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.

Epidemiology and prevention of cardiovascular disease in the Seychelles Islands (Indian Ocean)

This article presents selected findings and lessons from a cardiovascular research and prevention program initiated in 1989 in the Republic of Seychelles, a country in demographic and epidemiological transition. Rapid and sustained aging of the population (e.g., two-fold increase of people aged 30-39 from 1979 to 1995) implies, over the next few decades, further dramatic increase of the burden of chronic diseases, particularly cardiovascular disease (CVD). Epidemiological surveillance shows high age-specific rates of CVD (particularly stroke), high prevalence of peripheral atherosclerosis (plaques in carotid and femoral arteries), high prevalence of classical modifiable risk factors in the adult population (particularly hypertension), and substantial proportions of children with overweight. Stagnant life expectancy in men and an increase in women have been observed over the last two decades; this occurred despite largely improved health services and reduced infant mortality rates, and may reflect the large CVD burden found in middle-aged men (less so in middle-aged women). A national program of prevention of CVD has been initiated since 1991, which includes a mix of interventions to reduce risk factors in the general population and in high-risk individuals. Substantial research to back the prevention program indeed shows, at the moment, epidemiological patterns in Seychelles similar to those observed in Western countries (e.g., an association between peripheral atherosclerosis [as a proxy of CVD] and low density lipoprotein-cholesterol, smoking, diabetes, and [inversely] walking). This clearly supports the view that promotion of healthy lifestyles and control of conventional risk factors should be the main targets for CVD prevention and control.

Factors associated with clinical leptospirosis: a population-based case-control study in the Seychelles (Indian Ocean).

BACKGROUND: In Western countries, leptospirosis is uncommon and mainly occurs in farmers and individuals indulging in water-related activities. In tropical countries, leptospirosis can be up to 1000 times more frequent and risk factors for this often severe disease may differ. METHODS: We conducted a one-year population-based matched case-control study to investigate the frequency and associated factors of leptospirosis in the entire population of Seychelles. RESULTS: A total of 75 patients had definite acute leptospirosis based on microagglutination test (MAT) and polymerase chain reaction (PCR) assay (incidence: 101 per 100,000 per year; 95% confidence interval [CI]: 79-126). Among the controls, MAT was positive in 37% (past infection) and PCR assay in 9% (subclinical infection) of men aged 25-64 with manual occupation. Comparing cases and controls with negative MAT and PCR, leptospirosis was associated positively with walking barefoot around the home, washing in streams, gardening, activities in forests, alcohol consumption, rainfall, wet soil around the home, refuse around the home, rats visible around the home during day time, cats in the home, skin wounds and inversely with indoor occupation. The considered factors accounted for as much as 57% of the variance in predicting the disease. CONCLUSION: These data indicate a high incidence of leptospirosis in Seychelles. This suggests that leptospires are likely to be ubiquitous and that effective leptospirosis control in tropical countries needs a multifactorial approach including major behaviour change by large segments of the general public.

Heritability of renal function in hypertensive families of African descent in the Seychelles (Indian Ocean).

BACKGROUND: We estimated the heritability of three measures of glomerular filtration rate (GFR) in hypertensive families of African descent in the Seychelles (Indian Ocean). METHODS: Families with at least two hypertensive siblings and an average of two normotensive siblings were identified through a national hypertension register. Using the ASSOC program in SAGE (Statistical Analysis in Genetic Epidemiology), the age- and gender-adjusted narrow sense heritability of GFR was estimated by maximum likelihood assuming multivariate normality after power transformation. ASSOC can calculate the additive polygenic component of the variance of a trait from pedigree data in the presence of other familial correlations. The effects of body mass index (BMI), blood pressure, natriuresis, along with sodium to potassium ratio in urine and diabetes, were also tested as covariates. RESULTS: Inulin clearance, 24-hour creatinine clearance, and GFR based on the Cockcroft-Gault formula were available for 348 persons from 66 pedigrees. The age- and gender-adjusted correlations (+/- SE) were 0.51 (+/- 0.04) between inulin clearance and creatinine clearance, 0.53 (+/- 0.04) between inulin clearance and Cockcroft-Gault formula and 0.66 (+/- 0.03) between creatinine clearance and Cockcroft-Gault formula. The age- and gender-adjusted heritabilities (+/- SE) of GFR were 0.41 (+/- 0.10) for inulin clearance, 0.52 (+/- 0.13) for creatinine clearance, and 0.82 (+/- 0.09) for Cockcroft-Gault formula. Adjustment for BMI slightly lowered the correlations and heritabilities for all measurements whereas adjustment for blood pressure had virtually no effect. CONCLUSION: The significant heritability estimates of GFR in our sample of families of African descent confirm the familial aggregation of this trait and justify further analyses aimed at discovering genetic determinants of GFR.

HTLV-I infection in the South West Indian Ocean islands, particularly in La Réunion and the Seychelles

Data on HTLV-I are scarce in several Southwest Indian Ocean islands except for La Réunion and The Seychelles. The two cases of HTLV-I have been confirmed by Western-Blot in La Réunion, among blood donors. In Seychelles (87 400 inhabitants in 2012), where blood donors and some other cases are screened, HTLV-I was confirmed with a line immune assay in 43 persons and at least 10-20 patients are known to have tropical spastic paraparesia or adult T-cell lymphoma associated with HTLV-I. In the south-west Indian Ocean, a possibly important other issue may be co-infection of HTLV-1 with the Strongyloides stercoralis roundworm, which is endemic in all countries of the region and which can sometimes lead to severe symptomatic infestation.

The Carboniferous Baralacha La basaltic dykes (Upper Lahul, Ladakh): remnants of an early rifting event along the Indian northern plate

The Lower Carboniferous Baralacha La basaltic dykes were emplaced along transtensional faults. The basalts exhibit tholeiitic and alkaline affinities. The tholeiites are TiO2-poor, moderately enriched in light rare earth (LREE), and display Nb and Ta negative and Th positive anomalies. The alkali basalts, compared to the tholeiites, have higher TiO2, rare earth and highly incompatible trace element contents and greater LREE enrichments. The Nd and Pb isotope compositions of the Baralacha La basalts suggest that they derive from the partial melting of an enriched OIB mantle source. characterized by a HIMU component, and contaminated by the lower continental crust. The Baralacha La dyke swarm represent the remnants of an early rifting event on the northern Indian passive margin.

Exhumation history of the NW Indian Himalaya revealed by fission track and 40Ar/39Ar ages

New fission track and Ar/Ar geochronological data provide time constraints on the exhumation history of the Himalayan nappes in the Mandi (Beas valley) - Tso Monad transect of the NW Indian Himalaya. Results from this and previous studies suggest that the SW-directed North Himalayan nappes were emplaced by detachment from the underthrusted upper Indian crust by 55 Ma and metamorphosed by ca. 48-40 Ma. The nappe stack was subsequently exhumed to shallow upper crustal depths (<10 km) by 40-30 Ma in the Tso Monad dome (northern section of the transect) and by 30-20 Ma close to frontal thrusts in the Baralacha La region. From the Oligocene to the present, exhumation continued slowly.

Frequency and impact of autosomal dominant polycystic kidney disease in the Seychelles (Indian Ocean).

BACKGROUND: As little such data is available in African populations, we investigated the prevalence of ADPKD and the impact of the disease in the Seychelles islands, where approximately 65% of the population is of African descent and 30% of Caucasian or mixed descent. METHODS: Prevalent cases were identified over a 3-year period by requesting all the doctors in the country (most of them are employed within a national health system) to refer all presumed or confirmed cases and by systematically examining the family members of all confirmed cases. The diagnosis was based on standard criteria including ultrasonographic findings and family history. RESULTS: Forty-two cases were identified in this population of 74,331 inhabitants, a total prevalence (per 100,000 total population) of 57 (95% CI, 41-76). All but one of the cases were of Caucasian descent so that the prevalence rates of the disease in the populations of Black and Caucasian descents were respectively 2 (0-11) and 184 (132-249). The prevalence rates of the gene(s) carriers were estimated to be 75 (45-117) in the total population respectively 6 (0-33) and 236 (140-372) in the Black and Caucasian populations. Haplotype analysis in 58 cases from three families showed a common DNA fragment in all affected individuals. Cases had significantly higher blood pressure compared to the general population and 21% had serum creatinine higher than 120 mumol/l. Among the established pedigrees, mean age of death between 1960 and 1995 (haemodialysis was introduced in 1992) was younger in subjects with than those without ADPKD (50.5 vs 67.7 years; P < 0.001). CONCLUSIONS: In the Seychelles, ADPKD clusters in the Caucasian population (possibly a founder effect), is rare in individuals of black descent, and is associated with substantial clinical and survival impact.