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.

Biological materials in colorectal surgery: current applications and potential for the future.

Biological materials are increasingly used in abdominal surgery for ventral, pelvic and perineal reconstructions, especially in contaminated fields. Future applications are multi-fold and include prevention and one-step closure of infected areas. This includes prevention of abdominal, parastomal and pelvic hernia, but could also include prevention of separation of multiple anastomoses, suture- or staple-lines. Further indications could be a containment of infected and/or inflammatory areas and protection of vital implants such as vascular grafts. Reinforcement patches of high-risk anastomoses or unresectable perforation sites are possibilities at least. Current applications are based mostly on case series and better data is urgently needed. Clinical benefits need to be assessed in prospective studies to provide reliable proof of efficacy with a sufficient follow-up. Only superior results compared with standard treatment will justify the higher costs of these materials. To date, the use of biological materials is not standard and applications should be limited to case-by-case decision.

The clinical and biological impact of new pathogen inactivation technologies on platelet concentrates.

Since 1990, several techniques have been developed to photochemically inactivate pathogens in platelet concentrates, potentially leading to safer transfusion therapy. The three most common methods are amotosalen/UVA (INTERCEPT Blood System), riboflavin/UVA-UVB (MIRASOL PRT), and UVC (Theraflex-UV). We review the biology of pathogen inactivation methods, present their efficacy in reducing pathogens, discuss their impact on the functional aspects of treated platelets, and review clinical studies showing the clinical efficiency of the pathogen inactivation methods and their possible toxicity.

Influence of transport and time on blood variables commonly measured for the athlete biological passport.

Some recent studies have characterized the stability of blood variables commonly measured for the Athlete Biological Passport. The aim of this study was to characterize the impact of different shipments conditions and the quality of the results returned by the haematological analyzer. Twenty-two healthy male subjects provided five EDTA tubes each. Four shipment conditions (24, 36, 48, 72 h) under refrigerated conditions were tested and compared to a set of samples left in the laboratory also under refrigerated conditions (group control). All measurements were conducted using two Sysmex XT-2000i analyzers. Haemoglobin concentration, reticulocytes percentage, and OFF-score numerical data were the same for samples analyzed just after collection and after a shipment under refrigerated conditions up to 72 h. Detailed information reported especially by the differential (DIFF) channel scatterplot of the Sysmex XT-2000i indicated that there were signs of blood deterioration, but were not of relevance for the variables used in the Athlete Biological Passport. As long as the cold chain is guaranteed, the time delay between the collection and the analyses of blood variables can be extended. Copyright© 2015 John Wiley & Sons, Ltd.