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.

The History of Rome in Painting

There are many paths to reach Rome, immense field open to the eye through the centuries and days, where the presence of the story is haunting. All the artists came to Rome: Italians of various Italian and also French, Dutch, Flemish, Spanish, English and Americans. These painters whose works tell its long history for having lived in the glare of light forever are the Roman pantheon of arts: what are all the anonymous authors of the frescoes of ancient Rome and medieval, but Fabriano, Cimabue , Giotto, Botticelli, Raphael, Giulio Romano, Michelangelo, Caravaggio, Guido Reni, Guercino, Titian, Vasari, Velasquez, Le Nain, Poussin, Zuccari, Van Wittel, Eckersberg, Giraudet, David, Panini, Hubert Robert, Reynolds, Fuseli, Ingres, Sargent, Caffi, Vernet, Turner, Corot, Caffi, De Chirico, etc..

Discordances between phylogenetic and morphological patterns in alpine leaf beetles attest to an intricate biogeographic history of lineages in postglacial Europe.

Pleistocene glacial and interglacial periods have moulded the evolutionary history of European cold-adapted organisms. The role of the different mountain massifs has, however, not been accurately investigated in the case of high-altitude insect species. Here, we focus on three closely related species of non-flying leaf beetles of the genus Oreina (Coleoptera, Chrysomelidae), which are often found in sympatry within the mountain ranges of Europe. After showing that the species concept as currently applied does not match barcoding results, we show, based on more than 700 sequences from one nuclear and three mitochondrial genes, the role of biogeography in shaping the phylogenetic hypothesis. Dating the phylogeny using an insect molecular clock, we show that the earliest lineages diverged more than 1 Mya and that the main shift in diversification rate occurred between 0.36 and 0.18 Mya. By using a probabilistic approach on the parsimony-based dispersal/vicariance framework (MP-DIVA) as well as a direct likelihood method of state change optimization, we show that the Alps acted as a cross-roads with multiple events of dispersal to and reinvasion from neighbouring mountains. However, the relative importance of vicariance vs. dispersal events on the process of rapid diversification remains difficult to evaluate because of a bias towards overestimation of vicariance in the DIVA algorithm. Parallels are drawn with recent studies of cold-adapted species, although our study reveals novel patterns in diversity and genetic links between European mountains, and highlights the importance of neglected regions, such as the Jura and the Balkanic range.

Family history of cancer: pooled analysis in the International Head and Neck Cancer Epidemiology Consortium.

Alcohol and tobacco consumption are well-recognized risk factors for head and neck cancer (HNC). Evidence suggests that genetic predisposition may also play a role. Only a few epidemiologic studies, however, have considered the relation between HNC risk and family history of HNC and other cancers. We pooled individual-level data across 12 case-control studies including 8,967 HNC cases and 13,627 controls. We obtained pooled odds ratios (OR) using fixed and random effect models and adjusting for potential confounding factors. All statistical tests were two-sided. A family history of HNC in first-degree relatives increased the risk of HNC (OR=1.7, 95% confidence interval, CI, 1.2-2.3). The risk was higher when the affected relative was a sibling (OR=2.2, 95% CI 1.6-3.1) rather than a parent (OR=1.5, 95% CI 1.1-1.8) and for more distal HNC anatomic sites (hypopharynx and larynx). The risk was also higher, or limited to, in subjects exposed to tobacco. The OR rose to 7.2 (95% CI 5.5-9.5) among subjects with family history, who were alcohol and tobacco users. A weak but significant association (OR=1.1, 95% CI 1.0-1.2) emerged for family history of other tobacco-related neoplasms, particularly with laryngeal cancer (OR=1.3, 95% CI 1.1-1.5). No association was observed for family history of nontobacco-related neoplasms and the risk of HNC (OR=1.0, 95% CI 0.9-1.1). Familial factors play a role in the etiology of HNC. In both subjects with and without family history of HNC, avoidance of tobacco and alcohol exposure may be the best way to avoid HNC.

The evolutionary history of the CD209 (DC-SIGN) family in humans and non-human primates

The CD209 gene family that encodes C-type lectins in primates includes CD209 (DC-SIGN), CD209L (L-SIGN) and CD209L2. Understanding the evolution of these genes can help understand the duplication events generating this family, the process leading to the repeated neck region and identify protein domains under selective pressure. We compiled sequences from 14 primates representing 40 million years of evolution and from three non-primate mammal species. Phylogenetic analyses used Bayesian inference, and nucleotide substitutional patterns were assessed by codon-based maximum likelihood. Analyses suggest that CD209 genes emerged from a first duplication event in the common ancestor of anthropoids, yielding CD209L2 and an ancestral CD209 gene, which, in turn, duplicated in the common Old World primate ancestor, giving rise to CD209L and CD209. K(A)/K(S) values averaged over the entire tree were 0.43 (CD209), 0.52 (CD209L) and 0.35 (CD209L2), consistent with overall signatures of purifying selection. We also assessed the Toll-like receptor (TLR) gene family, which shares with CD209 genes a common profile of evolutionary constraint. The general feature of purifying selection of CD209 genes, despite an apparent redundancy (gene absence and gene loss), may reflect the need to faithfully recognize a multiplicity of pathogen motifs, commensals and a number of self-antigens

History of biological warfare and bioterrorism.

Bioterrorism literally means using microorganisms or infected samples to cause terror and panic in populations. Bioterrorism had already started 14 centuries before Christ, when the Hittites sent infected rams to their enemies. However, apart from some rare well-documented events, it is often very difficult for historians and microbiologists to differentiate natural epidemics from alleged biological attacks, because: (i) little information is available for times before the advent of modern microbiology; (ii) truth may be manipulated for political reasons, especially for a hot topic such as a biological attack; and (iii) the passage of time may also have distorted the reality of the past. Nevertheless, we have tried to provide to clinical microbiologists an overview of some likely biological warfare that occurred before the 18th century and that included the intentional spread of epidemic diseases such as tularaemia, plague, malaria, smallpox, yellow fever, and leprosy. We also summarize the main events that occurred during the modern microbiology era, from World War I to the recent 'anthrax letters' that followed the World Trade Center attack of September 2001. Again, the political polemic surrounding the use of infectious agents as a weapon may distort the truth. This is nicely exemplified by the Sverdlovsk accident, which was initially attributed by the authorities to a natural foodborne outbreak, and was officially recognized as having a military cause only 13 years later.