Why is space 3-dimensional? The fi rst answer to this question, entirely based on Physics, was given by Ehrenfest, in 1917, who showed that the stability requirement for n-dimensional two-body planetary system very strongly constrains space dimensionality, favouring 3-d. This kind of approach will be generically called "stability postulate" throughout this paper and was shown by Tangherlini, in 1963, to be still valid in the framework of general relativity as well as for quantum mechanical hydrogen atom, giving the same constraint (...) for space{dimensionality. In the present work, before criticizing this methodology, a brief discussion has been introduced, aimed at stressing and clarifying some general physical aspects of the problem of how to determine the number of space dimensions. Then, the epistemological consequences of Ehrenfest's methodology are critically reviewed. An alternative procedure to get at the proper number of dimensions, in which the stability postulate - and the implicit singularities in three-dimensional physics - are not an essential part of the argument, is proposed. In this way, the main epistemological problems contained in Ehrenfest's original idea are avoided. The alternative methodology proposed in this paper is realized by obtaining and discussing the n-dimensional quantum theory as expressed in Planck's law, de Broglie relation and the Heisenberg uncertainty relation. As a consequence, it is possible to propose an experiment, based on thermal neutron di raction by crystals, to directly measure space dimensionality. Finally the distinguished role of Maxwell's electromagnetic theory in the determination of space dimensionality is stressed. (shrink)

In this article it is shown that a careful analysis of Kant 's Gedanken von der wahren Schätzung der lebendigen Kräfte und Beurtheilung der Beweise leads to a conclusion that does not match the usually accepted interpretation of Kant 's reasoning in 1747, according to which the young Kant supposedly establishes a relationship between the tridimensionality of space and Newton's law of gravitation. Indeed, it is argued that this text does not yield a satisfactory explanation of space dimensionality, and actually (...) restricts itself to justifying the tridimensionality of extension. (shrink)

Metascientific criteria used for explaining or constraining physical space dimensionality and their historical relationship to prevailing causal systems are discussed. The important contributions by Aristotle, Kant and Ehrenfest to the dimensionality of space problem are considered and shown to be grounded on different causal explanations: causa materialis for Aristotle, causa efficiens for young Kant and an ingenious combination of causa efficiens and causa formalis for Ehrenfest. The prominent and growing rôle played by causa formalis in modern physical approaches to this (...) problem is emphasized. (shrink)

Within the general discussion of space and its dimensionality, Aristotle's position is of the greatest relevance, as one will have the opportunity to argue and discuss in this article.

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the influences of three-dimensionality in the solar system stability and the origin of life on Earth are discussed. New constraints on space dimensionality and on its invariance in very large spatial and temporal scales are also stressed.

The aim of this workshop was to ask potential end-users of the citizens’ information pack on legal and ethical issues around ICTs the following questions: What is your knowledge of the EU’s General Data Protection Regulation, and what actions have you taken in response to these regulations? What challenges are you experiencing in ensuring the protection and security of your project data, and compliance with the GDPR, within existing data management processes/systems? What information/tools/resources do you need to overcome these challenges? (...) What are the best formats/channels for receiving, sharing and acting upon this information? What is the most appropriate structure/format for the citizens’ information pack? (shrink)

ICTs, personal data, digital rights, the GDPR, data privacy, online security… these terms, and the concepts behind them, are increasingly common in our lives. Some of us may be familiar with them, but others are less aware of the growing role of ICTs and data in our lives - and the potential risks this creates. These risks are even more pronounced for vulnerable groups in society. People can be vulnerable in different, often overlapping, ways, which place them at a disadvantage (...) to the majority of citizens; Table 3 in this guide presents some of the many forms and causes of vulnerability. As a result, vulnerable people need greater support to navigate the digital world, and to ensure that they are able to exercise their rights. This guide explains where such support can be found, and also answers the following questions: - What are the main ethical and legal issues around ICTs for vulnerable citizens? - Who is vulnerable in Europe? - How do issues around ICTs affect vulnerable people in particular? This guide is a resource for members of vulnerable groups, people who work with vulnerable groups, and citizens more broadly. It is also useful for data controllers1 who collect data about vulnerable citizens. While focused on citizens in Europe, it may be of interest to people in other parts of the world. It forms part of the Citizens’ Information Pack produced by the PANELFIT project, and is available in English, French, German, Italian and Spanish. You are welcome to translate this guide into other languages. Please send us a link to online versions in other languages, so that we can add them to the project website. (shrink)

Space is one of the most fundamental concepts over which scientific knowledge has been constructed. But it is also true that space concepts extrapolate by far the scientific domain, and permeate many other branches of human knowledge. Those are fascinating aspects that could di per se justify the compilation of a long bibliography. Another one is the passion for books. My interest in some physical, historical and philosophical problems concerning the concept of space in Physics, and its properties, can be (...) traced back to the early 1980. Since that time, I have being studying, with several collaborators, the influence of space dimensionality in different physical phenomena, like the Casimir Effect, neutron diffraction, Cosmic Microwave Background Radiation and the stability of Schrödinger’s and Dirac’s hydrogen atom in arbitrary number of dimensions, as well as epistemological aspects of the works of Kant, Ehrenfest an others on this particular subject. Meanwhile, I gave lectures about the History of the Concepts of Space in Physics at the Centro Brasileiro de Pesquisas Físicas (CBPF), at the Program of History of Sciences, Technics and Epistemology of the Federal University of Rio the Janeiro (UFRJ) and also at the Physics Institute of the State University of Rio de Janeiro (UERJ). As a consequence of both this interest and my love for books, I continuously bought books on space for my personal library which contains now quite one half of all the books quoted here. In 1996, Roberto Moreira and I published the Sources for the History of Space concepts in Physics: From 1845 to 1995 in the series Notas de Física of the CBPF (NF # 084/96), which is still available online. This was a first initiative to share our bibliography on space. At that time, it contained 1075 references, including 414 books entirely devoted to space, 380 articles in periodical journals and proceedings and 281 miscellaneous citations. After fifteen years, I decided to focus my attention here to collect what in my opinion are the 601 essential books which could be useful for anyone interested on learning about space. An important restriction is imposed here by language: only texts written in English, French, German, Italian, Spanish, Portuguese and Latin were considered. References are given in chronological order covering the period between 1739 and 2010. For each year, the books are listed in alphabetical order of authors’ name. An onomastic index is included at the end of the book. -/- Francisco Caruso Rio de Janeiro, October 2011 . (shrink)