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.

Dalí et le dynamisme des formes. L'élaboration de l'activité « paranoïaque-critique » dans le contexte socioculturel des années 1920-1930

RESUME Dalí et le dynamisme des formes. L'élaboration de l'activité « paranoïaque-critique » dans le contexte socioculturel des années 1920-1930 Rendre à nouveau lisibles des textes dont on ne sait plus reconnaître les enjeux historiques et cognitifs, tel est le principal défi que cet ouvrage consacré aux écrits surréalistes de Dalí se propose de relever. La thèse fait ressortir l'image sans doute un peu déroutante d'un créateur stratège qui, assimilant de manière originale les savoirs les plus variés et dialoguant avec les intellectuels de son temps, propose au tournant des années 1930 une théorie du surréalisme novatrice, capable de redynamiser un groupe en pleine crise. L'étude, combinant des perspectives sociologiques et linguistiques, explore tout d'abord les écrits à caractère manifestaire et dessine les traits conceptuels et stylistiques qui font la singularité du projet de Dalí dans le cadre du mouvement surréaliste. S'inspirant des images-devinettes, de la production des fous, de l'interprétation des figures aux formes indéterminées, le Catalan conçoit une méthode créative et cognitive qui se fonde sur une pensée subconsciente active, schématisant et fertilisant automatiquement toute donnée perçue. Dans le domaine de la peinture, ce sont les formes des objets qui sont surdéterminées par les désirs subconscients du créateur et du spectateur et qui acquièrent ainsi des significations inattendues. Dans le domaine de l'écriture, ce sont les formes sonores et graphiques des mots ou encore l'ossature discursive qui, investies par les fantasmes de l'écrivain et du lecteur, génèrent une multitude d'images. A l'aune des modes de connaissance propres à l'époque, l'étude porte ensuite sur deux modèles de pensée - le paradigme photographique et l'imaginaire lié à la notion d'espace-temps développée par Einstein dans le cadre de la théorie de la relativité générale - qui sont en vogue pendant les années 1930 et que le peintre se réapproprie pour signifier la dimension « révélatrice » et « objective » de ses oeuvres. Premièrement, pour penser la méthode « paranoïaque-critique », le Catalan reprend et détourne les phases de production du cliché : loin de reproduire fidèlement le visible, le dispositif photographique dalinien permet de révéler les pensées subconscientes. Deuxièmement, dès 1933-1934, Dalí reformule le modèle de l'espace-temps de la relativité générale d'Einstein pour penser la façon dont une entité invisible (le fantasme) s'objective et se matérialise dans la réalité extérieure. L'étude du dynamisme psychique conféré par Dalí aux formes des objets, aux formes verbales et picturales permet finalement de mettre en lumière le foisonnement mais aussi l'extrême cohérence de l'univers surréaliste du Catalan, et de souligner la valeur de l'approche « paranoïaque-critique » de la réalité tant sur le plan de l'histoire culturelle que sur le plan de la connaissance.

Space-time within general relativity : a structural realist understanding

ABSTRACT This dissertation investigates the, nature of space-time as described by the theory of general relativity. It mainly argues that space-time can be naturally interpreted as a physical structure in the precise sense of a network of concrete space-time relations among concrete space-time points that do not possess any intrinsic properties and any intrinsic identity. Such an interpretation is fundamentally based on two related key features of general relativity, namely substantive general covariance and background independence, where substantive general covariance is understood as a gauge-theoretic invariance under active diffeomorphisms and background independence is understood in the sense that the metric (or gravitational) field is dynamical and that, strictly speaking, it cannot be uniquely split into a purely gravitational part and a fixed purely inertial part or background. More broadly, a precise notion of (physical) structure is developed within the framework of a moderate version of structural realism understood as a metaphysical claim about what there is in the world. So, the developement of this moderate structural realism pursues two main aims. The first is purely metaphysical, the aim being to develop a coherent metaphysics of structures and of objects (particular attention is paid to the questions of identity and individuality of these latter within this structural realist framework). The second is to argue that moderate structural realism provides a convincing interpretation of the world as described by fundamental physics and in particular of space-time as described by general relativity. This structuralist interpretation of space-time is discussed within the traditional substantivalist-relationalist debate, which is best understood within the broader framework of the question about the relationship between space-time on the one hand and matter on the other. In particular, it is claimed that space-time structuralism does not constitute a 'tertium quid' in the traditional debate. Some new light on the question of the nature of space-time may be shed from the fundamental foundational issue of space-time singularities. Their possible 'non-local' (or global) feature is discussed in some detail and it is argued that a broad structuralist conception of space-time may provide a physically meaningful understanding of space-time singularities, which is not plagued by the conceptual difficulties of the usual atomsitic framework. Indeed, part of these difficulties may come from the standard differential geometric description of space-time, which encodes to some extent this atomistic framework; it raises the question of the importance of the mathematical formalism for the interpretation of space-time.

Botulinum toxin A in non-dystonic tremors.

The present pilot study evaluated the effect of botulinum toxin A on primarily non-dystonic tremors using accelerometry in a single-blind, placebo-controlled design. Resting, postural, intention, or head tremor were assessed before and approximately 1 month after intramuscular saline and botulinum toxin A (25-50 U) respectively. Half of the patients showed > or = 30% placebo effect. Tremor in 10 of 17 patients (60%) studied improved further after botulinum toxin A (range 30-95%), exceeding the placebo effect by > or = 30%. Nine patients demonstrated clinically significant focal weakness in the extensor muscles after botulinum toxin A which interfered with fine movements. Patients were subdivided into PD-like and ET-like tremor(s). Both groups experienced large placebo effects for resting tremor, with little or no further improvement after botulinum toxin A. The improvement in postural tremor after botulinum toxin A, of 40% in the PD-like and 57% in the ET-like groups, however, was approximately twice that of placebo. In conclusion, botulinum toxin A exerts a modest tremorlytic effect, however the dose, and its distribution over the sites injected, need to be optimised to minimise focal weakness.

Distinguishing general concepts from individuals: an automatic coarse-grained classifier

Named entity recognizers are unable to distinguish if a term is a general concept as "scientist" or an individual as "Einstein". In this paper we explore the possibility to reach this goal combining two basic approaches: (i) Super Sense Tagging (SST) and (ii) YAGO. Thanks to these two powerful tools we could automatically create a corpus set in order to train the SuperSense Tagger. The general F1 is over 76% and the model is publicly available.

Oral rivaroxaban for symptomatic venous thromboembolism.

BACKGROUND: Rivaroxaban, an oral factor Xa inhibitor, may provide a simple, fixed-dose regimen for treating acute deep-vein thrombosis (DVT) and for continued treatment, without the need for laboratory monitoring. METHODS: We conducted an open-label, randomized, event-driven, noninferiority study that compared oral rivaroxaban alone (15 mg twice daily for 3 weeks, followed by 20 mg once daily) with subcutaneous enoxaparin followed by a vitamin K antagonist (either warfarin or acenocoumarol) for 3, 6, or 12 months in patients with acute, symptomatic DVT. In parallel, we carried out a double-blind, randomized, event-driven superiority study that compared rivaroxaban alone (20 mg once daily) with placebo for an additional 6 or 12 months in patients who had completed 6 to 12 months of treatment for venous thromboembolism. The primary efficacy outcome for both studies was recurrent venous thromboembolism. The principal safety outcome was major bleeding or clinically relevant nonmajor bleeding in the initial-treatment study and major bleeding in the continued-treatment study. RESULTS: The study of rivaroxaban for acute DVT included 3449 patients: 1731 given rivaroxaban and 1718 given enoxaparin plus a vitamin K antagonist. Rivaroxaban had noninferior efficacy with respect to the primary outcome (36 events [2.1%], vs. 51 events with enoxaparin-vitamin K antagonist [3.0%]; hazard ratio, 0.68; 95% confidence interval [CI], 0.44 to 1.04; P<0.001). The principal safety outcome occurred in 8.1% of the patients in each group. In the continued-treatment study, which included 602 patients in the rivaroxaban group and 594 in the placebo group, rivaroxaban had superior efficacy (8 events [1.3%], vs. 42 with placebo [7.1%]; hazard ratio, 0.18; 95% CI, 0.09 to 0.39; P<0.001). Four patients in the rivaroxaban group had nonfatal major bleeding (0.7%), versus none in the placebo group (P=0.11). CONCLUSIONS: Rivaroxaban offers a simple, single-drug approach to the short-term and continued treatment of venous thrombosis that may improve the benefit-to-risk profile of anticoagulation. (Funded by Bayer Schering Pharma and Ortho-McNeil; ClinicalTrials.gov numbers, NCT00440193 and NCT00439725.).