Mathematical practice, crowdsourcing, and social machines

The highest level of mathematics has traditionally been seen as a solitary endeavour, to produce a proof for review and acceptance by research peers. Mathematics is now at a remarkable inflexion point, with new technology radically extending the power and limits of individuals. Crowdsourcing pulls together diverse experts to solve problems; symbolic computation tackles huge routine calculations; and computers check proofs too long and complicated for humans to comprehend. Mathematical practice is an emerging interdisciplinary field which draws on philosophy and social science to understand how mathematics is produced. Online mathematical activity provides a novel and rich source of data for empirical investigation of mathematical practice - for example the community question answering system {\it mathoverflow} contains around 40,000 mathematical conversations, and {\it polymath} collaborations provide transcripts of the process of discovering proofs. Our preliminary investigations have demonstrated the importance of "soft" aspects such as analogy and creativity, alongside deduction and proof, in the production of mathematics, and have given us new ways to think about the roles of people and machines in creating new mathematical knowledge. We discuss further investigation of these resources and what it might reveal. Crowdsourced mathematical activity is an example of a "social machine", a new paradigm, identified by Berners-Lee, for viewing a combination of people and computers as a single problem-solving entity, and the subject of major international research endeavours. We outline a future research agenda for mathematics social machines, a combination of people, computers, and mathematical archives to create and apply mathematics, with the potential to change the way people do mathematics, and to transform the reach, pace, and impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent Computer Mathematics, CICM 2013, July 2013 Bath, U

Derivations of the Born Rule

The Born rule, a cornerstone of quantum theory usually taken as a postulate, continues to attract numerous attempts for its derivation. A critical review of these derivations, from early attempts to very recent results, is presented. It is argued that the Born rule cannot be derived from the other postulates of quantum theory without some additional assumptions

Características del liderazgo pedagógico del directivo docente de la I.E. de Jesús del municipio de Concordia

Esta investigación abordó el liderazgo pedagógico, específicamente el liderazgo directivo, su papel dentro del proceso pedagógico de la institución educativa está justificado por la relevancia que tiene en la gestión curricular, entre otras funciones, pues permite que las instituciones educativas - I.E marchen adecuadamente y alcancen mayores logros para todos los estudiantes. El objetivo consistió en identificar las características del liderazgo pedagógico del directivo docente de la I.E de Jesús del municipio de Concordia. Para esto se consideró una investigación enmarcada dentro del enfoque cualitativo de tipo descriptivo, el método fue estudio de caso. Los instrumentos que se utilizaron fueron, la entrevista, el diario de campo y el grupo focal. Con base en los resultados obtenidos en las entrevistas se destacan aspectos importantes de la comunicación y el liderazgo, vinculados a la gestión administrativa de la I.E. La investigación muestra la importancia que tiene el liderazgo pedagógico del directivo docente como elemento clave en el desarrollo y funcionamiento pedagógico-curricular de la I.E.This research addressed pedagogical leadership, such as one that focuses on the directive role, specifically on his role in the educational process on the educative institution; the relevance it's justified for this process for function properly on the institutions to and achieve greater achievements for all students. The objective was to identify the pedagogical leadership from the educative director of the Educative Institution of Jesus from the Concordia municipality. For this, was considered an investigation framed within the qualitative approach of descriptive type, the method was a study case. The instruments used were interview, field diaries and focus group. Based on the interview results obtained, important aspects of communication and leadership were highlighted, linked to the development processes on the educative institution. The research shows the importance on a pedagogical leadership of the teaching director as a key element within the institution.Magíster en EducaciónMaestrí

Uniting model theory and the universalist tradition of logic: Carnap's early axiomatics

We shift attention from the development of model theory for demarcated languages to the development of this theory for fragments of a language. Although it is often assumed that model theory for demarcated languages is not compatible with a universalist conception of logic, no one has denied that model theory for fragments of a language can be compatible with that conception. It thus seems unwarranted to ignore the universalist tradition in the search for the origins and development of model theory. This point is illustrated by Carnap's early semantics and model theory, which he developed within a type theoretical framework and which stand out both for their universalistic treatment and for certain idiosyncratic technicalities by which the construction is supported. One special property is that individuals are context relative in Carnap's system. This leads to a model theory in which the model domains are more flexible than has been suggested in the literature. © 2014 Springer Science+Business Media Dordrecht

Why Innovative Design Requires New Scientific Foundations for Manageable Identities of Systems

International audienceWhen can we state that things are identical or different? This is a key issue in structuring humans' representations and making plausible predictions with potentially major implications, as demonstrated in high-tech industries such as those studied here. The identity of things is not a natural and absolute relationship just waiting to be stated once and for all. Rather, it is an artificial and short-lived one, relative to available knowledge or experience, and should be memorized as such using well-suited semantics. Standard rationality enables designers to manage consistent identities according to a fixed state of understanding only. If that state is updated to reflect current changes of things or environments coupled with innovation, they must adopt a relevant non standard rationality based on new scientific foundations