic value. Ultimately, the varieties of hijab , including the full-faced burqa and niqab , are complex assemblages of meaning that speak to the multitudinous flows of Islamic identities over time and space. As Gökariksel and McLarney observe, “Wearing a certain style of veil may simultaneously be a disciplinary practice crucial to the cultivation of piety (Mahmood 2005; Gokariksel 2009) and a gendered performance of social distinction in terms of class, taste, and urbanity (White 1999; Navaro-Yashin 2002; Gokariksel and Secor 2009) or of ethnicity and race (Dwyer 1999).”(15) The ideological marketplace from which the varieties of hijab ebb and flow serves both as a reflection of the ever-present materiality and dynamic functionality of spiritual economies, which are derivative of the equally ubiquitous flows of transnational capital driving agency and representationality within our historical moment. Keeping these dual, yet deeply interconnected, capital ecologies as the site of exploration for how the veil is represented within public space, one might begin to sense what lurks behind such veiled agendas. Examining the symbolic and representational nature of the Islamic “veil” in its various forms, this project situates the decidedly political contestations of public space at stake in the French ban alongside recent condemnations of multiculturalism as calculated efforts to re-distribute the sensible so as to valorize national identity within increasingly transnational and globalized socio-economic spaces, which collapse exchange values between distinct, yet interwoven, economies of (cultural/material/spiritual) capital. As the discourses on the veil rely upon representational imag(in)ings, it seems fitting to explore the political economy and art of the veil through the phenomenon of street art, which, much like hijab , is a complex assemblage of meaning of sensation mired in representationality and capital exchange. As street artists have taken up hijab in various forms, the movement offers a lens with which to situate critical responses to the veil debate across both spiritual and material economies. Situating this street art both aesthetically and historically, Lewisohn explains, “'Street art' is a sub-genre of graffiti writing and owes much to its predecessor. Though there is a good deal of crossover between the genres, they are distinct and separate in their own right.”(16) Evolving out of the graffiti explosion of the late 1970's and 1980's, street art broke the unspoken rules of the artistic underground by challenging and re-examining one's sensory experience of art in public space by experimenting with both content and form in ways that harken back to the Situationist International, which as a collective challenged one's experience of urban space through various media and experiential phenomena. Again, Lewisohn observes, “It's important to note street art's break with the tradition of the tag, and its focus on visual symbols that embrace a much wider range of media than graffiti writers would use.”(17) From stencils to prints and murals to one-liners, street artists developed a reputation for critical social and political commentary, and while it is certainly the case that not all street art is intentionally political, in challenging the normative “regime of visibility,” as Rancière puts it, of public space, street artists—even if unconsciously—call into question the common sensory experience of the politics underlying the formation of (nationalist) space.(18) Indeed, Rancière refers to the partisan sensory managers as “police,” who ultimately forge “the rules governing the circulation of appearances, of their visibility and audibility, and the proper distribution of bodies therein.”(19) As such, one can sense that street art's relationship with the police is tenous for a variety of reasons. Writing about his own experience as a street artist, Shepard Fairey observes, “With street art, there's no committee deciding whether I can put my work up on the street, there's no censorship, and I have total freedom of expression, and that concept of freedom is expressed just by using the street as a medium.”(20) As Fairey and other street artists demonstrate, the medium, to paraphrase Marshall McLuhan, is the most glaring aspect of street art's message, and even as it now finds itself in galleries and usurped by private collectors, the ethos of the movement remains relavent to politics as it is, first and foremost, concerned with the configuration and experience of space. Just as examining the punishments for breaking the veil ban can map the terrain of French politics, a representational genealogy of street artist's deployment of hijab and female Muslim identity can assist in mining the depths of public space as a site of bio-political control and contestation in light of recent events in France and the rising tide of anti-multiculturalist rhetoric across Europe, even though the Islamic presence there is radically heterogenous. Using the work of Shepard Fairey, Princess Hijab, br1, and Banksy, this paper sets out to answer a number of key questions concerning the deployment of hijab, and female Islamic identity in particular, within street art as a movement now integral to and critical of the economies of exchange underlying global capitalism, which as a force of influence cannot be underestimated as a driver in the resurgence of nationalist biopolitical governmentalities. Although there exists a litany of artists to choose from, the aforementioned quartet of designers integrate hijab into their work in a seminal and critical fashion, and all have been working with the veil in some way prior to the French ban, which grants some additional context to their usage of it as a symbol in regards to the breakdown of multiculturalism across Europe, even if unconsciously. Although each artist depicts various amalgamations of hijab in their respective corpus, they share common tropes that raise significant questions concerning the veil debate, namely: what are the conditions of possibility for hijab to become a marker of Islamic identity within public space? How can we make sense of the representational topologies within street art's utilization of the hijab and female Islamic identity in light of the French ban? How might these aesthetic imag(in)ings simultaneously inhabit and combat normative discourses concerning hijab , multiculturalism, female Islamic identity, and public space? With these considerations as a backdrop, it is first necessary to outline more fully the hijab as a representative marker of female Islamic identity. The (Veiled) Writing on the Wall

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Aesthetic experience has been relativized and marginalized by recent social and cultural theory. As less attention has been paid to understanding the nature of aesthetic experience than mapping the distributed social correlates of tastes, its transformative potential and capacity to animate actors’ imaginations and actions goes unexplored. In this paper we draw upon a large number of in-depth interviews with performing arts audiences around Australia to investigate the language and discourse used to describe aesthetic experiences. In particular, we (...) begin with theorizations of the subject-object nexus within object-relations theory to consider the transformative potential of aesthetic experience. Using these literatures, and extending them to others within sociology of the arts and materiality, our focus is on the way aesthetic experience can fuse human subjects with aesthetic objects. We examine how viewers take an aesthetic object into themselves and in turn project themselves into the aesthetic object by various visual and imaginative techniques. Our theoretical and empirical analysis bears out the constructive and productive capacity of aesthetic experience. (shrink)

Exploratory analysis is an area of increasing interest in the computational linguistics arena. Pragmatically speaking, exploratory analysis may be paraphrased as natural language processing by means of analyzing large corpora of text. Concerning the analysis, appropriate means are statistics, on the one hand, and artificial neural networks, on the other hand. As a challenging application area for exploratory analysis of text corpora we may certainly identify text databases, be it information retrieval or information filtering systems. With this paper we present (...) recent findings of exploratory analysis based on both statistical and neural models applied to legal text corpora. Concerning the artificial neural networks, we rely on a model adhering to the unsupervised learning paradigm. This choice appears naturally when taking into account the specific properties of large text corpora where one is faced with the fact that input-output-mappings as required by supervised learning models cannot be provided beforehand to a satisfying extent. This is due to the fact of the highly changing contents of text archives. In a nutshell, artificial neural networks count for their highly robust behavior regarding the parameters for model optimization. In particular, we found statistical classification techniques much more susceptible to minor parameter variations than unsupervised artificial neural networks. In this paper we describe two different lines of research in exploratory analysis. First, we use the classification methods for concept analysis. The general goal is to uncover different meanings of one and the same natural language concept. A task that, obviously, is of specific importance during the creation of thesauri. As a convenient environment to present the results we selected the legal term of neutrality, which is a perfect representative of a concept having a number of highly divergent meanings. Second, we describe the classification methods in the setting of document classification. The ultimate goal in such an application is to uncover semantic similarities of various text documents in order to increase the efficiency of an information retrieval system. In this sense, document classification has its fixed position in information retrieval research from the very beginning. Nowadays renewed massive interest in document classification may be witnessed due to the appearance of large-scale digital libraries. (shrink)

Spatial, physical, and semantic magnitude dimensions can influence action decisions in human cognitive processing and interact with each other. For example, in the SNARC effect, semantic numerical magnitude facilitates left-hand or right-hand responding dependent on the small or large magnitude of number symbols. SNARC-like interactions of numerical magnitudes with the radial spatial dimension (depth) were postulated from early on. Usually, the SNARC effect in any direction is investigated using fronto-parallel computer monitors for presentation of stimuli. In such 2D setups, (...) however, the metaphorical and literal interpretation of the radial depth axis with seemingly close / far stimuli or responses are not distinct. Hence, it is difficult to draw clear conclusions with respect to the contribution of different spatial mappings to the SNARC effect. In order to disentangle the different mappings in a natural way, we studied parametrical interactions between semantic numerical magnitude, horizontal directional responses, and perceptual distance by means of stereoscopic depth in an immersive virtual reality (VR). Two VR experiments show horizontal SNARC effects across all spatial displacements in traditional latency measures and kinematic response parameters. No indications of a SNARC effect along the depth axis, as it would be predicted by a direct mapping account, were observed, but the results show a non-linear relationship between horizontal SNARC slopes and physical distance. Steepest SNARC slopes were observed for digits presented close to the hands. We conclude that spatial-numerical processing is susceptible to effector-based processes but relatively resilient to task-irrelevant variations of radial-spatial magnitudes. (shrink)

We agree with Nuñez that the Mundurucu do not master the formal propreties of number lines and logarithms, but as the term "intuition" implies, they spontaneously experience a logarithmic mapping of number to space as natural and "feeling right.".

This article turns towards the spatial life of ‘digital infrastructures’, i.e. code, protocols, standards, and data formats that are hidden from view in everyday applications of computational technologies. It does so by drawing on the version control system Git as a case study, and telling the story of its initial development in order to reconstruct the circumstances and technical considerations surrounding its conception. This account engages with computational infrastructures on their own terms by adopting the figure of the ‘stack’ to (...) frame a technically informed analysis, and exploring its implications for a different kind of geographic inquiry. Drawing on topology as employed by Law and Mol, attention is given to the multiplicity of spatialities and temporalities enrolled in digital infrastructures in general, and Git specifically. Along the lines of the case study and by reading it against other literatures, this notion of topology is expanded to include the material performation of fundamentally arbitrary, more-than-human topologies, as well as their nested articulation, translation and negotiation within digital infrastructures. (shrink)

In this paper, we highlight some problems for accounts of disability and enhancement that have not been sufficiently addressed in the literature. The reason, we contend, is that contemporary debates that seek to define, characterise or explain the normative valence of disability and enhancement do not pay sufficient attention to a wide range of cases, and the transition between one state and another. In section one, we provide seven cases that might count as disability or enhancement. We explain why each (...) case might count, and on what basis, and why it is been neglected. Each case is explained as a transition in what we call capacity space. We then argue that no definition of disability or enhancement addresses all of these cases, except for strict welfarist accounts of disability that do not rely on a depiction of any particular capacity. We argue further, however, that this is a serious deficiency of welfarist conceptions of disability. We then address objections to our account. (shrink)

This study examines the complex relation between spatial experience and aesthetic experience. It is argued that spatial experience specifically in the context of everyday spaces makes it possible to experience them aesthetically as well. A wide selection of research ranging from environmental and philosophical aesthetics to architectural theory, psychology, human geography, and other relevant disciplines is employed in order to achieve a more detailed picture of how spatial experience is formed in the first place. This experience is described mainly in (...) terms of phenomenology but is then related to other ways of understanding experiences and their prerequisites. -/- Different notions of space and spatiality and a more comprehensive articulation of the relation of perception to spatial experience, sensory perception, and how senses contribute to spatial experience are in the focus of attention at the beginning of the study. Different experiential layers that can be distinguished within the space which is closest experienced are explored. Interaction with environment is discussed and the notion of preaesthetic is presented to clarify the relation between the two different types of experiences. Following this, the notion of preaesthetic is studied against eminent notions such as aesthetic attitude and aesthetic engagement that show elements that have traditionally been considered to either lead to or define aesthetic experiences. -/- This study shows that the effect that spatial experience has on revealing aesthetic potentialities in everyday environments is far more complicated than has previously been understood. Due to its contingent qualities, spatial experience sometimes leads to "failed" aesthetic experiences even in situations where there is obvious aesthetic potentiality. Even though there are some overlapping qualities in spatial and aesthetic experiences, they cannot thus be equated, as has more or less been done in different branches studying the topics of art and architectural experiences, for example. In the final part of the study, some possible directions for future research are pointed out and the application possibilities of these new developments in aesthetic theory are presented by short case studies, in which a closer look is taken into a chosen set of urban everyday spaces. (shrink)

This textbook is designed for an Introduction to Proofs course organized around the themes of number and space. Concepts are illustrated using both geometric and number examples, while frequent analogies and applications help build intuition and context in the humanities, arts, and sciences. Sophisticated mathematical ideas are introduced early and then revisited several times in a spiral structure, allowing students to progressively develop rigorous thinking. Throughout, the presentation is enlivened with whimsical illustrations, apt quotations, and glimpses of (...) mathematical history and culture. Early chapters integrate an introduction to sets, logic, and beginning proof techniques with a first exposure to more advanced mathematical structures. The middle chapters focus on equivalence relations, functions, and induction. Carefully chosen examples elucidate familiar topics, such as natural and rational numbers and angle measurements, as well as new mathematics, such as modular arithmetic and beginning graph theory. The book concludes with a thorough exploration of the cardinalities of finite and infinite sets and, in two optional chapters, brings all the topics together by constructing the real numbers and other complete metric spaces. Designed to foster the mental flexibility and rigorous thinking needed for advanced mathematics, Introduction to Mathematics suits either a lecture-based or flipped classroom. A year of mathematics, statistics, or computer science at the university level is assumed, but the main prerequisite is the willingness to engage in a new challenge. (shrink)

We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state and \ to \ or \ in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, notably Souriau’s (...) moment map, the Mardsen–Weinstein symplectic reduction, the symplectic “category” introduced by Weinstein, and the conjecture according to which “quantization commutes with reduction”. By using the generalization of this conjecture to the non-zero coadjoint orbits of an abelian Hamiltonian action, we argue that phase invariance in quantum mechanics and gauge invariance have a common geometric underpinning, namely the symplectic reduction formalism. This stance points towards a gauge-theoretical interpretation of Heisenberg indeterminacy principle. We revisit this principle in the light of the difference between the set-theoretic points of a phase space and its category-theoretic symplectic points. (shrink)

A growing number of people are relying on technologies like Google Maps not only to navigate and locate themselves in cartographic space but also to search, discover and evaluate urban places. While the spatial data that underlies such technology frequently appears as a combination of Google-created maps and locational information passively collected from mobile (GPS-enabled) devices, in this article we argue that for such systems to function as both useful tools for exploration for users and sources of revenue, (...) users must actively produce massive quantities of granular spatial data that would otherwise be significantly more difficult and expensive to collect. The production of this qualitative information about places constitutes significant unremunerated affective labour. In this article, we build on the tradition of feminist geographies, especially feminist and critical Geographic Information Systems (GIS), to examine how the labour done by gendered, raced and often classed members of a local community is alienated by Google (i.e. Alphabet, Inc.) to produce commodified spatial data/media in the Local Guides platform. We analyse how Google’s presentation of the platform hails women as care labourers—sharing their thoughts, feelings and knowledge of place for free in the name of supporting and caring for a community, however vaguely it may be constituted. At the same time, we argue that digital labour that produces the Local Guides platform draws from and reproduces specific gendering of spaces. We draw on a case study of a commercial corridor in the US city of Worcester, Massachusetts to show how the dialectic between affective digital labour and urban space has material effects on the production of raced, classed and gendered spaces and places. The article concludes with a call to maintain critical, feminist engagements with these types of platforms in order to further develop forms of digital praxis towards more just cities. (shrink)

In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field${\mathbf {No}}$of surreal numbers was brought to the fore by the first author and employed to provide necessary and sufficient conditions for an ordered field (ordered$K$-vector space) to be isomorphic to an initial subfield ($K$-subspace) of${\mathbf {No}}$, i.e. a subfield ($K$-subspace) of${\mathbf {No}}$that is an initial subtree of${\mathbf {No}}$. In this sequel, analogous results are established forordered exponential fields, making use of a slight generalization of Schmeling’s conception (...) of atransseries field. It is further shown that a wide range of ordered exponential fields are isomorphic to initial exponential subfields of$({\mathbf {No}}, \exp )$. These include all models of$T({\mathbb R}_W, e^x)$, where${\mathbb R}_W$is the reals expanded by aconvergent Weierstrass system W. Of these, those we calltrigonometric-exponential fieldsare given particular attention. It is shown that the exponential functions on the initial trigonometric-exponential subfields of${\mathbf {No}}$, which includes${\mathbf {No}}$itself, extend tocanonicalexponential functions on theirsurcomplexcounterparts. The image of the canonical map of the ordered exponential field${\mathbb T}^{LE}$oflogarithmic-exponentialtransseries into${\mathbf {No}}$is shown to be initial, as are the ordered exponential fields${\mathbb R}((\omega ))^{EL}$and${\mathbb R}\langle \langle \omega \rangle \rangle $. (shrink)

Objective: Tangent Space Mapping using the geometric structure of the covariance matrices is an effective method to recognize multiclass motor imagery. Compared with the traditional CSP method, the Riemann geometric method based on TSM takes into account the nonlinear information contained in the covariance matrix, and can extract more abundant and effective features. Moreover, the method is an unsupervised operation, which can reduce the time of feature extraction. However, EEG features induced by MI mental activities of different subjects (...) are not the same, so selection of subject-specific discriminative EEG frequency components play a vital role in the recognition of multiclass MI. In order to solve the problem, a discriminative and multi-scale filter bank tangent space mapping algorithm is proposed in this article to design the subject-specific Filter Bank so as to effectively recognize multiclass MI tasks. Methods: On the 4-class BCI competition IV-2a dataset, first, a non-parametric method of multivariate analysis of variance based on the sum of squared distances is used to select discriminative frequency bands for a subject; next, a multi-scale FB is generated according to the range of these frequency bands, and then decompose multi-channel EEG of the subject into multiple sub-bands combined with several time windows. Then TSM algorithm is used to estimate Riemannian tangent space features in each sub-band and finally a liner Support Vector Machines is used for classification. Main Results: The analysis results show that the proposed discriminative FB enhances the multi-scale TSM algorithm, improves the classification accuracy and reduces the execution time during training and testing. On the 4-class BCI competition IV-2a dataset, the average session to session classification accuracy of nine subjects reached 77.33 ± 12.3%. When the training time and the test time are similar, the average classification accuracy is 2.56% higher than the latest TSM method based on multi-scale filter bank analysis technology. When the classification accuracy is similar, the training speed is increased by more than three times, and the test speed is increased two times more. Compared with Supervised Fisher Geodesic Minimum Distance to the Mean, another new variant based on Riemann geometry classifier, the average accuracy is 3.36% higher, we also compared with the latest Deep Learning method, and the average accuracy of 10-fold cross validation improved by 2.58%. Conclusion: Research shows that the proposed DMFBTSM algorithm can improve the classification accuracy of MI tasks. Significance: Compared with the MFBTSM algorithm, the algorithm proposed in this article is expected to select frequency bands with good separability for specific subject to improve the classification accuracy of multiclass MI tasks and reduce the feature dimension to reduce training time and testing time. (shrink)

Aboutness has been studied from any number of angles. Brentano made it the defining feature of the mental. Phenomenologists try to pin down the aboutness-features of particular mental states. Materialists sometimes claim to have grounded aboutness in natural regularities. Attempts have even been made, in library science and information theory, to operationalize the notion. But it has played no real role in philosophical semantics. This is surprising; sentences have aboutness-properties if anything does. Aboutness is the first book to examine (...) through a philosophical lens the role of subject matter in meaning. A long-standing tradition sees meaning as truth-conditions, to be specified by listing the scenarios in which a sentence is true. Nothing is said about the principle of selection--about what in a scenario gets it onto the list. Subject matter is the missing link here. A sentence is true because of how matters stand where its subject matter is concerned. Stephen Yablo maintains that this is not just a feature of subject matter, but its essence. One indicates what a sentence is about by mapping out logical space according to its changing ways of being true or false. The notion of content that results--directed content--is brought to bear on a range of philosophical topics, including ontology, verisimilitude, knowledge, loose talk, assertive content, and philosophical methodology. Written by one of today's leading philosophers, Aboutness represents a major advance in semantics and the philosophy of language. (shrink)

I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not require the (...) binary relation reflecting an agent’s comparative judgments to be reflexive, complete or even transitive, and it applies to an absolutely arbitrary collection of gambles, free of structural conditions (e.g., closure, measurability, etc.). Moreover, unlike de Finetti’s criterion of coherence, the qualitative criterion respects the principle of weak dominance, a standard of rational decision making that obliges an agent to reject a gamble that is possibly worse and certainly no better than another gamble available for choice. Despite these weak assumptions, I establish a qualitative analogue of de Finetti’s Fundamental Theorem of Prevision, from which it follows that any coherent system of comparative expectations can be extended to a weakly ordered coherent system of comparative expectations over any collection of gambles containing the initial set of gambles of interest. The extended weakly ordered coherent system of comparative expectations satisfies familiar additivity and scale invariance postulates (i.e., independence) when the extended collection forms a linear space. In the course of these developments, I recast de Finetti’s quantitative account of coherent prevision in the qualitative framework adopted in this article. I show that comparative previsions satisfy qualitative analogues of de Finetti’s famous bookmaking theorem and his Fundamental Theorem of Prevision.The results of this article complement those of another article (Pedersen, Strictly coherent preferences, no holds barred, Manuscript, 2013). I explain how those results entail that any coherent weakly ordered system of comparative expectations over a unital linear space can be represented by an expectation function taking values in a (possibly non-Archimedean) totally ordered field extension of the system of real numbers. The ordered field extension consists of formal power series in a single infinitesimal, a natural and economical representation that provides a relief map tracing numerical non-Archimedean features to qualitative non-Archimedean features. (shrink)

In a recent opinion piece, Denis Duboule has claimed that the increasing shift towards systems biology is driving evolutionary and developmental biology apart, and that a true reunification of these two disciplines within the framework of evolutionary developmental biology may easily take another 100 years. He identifies methodological, epistemological, and social differences as causes for this supposed separation. Our article provides a contrasting view. We argue that Duboule’s prediction is based on a one-sided understanding of systems biology as a science (...) that is only interested in functional, not evolutionary, aspects of biological processes. Instead, we propose a research program for an evolutionary systems biology, which is based on local exploration of the configuration space in evolving developmental systems. We call this approach—which is based on reverse engineering, simulation, and mathematical analysis—the natural history of configuration space. We discuss a number of illustrative examples that demonstrate the past success of local exploration, as opposed to global mapping, in different biological contexts. We argue that this pragmatic mode of inquiry can be extended and applied to the mathematical analysis of the developmental repertoire and evolutionary potential of evolving developmental mechanisms and that evolutionary systems biology so conceived provides a pragmatic epistemological framework for the EvoDevo synthesis. (shrink)