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

Searching for a Common Ancestry: Linguistic and Biological Analogies in Comic Art

Sometimes comic book readers randomly encounter images in a comic that closely resemble images in other comics. This artwork could appear to the reader to have been copied, even directly 'lifted' from older or better-known comics. Sometimes, however, it does seem like any similarities have been generated independently, by chance or serendipity. In this note we draw on the work of Umberto Eco, William Lethaby, Walter Benjamin and Carl Jung to describe a multidisciplinary conceptual framework to analyse similar images using a heuristic approach involving two analogy concepts drawn from two different disciplines: linguistics and biology. When the origin of similarity between images is well documented, we propose the linguistic analogy approach can explain the phenomenon of recurrent images. When the similarity between two images appears to be unexplainable, or the result of mere chance, we propose that the concept of biological analogy can be helpful to explain the superficial resemblance of elements that have different origins

Fregean Logical Graphs

In \u201cGedankengef\ufcge\u201d Frege says that any two sentences of the form \u201cA and B\u201d and \u201cB and A\u201d have the same sense. In a 1906 letter to Husserl he says that sentences with the same sense should be represented in a perfect notation by one and the same formula. Frege\u2019s own notation, just like any linear notation for sentential logic, is not perfect in this sense, because in it \u201cA and B\u201d and \u201cB and A\u201d are represented by distinct formulas, as is any pair of logically equivalent compound conditionals. A notation for the sentential calculus that meets Frege\u2019s worries about conjunction, and indeed about any symmetric relation that there may be occasion to symbolize, is Peirce\u2019s Alpha graphs

Never Mind The Iguana, What About The Tortoise? Models in Adaptive Behaviour

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Significant New Records of Amphibians and Reptiles From Georgia, USA

Distributional maps found in Amphibians and Reptiles of Georgia (Jensen et al. 2008), along with subsequent geographical distribution notes published in Herpetological Review, serve as essential references for county-level occurrence data for herpetofauna in Georgia. Collectively, these resources aid biologists by helping to identify distributional gaps for which to target survey efforts. Herein we report newly documented county records for a variety of amphibian and reptile species in Georgia. All records below were verified by David Bechler (VSU), Nikole Castleberry (GMNH), David Laurencio (AUM), Lance McBrayer (GSU), and David Steen (SRSU), and datum used was WGS84. Standard English names follow Crother (2012)