The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Gregory J. Chaitin - One of the best experts on this subject based on the ideXlab platform.
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irreducible complexity in Pure Mathematics
From ontos verlag: Publications of the Austrian Ludwig Wittgenstein Society - New Series, 2013Co-Authors: Gregory J. Chaitin, Gregory J. ChaitinAbstract:I'll review the history of metaMathematics, including the ideas of David Hilbert, Kurt Goedel, Alan Turing, and Emile Borel, leading to my own work on incompleteness, randomness, algorithmic information and complexity, that can be traced back to Leibniz's 1686 Discours de metaphysique.
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the halting probability omega irreducible complexity in Pure Mathematics
Milan Journal of Mathematics, 2007Co-Authors: Gregory J. ChaitinAbstract:Some Godel centenary reflections on whether incompleteness is really serious, and whether Mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information.
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The Halting Probability Omega: Irreducible Complexity in Pure Mathematics
arXiv: History and Overview, 2006Co-Authors: Gregory J. ChaitinAbstract:Some Goedel centenary reflections on whether incompleteness is really serious, and whether Mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given Monday, October 30, 2006, at the University of Milan.]
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Irreducible Complexity in Pure Mathematics
arXiv: History and Overview, 2004Co-Authors: Gregory J. ChaitinAbstract:By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to show that there can never be a "theory of everything" for all of Mathematics.
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lecture undecidability randomness in Pure Mathematics
2002Co-Authors: Gregory J. ChaitinAbstract:I have shown that God not only plays dice in physics, but even in Pure Mathematics, in elementary number theory, in arithmetic! My work is a fundamental extension of the work of Godel and Turing on undecidability in Pure Mathematics. I show that not only does undecidability occur, but in fact sometimes there is complete randomness, and mathematical truth becomes a perfect coin toss.
Lisa Mcgrath - One of the best experts on this subject based on the ideXlab platform.
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Open-access writing: An investigation into the online drafting and revision of a research article in Pure Mathematics
English for Specific Purposes, 2016Co-Authors: Lisa McgrathAbstract:ESP research has provided an account of research articles (RAs) across disciplines using both text-analytical methods and ethnographically-oriented approaches. This study explores what additional insights are gained into the genre from the study of a collaboratively produced RA in Pure Mathematics, negotiated via an open-access research blog. The data consists of 659 thread comments posted by blog participants as they engage with the research and writing up process. Facets of research-based writing that preoccupy the blog participants are revealed, as well as how decisions pertaining to genre and dissemination outlets are made. In addition, blog posts point to how the RA is adjusted to cater for the more diverse readership that open-access knowledge dissemination may entail. The findings provide support for results of existing genre analyses of RAs in Pure Mathematics, and offer new insights into writing for publication practices in the discipline. Potential pedagogical applications of the findings are proposed.
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The Theoretical Research Article as a Reflection of Disciplinary Practices: The Case of Pure Mathematics.
Applied Linguistics, 2013Co-Authors: Maria Kuteeva, Lisa McgrathAbstract:Recent years have seen an interest in the generic structure of empirical research articles across a variety of disciplines. However, significantly less attention has been given to theoretical articles. This study aims to begin to address this imbalance by presenting the results of an investigation into the organizational and rhetorical structure of theoretical Pure Mathematics research articles. The data set combines a close analysis of 22 peer-reviewed articles and semi-structured interviews with their authors. While there is considerable variation in terms of the major section headings and content, the results reveal an overall structure that differs from a typical empirical research article. We argue that this alternative structure is produced by the dual argumentation—mathematical and meta-mathematical—which runs throughout the text. Moreover, triangulation with the interview data indicates that the structural patterns of the theoretical Pure Mathematics research article can be viewed as a reflection of the research practices and epistemology of the discipline.
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Stance and engagement in Pure Mathematics research articles: Linking discourse features to disciplinary practices
English for Specific Purposes, 2012Co-Authors: Lisa Mcgrath, Maria KuteevaAbstract:Recent ESP research into academic writing has shown how writers convey their stance and interact with readers across different disciplines. However, little research has been carried out into the disciplinary writing practices of the Pure Mathematics academic community from an ESP genre analysis perspective. This study begins to address this gap by applying Hyland’s stance and engagement framework to Pure Mathematics research articles. The data consists of a corpus of 25 articles collected from five authors and semi-structured interviews with the same authors. The results of the corpus analysis reveal a low number of hedges and attitude markers compared to other hard and soft disciplines, but higher than expected shared knowledge and reader references. Furthermore, triangulation with interview data suggests that the epistemology and research practices of the discourse community can account for these frequency patterns, and that writers are conscious of the need to situate oneself within the norms of the discourse community by adhering to disciplinary writing conventions. The study also confirms that Hyland’s framework can be usefully applied to Pure Mathematics research articles, although the boundaries between categories in the taxonomy are fuzzier than a stance/engagement dichotomy might suggest.
Maria Kuteeva - One of the best experts on this subject based on the ideXlab platform.
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The Theoretical Research Article as a Reflection of Disciplinary Practices: The Case of Pure Mathematics.
Applied Linguistics, 2013Co-Authors: Maria Kuteeva, Lisa McgrathAbstract:Recent years have seen an interest in the generic structure of empirical research articles across a variety of disciplines. However, significantly less attention has been given to theoretical articles. This study aims to begin to address this imbalance by presenting the results of an investigation into the organizational and rhetorical structure of theoretical Pure Mathematics research articles. The data set combines a close analysis of 22 peer-reviewed articles and semi-structured interviews with their authors. While there is considerable variation in terms of the major section headings and content, the results reveal an overall structure that differs from a typical empirical research article. We argue that this alternative structure is produced by the dual argumentation—mathematical and meta-mathematical—which runs throughout the text. Moreover, triangulation with the interview data indicates that the structural patterns of the theoretical Pure Mathematics research article can be viewed as a reflection of the research practices and epistemology of the discipline.
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Stance and engagement in Pure Mathematics research articles: Linking discourse features to disciplinary practices
English for Specific Purposes, 2012Co-Authors: Lisa Mcgrath, Maria KuteevaAbstract:Recent ESP research into academic writing has shown how writers convey their stance and interact with readers across different disciplines. However, little research has been carried out into the disciplinary writing practices of the Pure Mathematics academic community from an ESP genre analysis perspective. This study begins to address this gap by applying Hyland’s stance and engagement framework to Pure Mathematics research articles. The data consists of a corpus of 25 articles collected from five authors and semi-structured interviews with the same authors. The results of the corpus analysis reveal a low number of hedges and attitude markers compared to other hard and soft disciplines, but higher than expected shared knowledge and reader references. Furthermore, triangulation with interview data suggests that the epistemology and research practices of the discourse community can account for these frequency patterns, and that writers are conscious of the need to situate oneself within the norms of the discourse community by adhering to disciplinary writing conventions. The study also confirms that Hyland’s framework can be usefully applied to Pure Mathematics research articles, although the boundaries between categories in the taxonomy are fuzzier than a stance/engagement dichotomy might suggest.
Lishan Liu - One of the best experts on this subject based on the ideXlab platform.
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Pure Mathematics | RESEARCH ARTICLE Properties and inequalities for the (h , h 2 )- and (h 1 , h 2 , m)-GA-convex functions
2016Co-Authors: Lishan LiuAbstract:1 * and Feng Qi 2,3 Abstract: In the paper, the authors introduce definitions of the (h 1 ,h 2 )-GA-convex functions and the (h 1 ,h 2 ,m)-GA-convex functions, discuss some properties of these kinds of functions, establish some integral inequalities for these functions, and ap- ply these inequalities to construct several more inequalities. Subjects: Advanced Mathematics; Analysis-Mathematics; Mathematical Analysis; Mathematics & Statistics; Pure Mathematics; Real Functions; Science
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Pure Mathematics | RESEARCH ARTICLE Attribute topologies based similarity
2016Co-Authors: T. N. Alharthi, M. A. Elsafty, Lishan LiuAbstract:2 * Abstract: In this work, we generated more topologies based on similarity relation for an information system and we found lower and upper approximations. This paper discussed two approaches for determining accuracy with Yao's method and Pawlak's method of qualitative data. From both ideas, it is seen that due to the un- certainty and vagueness of qualitative data, we get many topologies on one or two attributes. We determined the accuracies by the new method; this method showed the difference between one or two attributes. This method is clarified by application.
Robert Tavernor - One of the best experts on this subject based on the ideXlab platform.
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Measure, metre, irony: reuniting Pure Mathematics with architecture
Architectural Research Quarterly, 2002Co-Authors: Robert TavernorAbstract:The human body once provided the fundamental measurements by which to gauge human creations – but the metric system offers ‘mere number without concrete being’. A synthesis is needed.Measure: mens (L – mind), mensurare = measuring/measureMetre: metron (Gk), metrum (L – measuring rod), mètre (Fr) = metreIrony: eironeia (Gk – simulated ignorance), eiron – dissembler and simulator of power = ironyNo civilization has existed without measures, and each has described measures in a manner specific to its needs. To exist at all, measures must be practical and useful, and most have their origins in everyday experience. At some stage in the development of a civilized society measures will be refined, standardized and regulated and represented physically. To endure and be accepted by hundreds, thousands, even millions of people – across great civilizations and around the globe – measures must reflect and extend the authority of leaders. Measure is therefore a statement and record of the changing balance of power and independence. It is an expression of culture.
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measure metre irony reuniting Pure Mathematics with architecture
Arq-architectural Research Quarterly, 2002Co-Authors: Robert TavernorAbstract:Measures in Western society were once mostly derived from the notion of the ideal male body, its qualities and proportions as well as its dimensions. These were represented in classical sculptures and buildings, artefacts that have influenced art and architecture into modern times. However, during the European Enlightenment the body as measuring standard was criticised. Scientists and politicians became intent on providing a system of rational, universal measures independent of the human body, and the metre rod was formulated. This paper argues that measure needs to be recognised as more than an abstract calibrated length of inert material: it is a deliberate consequence of human thought and simulator of power. The metric system has almost universal authority but it is no more rational than the idealised body that once dominated the ancient world. Indeed, I will argue that it might be better understood as the measure of all irony.
