A parasitological view of non-constructible sets

The genetic code, the primary manifestation of life, and, on the other hand, language, the universal endowment of humanity and its momentous leap from genetics to civilization, are the two fundamental stores of information transmissible from the ancestry to the progeny, the molecular succession, which ensures the transfer of hereditary messages from the cells of one generation to the next generation, and the verbal legacy as a necessary prerequisite of cultural tradition. Divergent terminologies direct attention to different pattemings; and finding a logically convincing test, acceptable all around, that can determine whether one such system of terms is superior to its rivals, is often impossible. Yet the slow processes of evolution presumably apply to human societies and their symbolic systems as much as to human bodies, so that when logic cannot decide, survival eventually will

Spontaneous Meta-Arithmetic as the First Step Toward School Algebra

Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the “official” algebraic form of talk. In this paper we take a look at the very beginning of this process. Preliminary analyses of data have shown, unsurprisingly, that while reflecting on arithmetic processes and relations, the uninitiated 7th graders were employing colloquial means, which could not protect them against occasional ambiguities. More unexpectedly, this spontaneous meta-arithmetic, although not supported by any previous algebraic schooling, displayed some algebra-like features, not to be normally found in everyday discourses

An Introduction to Critical Thinking and Symbolic Logic Volume 1: Formal Logic

This textbook has developed over the last few years of teaching introductory symbolic logic and critical thinking courses. It has been truly a pleasure to have benefited from such great students and colleagues over the years. As we have become increasingly frustrated with the costs of traditional logic textbooks (though many of them deserve high praise for their accuracy and depth), the move to open source has become more and more attractive. We're happy to provide it free of charge for educational use. With that being said, there are always improvements to be made here and we would be most grateful for constructive feedback and criticism. We have chosen to write this text in LaTex and have adopted certain conventions with symbols. Certainly many important aspects of critical thinking and logic have been omitted here, including historical developments and key logicians, and for that we apologize. Our goal was to create a textbook that could be provided to students free of charge and still contain some of the more important elements of critical thinking and introductory logic. To that end, an additional benefit of providing this textbook as a Open Education Resource (OER) is that we will be able to provide newer updated versions of this text more frequently, and without any concern about increased charges each time. We are particularly looking forward to expanding our examples, and adding student exercises. We will additionally aim to continually improve the quality and accessibility of our text for students and faculty alike. We have included a bibliography that includes many admirable textbooks, all of which we have benefited from. The interested reader is encouraged to consult these texts for further study and clarification. These texts have been a great inspiration for us and provide features to students that this concise textbook does not. We would both like to thank the philosophy students at numerous schools in the Puget Sound region for their patience and helpful suggestions. In particular, we would like to thank our colleagues at Green River College, who have helped us immensely in numerous different ways. Please feel free to contact us with comments and suggestions. We will strive to correct errors when pointed out, add necessary material, and make other additional and needed changes as they arise. Please check back for the most up to date version

A Non-Parametric Approach to Spatial Causality

The purpose of this paper is to show the capacity of a new non-parametric test based on symbolic entropy and symbolic dynamics to deal with the detection of linear and non-linear spatial causality. The good performance of the new test in detecting spatial causality and causal weighting matrix is notable and gives rise to an expectation that it may form a adequate tool for constructive specification searches.Causality; Spatial Dependence; Spatial Weight Matrices

Education in cartography: what is the status of young people's map-reading skills?

Due to recent technological progress, maps have become more popular than ever before. This is especially true for young people, who interact with these technologies on a daily basis. Therefore, it is essential that these potential map users possess sufficient knowledge and skills to process the content of cartographic products. A user study was conducted during which pupils (aged 11-18years) and geography students (>18years) had to solve a number of cartography questions using topographic maps. The data were analyzed statistically, taking into account a number of potentially influencing factors (user characteristics) on the participants' results: age, gender, youth club membership, knowledge about the area, among others. The results show a rising trend in the pupils' scores with increasing age, which can be explained by education in cartography at school. Geography students perform much better, but no influence of any other user characteristics was detected. For pupils, knowledge about the area and gender might be considered as influencing factors. However, the detected influence of gender depends on the scoring system

Designing Multi-Scale Maps: Lessons Learned from Existing Practices

International audienceMapping applications display multi-scale maps where zooming in and out triggers the display of different maps at different scales. Multi-scale maps strongly augmented the potential uses of maps, compared to the traditional single-scaled paper maps. But the exploration of the multi-scale maps can be cognitively difficult for users because the content of the maps can be very different at different scales. This paper seeks to identify the factors in the design of map content and style that increase or decrease the exploration cognitive load, in order to improve multi-scales map design. We studied sixteen existing examples of multi-scale maps to identify these factors that influence a fluid zooming interaction. Several different analyses were conducted on these sixteen multiscale maps. We first conducted a guided visual exploration of the maps, and a detailed study of the scales of the maps, to identify general trends of good practices (e.g. the WMTS standard that defines zoom levels is widely used) and potential ways of improvement (e.g. a same map is often used at multiple successive zoom levels). Then, we focused on the visual complexity of the multi-scale maps by analyzing how it varies, continuously or not, across scales, using clutter measures, which showed a peak of complexity at zoom level 12 of the WMTS standard. Finally, we studied how buildings and roads are subject to abstraction changes across scales (e.g. at what zoom level individual buildings turn into built-up areas), which can be one of the causes of exploration difficulties. We identified some good practices to reduce the impact of abstraction changes, for instance by mixing different levels of abstraction in the same map.Les applications cartographiques actuelles affichent des cartes multi-échelles, dans lesquelles une interaction de zoom avant ou arrière déclenche l'affichage d'une nouvelle carte à plus grande ou plus petite échelle. Ces cartes multi-échelles permettent des utilisations beaucoup plus vastes et diverses que les traditionnelles cartes topographiques imprimées sur papier. Mais l'exploration interactive de ces cartes peut entrainer une charge cognitive assez lourde car le contenu des cartes peut varier très fortement entre les différentes échelles, et il devient difficile de se repérer. Cet article cherche à identifier les facteurs du design cartographique qui influent sur cette charge cognitive lors d'un changement d'échelle, avec pour objectif à long terme d'améliorer les pratiques de conception de cartes multi-échelles. Nous avons ainsi étudié seize exemples de cartes multi-échelles pour identifier les facteurs permettant d'influer sur la fluidité du zoom. Plusieurs analyses différentes ont été menées sur ces seize cartes. Nous avons d'abord réalisé une analyse visuelle de ces cartes selon divers critères, et une étude détaillée des différentes échelles utilisées, afin d'identifier des tendances (comme l'utilisation massive du standard WMTS), ou des pistes d'amélioration (par exemple, l'utilisation d'une même carte à plusieurs échelles parait sous-optimale). Nous avons ensuite mesuré la variation de complexité visuelle des cartes quand les échelles varient à l'aide de mesures de l'effet de ≪ clutter ≫ ce qui a notamment montré un pic de complexité pour les cartes présentées au niveau de zoom n∘12 du standard WMTS. Enfin, nous avons étudié les changements de niveau d'abstraction spécifiquement sur les thèmes ≪ bâti ≫ et ≪ routes ≫ (par exemple à quelle échelle la représentation des bâtiments individuels est remplacée par une représentation de l'aire urbaine), ce qui a permis de mettre en valeur une cause possible de ces difficultés d'exploration. Des bonnes pratiques ont été identifiées pour une meilleure transition entre les niveaux d'abstraction, notamment en les combinant dans une même carte à une échelle de transition

From quasi-variable thinking to algebraic thinking: A study with grade 4 students

This communication presents a study that is part of a broader teaching experiment research that focus on the development students’ algebraic thinking in one grade 4 class. The particular goal of this communication is to analyze students’ algebraic thinking when they explore numerical equalities with two unknown quantities. Data collection focuses on the students’ work on one task in the classroom, and is based on participant observation and on the analyses of students’ worksheets. We conclude that students are starting to evidence the emergence of algebraic thinking by expressing the generalization of the numerical relationships in different representations.FCT - Fundação para a Ciência e Tecnologi