Essential Incompleteness of Arithmetic Verified by Coq

A constructive proof of the Goedel-Rosser incompleteness theorem has been completed using the Coq proof assistant. Some theory of classical first-order logic over an arbitrary language is formalized. A development of primitive recursive functions is given, and all primitive recursive functions are proved to be representable in a weak axiom system. Formulas and proofs are encoded as natural numbers, and functions operating on these codes are proved to be primitive recursive. The weak axiom system is proved to be essentially incomplete. In particular, Peano arithmetic is proved to be consistent in Coq's type theory and therefore is incomplete.Comment: This paper is part of the proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics (TPHOLs 2005). For the associated Coq source files see the TeX sources, or see <http://r6.ca/Goedel20050512.tar.gz

An Investigation into the Effect of Hydrodynamic Cavitation on Diesel using Optical Extinction

A conventional diesel and paraffinic-rich model diesel fuel were subjected to sustained cavitation in a custom-built high-pressure recirculation flow rig. Changes to the spectral extinction coefficient at 405 nm were measured using a simple optical arrangement. The spectral extinction coefficient at 405 nm for the conventional diesel sample was observed to increase to a maximum value and then asymptotically decrease to a steady-state value, while that for the paraffinic-rich model diesel was observed to progressively decrease. It is suggested that this is caused by the sonochemical pyrolysis of mono-aromatics to form primary soot-like carbonaceous particles, which then coagulate to form larger particles, which are then trapped by the filter, leading to a steady-state spectral absorbance

Spaces of visibility in the smart city: flagship urban spaces and the smart urban imaginary

This is the author accepted manuscript. The final version is available from SAGE Publications via the DOI in this record.Smart urbanism is a currently popular and widespread way of conceptualising the future city. At the same time, the smart city is critiqued by several scholars as difficult to define, and as being almost invisible to the naked eye. The paper explores two urban spaces through which the smart city is rendered visible, in two UK cities that are prominent sites for smart urban experimentation and development. Bristol’s Data Dome, and Glasgow’s Operations Centre are analysed in light of their iconic nature. The paper develops a conceptual understanding of these flagship spaces of the actually existing smart cities through three interrelated conceptual lenses. Firstly, they are understood as a videological type of Leibniz’s concept of the windowless monad. Secondly, they are conceptualised as examples of banal and serialised architecture. Thirdly, these spaces and their attendant buildings are understood as totemic assemblages that point to newly emergent forms of elite urban power.This work was supported by the Economic and Social Research Council (grant number ES/L015978/2), ‘Smart eco-cities for a green economy: a comparative study of Europe and China (SMART-ECO).

Critical research on eco-cities? A walk through the Sino-Singapore Tianjin Eco-City, China

This article uses the narrative tool of a walk through Tianjin Eco-City, China, as an entry point in raising and discussing key questions in contemporary eco-city research. Eco-city projects are becoming increasingly prevalent in policy and political-economic discourses in a variety of locations as new urban spaces where blueprints for low carbon economies can be trialled. In light of this, the article highlights the key necessity of, firstly, considering scale when analyzing eco-city 'futures'. Secondly, the article argues for the need to interrogate eco-cities' definitions, as well as evaluation, performance and monitoring frameworks, as this will aid in critical analyses of the marketing, presentation and actually built urban environments in eco-city projects. Thirdly, the question of internal social resilience and the emergence of communities within newly-built eco-cities needs to be assessed: this is of crucial importance in light of the exclusive, gated nature of several flagship eco-city projects under construction at the time of writing. Lastly, the article argues that research on eco-city projects needs to consider not only the high-tech, new urban environments materialized as eco-cities, but also the production and reproduction of large, often transient populations of low-paid workers who build eco-cities and who form what the article calls the 'new urban poor', forming 'workers' cities' on the edges of flagship 'sustainable' urban projects worldwide. </p

Future cities: moving from technical to human needs

This is the author accepted manuscript. The final version is available from Palgrave Macmillan via the DOI in this record.The article argues for a foregrounding of human needs at the heart of urban societal futures. While economic, technical and environmental imperatives are understandably the focus of policymaking and governance arrangements at national and supra-national scales, defining and targeting priorities in the ‘ordinary’ city is key. The argument is that it is now time to place basic human needs (as enshrined both in international agreements and in the more prosaic conditions of specific cities) at the centre of thinking and planning for future cities. The piece therefore proposes that plans for urban futures start from an elaboration of contextually sensitive as well as internationally negotiated needs rather than from macro-scale and potentially ephemeral visions of glittering technological future metropoles.This work was supported by the Economic and Social Research Council [grant number ES/L015978/1 and ES/N014138/2

Smart Cities: Towards a New Citizenship Regime? A Discourse Analysis of the British Smart City Standard

Growing practice interest in smart cities has led to calls for a less technology-oriented and more citizen-centric approach. In response, this articles investigates the citizenship mode promulgated by the smart city standard of the British Standards Institution. The analysis uses the concept of citizenship regime and a mixture of quantitative and qualitative methods to discern key discursive frames defining the smart city and the particular citizenship dimensions brought into play. The results confirm an explicit citizenship rationale guiding the smart city (standard), although this displays some substantive shortcomings and contradictions. The article concludes with recommendations for both further theory and practice development