Continuous Truth II: Reflections

Abstract. In the late 1960s, Dana Scott first showed how the Stone-Tarski topological interpretation of Heyting’s calculus could be extended to model intuitionistic analysis; in particular Brouwer’s continuity prin-ciple. In the early ’80s we and others outlined a general treatment of non-constructive objects, using sheaf models—constructions from topos theory—to model not only Brouwer’s non-classical conclusions, but also his creation of “new mathematical entities”. These categorical models are intimately related to, but more general than Scott’s topological model. The primary goal of this paper is to consider the question of iterated extensions. Can we derive new insights by repeating the second act? In Continuous Truth I, presented at Logic Colloquium ’82 in Florence, we showed that general principles of continuity, local choice and local com-pactness hold in the gros topos of sheaves over the category of separable locales equipped with the open cover topology. We touched on the question of iteration. Here we develop a more gen-eral analysis of iterated categorical extensions, that leads to a reflection schema for statements of predicative analysis. We also take the opportunity to revisit some aspects of both Continuous Truth I and Formal Spaces (Fourman & Grayson 1982), and correct two long-standing errors therein

Homebuyers and the representation of spatial markets by information providers

Purpose – The purpose of this paper is to renew a research agenda considering the impact that information providers’ processes are having on the housing market; in particular to develop a research agenda around the role of the Internet in shaping households’ perceptions of the spatial nature of housing markets. Design/methodology/approach – This paper reviews the existing literature. It uses preliminary extensive survey findings about the role of the Internet in housing search to hypothesise ways in which households may be affected by this transition. Findings – Not applicable – other than evidence for the growth in the importance of the Internet in shaping households’ housing search. Practical implications – First, the academy needs to readdress the theory surrounding information acquisition and use insights from economics, sociology and psychology to understand these processes. Second, local authorities and academics should analyse the impact of Internet use on housing market boundaries (and the profound subsequent impact on policy traction). Third, estate agents should reconsider the role of the Internet in shaping housing markets and provide a critical response to the large property search engines. Originality/value – This paper reviews the literature and explores the necessity of a renewed interest in research on the role of information sources in framing and constraining housing search behaviour

Dynamics of an Unbounded Interface Between Ordered Phases

We investigate the evolution of a single unbounded interface between ordered phases in two-dimensional Ising ferromagnets that are endowed with single-spin-flip zero-temperature Glauber dynamics. We examine specifically the cases where the interface initially has either one or two corners. In both examples, the interface evolves to a limiting self-similar form. We apply the continuum time-dependent Ginzburg-Landau equation and a microscopic approach to calculate the interface shape. For the single corner system, we also discuss a correspondence between the interface and the Young tableau that represents the partition of the integers.Comment: 9 pages, 11 figures, 2-column revtex4 format. V2: references added and discussion section expanded slightly. Final version for PRE. V3: A few small additional editorial change

Materializing digital collecting: an extended view of digital materiality

If digital objects are abundant and ubiquitous, why should consumers pay for, much less collect them? The qualities of digital code present numerous challenges for collecting, yet digital collecting can and does occur. We explore the role of companies in constructing digital consumption objects that encourage and support collecting behaviours, identifying material configuration techniques that materialise these objects as elusive and authentic. Such techniques, we argue, may facilitate those pleasures of collecting otherwise absent in the digital realm. We extend theories of collecting by highlighting the role of objects and the companies that construct them in materialising digital collecting. More broadly, we extend theories of digital materiality by highlighting processes of digital material configuration that occur in the pre-objectification phase of materialisation, acknowledging the role of marketing and design in shaping the qualities exhibited by digital consumption objects and consequently related consumption behaviours and experiences

Microflares and the Statistics of X-ray Flares

This review surveys the statistics of solar X-ray flares, emphasising the new views that RHESSI has given us of the weaker events (the microflares). The new data reveal that these microflares strongly resemble more energetic events in most respects; they occur solely within active regions and exhibit high-temperature/nonthermal emissions in approximately the same proportion as major events. We discuss the distributions of flare parameters (e.g., peak flux) and how these parameters correlate, for instance via the Neupert effect. We also highlight the systematic biases involved in intercomparing data representing many decades of event magnitude. The intermittency of the flare/microflare occurrence, both in space and in time, argues that these discrete events do not explain general coronal heating, either in active regions or in the quiet Sun.Comment: To be published in Space Science Reviews (2011

An Observational Overview of Solar Flares

We present an overview of solar flares and associated phenomena, drawing upon a wide range of observational data primarily from the RHESSI era. Following an introductory discussion and overview of the status of observational capabilities, the article is split into topical sections which deal with different areas of flare phenomena (footpoints and ribbons, coronal sources, relationship to coronal mass ejections) and their interconnections. We also discuss flare soft X-ray spectroscopy and the energetics of the process. The emphasis is to describe the observations from multiple points of view, while bearing in mind the models that link them to each other and to theory. The present theoretical and observational understanding of solar flares is far from complete, so we conclude with a brief discussion of models, and a list of missing but important observations.Comment: This is an article for a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011

Some remarks on extending bar induction

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