On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

Seizures after single-agent overdose with pharmaceutical drugs: Analysis of cases reported to a poison center.

Abstract Context. Seizures during intoxications with pharmaceuticals are a well-known complication. However, only a few studies report on drugs commonly involved and calculate the seizure potential of these drugs. Objectives. To identify the pharmaceutical drugs most commonly associated with seizures after single-agent overdose, the seizure potential of these pharmaceuticals, the age-distribution of the cases with seizures and the ingested doses. Methods. A retrospective review of acute single-agent exposures to pharmaceuticals reported to the Swiss Toxicological Information Centre (STIC) between January 1997 and December 2010 was conducted. Exposures which resulted in at least one seizure were identified. The seizure potential of a pharmaceutical was calculated by dividing the number of cases with seizures by the number of all cases recorded with that pharmaceutical. Data were analyzed using descriptive statistics. Results. We identified 15,441 single-agent exposures. Seizures occurred in 313 cases. The most prevalent pharmaceuticals were mefenamic acid (51 of the 313 cases), citalopram (34), trimipramine (27), venlafaxine (23), tramadol (15), diphenhydramine (14), amitriptyline (12), carbamazepine (11), maprotiline (10), and quetiapine (10). Antidepressants were involved in 136 cases. Drugs with a high seizure potential were bupropion (31.6%, seizures in 6 of 19 cases, 95% CI: 15.4-50.0%), maprotiline (17.5%, 10/57, 95% CI: 9.8-29.4%), venlafaxine (13.7%, 23/168, 95% CI: 9.3-19.7%), citalopram (13.1%, 34/259, 95% CI: 9.5-17.8%), and mefenamic acid (10.9%, 51/470, 95% CI: 8.4-14.0%). In adolescents (15-19y/o) 23.9% (95% CI: 17.6-31.7%) of the cases involving mefenamic acid resulted in seizures, but only 5.7% (95% CI: 3.3-9.7%) in adults (≥ 20y/o; p < 0.001). For citalopram these numbers were 22.0% (95% CI: 12.8-35.2%) and 10.9% (95% CI: 7.1-16.4%), respectively (p = 0.058). The probability of seizures with mefenamic acid, citalopram, trimipramine, and venlafaxine increased as the ingested dose increased. Conclusions. Antidepressants were frequently associated with seizures in overdose, but other pharmaceuticals, as mefenamic acid, were also associated with seizures in a considerable number of cases. Bupropion was the pharmaceutical with the highest seizure potential even if overdose with bupropion was uncommon in our sample. Adolescents might be more susceptible to seizures after mefenamic acid overdose than adults. "Part of this work is already published as a conference abstract for the XXXIV International Congress of the European Association of Poisons Centres and Clinical Toxicologists (EAPCCT) 27-30 May 2014, Brussels, Belgium." Abstract 8, Clin Toxicol 2014;52(4):298.

L'hystérie : une entité historique, un trouble psychiatrique ou une maladie neurologique? [Hysteria : an historical entity, a psychiatric condition or a neurological disease?]

Il a été suggéré que l'hystérie avait disparu et n'était qu'un concept ancien, stigmatisant et péjoratif, voire erroné, reflétant l'incapacité de la communauté médicale à établir parfois un diagnostic. Actuellement ces troubles, appelés troubles dissociatifs ou de conversion, restent pourtant une réalité clinique fréquente et invalidante pour les patients. Plusieurs études et revues ont tenté de mieux décrire la présentation clinique, mais également de mieux comprendre les mécanismes neurobiologiques impliqués dans ces troubles grâce au développement de certaines techniques d'imagerie cérébrale. Si les corrélats neurobiologiques sont mieux compris, des traitements efficaces manquent encore et seule une prise en charge multidisciplinaire (généralistes, neurologues et psychiatres) et individualisée peut apporter un bénéfice au patient. It has been suggested that hysteria had waned and was an old-fashioned, stigmatizing and false concept, reflecting the incapacity of the medical community to establish a diagnosis in certain situations. Nowadays, however, those disturbances, now referred to as conversion or dissociative disorders, still remain a frequent and incapacitating condition that every clinician faces. These past decades, several studies have tried to better describe their clinical presentation and their neurobiological mechanisms, with the help of the development of new neuroimaging techniques. If the neurobiological correlates are now better understood, efficient treatments are still lacking and only a multidisciplinary (general practitioners, neurologists and psychiatrists) and individually-tailored therapy might be beneficial to the patients.

An epidemiological and clinical approach to adolescent suicide. A comparison between suicidal and non-suicidal clinical groups in a health foundation center for French students.

Suicidal behaviour among young people represents a major public health problem. This study seeks to compare the major sociological, clinical, schooling and family features of suicidal and non-suicidal subgroups of adolescents hospitalised in the Health Foundation Center for French Students of neufmoutiers en Brie (France). All these adolescents suffered from the severe mental disorders. The adolescents from the suicidal subgroup presented significantly fewer psychoses and more mood disorders than those of the non-suicidal subgroup. Half of the patients from the suicidal subgroup presented some features of personality disorders, mostly borderline personality disorders. Nevertheless, their global functioning was more frequently improved between admission and discharge than was the case for the non-suicidal group.

Historical Profile of Water Regime in Switzerland (1870-2000).

Analyse comparée de la formation et des effets des régimes institutionnels de ressources naturelles en Suisse. Partant du constat de l'accroissement significatif et généralisé de la consommation des ressources naturelles, le projet a pour ambition d'examiner, dans le cas de la Suisse, quels sont les types de régimes institutionnels -régimes composés de l'ensemble des droits de propriété de disposition et d'usages s'appliquant aux différentes ressources naturelles, de même que des politiques publiques d'exploitation et de protection les régulant- susceptibles de prévenir des processus de surexploitation et de dégradation de ces ressources. Dans le cadre de ce projet de recherche financé par le Fonds national suisse de la recherche scientifique (FNRS), il s'agit, dans un premier temps, d'analyser les trajectoires historiques d'adaptation et de changements des régimes institutionnels des différentes ressources sur une durée d'environ un siècle (1900-2000). C'est l'objet des différents screenings. Dans un second temps et à l'aide d'études de cas, ces transformations de (ou au sein des) régimes institutionnels sont analysées sous l'angle de leurs effets sur l'état de la ressource. L'ambition finale de cette recherche est de comprendre les conditions l'émergence de "régimes intégrés" capables de prendre en compte un nombre croissant de groupes d'usagers agissant à différents niveaux (géographiques et institutionnels) et ayant des usages de plus en plus hétérogènes et concurrents de ces différentes ressources. Le champ empirique de la recherche porte plus particulièrement sur cinq ressources que sont: l'eau,l'air, le sol, le paysage et la forêt.

Ethiques de la description: naissance de l'imagination typologique en France, dans le roman et la sociologie (1820-1860)

Résumé: Ce travail d'histoire comparée de la littérature et de la sociologie s'interroge sur l'émergence de la notion de type dans les pratiques de description du monde social au cours des années 1820-1860. A partir de l'analyse des opérations de schématisation engagées par Honoré Balzac dans La Comédie humaine et par Frédéric Le Play dans Les Ouvriers européens, soit deux oeuvres que tout semble éloigner du point de vue de leurs ambitions, de leur forme, et de la trajectoire de leur auteur, mais qui toutes deux placent cependant la typification au centre de leur dispositif, il s'est agi de produire une histoire de l'imagination typologique, et des ontologies, sociales ou non, qui lui furent associées. Aussi le corpus intègre-t-il des textes d'histoire naturelle, de sciences médicales, d'histoire, de chimie, de géologie, de métallurgie, et, bien évidemment, les genres du roman sentimental, du roman historique et de la littérature panoramique, ainsi que les enquêtes ouvrières et la statistique. Abstract: This work offers a compared history of literature and sociology in France between 1820 and 1860. During that period, the notion of type appears in the literary and sociological descriptions of social reality, and becomes more and more central in the apprehension of the differenciations among classes, communities or groups. Based on the analysis of Honoré Balzac's La Comédie humaine and Frédéric Le Play's Les Ouvriers européens, this study shows that these two series of novels and of workers' monographies put typification at the center of their descriptive ambition. More broadly, it proposes a history of the uses of a typological imagination and of the ontologies, above all social, that were underlying them. That is why the texts also taken into account in this study ranges from natural history, medical sciences, history, chemistry geology and metallurgy, to the sentimental novel, the historical novel and the panoramic literature, as well as social inquiries and statistics.

Evolution des transferts interhospitaliers au départ d'un centre hospitalier universitaire suisse [Trends in interhospital transfers from a Swiss university hospital center].

OBJECTIVE: Research on interhospital transfers provides a basis for describing and quantifying patient flow and its evolution over time, offering an insight into hospital organization and management and hospital overcrowding. The purpose of this study was to conduct a qualitative and quantitative analysis of patient flow and to examine trends over an eight-year period. METHODS: A retrospective descriptive study of interhospital transfers was conducted between 2003 and 2011 based on an analysis of demographic, medical and operational characteristics. Ambulance transfers and transfers requiring physician assistance were analyzed separately. RESULTS: The number of interhospital transfers increased significantly over the study period,from 4,026 in 2003 to 6,481 in 2011 (+60.9%). The number of ambulance transfers increased by almost 300% (616 in 2003 compared to 2,460 in 2011). Most of the transfers (98%) were to hospitals located less than 75 km from the university hospital (median: 24 km, 5-44). In 2011, 24% of all transfers were to psychiatric institutions. 26% of all transfer cases were direct transfers from the emergency department. An increasing number of transfers required physician assistance. 18% of these patients required ventilatory support, whole 9.8% required vasoactive drugs. 11.6% of these transfers were due to hospital overcrowding. Conclusion: The study shows that there has been a significant increase in interhospital transfers. This increase is related to hospital overcrowding and to the network-based systems governing patient care strategies.