From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

Exertional heat stroke in a marathon runner with extensive healed deep burns: a case report

Exertional heat illness typically occurs over hours in younger athletic patients or military recruits who exercise at elevated temperatures for a sufficient period of time to cause the rate of heat production to exceed the capacity of the body to dissipate heat. Since the physiological response to exercise includes cutaneous vasodilation and sweating, any limitation of such a response can cause rapid hyperthermia and thus heat stroke. One such condition is extensive burns healed by cicatrisation of the skin where the scar and grafted skin surface do not have functional sweat glands and are unable to lose heat in response to high temperatures. The authors report one unique case of a female marathon runner with exertional heat stroke who had recovered from deep second and third degree burns over approximately 50% of her body a few years ago

The "Artificial Mathematician" Objection: Exploring the (Im)possibility of Automating Mathematical Understanding

Reuben Hersh confided to us that, about forty years ago, the late Paul Cohen predicted to him that at some unspecified point in the future, mathematicians would be replaced by computers. Rather than focus on computers replacing mathematicians, however, our aim is to consider the (im)possibility of human mathematicians being joined by “artificial mathematicians” in the proving practice—not just as a method of inquiry but as a fellow inquirer

Approaching Proof in the Classroom Through the Logic of Inquiry

The paper analyses a basic gap, highlighted by most of the literature concerning the teaching of proofs, namely, the distance between students' argumentative and proving processes. The analysis is developed from both epistemological and cognitive standpoints: it critiques the Toulmin model of reasoning and introduces a new model, the Logic of Inquiry of Hintikka, more suitable for bridging this gap. An example of didactical activity within Dynamic Geometry Environments is sketched in order to present a concrete illustration of this approach and to show the pedagogical effectiveness of the model

Humic Substances Enhance Chlorothalonil Phototransformation via Photoreduction and Energy Transfer

ABSTRACT: The photodegradation of chlorothalonil, a polychlorinated aromatic fungicide widely used in agriculture, was investigated under ultraviolet–visible irradiation in the presence and absence of different humic substances that significantly enhance the chlorothalonil phototransformation. On the basis of a kinetic model, an analytical study, the effect of scavengers, the chlorothalonil phosphorescence measurement, and varying irradiation conditions, it was possible to demonstrate that this accelerating effect is due to their capacity to reduce the chlorothalonil triplet state via H-donor reaction and to energy transfer from the triplet humic to ground state chlorothalonil. Energy transfer occurs at wavelengths below 450 nm and accounts for up to 30% of the reaction in deoxygenated medium upon irradiation with polychromatic light (300–450 nm). This process is more important with Elliott humic and fulvic acids and with humic acids extracted from natural carbonaceous material than with Nordic NOM and Pahokee peat humic acids. The obtained results are of high relevance to understanding the processes involved in chlorothalonil phototransformation and the photoreactivity of humic substances. Chlorothalonil is one of the rare molecules shown to react by energy transfer from excited humic substances

How to think about informal proofs

This document is the Accepted Manuscript version of the following article: Brendan Larvor, ‘How to think about informal proofs’, Synthese, Vol. 187(2): 715-730, first published online 9 September 2011. The final publication is available at Springer via doi:10.1007/s11229-011-0007-5It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the fieldPeer reviewedFinal Accepted Versio

Current Advances in Internet of Underground Things

The latest developments in Internet of Underground Things are covered in this chapter. First, the IOUT Architecture is discussed followed by the explanation of the challenges being faced in this paradigm. Moreover, a comprehensive coverage of the different IOUT components is presented that includes communications, sensing, and system integration with the cloud. An in-depth coverage of the applications of the IOUT in various disciplines is also surveyed. These applications include areas such as decision agriculture, pipeline monitoring, border control, and oil wells