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.

Use of LIDAR in landslide investigations: A review

This paper presents a short history of the appraisal of laser scanner technologies in geosciences used for imaging relief by high-resolution digital elevation models (HRDEMs) or 3D models. A general overview of light detection and ranging (LIDAR) techniques applied to landslides is given, followed by a review of different applications of LIDAR for landslide, rockfall and debris-flow. These applications are classified as: (1) Detection and characterization of mass movements; (2) Hazard assessment and susceptibility mapping; (3) Modelling; (4) Monitoring. This review emphasizes how LIDARderived HRDEMs can be used to investigate any type of landslides. It is clear that such HRDEMs are not yet a common tool for landslides investigations, but this technique has opened new domains of applications that still have to be developed.

Altruism - a philosophical analysis

Altruism is a malleable notion that is understood differently in various disciplines. The common denominator of most definitions of altruism is the idea of unidirectional helping behaviour. However, a closer examination reveals that the term altruism sometimes refers to the outcomes of a helping behaviour for the agent and its neighbours - i.e. reproductive altruism - and sometimes to what motivates the agent to help others - i.e. psychological altruism. Since these perspectives on altruism are crucially different, it is important to use a clear terminology to avoid confusion. In particular, we show that the notion of altruism used by biologists profoundly differs from the ones used by philosophers, psychologists and economists in cross-disciplinary debates about human altruism.

A new method for geoelectrical investigations underwater

A new electrical method is proposed for determining the apparent resistivity of multi-earth layers located underwater. The method is based on direct current geoelectric sounding principles. A layered earth model is used to simulate the stratigraphic target. The measurement array is of pole-pole type; it is located underwater and is orientated vertically. This particular electrode configuration is very useful when conventional electrical methods cannot be used, especially if the water depth becomes very important. The calculated apparent resistivity shows a substantial quality increase in the measured signal caused by the underwater targets, from which little or no response is measured using conventional surface electrode methods. In practice, however, different factors such as water stratification, underwater streams or meteorological conditions complicate the interpretation of the field results. A case study is presented, where field surveys carried out on Lake Geneva were interpreted using the calculated apparent resistivity master-curves.

Blood, urine and vitreous isopropyl alcohol as biochemical markers in forensic investigations.

Isopropyl alcohol (IPA) is widely used as an industrial solvent and cleaning fluid. After ingestion or absorption, IPA is converted into acetone by alcohol dehydrogenase. However, in ketosis, acetone can be reduced to IPA. The aim of this study was to investigate blood IPA and acetone concentrations in a series of 400 medico-legal autopsies, including cases of diabetic ketoacidosis, hypothermia and alcohol misuse-related deaths, to illustrate the extent of ketosis at the time of death. Vitreous glucose, blood 3-β-hydroxybutyrate (3HB) and acetoacetate (AcAc) concentrations were also determined systematically. Additionally, vitreous and urine IPA, acetone, 3HB and AcAc concentrations as well as other biochemical markers, including glycated hemoglobin and carbohydrate-deficient transferrin (CDT) were also determined in selected cases. The results of this study indicate that ketosis is characterized by the presence of IPA resulting from the acetone metabolism and that IPA can be detected in several substrates. These findings confirm the importance of the systematic determination of IPA and acetone levels that is used to quantify biochemical disturbances and the importance of ketosis at the time of death.

The philosophical foundations of classical "rDzogs chen" in Tibet : investigating the distinction between dualistic mind (sems) and primordial knowing (ye shes)

While the syncretistic Tibetan tradition known as rDzogs chen ("Great Perfection") has attracted considerable attention over the past few decades, its philosophical foundations remain largely unknown to those unacquainted with its primary sources. This thesis looks at the essentials of rDzogs chen philosophy through the lens of two principal distinctions that the tradition has considered indispensable for understanding its distinctive views and practices: dualistic mind (sems) versus primordial knowing (ye shes) and dharmakâya versus the 'ground of all' (kun gzhi) conditioned experience. Arguing that the distinctions provided classical rDzogs chen scholars with a crucial framework for (a) articulating the necessary conditions of nondual primordial knowing, the conditio sine qua non of rNying ma soteriology, and (b) schematizing the relationship between the exoteric and esoteric vehicles of Indian Buddhism within a unifying conception of the Buddhist path as the progressive disclosure of primordial knowing, the thesis shows how the rDzogs chen philosophy of mind has been integral to the tradition's complex soteriology. The thesis consists of two parts: (1) a detailed philosophical investigation of the distinctions and (2) an anthology of previously untranslated Tibetan materials on the distinctions accompanied by critical editions and introductions. The first part systematically invesigates the nature and scope of the distinctions and traces their evolution and complex relationships with Indian Buddhist Cittamâtra, Madhyamaka, Pramàriavàda, and Vajrayâna views. It concludes with an exploration of some soteriological implications of the mind/primordial knowing distinction that became central to rDzogs chen path hermeneutics in the classical period as authors of rDzogs chen path summaries used this distinction to reconcile progressivist sutric and non-progressivist tantric models of the Buddhist path. The translations and texts included in part two of the thesis consist of (a) a short treatise from Klong chen pa's Miscellaneous Writings entitled Sems dang ye shes kyi dris lan (Reply to Questions Concerning Mind and Primordial Knowing), (b) selected passages on the distinctions from this author's monumental summary of the rDzogs chen snying thig system, the Theg mchog mdzod (Treasury of the Supreme Vehicle), and (c) an excerpt on rDzogs chen distinctions taken from 'Jigs med gling pa's (1729-1798) 18th century Klong chen sNying thig path summary entitled Treasury of Qualities (Yon tan mdzod) along with a word-by- word commentary by Yon tan rgya mtsho (b. 19th c.).

Investigations on carbon isotope ratios and concentrations of urinary formestane.

The aromatase inhibitor formestane (4-hydroxy-androst-4-ene-3,17-dione, F) is prohibited in sports by the World Anti-Doping Agency (WADA). F possesses only weak androgenic properties and is presumed to be employed in order to suppress estrogen production during the illicit intake of anabolic steroids by athletes. Former studies additionally showed that F is an endogenous steroid produced in low amounts. According to the regulations of WADA, urinary concentrations above 100 ng/ml are assumed to be due to ingestion of F. To distinguish between endogenous or exogenous sources of urinary F, isotope ratio mass spectrometry (IRMS) is the method of choice. Therefore, a method to determine the carbon isotope ratio (CIR) of F in urine samples was developed and validated. Routine samples (n = 42) showing concentrations of F above 5 ng/ml were investigated and enabled elucidation of the CIR of endogenous F and subsequent the calculation of a reference limit. A reference population encompassing n = 90 males and females was investigated regarding endogenous concentrations of F. An excretion study with one male volunteer was conducted to test and validate the developed method and to identify possible impact of F administration on other endogenous steroids. By CIR determination of F it is clearly possible to elucidate its endogenous or exogenous source. Taking into account the CIR of other target analytes like testosterone, a differentiation between F and androstenedione intake is possible. In 2011, the first exogenous F below the WADA threshold could be detected by means of the developed IRMS method.

Synchrotron-based X-ray tomographic microscopy for rock physics investigations

Synchrotron radiation X-ray tomographic microscopy is a nondestructive method providing ultra-high-resolution 3D digital images of rock microstructures. We describe this method and, to demonstrate its wide applicability, we present 3D images of very different rock types: Berea sandstone, Fontainebleau sandstone, dolomite, calcitic dolomite, and three-phase magmatic glasses. For some samples, full and partial saturation scenarios are considered using oil, water, and air. The rock images precisely reveal the 3D rock microstructure, the pore space morphology, and the interfaces between fluids saturating the same pore. We provide the raw image data sets as online supplementary material, along with laboratory data describing the rock properties. By making these data sets available to other research groups, we aim to stimulate work based on digital rock images of high quality and high resolution. We also discuss and suggest possible applications and research directions that can be pursued on the basis of our data.

Identification concept and the use of probabilities in forensic odontology--an approach by philosophical discussion.

This paper questions the practitioners' deterministic approach(es) in forensic identification and notes the limits of their conclusions in order to encourage a discussion to question current practices. With this end in view, a hypothetical discussion between an expert in dentistry and an enthusiastic member of a jury, eager to understand the scientific principles of evidence interpretation, is presented. This discussion will lead us to regard any argument aiming at identification as probabilistic.