The Axioms of Wisdom

Following a suggestion of Brouwer an axiomatic definition of wisdom is proposed.

Perspex machine VIII: axioms of transreal arithmetic

Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometry with the Turing Machine. Here we axiomatise the algebraic structure of transreal arithmetic so that it provides a total arithmetic on any appropriate set of numbers. This opens up the possibility of specifying a version of floating-point arithmetic that does not have any arithmetical exceptions and in which every number is a first-class citizen. We find that literal numbers in the axioms are distinct. In other words, the axiomatisation does not require special axioms to force non-triviality. It follows that transreal arithmetic must be defined on a set of numbers that contains{-8,-1,0,1,8,&pphi;} as a proper subset. We note that the axioms have been shown to be consistent by machine proof.

Exploring the impact of social axioms on firm reputation: a stakeholder perspective

This study proposes a model of how deeply held beliefs, known as ‘social axioms, moderate the interaction between reputation, its causes and consequences with stakeholders. It contributes to the stakeholder relational field of reputation theory by explaining why the same organizational stimuli lead to different individual stakeholder responses. The study provides a shift in reputation research from organizational-level stimuli as the root causes of stakeholder responses to exploring the interaction between individual beliefs and organizational stimuli in determining reputational consequences. Building on a conceptual model that incorporates product/service quality and social responsibility as key reputational dimensions, the authors test empirically for moderating influences, in the form of social axioms, between reputation-related antecedents and consequences, using component-based structural equation modelling (n = 204). In several model paths, significant differences are found between responses of individuals identified as either high or low on social cynicism, fate control and religiosity. The results suggest that stakeholder responses to reputation-related stimuli can be systematically predicted as a function of the interactions between the deeply held beliefs of individuals and these stimuli. The authors offer recommendations on how strategic reputation management can be approached within and across stakeholder groups at a time when firms grapple with effective management of diverse stakeholder expectations.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Geometry without axioms; or the first book of Euclid's elements. With alterations and familiar notes; and an intercalary book in which the straight line and plane are derived from properties of the sphere ... To which is added an appendix ...

Mode of access: Internet.

Researching the 'reception' of indigenous affairs in Australia

The Reporting and Reception of Indigenous Issues in the Australian Media was a three year project financed by the Australian government through its Australian Research Council Large Grants Scheme and run by Professor John Hartley (of Murdoch and then Edith Cowan University, Western Australia). The purpose of the research was to map the ways in which indigeneity was constructed and circulated in Australia's mediasphere. The analysis of the 'reporting' element of the project was almost straightforward: a mixture of content analysis of a large number of items in the media, and detailed textual analysis of a smaller number of key texts. The discoveries were interesting - that when analysis approaches the media as a whole, rather than focussing exclusively on news or serious drama genres, then representation of indigeneity is not nearly as homogenous as has previously been assumed. And if researchers do not explicitly set out to uncover racism in every text, it is by no means guaranteed they will find it1. The question of how to approach the 'reception' of these issues - and particularly reception by indigenous Australians - proved to be a far more challenging one. In attempting to research this area, Hartley and I (working as a research assistant on the project) often found ourselves hampered by the axioms that underlie much media research. Traditionally, the 'reception' of media by indigenous people in Australia has been researched in ethnographic ways. This research repeatedly discovers that indigenous people in Australia are powerless in the face of new forms of media. Indigenous populations are represented as victims of aggressive and powerful intrusions: ‘What happens when a remote community is suddenly inundated by broadcast TV?’; ‘Overnight they will go from having no radio and television to being bombarded by three TV channels’; ‘The influence of film in an isolated, traditionally oriented Aboriginal community’2. This language of ‘influence’, ‘bombarded’, and ‘inundated’, presents metaphors not just of war but of a war being lost. It tells of an unequal struggle, of a more powerful force impinging upon a weaker one. What else could be the relationship of an Aboriginal audience to something which is ‘bombarding’ them? Or by which they are ‘inundated’? This attitude might best be summed up by the title of an article by Elihu Katz: ‘Can authentic cultures survive new media?’3. In such writing, there is little sense that what is being addressed might be seen as a series of discursive encounters, negotiations and acts of meaning-making in which indigenous people — communities and audiences —might be productive. Certainly, the points of concern in this type of writing are important. The question of what happens when a new communication medium is summarily introduced to a culture is certainly an important one. But the language used to describe this interaction is a misleading one. And it is noticeable that such writing is fascinated with the relationship of only traditionally-oriented Aboriginal communities to the media of mass communication.

Tutorial facilitation in the humanities based on the tenets of Carl Rogers

This article introduces a model for group facilitation in the humanities based on Carl Rogers’s model for group psychotherapy. Certain aspects of Rogers’s reflective learning strategies are re-appraised and principles, specific only to psychotherapy, are introduced. Five of Rogers’s axioms are applied to the tutorial discussion model: a non-directive approach, climate-setting, facilitation, reflective listening and positive regard. The model, which has been trialed in tutorials at The University of Queensland, encourages self-direction, active learning and critical thinking.

Non-monotonic Reasoning and the Reversibility of Belief Change

Traditional approaches to nonmonotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some of these difficulties. Here we show that RPMs are not adequate to handle iterated belief change. Specifically, we show that RPMs do not always allow for the reversibility of belief change. This result indicates the need for numerical strengths of belief.

Producing the NAPLAN Machine: A Schizoanalytic Cartography

Everything revolves around desiring-machines and the production of desire… Schizoanalysis merely asks what are the machinic, social and technical indices on a socius that open to desiring-machines (Deleuze & Guattari, 1983, pp. 380-381). Achievement tests like NAPLAN are fairly recent, yet common, education policy initiatives in much of the Western world. They intersect with, use and change pre-existing logics of education, teaching and learning. There has been much written about the form and function of these tests, the ‘stakes’ involved and the effects of their practice. This paper adopts a different “angle of vision” to ask what ‘opens’ education to these regimes of testing(Roy, 2008)? This paper builds on previous analyses of NAPLAN as a modulating machine, or a machine characterised by the increased intensity of connections and couplings. One affect can be “an existential disquiet” as “disciplinary subjects attempt to force coherence onto a disintegrating narrative of self”(Thompson & Cook, 2012, p. 576). Desire operates at all levels of the education assemblage, however our argument is that achievement testing manifests desire as ‘lack’; seen in the desire for improved results, the desire for increased control, the desire for freedom, the desire for acceptance to name a few. For Deleuze and Guattari desire is irreducible to lack, instead desire is productive. As a productive assemblage, education machines operationalise and produce through desire; “Desire is a machine, and the object of the desire is another machine connected to it”(Deleuze & Guattari, 1983, p. 26). This intersection is complexified by the strata at which they occur, the molar and molecular connections and flows they make possible. Our argument is that when attention is paid to the macro and micro connections, the machines built and disassembled as a result of high-stakes testing, a map is constructed that outlines possibilities, desires and blockages within the education assemblage. This schizoanalytic cartography suggests a new analysis of these ‘axioms��� of testing and accountability. It follows the flows and disruptions made possible as different or altered connections are made and as new machines are brought online. Thinking of education machinically requires recognising that “every machine functions as a break in the flow in relation to the machine to which it is connected, but at the same time is also a flow itself, or the production of flow, in relation to the machine connected to it”(Deleuze & Guattari, 1983, p. 37). Through its potential to map desire, desire-production and the production of desire within those assemblages that have come to dominate our understanding of what is possible, Deleuze and Guattari’s method of schizoanalysis provides a provocative lens for grappling with the question of what one can do, and what lines of flight are possible.

Respite & Recoery at Al Wakra

International Design Competition for Qatar Psychiatric Hospital. The scheme for the Al Wakra Respite and Recovery Centre delivers on an all-in attitude toward evidence-based design. It sets new benchmarks in so many ways: the way it allows excellent separation between patient cohorts without unnecessary or visible restrictions; the way it allows sharing of most of the clinical kit and spaces; the way services reticulation and facilities management takes place without compromising security and safety; the ways It abandons the institutional axioms that are still so ubiquitous elsewhere, so it can appear as the friendly, welcoming and wholesome; the way it allows incredible flexibility to allow changes or flexion on the fly; the way it has such ‘good bones’ for more structural changes as the future unfolds. But most importantly, the scheme will be exemplary in the way the building itself plays a role in promoting the recovery and mental well-being of its residents. Like no other, the Centre will rise to the challenges of supporting and inspiring an exemplary mental health service and promote the well-being of the patients. The 160 bed scheme allows for 43,000m2 of landscape, packed with wholesome things to do and experience. The Aspire zone even has stables and a falconry, both to celebrate the love that Qatari people have for horses and birds.

WISENOM. A formal organic chemical nomenclature system

A formal chemical nomenclature system WISENOM based on a context-free grammar and graph coding is described. The system is unique, unambiguous, easily pronounceable, encodable, and decodable for organic compounds. Being a formal system, every name is provable as a theorem or derivable as a terminal sentence by using the basic axioms and rewrite rules. The syntax in Backus-Naur form, examples of name derivations, and the corresponding derivation trees are provided. Encoding procedures to convert connectivity tables to WISENOM, parsing, and decoding are described.

A knowledge-based clustering scheme

In this paper the notion of conceptual cohesiveness is precised and used to group objects semantically, based on a knowledge structure called ‘cohesion forest’. A set of axioms is proposed which should be satisfied to make the generated clusters meaningful.

A comparison between conceptual clustering and conventional clustering

Clustering is a process of partitioning a given set of patterns into meaningful groups. The clustering process can be viewed as consisting of the following three phases: (i) feature selection phase, (ii) classification phase, and (iii) description generation phase. Conventional clustering algorithms implicitly use knowledge about the clustering environment to a large extent in the feature selection phase. This reduces the need for the environmental knowledge in the remaining two phases, permitting the usage of simple numerical measure of similarity in the classification phase. Conceptual clustering algorithms proposed by Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] and Stepp and Michalski [Artif. Intell., pp. 43–69 (1986)] make use of the knowledge about the clustering environment in the form of a set of predefined concepts to compute the conceptual cohesiveness during the classification phase. Michalski and Stepp [IEEE Trans. PAMI, PAMI-5, 396–410 (1983)] have argued that the results obtained with the conceptual clustering algorithms are superior to conventional methods of numerical classification. However, this claim was not supported by the experimental results obtained by Dale [IEEE Trans. PAMI, PAMI-7, 241–244 (1985)]. In this paper a theoretical framework, based on an intuitively appealing set of axioms, is developed to characterize the equivalence between the conceptual clustering and conventional clustering. In other words, it is shown that any classification obtained using conceptual clustering can also be obtained using conventional clustering and vice versa.