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.

Cooperation among selfish individuals in insect societies

Kin selection is the key to understanding the evolution of cooperation in insect societies. However, kin selection also predicts potential kin conflict, and understanding how these conflicts are resolved is a major goal of current research on social insects

E-Cigarettes: A Review of New Trends in Cannabis Use.

The emergence of electronic cigarettes (e-cigs) has given cannabis smokers a new method of inhaling cannabinoids. E-cigs differ from traditional marijuana cigarettes in several respects. First, it is assumed that vaporizing cannabinoids at lower temperatures is safer because it produces smaller amounts of toxic substances than the hot combustion of a marijuana cigarette. Recreational cannabis users can discretely "vape" deodorized cannabis extracts with minimal annoyance to the people around them and less chance of detection. There are nevertheless several drawbacks worth mentioning: although manufacturing commercial (or homemade) cannabinoid-enriched electronic liquids (e-liquids) requires lengthy, complex processing, some are readily on the Internet despite their lack of quality control, expiry date, and conditions of preservation and, above all, any toxicological and clinical assessment. Besides these safety problems, the regulatory situation surrounding e-liquids is often unclear. More simply ground cannabis flowering heads or concentrated, oily THC extracts (such as butane honey oil or BHO) can be vaped in specially designed, pen-sized marijuana vaporizers. Analysis of a commercial e-liquid rich in cannabidiol showed that it contained a smaller dose of active ingredient than advertised; testing our laboratory-made, purified BHO, however, confirmed that it could be vaped in an e-cig to deliver a psychoactive dose of THC. The health consequences specific to vaping these cannabis preparations remain largely unknown and speculative due to the absence of comprehensive, robust scientific studies. The most significant health concerns involve the vaping of cannabinoids by children and teenagers. E-cigs could provide an alternative gateway to cannabis use for young people. Furthermore, vaping cannabinoids could lead to environmental and passive contamination.