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.

Procura-se identificar algumas das origens históricas do negacionismo, dando ênfase aos seus aspectos filosóficos. Apresenta-se uma revisão de alguns conceitos basilares como os de verdade e episteme, destacando o quanto foram importantes na História das Ideias e na Filosofia Ocidental. Analisa-se, ainda que de forma resumida, o aspecto social da questão, por meio da compreensão da mudança do sujeito e suas relações de trabalho ao longo da História, principalmente no período pós-industrial. Por fim, discute-se a práxis negacionista, destacando suas principais (...) influências filosóficas e consequências. (shrink)

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.

Name der Zeitschrift: Kant-Studien Jahrgang: 106 Heft: 4 Seiten: 547-560.

L'idea di relazionare la dimensionalità dello spazio ad una legge fisica, contenuta nel primo scritto di Kant "Pensieri sulla veridica estima delle forze vive", svela un modo di guardare i rapporti tra Fisica e Matematica così nuovo ed originale che potè essere sviluppato e compreso nella sua plenitudine soltanto nel secolo XX. Ci riferiamo qui ala prospettiva aperta da Ehrenfest nel suo "In what way does it become manifest in the fundamental laws of physics that space has three dimensions?". In (...) questo saggio si cerca di comprendere alcune delle radici fisiche, filosofiche e teologiche dell’approccio di Kant a questo problema, e la sua inserzione nel dibattito delle idee che sostengono la concezione meccanicista del Mondo. In primo luogo, si sottolinea che da una lettura attenta del suo Gedanken von der wahren Schätzung der lebendigen Kräfte si può concludere che - al contrario di quanto viene normalmente creduto - Kant non riuscì a dimostrare la sua congettura che la tridimensionalità dello spazio possa essere fondata sulla legge di gravitazione di Newton, secondo la quale la forza tra due corpi va come l'inverso del quadrato della distanza che li separa; in realtà, egli si limitò a giustificare la tridimensionalità della estensione. Dopo aver considerato la distinzione fra estensione e spazio, si fa notare che la catena logica della congettura del giovane Kant, presuppone la forza come concetto basilare, intrinseco alle sostanze. È mediante questa forza che si stabiliscono le relazioni tra le sostanze, le quali, a sua volta, creano l'ordine su cui viene basato il concetto di spazio. Si deve badare che la coerenza del suo argomento richiede, in ultima analisi, concepire la percezione, cioè, l'interazione fra le sostanze e l'anima, come risultato della medesima forza di lunga portata. Inoltre, si dimostra che l'argomento di Kant non poteva essere costrutto su una intelaiatura puramente newtoniana nel 1747. Infatti, egli costruì sua dimostrazione a partire da una concezione del mondo basata sul legato di Cartesio (soprattutto l'idea di um ordine cosmico) e Leibniz (l'esistenza di una forza che precede l'estensione e l'idea di spazio relativo) alla quale sovrappone, in modo ibrido, la legge di gravitazione di Newton. Si argomenta che questa scelta fu fortemente influenzata da alcune idee teologiche del Giovane Kant che divergono da quelle di Cartesio, Newton e Leibniz. Fu questo carattere ibrido del suo approccio che permise a Kant di trattare la questione della dimensionalità dello spazio come un problema di fisica, ma, che, allo stesso tempo, a causa delle sue limitazioni intrinsiche, portò Kant a provare appena la tridimensionalità della estensione. (shrink)

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)

A solução do problema educacional brasileiro passa, necessariamente, por duas etapas, que se resumem essencialmente na busca da revalorização do Saber. Independente de qualquer política ministerial, este é o compromisso maior que deveria brotar espontaneamente de toda a comunidade acadêmico-científica. As duas etapas a que nos referimos pouco dependem de verbas e são: a conscientização da responsabilidade e do papel de liderança que cabe a esta comunidade na busca desta solução; a sua capacidade de promover, nas Universidades, uma ampla e (...) profunda reestruturação dos currículos de Licenciatura. (shrink)

Recent scholarship has recognized some thematic connections related to onto-cosmological issues between two late Platonic dialogues, such as Philebus and Timaeus, and has tried to explain them in different ways. The aim of this paper is to contribute to such a debate by analysing an ancient exegesis of Timaeus 35a1-b4, that of Plutarch of Chaeronea, which made use of the ontological sections of the Philebus in his treatise on the cosmogony of the Timaeus. More specifically, this analysis will show that (...) the notions of ‘limit’ and ‘unlimitedness’ played a decisive role in the shaping of the “essence” of the world-soul according to Plutarch. (shrink)