Topological aggregation, the twin paradox and the No Show paradox

International audienceConsider the framework of topological aggregation introduced by Chichilnisky (1980). We prove that in this framework the Twin Paradox and the No Show Paradox cannot be avoided. Anonymity and unanimity are not needed to obtain these results

Introduction: Creating new worlds out of old texts

Despite initial expectations that globalization would eradicate the need for geographical space and distance, "maps matter" today in ways that were unimaginable a mere two decades ago. Technological advances have brought to the fore an entirely new set of methods for representing and interacting with spatial formations, while the ever-increasing mobility of ideas, capital, and people has created a world in which urban and regional inequalities are being heightened at an accelerating pace. As a result, the ability of any given place to reap the benefits of global socio-technical flows mainly hinges on the forging of connections that can transcend the limits of its material location. In contrast to the traditional "topographic" perspective, the territorial extent of economic and political realms is being increasingly conceived through a "topological" lens: as a set of overlapping reticulations in which the nature and frequency of links among different sites matter more than the physical distances between them. At the same time, a parallel stream of innovation has revolutionized the understanding of space in disciplines such as history, archaeology, classics, and linguistics. Much of this work has been concentrated in the burgeoning field of the "digital humanities", which has been persistently breaking new ground in the conceptualization of past and present places. When seen in the context of globalization-induced dynamics, such developments emphasize the need for developing cartographic approaches that can bring out the inherently networked structure of social space via a lens that is both theoretically integrative and heuristically sharp. We have decided to respond to these analytical and methodological challenges by focusing on ancient Greek literature: a corpus of work that has often been characterized as being free of the constraints imposed by post-Enlightenment cartography, despite setting the foundations of many contemporary map-making methods. In the 12 chapters that follow, we highlight the rich array of representational devices employed by authors from this era, whose narrative depictions of spatial relations defy the logic of images and surfaces that dominates contemporary cartographic thought. There is a particular focus on Herodotus' Histories - a text that is increasingly taken up by classicists as the example of how ancient perceptions of space may have been rather different to the cartographic view that we tend to assume. But this volume also considers the spatial imaginary through the lens of other authors (e.g. Aristotle), genres (e.g. hymns), cultural contexts (e.g. Babylon), and disciplines (e.g. archaeology), with a view to stimulating a broad-based discussion among readers and critics of Herodotus and ancient Greek literature and culture more generally. In fact, many of the disciplinary and conceptual perspectives explored here are at their inception, and have a more general relevance for the wider community of humanities and social science researchers interested in novel mapping techniques. The resulting juxtaposition of more "traditional", philological discussions of space with chapters dedicated to the exploration of new technologies may jar or appear uneven, especially since we have not set out to privilege one method over another. But it is through viewing these different approaches in the round and reading them alongside each other that, we maintain, we can best disrupt customary ways of thinking (and writing) about space and catch a glimpse of new possibilities

Metasemantics and fuzzy mathematics

The present thesis is an inquiry into the metasemantics of natural languages, with a particular focus on the philosophical motivations for countenancing degreed formal frameworks for both psychosemantics and truth-conditional semantics. Chapter 1 sets out to offer a bird's eye view of our overall research project and the key questions that we set out to address. Chapter 2 provides a self-contained overview of the main empirical findings in the cognitive science of concepts and categorisation. This scientific background is offered in light of the fact that most variants of psychologically-informed semantics see our network of concepts as providing the raw materials on which lexical and sentential meanings supervene. Consequently, the metaphysical study of internalistically-construed meanings and the empirical study of our mental categories are overlapping research projects. Chapter 3 closely investigates a selection of species of conceptual semantics, together with reasons for adopting or disavowing them. We note that our ultimate aim is not to defend these perspectives on the study of meaning, but to argue that the project of making them formally precise naturally invites the adoption of degreed mathematical frameworks (e.g. probabilistic or fuzzy). In Chapter 4, we switch to the orthodox framework of truth-conditional semantics, and we present the limitations of a philosophical position that we call "classicism about vagueness". In the process, we come up with an empirical hypothesis for the psychological pull of the inductive soritical premiss and we make an original objection against the epistemicist position, based on computability theory. Chapter 5 makes a different case for the adoption of degreed semantic frameworks, based on their (quasi-)superior treatments of the paradoxes of vagueness. Hence, the adoption of tools that allow for graded membership are well-motivated under both semantic internalism and semantic externalism. At the end of this chapter, we defend an unexplored view of vagueness that we call "practical fuzzicism". Chapter 6, viz. the final chapter, is a metamathematical enquiry into both the fuzzy model-theoretic semantics and the fuzzy Davidsonian semantics for formal languages of type-free truth in which precise truth-predications can be expressed

The dialectic as driver of complexity in urban and social systems

This chapter considers what can be learned from the study of urban systems considered as complex networks of spatial relations that might shed light on the rapid acceleration in human progress after their first invention around 10,000 BC. Using Hillier’s key notion of the objective subject, Karl Marx and Vilfredo Pareto’s distinct notions of the dialectic are reviewed. The contribution of space syntax research to consideration of the objective and subjective experience of urban systems is described, before finally proposing a dynamic bi-directional process in which the dialectic delivers continued progress in human development

The Translocal Event and the Polyrhythmic Diagram

This thesis identifies and analyses the key creative protocols in translocal performance practice, and ends with suggestions for new forms of transversal live and mediated performance practice, informed by theory. It argues that ontologies of emergence in dynamic systems nourish contemporary practice in the digital arts. Feedback in self-organised, recursive systems and organisms elicit change, and change transforms. The arguments trace concepts from chaos and complexity theory to virtual multiplicity, relationality, intuition and individuation (in the work of Bergson, Deleuze, Guattari, Simondon, Massumi, and other process theorists). It then examines the intersection of methodologies in philosophy, science and art and the radical contingencies implicit in the technicity of real-time, collaborative composition. Simultaneous forces or tendencies such as perception/memory, content/ expression and instinct/intellect produce composites (experience, meaning, and intuition- respectively) that affect the sensation of interplay. The translocal event is itself a diagram - an interstice between the forces of the local and the global, between the tendencies of the individual and the collective. The translocal is a point of reference for exploring the distribution of affect, parameters of control and emergent aesthetics. Translocal interplay, enabled by digital technologies and network protocols, is ontogenetic and autopoietic; diagrammatic and synaesthetic; intuitive and transductive. KeyWorx is a software application developed for realtime, distributed, multimodal media processing. As a technological tool created by artists, KeyWorx supports this intuitive type of creative experience: a real-time, translocal “jamming” that transduces the lived experience of a “biogram,” a synaesthetic hinge-dimension. The emerging aesthetics are processual – intuitive, diagrammatic and transversal

Thinking time through difference and repetition: duration, memory, perception and the virtual time of media events

"This dissertation examines two ways by which duration can come to be experienced in analog cinema and digital installations: the interstice and the fold. Whereas the interstice is a material fissure that brings about temporal disruptions between shots/images, the fold is the ontological ground upon which the continuous relations between image and mind arise. These two conceptual figures of time are contradictory, asymmetrical and unequal, giving rise to the question: how might duration be examined from two contrasting and contradictory points of view? If interstices present temporal disjunctions, how might temporal continuities also be a valid point of view? The fold introduces a difference by which a different type of thinking might occur about duration: it introduces a rupture in the orientation of thought about the interstice. Each figure is a different node of thinking of the rhizome, making up the multiplicity by which duration can come under scrutiny in media-objectiles. Each is part of the difference that constitutes the whole. Time is also the method and process by which duration is examined. As method, time is examined through the difference and repetition of the image. Important to the return is the nature of what returns: does the return bring about the same duration, or does it bring difference? Whereas the time-images of cinema give rise to movements between pasts and futures, the digital installations examined give rise to a continual ""now,"" or to presentism. The digital-image as the returning difference to the analog-image presents its ontological difference, producing a different image of time. As process, the lived time of media-events queries the type of duration endured in nonlinear, asynchronous time. Pivoting between pasts and futures, this open and free time of duration gives rise to memories and visions in the experience of media. The media examples discussed are Claire Denis' s film L'lntrus (2004), Susan Collins's installations Glenlandia, Fenlandia and The Spectroscope (2004-7), Andrei Tarkovsky's film Mirror (1975), Sound Research Laboratories's performance in Barcelona (1991), Granular Synthesis's performances Modell 5 (1997) and POL (1998) and Toni Dove's interactive cinema Spectropia (2008).

The Mathematization of Macroeconomics: A Recursive Revolution

Frank Ramsey's classic framing of the dynamics of optimal savings, [51] as one to be solved as a problem in the calculus of variations and Ragnar Frisch's imaginative invoking of a felicitous Wicksellian metaphor to provide the impulse-propagation dichotomy, in a stochastic dynamic framework, for the tackling the problem of business cycles [17], have come to be considered the twin fountainheads of the mathematization of macroeconomics in its dynamic modes - at least in one dominant tradition. The intertemporal optimization framework of a rational agent, viewed as a signal processor, facing the impulses that are propagated through the mechanisms of a real economy, provide the underpinnings of the stochastic dynamic general equilibrium (SDGE) model that has become the benchmark and frontier of current macroeconomics. In this paper, on the 80th anniversary of Ramsey's classic and the 75th anniversary of Frisch's Cassel Festschrift contribution, an attempt is made to characterize the mathematization of macroeconomics in terms of the frontier dominance of recursive methods. There are, of course, other - probably more enlightened - ways to tell this fascinating story. However, although my preferred method would have been to tell it as an evolutionary development, since I am not sure that where we are represents progress, from where we were, say 60 years ago, I have chosen refuge in some Whig fantasies.Macrodynamics, Mathematical Economics, Dynamic Economics, Computational Economics.