6 research outputs found

    Towards a classification of continuity and on the emergence of generality

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    This dissertation has for its primary task the investigation, articulation, and comparison of a variety of concepts of continuity, as developed throughout the history of philosophy and a part of mathematics. It also motivates and aims to better understand some of the conceptual and historical connections between characterizations of the continuous, on the one hand, and ideas and commitments about what makes for generality (and universality), on the other. Many thinkers of the past have acknowledged the need for advanced science and philosophy to pass through the “labyrinth of the continuum” and to develop a sufficiently rich and precise model or description of the continuous; but it has been far less widely appreciated how the resulting description informs our ideas and commitments regarding how (and whether) things become general (or how we think about universality). The introduction provides some motivation for the project and gives some overview of the chapters. The first two chapters are devoted to Aristotle, as Aristotle’s Physics is arguably the foundational book on continuity. The first two chapters show that Aristotle\u27s efforts to understand and formulate a rich and demanding concept of the continuous reached across many of his investigations; in particular, these two chapters aim to better situate certain structural similarities and conceptual overlaps between his Posterior Analytics and his Physics, further revealing connections between the structure of demonstration or proof (the subject of logic and the sciences) and the structure of bodies in motion (the subject of physics and study of nature). This chapter also contributes to the larger narrative about continuity, where Aristotle emerges as one of the more articulate and influential early proponents of an account that aligns continuity with closeness or relations of nearness. Chapter 3 is devoted to Duns Scotus and Nicolas Oresme, and more generally, to the Medieval debate surrounding the “latitude of forms” or the “intension and remission of forms,” in which concerted efforts were made to re-focus attention onto the type of continuous motions mostly ignored by the tradition that followed in the wake of Aristotelian physics. In this context, the traditional appropriation of Aristotle’s thoughts on unity, contrariety, genera, forms, quantity and quality, and continuity is challenged in a number of important ways, reclaiming some of the largely overlooked insights of Aristotle into the intimate connections between continua and genera. By realizing certain of Scotus’s ideas concerning the intension and remission of qualities, Oresme initiates a radical transformation in the concept of continuity, and this chapter argues that Oresme’s efforts are best understood as an early attempt at freeing the concept of continuity from its ancient connection to closeness. Chapters 4 and 5 are devoted to unpacking and re-interpreting Spinoza’s powerful theory of what makes for the ‘oneness’ of a body in general and how ‘ones’ can compose to form ever more composite ‘ones’ (all the way up to Nature as a whole). Much of Spinoza reads like an elaboration on Oresme’s new model of continuity; however, the legacy of the Cartesian emphasis on local motion makes it difficult for Spinoza to give up on closeness altogether. Chapter 4 is dedicated to a closer look at some subtleties and arguments surrounding Descartes’ definition of local motion and ‘one body’, and Chapter 5 builds on this to develop Spinoza’s ideas about how the concept of ‘one body’ scales, in which context a number of far-reaching connections between continuity and generality are also unpacked. Chapter 6 leaves the realm of philosophy and is dedicated to the contributions to the continuitygenerality connection from one field of contemporary mathematics: sheaf theory (and, more generally, category theory). The aim of this chapter is to present something like a “tour” of the main philosophical contributions made by the idea of a sheaf to the specification of the concept of continuity (with particular regard for its connections to universality). The concluding chapter steps back and discusses a number of distinct characterizations of continuity in more abstract and synthetic terms, while touching on some of the corresponding representations of generality to which each such model gives rise. This chapter ends with a brief discussion of some of the arguments that have been deployed in the past to claim that continuity (or discreteness) is “better.

    Towards a GIS-based Multiscale Visibility Assessment Method for Solar Urban Planning

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    Urban areas are facing a growing deployment of solar photovoltaic and thermal tech-nologies on building envelopes, both on roofs and on façades, essential for the realization of the Swiss Energy Strategy 2050. This process often occurs regardless of the desirable archi-tectural integration quality in a given urban context, which depends on socio-cultural sensitivi-ty and on the visibility of the solar modules from the public space. Visibility and visual impact are recurrent decisional factors in spatial planning processes, with practical implications in-cluding touristic and real estate promotion, outdoor human comfort, way finding, public feeling of security and advertisement. In this thesis, the definition of visibility under a geometrical, physical and psycho-physiological perspective is explored, several quantitative indicators being described and test-ed. The objective is to provide a scale-dependent methodology to assess the visibility of build-ing envelope surfaces exposed to solar radiation, which could host solar modules, in urban areas. A visibility index is determined for inclusion as a variable in a multi criteria method, cover-ing areas from the strategic broad territorial scale to the district level, including neighborhoods and clusters of buildings. Accomplished research includes the estimation of public visual inter-est on the basis of crowd-sourced photographic databases, complementing geometry-based parameters such as cumulative viewsheds and solid angles. At each scale, the visibility index is systematically overlapped on an urban sensitivity layer issued from land use and on a spatial representation of the solar energy generation potential, at an appropriate level of detail. Results indicate that stakeholders can reasonably expect to harvest a serious amount of solar energy by means of building integrated solar systems without crucially affecting public perception. In the study area located in the city of Geneva (Switzerland), more than 50 m2 / building of non-visible envelope surface receiving sufficient solar radiation for an economically viable solar re-furbishment is available over half of the buildings. Solar thermal collectors or PV panels in-stalled on scarcely visible surfaces, mainly situated in courtyards, far from the streets or in deep urban canyons, could cover about 10% of the annual heating demand or alternatively, the same share of electricity needs on a district basis. At the same time, plenty of highly visible areas remain available for high-end solar deployments, which could also serve pilot and demonstration purposes

    Temporality in Designed Landscapes: the theory and its practice in works of some major landscape designers 1945-2005

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    This study analyses temporality in designed landscapes. The meaning of temporality is explored, taking us beyond common conceptualisations of time. Temporality, invariably poorly understood in a landscape context, and previously acknowledged as being important, but with only limited explicit discourse, is examined through the lens of a fresh theoretical articulation of temporality pertaining to designed landscapes. A phenomenological approach becomes imperative; and is employed in probing the work, through writing, of several eminent landscape designers between 1945 and 2005. These designers’ works are analysed through the texts, and with support from images of the works, for characteristics of temporality. Textual material offered a broad range of verbal articulation of these characteristics. Some designed landscapes are described with explicit verbalisation of their temporal qualities: others require analysis to discover their temporal qualities from text that is only mildly suggestive. The heterochronous characteristics of temporality expressed in these designers’ works are named and ordered within five themes: tempo, process, duration, imagination and layers. Theoretical understanding of temporality builds with identification of its applications in designed landscapes

    Conditional toggle mappings: principles and applications

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    International audienceWe study a class of mathematical morphology filters to operate conditionally according to a set of pixels marked by a binary mask. The main contribution of this paper is to provide a general framework for several applications including edge enhancement and image denoising, when it is affected by salt-and-pepper noise. We achieve this goal by revisiting shock filters based on erosions and dilations and extending their definition to take into account the prior definition of a mask of pixels that should not be altered. New definitions for conditional erosions and dilations leading to the concept of conditional toggle mapping. We also investigate algebraic properties as well as the convergence of the associate shock filter. Experiments show how the selection of appropriate methods to generate the masks lead to either edge enhancement or salt-and-pepper denoising. A quantitative evaluation of the results demonstrates the effectiveness of the proposed methods. Additionally, we analyse the application of conditional toggle mapping in remote sensing as pre-filtering for hierarchical segmentation

    Virtual Mathematics: the logic of difference

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    Of all twentieth century philosophers, it is Gilles Deleuze whose work agitates most forcefully for a worldview privileging becoming over being, difference over sameness; the world as a complex, open set of multiplicities. Nevertheless, Deleuze remains singular in enlisting mathematical resources to underpin and inform such a position, refusing the hackneyed opposition between ‘static’ mathematical logic versus ‘dynamic’ physical world. This is an international collection of work commissioned from foremost philosophers, mathematicians and philosophers of science, to address the wide range of problematics and influences in this most important strand of Deleuze’s thinking. Contributors are Charles Alunni, Alain Badiou, Gilles Châtelet, Manuel DeLanda, Simon Duffy, Robin Durie, Aden Evens, Arkady Plotnitsky, Jean-Michel Salanskis, Daniel Smith and David Webb

    CWI Self-evaluation 1999-2004

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