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.

Influence of local environmental olfactory cues on place learning in rats

The aim of the present study was to assess the influence of local environmental olfactory cues on place learning in rats. We developed a new experimental design allowing the comparison of the use of local olfactory and visual cues in spatial and discrimination learning. We compared the effect of both types of cues on the discrimination of a single food source in an open-field arena. The goal was either in a fixed or in a variable location, and could be indicated by local olfactory and/or visual cues. The local cues enhanced the discrimination of the goal dish, whether it was in a fixed or in a variable location. However, we did not observe any overshadowing of the spatial information by the local olfactory or visual cue. Rats relied primarily on distant visuospatial information to locate the goal, neglecting local information when it was in conflict with the spatial information.

Are relationship patterns with significant others reenacted with the therapist?: a study of early transference reactions.

This study examines how patients' relationship patterns are reenacted with the therapist during the first sessions of psychotherapy. Forty (N = 40) outpatients treated with a Brief Psychodynamic Intervention were included in the study. Their narratives of relationship episodes with significant others (e.g., mother, father, romantic partner, colleagues) were compared with relationship episodes with their therapist using the Core Conflictual Relationship Theme method. The Core Conflictual Relationship Theme focuses on 3 aspects of patients' relationship narratives: what the patient wants from others or from self; how others react to his/her wish; and how the patient consequently reacts. Results showed that 60% of patients display similar relationship patterns with their therapist and with significant others. The patterns that were reenacted with the therapist were not the most pervasive ones but were similar to those found in relationship episodes involving parents or romantic partners. These findings provide some support for the clinical concept of repetition of internalized relational patterns with the therapist very early in psychotherapy. Clinical implications are discussed.

Sex-dependent selection on an autosomal melanic female ornament promotes the evolution of sex ratio bias.

Sex-dependent selection often leads to spectacularly different phenotypes in males and females. In species in which sexual dimorphism is not complete, it is unclear which benefits females and males derive from displaying a trait that is typical of the other sex. In barn owls (Tyto alba), females exhibit on average larger black eumelanic spots than males but members of the two sexes display this trait in the same range of possible values. In a 12-year study, we show that selection exerted on spot size directly or on genetically correlated traits strongly favoured females with large spots and weakly favoured males with small spots. Intense directional selection on females caused an increase in spot diameter in the population over the study period. This increase is due to a change in the autosomal genes underlying the expression of eumelanic spots but not of sex-linked genes. Female-like males produced more daughters than sons, while male-like females produced more sons than daughters when mated to a small-spotted male. These sex ratio biases appear adaptive because sons of male-like females and daughters of female-like males had above-average survival. This demonstrates that selection exerted against individuals displaying a trait that is typical of the other sex promoted the evolution of specific life history strategies that enhance their fitness. This may explain why in many organisms sexual dimorphism is often not complete.

Présentation de l'adaptation française de « l'échelle de coparentage » de McHale pour familles avec jeunes enfants [Presentation of the french adaptation of McHale's coparenting scale for families with young children.]

The aim of this paper is to present McHale's coparenting scale,a self-administered questionnaire enabling assessment of the quality of coparenting, and first steps in structural and construct validation of the French version. A total of 41 French speaking Swiss families and 84 US families completed this questionnaire and the Dyadic Adjustment Scale, a measure of marital satisfaction. The results of the Swiss families correspond to those of US families: first, items distributed into four factors (family integrity, conflict, affection and disparagement) and second, a partial link was found between quality of coparenting and marital adjustment. This finding supports the construct validity of the questionnaire, reflecting the established link between these two family sub-systems. Given that coparenting quality has a major influence on children's socio-affective development, the questionnaire will find great use in assessing not just negative features of coparenting, such as conflicts and disparagement, but also positive components such as warmth and support. This will be an important asset for research as well as clinical purposes.

The vigilance components of begging and sibling competition

The conflict between siblings over how parental resources are divided has promoted the evolution of specific behaviour to outcompete each other. Young animals look out for parents' arrival in order to start begging as quickly as possible, since a rapid begging reaction increases the likelihood of being fed before nestmates. If the young can physically intercept the parents, selection might be operating on the offspring ability to monitor parent arrival (vigilance towards parents) and any sudden modifications in siblings' behaviour (vigilance towards siblings). To investigate the adaptive value of nestling vigilance in the context of family interactions, we recorded which direction barn owl Tyto alba siblings were facing in 89 two-chick broods before the first parental feeding visit of the night. Nestlings were more vigilant towards nest entrance than expected by chance suggesting that vigilance towards parents is an important component of sibling competition. When positioned near the nest-box entrance where parents predictably deliver food, the younger individual (i.e. junior) looked more towards the entrance than its older sibling. Thus, when the likelihood of obtaining a food item is relatively high, juniors are more vigilant than seniors to detect the incoming parent. When positioned at the back of the nest, the senior looked relatively more frequently towards its sibling than the junior did in the same situation. This suggests that when the likelihood of obtaining a food item is relatively low, seniors are more vigilant than juniors to observe their sibling. Because vigilance was not related to hunger level and prey obtaining, we propose the hypothesis that vigilance towards parents and siblings only indirectly influences the outcome of sibling competition.

Will climate change drive alien invasive plants into areas of high protection value? An improved model-based regional assessment to prioritise the management of invasions.

Species distribution models (SDMs) studies suggest that, without control measures, the distribution of many alien invasive plant species (AIS) will increase under climate and land-use changes. Due to limited resources and large areas colonised by invaders, management and monitoring resources must be prioritised. Choices depend on the conservation value of the invaded areas and can be guided by SDM predictions. Here, we use a hierarchical SDM framework, complemented by connectivity analysis of AIS distributions, to evaluate current and future conflicts between AIS and high conservation value areas. We illustrate the framework with three Australian wattle (Acacia) species and patterns of conservation value in Northern Portugal. Results show that protected areas will likely suffer higher pressure from all three Acacia species under future climatic conditions. Due to this higher predicted conflict in protected areas, management might be prioritised for Acacia dealbata and Acacia melanoxylon. Connectivity of AIS suitable areas inside protected areas is currently lower than across the full study area, but this would change under future environmental conditions. Coupled SDM and connectivity analysis can support resource prioritisation for anticipation and monitoring of AIS impacts. However, further tests of this framework over a wide range of regions and organisms are still required before wide application.

Struggles for meaning and struggles for control: the diffusion of bandwagon technology in two institutional environments

In this thesis, I examine the diffusion process for a complex medical technology, the PET scanner, in two different health care systems, one of which is more market-oriented (Switzerland) and the other more centrally managed by a public agency (Quebec). The research draws on institutional and socio-political theories of the diffusion of innovations to examine how institutional contexts affect processes of diffusion. I find that diffusion proceeds more rapidly in Switzerland than in Quebec, but that processes in both jurisdictions are characterized by intense struggles among providers and between providers and public agencies. I show that the institutional environment influences these processes by determining the patterns of material resources and authority available to actors in their struggles to strategically control the technology, and by constituting the discursive resources or institutional logics on which actors may legitimately draw in their struggles to give meaning to the technology in line with their interests and values. This thesis illustrates how institutional structures and meanings manifest themselves in the context of specific decisions within an organizational field, and reveals the ways in which governance structures may be contested and realigned when they conflict with interests that are legitimized by dominant institutional logics. It is argued that this form of contestation and readjustment at the margins constitutes one mechanism by which institutional frameworks are tested, stretched and reproduced or redefined.

The role of queen pheromones in social insects: queen control or queen signal?

Queens and workers in social insect colonies can differ in reproductive goals such as colony-level sex allocation and production of males by workers. That the presence of queen(s) often seems to affect worker behaviour in situations of potential conflict has given rise to the idea of queen control over reproduction. In small colonies queen control is possible via direct aggression against workers, but in large colonies queens cannot be effectively aggressive towards all the workers. This, plus evidence that queen-produced chemicals affect worker behaviour, has led to the conclusion that physical intimidation has been replaced by pheromonal queen control, whereby queen(s) chemically manipulate workers into behaving in ways that increase the queen's fitness at the worker's expense. It is argued in this paper, however, that pheromonal queen control has never conclusively been demonstrated and is evolutionarily difficult to justify. Proposed examples of pheromonal control are more likely to be honest signals, with workers' responses increasing their own inclusive fitness. A series of experimental and field studies in which positive results would give prima facie evidence for pheromonal queen control is suggested. Finally, three terms are defined: (1) pheromonal queen control for workers or subordinate queens being chemically manipulated into acting against their own best interests; (2) pheromonal queen signal for situations where workers or subordinate queens react to queen pheromones in ways that increase their, and possibly the queens', inclusive fitness; and (3) pheromonal queen effect where changes in the workers' or subordinate queens' behaviour have an unknown consequence on their inclusive fitness.

Dietary lipids reduce the expression of carotenoid-based coloration in Lacerta vivipara

1. The importance of dietary lipids for carotenoid-based ornaments has rarely been investigated, although theory predicts that dietary lipids may control the development of these widespread animal signals. Dietary lipids have been suggested to enhance the expression of male carotenoid-based ornaments because they provide carotenoids with a hydrophobic domain that facilitates their absorption and transport. Dietary lipids may also enhance the uptake of tocopherols (vitamin E), which share common absorption and transport routes with carotenoids. Here, we test whether dietary lipids enhance carotenoid availability and male carotenoid-based colorations. We also explore the effects of dietary lipids on plasma tocopherol concentration, which allow disentangling between different pathways that may explain how dietary lipids affect ornamental expression. 2. Following a two-factorial design, we manipulated dietary access of naturally occurring fatty acids (oleic acid) and carotenoids (lutein and zeaxanthin) and measured its effects on the circulating concentrations of carotenoids (lutein and zeaxanthin) and vitamin E (α- and γ-(β-) tocopherols) and on the ventral, carotenoid-based coloration of male common lizards (Lacerta vivipara). 3. Lutein but not zeaxanthin plasma concentrations increased with carotenoid supplementation, which, however, did not affect coloration. Lipid intake negatively affected circulating concentrations of lutein and γ-(β-) tocopherol and led to significantly less orange colorations. The path analysis suggests that a relationship between the observed colour change and the change in plasma concentrations of γ-(β-) tocopherol may exist. 4. Our study shows for the first time that dietary lipids do not enhance but reduce the intensity of male carotenoid-based ornaments. Although dietary lipids affected plasma carotenoid concentration, its negative effect on coloration appeared to be linked to lower vitamin E plasma concentrations. These findings suggest that a conflict between dietary lipids and carotenoid and tocopherol uptake may arise if these nutrients are independently obtained from natural diets and that such conflict may reinforce signal honesty in carotenoid-based ornaments. They also suggest that, at least in the common lizard, sexual selection with respect to carotenoid-based coloration may select for males with low antioxidant capacity and thus for males of superior health.