The purpose of this thesis is to study the effects of hyperbolic transformations on the cubic that is determined by locus of centroids of the equilateral triangles in H² whose base coincides with the line y=0, and whose common vertex is at the origin. The derivation of the formulas within this work are based on the Poincaré disk model of H², where H² is understood to mean the hyperbolic plane. The thesis explores the properties of both the untransformed cubic (the original locus of centroids) and the transformed cubic (the original cubic taken under a linear fractional transformation).

The main purpose of this thesis is to explore the conditions of the existence and properties of the Euler line of a triangle in the hyperbolic plane. Poincaré's conformal disk model and Hermitian matrices were used in the analysis.ʹ

In this thesis the author presents a history of non-convergent series which, in the past, played an important role in mathematics. Euler's formula, Stirling's series and Poincare's theory are examined to show the development of asymptotic series, a subdivision of divergent series.

<div>Compelled by converging research in the natural sciences suggesting the stratigraphic nature of time, I argue for a temporal approach to the venerable problem of synthesis in evolutionary theory. Geneticist and pioneer of the Modern Synthesis (MS), Theodosius Dobzhansky (1900-1975), constructed one of the most powerful synthesis arguments in the history of evolutionary biology in the classic “Nothing in Biology Makes Sense Except in the Light of Evolution” (1973). I argue that nothing in evolution makes sense except in the light of time, such that the problem of evolutionary time plays a powerful role in making sense of the conceptual architecture of the Extended Evolutionary Synthesis (EES). The EES offers a strong alternative to the temporal and causal idealizations operating at the hardened core of the MS. I create the philosophical concept of stratigraphic time to strengthen connections between the four problem agendas or “causal catchalls” structuring the new synthesis: (1) developmental plasticity, (2) developmental bias, (3) inclusive inheritance, and (4) niche construction (Laland 2015 et al.). The dissertation is driven by two critical arguments (Chapters 1-3) concerning the subordination of time to process, and two constructive arguments (Chapters 4 and 5) concerning the nature of evolutionary time, which together attest to the conceptual strength of a temporal approach to the multiplicity of evolutionary problems pursued by the EES, and especially the connections between them. </div><div><br></div><div>Chapter 1, “Embracing the Problematic Structure of the Extended Evolutionary Synthesis,” explicates and evaluates the core assumptions of the EES in contrast with those of the MS, which has served as the dominant conceptual framework for evolutionary science and theory since the early twentieth century. Chapter 2, “Deep Time: The Forgotten Frontier,” critically argues that evolutionary time has been subordinated to evolutionary process, that the problem of evolutionary time must be revived after its eclipse at the origin of evolutionary theory, especially due to Darwin’s unnecessarily strict commitments to gradualism, adaptationism, and to the preeminence of natural selection. Chapter 3, “The Chronometric Subordination of Time to Movement in Philosophy, Science, and Society,” critically argues that the subordination of evolutionary time to process is primed by the chronometrically facilitated subordination of time to movement, what mathematician, physicist, and philosopher of science Henri Poincaré (1854-1912) called an unconscious opportunism in philosophical and scientific thought. The constructive arguments unfolded in Chapter 4, “The Continuous Variation of Evolutionary Contingency,” and Chapter 5, “Stratigraphic Time: The Synthesis of Deep and Developmental Rhythms,” attempt to respect causal thinking while conceptualizing evolutionary processes not according to causal laws but rather according to passive and active temporal syntheses (or modes of repetition), effectively delimiting causal thinking to a provisional conceptualization. Stratigraphic time enables conceptualization of the multiplicity of evolutionary process, driven by a new concept of evolutionary contingency. I argue that the roles of chance and causation in the EES are strengthened by concepts of difference and repetition, akin to the conceptual roles played by arrows and cycles of time in the formation of geological and evolutionary thought. These critical and constructive arguments are guided by Gilles Deleuze’s philosophy of time, which he conceptualizes under the rubric of repetition. The three passive and active temporal syntheses, or modes of repetition, Deleuze creates to think the nature of repetition provide conceptual tools for evolutionary synthesis through stratigraphic time. </div><div><br></div>

La somme romanesque que représente À la recherche du temps perdu se constitue au prix d’une « recherche » qui est à prendre au pied de la lettre, et qui instaure le sujet connaissant en savant-chercheur face à son objet de savoir. Proust fait en effet du « savoir » la condition même du talent, et fait entreprendre à son héros une exploration qui se présente en priorité comme étant une quête de savoirs. Ce travail se situe dans le sillage de l’épistémocritique qui étudie l’inscription dans le texte littéraire des savoirs en général, tout en insistant sur les savoirs qui relèvent de la science. Notre but est de dégager la posture épistémique qui caractérise le narrateur de la Recherche face aux divers savoirs qu’il récolte au cours de ses observations. Le parcours cognitif du narrateur est examiné suivant les quatre grandes étapes de sa recherche, que nous redéfinissons en termes de paradigmes : le paradigme de l’Exploration, qui définit une « épistémologie de l’observateur » ; le paradigme de la Communication, qui définit une « épistémologie de l’homme social » et une « épistémologie de l’homme moderne » ; le paradigme de l’Introspection, qui prépare à l’élaboration d’une « épistémologie du personnage intérieur » ; et enfin, le paradigme de la Vocation, qui rassemble les réponses trouvées par le narrateur à la plupart des questionnements qui auront jalonné son parcours cognitif. Ce dernier paradigme se présente sous la forme d’une « épistémologie de la création », d’une « épistémologie du réel » et d’une « épistémologie du hasard ». Car en dépit d’une démarche qui apparaît soumise aux médiations culturelles, la recherche du héros proustien se présente comme une « pensée de l’imprévisible » : fortement déterminée par la recherche cognitive du protagoniste, elle demeure pourtant irréductible à cette seule recherche. Nous dégageons, pour terminer, le statut réservé à la science et aux savoirs positifs en regard de la découverte de la vocation, mais aussi par rapport à l’élaboration d’une théorie de la création littéraire : ces deux grands domaines du savoir sont-ils considérés par Proust comme inconciliables avec une priorité évidente de l’un sur l’autre ou, au contraire, participent-ils tous deux d’une manière égale à la connaissance et à la création artistique ? / The comprehensive novelistic survey presented by À la recherche du temps perdu is worth a research to be taken literally and establishes the knowledgeable subject as a scholar-researcher against his object of knowledge. Proust makes of “knowledge” the condition of talent and engages his hero in an exploration that presents itself as a priority for being a quest for knowledge. The present essay follows in the wake of Epistemocritique, a discipline that studies the inscription of knowledge in the literary text in general, with a specific focus on knowledge related to science. Our aim is to bring forward the epistemic position that characterizes the narrator of À la recherche du temps perdu as he acquires various forms of knowledge in the course of his observations. The narrator’s cognitive path is examined with regard to the four main pillars of his quest, which we redefine in terms of paradigms: the paradigm of exploration, which defines an “epistemology of the observer”; the paradigm of communication, which defines an “epistemology of the social being”; the paradigm of Introspection which prepares for the elaboration of an “epistemology of the internal character”; and finally, the paradigm of vocation, which combines the answers to most of the questions that have marked the narrator’s cognitive path. This last paradigm presents itself as an “epistemology of creation”, an “epistemology of reality”, and an “epistemology of chance”. For, in spite of an approach that appears to be subject to cultural interventions, the quest by Proust’s main character appears as a thought of the unpredictable. Although strongly determined by the cognitive quest of the protagonist, it nevertheless remains irreducible to this sole quest. In conclusion, we emphasize the status reserved to science and to positive knowledge from the perspective of the discovery of vocation, but also in view of the elaboration of a theory of literary creation: does Proust consider these two areas of knowledge as irreconcilable, with one having an evident priority over the other, or, to the contrary, does he considers them as equal factors in knowledge and artistic creation?

Esse estudo apresenta a proposta de uma reconstrução metodológica da obra de Florian W. Znaniecki, intelectual polonês, com a finalidade de evitar a ocorrência de ecletismo metodológico em estudos de sociologia comparada. Nesse sentido, argumentamos em favor da forte presença dos fundamentos metodológicos propostos por Henri Poincaré na obra de Znaniecki, devendo ser um fato não negligenciável em análises de sua obra. / This study presents a proposal for methodological reconstruction of the work of Florian W. Znaniecki, Polish scholar, with the purpose of preventing the occurrence of methodological eclecticism in comparative sociological studies. In this sense, we argued in favor of the strong presence of methodological foundations proposed by Henri Poincaré in the work of Znaniecki, which shouldnt be a negligible fact in future analyses of his work.

Esse estudo apresenta a proposta de uma reconstrução metodológica da obra de Florian W. Znaniecki, intelectual polonês, com a finalidade de evitar a ocorrência de ecletismo metodológico em estudos de sociologia comparada. Nesse sentido, argumentamos em favor da forte presença dos fundamentos metodológicos propostos por Henri Poincaré na obra de Znaniecki, devendo ser um fato não negligenciável em análises de sua obra. / This study presents a proposal for methodological reconstruction of the work of Florian W. Znaniecki, Polish scholar, with the purpose of preventing the occurrence of methodological eclecticism in comparative sociological studies. In this sense, we argued in favor of the strong presence of methodological foundations proposed by Henri Poincaré in the work of Znaniecki, which shouldnt be a negligible fact in future analyses of his work.

La somme romanesque que représente À la recherche du temps perdu se constitue au prix d’une « recherche » qui est à prendre au pied de la lettre, et qui instaure le sujet connaissant en savant-chercheur face à son objet de savoir. Proust fait en effet du « savoir » la condition même du talent, et fait entreprendre à son héros une exploration qui se présente en priorité comme étant une quête de savoirs. Ce travail se situe dans le sillage de l’épistémocritique qui étudie l’inscription dans le texte littéraire des savoirs en général, tout en insistant sur les savoirs qui relèvent de la science. Notre but est de dégager la posture épistémique qui caractérise le narrateur de la Recherche face aux divers savoirs qu’il récolte au cours de ses observations. Le parcours cognitif du narrateur est examiné suivant les quatre grandes étapes de sa recherche, que nous redéfinissons en termes de paradigmes : le paradigme de l’Exploration, qui définit une « épistémologie de l’observateur » ; le paradigme de la Communication, qui définit une « épistémologie de l’homme social » et une « épistémologie de l’homme moderne » ; le paradigme de l’Introspection, qui prépare à l’élaboration d’une « épistémologie du personnage intérieur » ; et enfin, le paradigme de la Vocation, qui rassemble les réponses trouvées par le narrateur à la plupart des questionnements qui auront jalonné son parcours cognitif. Ce dernier paradigme se présente sous la forme d’une « épistémologie de la création », d’une « épistémologie du réel » et d’une « épistémologie du hasard ». Car en dépit d’une démarche qui apparaît soumise aux médiations culturelles, la recherche du héros proustien se présente comme une « pensée de l’imprévisible » : fortement déterminée par la recherche cognitive du protagoniste, elle demeure pourtant irréductible à cette seule recherche. Nous dégageons, pour terminer, le statut réservé à la science et aux savoirs positifs en regard de la découverte de la vocation, mais aussi par rapport à l’élaboration d’une théorie de la création littéraire : ces deux grands domaines du savoir sont-ils considérés par Proust comme inconciliables avec une priorité évidente de l’un sur l’autre ou, au contraire, participent-ils tous deux d’une manière égale à la connaissance et à la création artistique ? / The comprehensive novelistic survey presented by À la recherche du temps perdu is worth a research to be taken literally and establishes the knowledgeable subject as a scholar-researcher against his object of knowledge. Proust makes of “knowledge” the condition of talent and engages his hero in an exploration that presents itself as a priority for being a quest for knowledge. The present essay follows in the wake of Epistemocritique, a discipline that studies the inscription of knowledge in the literary text in general, with a specific focus on knowledge related to science. Our aim is to bring forward the epistemic position that characterizes the narrator of À la recherche du temps perdu as he acquires various forms of knowledge in the course of his observations. The narrator’s cognitive path is examined with regard to the four main pillars of his quest, which we redefine in terms of paradigms: the paradigm of exploration, which defines an “epistemology of the observer”; the paradigm of communication, which defines an “epistemology of the social being”; the paradigm of Introspection which prepares for the elaboration of an “epistemology of the internal character”; and finally, the paradigm of vocation, which combines the answers to most of the questions that have marked the narrator’s cognitive path. This last paradigm presents itself as an “epistemology of creation”, an “epistemology of reality”, and an “epistemology of chance”. For, in spite of an approach that appears to be subject to cultural interventions, the quest by Proust’s main character appears as a thought of the unpredictable. Although strongly determined by the cognitive quest of the protagonist, it nevertheless remains irreducible to this sole quest. In conclusion, we emphasize the status reserved to science and to positive knowledge from the perspective of the discovery of vocation, but also in view of the elaboration of a theory of literary creation: does Proust consider these two areas of knowledge as irreconcilable, with one having an evident priority over the other, or, to the contrary, does he considers them as equal factors in knowledge and artistic creation?

Made available in DSpace on 2016-04-28T14:16:19Z (GMT). No. of bitstreams: 1 Sonia Regina Tonetto.pdf: 1372040 bytes, checksum: 8041dda5cc94d8c48e9bf949419c38de (MD5) Previous issue date: 2014-03-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims to analyze the ideas about methods of teaching science in the early twentieth advocated by prominent scientists as Marcellin Berthelot, Paul Langevin and Henri Poincaré and the important contribution of these scientists in the reform of French teaching, 1902. Furthermore, we sought to understand the difficulties faced in teaching in French schools of that period, we sought to also to understand what these scientists believed to be the ideal science teaching method and the influence of positivist ideas in these discussions. We analyzed in particular the role of Co-operative Education of Mme Curie (1907-1908) and the objectives of the group of teachers, including Paul Langevin, which was involved in the discussions on the reform. This work was developed from the analysis of documents filed at the Institut Curie and at Bibliothèque Nationale de France, texts and books written by scholars and scientists, with direct and indirect participation in the reform, records of lectures, articles and manuscripts of the children who participated in the cooperative, as Isabelle Chavannes and Irène Curie / Este trabalho tem como objetivo analisar as ideias sobre métodos de ensino de ciências, no início do século XX, defendidas por cientistas de destaque, como Marcellin Berthelot, Paul Langevin e Henri Poincaré e a importante participação desses cientistas na reforma do ensino francês de 1902. Além disso, procurou-se entender as dificuldades enfrentadas no ensino nas escolas francesas daquele período, compreendendo o que esses cientistas acreditavam ser o método ideal para o ensino de ciências e a influência das ideias positivistas nessas discussões. Analisa-se em particular o papel da Cooperativa de Ensino de Mme Curie (1907-1908) e os objetivos do grupo de professores que, como Paul Langevin, se envolveu nos debates sobre a reforma. Este trabalho foi desenvolvido a partir da análise de documentos depositados no Institut Curie e na Bibliothèque Nationale de France, Paris, textos da época, livros escritos por estudiosos e cientistas com participação direta e indireta na reforma, registros de conferências, artigos publicados, manuscritos das crianças que participaram da cooperativa, como Isabelle Chavannes e Irène Curie

Transdisciplinarity emerged from the urge to grasp the elusive knowledge in the most fertile zone in between and beyond disciplines that escapes even the most elaborate interdisciplinary operations. While interdisciplinary protocol enables experts to operate within foreign disciplines, in the extreme case as diverse as art and science (by inviting artists into scientific departments and vice versa), the production of knowledge remains confined to particular domains. To transcend these confinements and access the knowledge that evades institutionalisation Basarab Nicolescu’s Manifesto of Transdisciplinarity sets up conditions for an open structure to be grown outside the current compartmentalisation into a living knowledge. This thesis imagines a possible evolution of transdisciplinarity into knowledge to be lived internally rather than learnt externally in order to overcome the anxiety in transcending the established culture of disciplinary research. By entering the transdisciplinary zone, the identity of experts-specialists dissolves, even the crudest separation into artists and scientists becomes obsolete. From the illusion of losing control over knowledge arises the fear of a return to archaic, mystic or even shamanic ways of knowing. Far from proposing a return to shamanism in its ancient forms this thesis imagines the way of polyphibianism – an imaginary solution to navigate efficiently the protoplasmic state of knowledge that would be indigenous to culture of disciplinary researchers. With every significant discovery the disciplinary researchers already intuitively trespass into the very zone that the Manifesto of Transdisciplinarity invites them to enter intentionally. From examination of documented introspective inquiries into their act of discovery the thesis infers the necessary sensibilities and adaptabilities of the individuals to cross the borders of their disciplines. Their seemingly lost identity is temporarily restored with the term polyphibian (analogous to amphibian) designating their ability to survive and explore multiple environments. With each change of circumstances in research a polyphibian adapts by swiftly reinventing its instinctive instruments, mutating its organs of knowing, indifferently to conventional habits of thought. Through their introspective writings this thesis investigates the polyphibic aptitude of Henri Poincaré, Henri Bergson and Marcel Duchamp to scout at the periphery of physics, metaphysics and ‘pataphysics, to intuitively anticipate the role of chance, chaos and complexity in both arts and sciences. A threshold of complexity has to be surpassed in order to bring the current apparatus of knowledge to life. Bergson’s insight on laughter and dreams suggests how intellect could transcend itself. The thesis proposes to consider laughter as faculty that could induce self-awareness in the intellectual apparatus while dreams are considered to facilitate self-organisation of intellect on higher orders of awareness. In Deleuzian manner of mutating Bergson’s work into Bergsonism, polyphibianism is a mutation in transcribing the code of Creative Evolution where Bergson insisted on interdependency between the theory of knowledge and the theory of evolution. The scholarly dispute on Bergsonian and anti-Bergsonian tendencies present in Marcel Duchamp’s work is revisited in the thesis by interpreting the higher dimensional Bride as a polyphibic organism of living knowledge with access to higher orders of awareness, able to guide the Bachelor’s apparatus of mechanical production and preservation of knowledge out of its predicament. Informed by peculiar Duchampian experiments that challenged both the domain of art and science the research projects in this thesis consist of an intervention at CERN that tested the impenetrability of institutionalised art-science collaborations and installation of the Interval of Suspended Judgement with high mathematical precision at the threshold between physics and ‘pataphysics. With these projects the problems of categorising researchers into artists and scientists are revealed. As Deleuze suggested, to effectively formulate the problem, to realize it in multiplicity of contexts, a new concept must be invented, a new organism must be conceived. This thesis gave birth to an imaginary organism of living knowledge in order to relieve the unnecessary anxieties and to fully engage in transdisciplinary research.