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 multicultural moment : the history of the idea and politics of multiculturalism in Sweden in comparative, transnational and biographical context, 1964–1975

The emergence of the idea of multiculturalism in Swedish public discourse and social science in the latter half of the 1960s and introduction of official multiculturalism in 1975 constituted a major intellectual and political shift in the post-war history of Sweden. The ambition of the 1975 immigrant and minority policy to enable the preservation of ethno-cultural minorities and to create a positive attitude towards the new multicultural society among the majority population was also incorporated into Swedish cultural, educational and media policies. The rejection of assimilationism and the new commitment to ethno-cultural diversity, the multicultural moment, has earned Sweden a place on the list of the early adopters of official multiculturalism, together with Canada and Australia. This compilation thesis examines the origins and early post-war history of the idea of multiculturalism as well as the interplay between idea and politics in the shift from a public ideal of homogeneity to an ideal of multiculturalism in Sweden. It does so from a range of conceptual, comparative, transnational, and biographical perspectives. The thesis consists of an introduction (Part I) and four previously published studies (Part II). The primary research result of the thesis concerns the agency involved in the break-through and formal establishment of the idea of multiculturalism in Sweden. Actors such as ethnic activists, experts and officials were instrumental in the introduction and establishment of multiculturalism in Sweden, as they also had been in Canada and in Australia. These actors have, however, not previously been recognized and analysed as significant idea-makers and political agents in the case of Sweden. The intertwined connections between activists, social scientists, linguists, and officials facilitated the transfer of the idea of multiculturalism from a publically contested idea to public policy via the way of The Swedish Trade Union Confederation, academia and the Royal Commission of Immigration. The thesis furthermore shows that the political success of the idea of multiculturalism, such as it was within the limits of the universalist social democratic welfare state, was dependent on whom the claims-makers were, the status and positions they held, and the way the idea of multiculturalism was conceptualised and used. It was also dependent on the migratory context of labour immigration in the 1960s and 1970s and on whose behalf the advocates of multiculturalism made their claims. The majority of the labour immigrants were Finnish citizens from the former eastern half of the kingdom of Sweden who were net contributors to the Swedish welfare state. This facilitated the recognition of their ethno-cultural difference, and, following the logic of universalism, the ethno-cultural difference of other minority groups in Sweden. The historical significance of the multicultural moment is still evident in the contemporary immigration and integration policies of Sweden. The affirmation of diversity continues to set Sweden apart from the rest of Europe, now more so than in the 1970s, even though the migratory context has changed radically in the last 40 years.

Hans Jürgen Eysenck. Life and work of one of the most infl uential scientist in the history of psychology

On this article, the biography and work of one of the most influential scientists in psychology history is briefl y introduced. With his work, he laid the bases for the scientific study not only on personality, but also on human behaviour. Hence, the most important contributions done by this author are highlighted in a wide range of areas of our discipline, as well as the vision he had about how psychology should be as a science. A series of considerations related to the current situation of scientific psychology in Argentina, lead us to the conclusion that it is essential to rescue his work from forgetfulness, apart from going back over some of his lines of research and thoughts. 

Digitisation, representation, and formalisation - Digital libraries of mathematics

One of the main tasks of the mathematical knowledge management community must surely be to enhance access to mathematics on digital systems. In this paper we present a spectrum of approaches to solving the various problems inherent in this task, arguing that a variety of approaches is both necessary and useful. The main ideas presented are about the differences between digitised mathematics, digitally represented mathematics and formalised mathematics. Each has its part to play in managing mathematical information in a connected world. Digitised material is that which is embodied in a computer file, accessible and displayable locally or globally. Represented material is digital material in which there is some structure (usually syntactic in nature) which maps to the mathematics contained in the digitised information. Formalised material is that in which both the syntax and semantics of the represented material, is automatically accessible. Given the range of mathematical information to which access is desired, and the limited resources available for managing that information, we must ensure that these resources are applied to digitise, form representations of or formalise, existing and new mathematical information in such a way as to extract the most benefit from the least expenditure of resources. We also analyse some of the various social and legal issues which surround the practical tasks.

Interregional migration 'wage premia': the case of creative and science and technology graduates in the UK

We analyze the migration behavior of graduates from UK universities with a focus on the salary benefits they receive from the migration process. We focus on sequential interregional migration and specifically examine the case of Science, Technology, Engineering and Mathematics (STEM) and Creative subject graduates. Our analysis differs from previous studies in that it accounts explicitly for migrant selectivity through propensity score matching, and it also classifies graduates into different migration behavior categories. Graduates were classified according to their sequential migration behavior first from their pre-university domicile to university and then from university to first job post-graduation. Our results show that ‘repeat migration’, as expected, is associated with the highest wage premium (around 15%). Other migration behaviors are also advantageous although this varies across different types of graduates. Creative graduates, for instance, do not benefit much from migration behaviors other than repeat migration. STEM graduates, on the contrary, benefit from both late migration and staying in the university area to work.

Genomic evidence for the Pleistocene and recent population history of Native Americans

How and when the Americas were populated remains contentious. Using ancient and modern genome-wide data, we found that the ancestors of all present-day Native Americans, including Athabascans and Amerindians, entered the Americas as a single migration wave from Siberia no earlier than 23 thousand years ago (ka) and after no more than an 8000-year isolation period in Beringia. After their arrival to the Americas, ancestral Native Americans diversified into two basal genetic branches around 13 ka, one that is now dispersed across North and South America and the other restricted to North America. Subsequent gene flow resulted in some Native Americans sharing ancestry with present-day East Asians (including Siberians) and, more distantly, Australo-Melanesians. Putative “Paleoamerican” relict populations, including the historical Mexican Pericúes and South American Fuego-Patagonians, are not directly related to modern Australo-Melanesians as suggested by the Paleoamerican Model.

Evolutionary history of Ramphastos toucans: Molecular phylogenetics, temporal diversification, and biogeography

The toucan genus Ramphastos (Piciformes: Ramphastidae) has been a model in the formulation of Neotropical paleobiogeographic hypotheses. Weckstein (2005) reported on the phylogenetic history of this genus based on three mitochondrial genes, but some relationships were weakly supported and one of the subspecies of R. vitellinus (citreolaemus) was unsampled. This study expands on Weckstein (2005) by adding more DNA sequence data (including a nuclear marker) and more samples, including R v. citreolaemus. Maximum parsimony, maximum likelihood, and Bayesian methods recovered similar trees, with nodes showing high support. A monophyletic R. vitellinus complex was strongly supported as the sister-group to R. brevis. The results also confirmed that the southeastern and northern populations of R. vitellinus ariel are paraphyletic. X v. citreolaemus is sister to the Amazonian subspecies of the vitellinus complex. Using three protein-coding genes (COI, cytochrome-b and ND2) and interval-calibrated nodes under a Bayesian relaxed-clock framework, we infer that ramphastid genera originated in the middle Miocene to early Pliocene, Ramphastos species originated between late Miocene and early Pleistocene, and intra-specific divergences took place throughout the Pleistocene. Parsimony-based reconstruction of ancestral areas indicated that evolution of the four trans-Andean Ramphastos taxa (R. v. citreolaemus, R. a. swainsonii, R. brevis and R. sulfuratus) was associated with four independent dispersals from the cis-Andean region. The last pulse of Andean uplift may have been important for the evolution of R. sulfuratus, whereas the origin of the other trans-Andean Ramphastos taxa is consistent with vicariance due to drying events in the lowland forests north of the Andes. Estimated rates of molecular evolution were higher than the ""standard"" bird rate of 2% substitutions/site/million years for two of the three genes analyzed (cytochrome-b and ND2). (C) 2009 Elsevier Inc. All rights reserved.

Phylogeography and evolutionary history of dengue virus type 3

In this study, we revisited the phylogeography of the three of major DENV-3 genotypes and estimated its rate of evolution, based on the analysis of the envelope (E) gene of 200 strains isolated from 31 different countries around the world over a time period of 50 years (1956-2006). Our phylogenetic analysis revealed a geographical subdivision of DENV-3 population in several country-specific clades. Migration patterns of the main DENV-3 genotypes showed that genotype I was mainly circumspect to the maritime portion of Southeast-Asia and South Pacific, genotype 11 stayed within continental areas in South-East Asia, while genotype III spread across Asia, East Africa and into the Americas. No evidence for rampant co-circulation of distinct genotypes in a single locality was found, suggesting that some factors, other than geographic proximity, may limit the continual dispersion and reintroduction of new DENV-3 variants. Estimates of the evolutionary rate revealed no significant differences among major DENV-3 genotypes. The mean evolutionary rate of DENV-3 in areas with long-term endemic transmissions (i.e., Indonesia and Thailand) was similar to that observed in the Americas, which have been experiencing a more recent dengue spread. We estimated the origin of DENV-3 virus around 1890, and the emergence of current diversity of main DENV-3 genotypes between the middle 1960s and the middle 1970s, coinciding with human population growth, urbanization, and massive human movement, and with the description of the first cases of DENV-3 hemorrhagic fever in Asia. (C) 2008 Elsevier B.V. All rights reserved.

Precambrian history of the Zona Transversal of the Borborema Province, NE Brazil: Insights from Sm-Nd and U-Pb geochronology

The Borborema Province has three major subprovinces. The northern subprovince lies north of the Patos shear zone and is comprised of Paleoproterozoic cratonic basement with Archean nuclei, plus overlying Neoproterozoic supracrustal rocks and Brasiliano plutonic rocks. The central subprovince occurs between the Patos and Pernambuco shear zones and is mainly comprised of the Zona Transversal. The southern subprovince occurs between the Pernamabuco shear zone and the Sao Francisco craton and is comprised of a tectonic collage of various blocks, terranes, or domains ranging in age from Archean to Neoproterozoic. This report focuses on the Zona Transversal, especially on Brasiliano rocks for which we have the most new information. Paleoproterozoic gneisses with ages of 2.0-2.2 Ga occur discontinuously throughout the Zona Transversal. The Cariris Velhos suite consists of metavolcanic, metasedimentary, and metaplutonic rocks yielding U-Pb zircon ages of 995-960 Ma. This suite is mainly confined to a 100 km wide belt that extends for more than 700 km within the Alto Pajeu terrane. Sm-Nd model ages in metaigneous rocks cluster about 1.3-1.6 Ga, indicating that older crust was involved in genesis of their magmas. Brasiliano supracrustal rocks dominate the Pianco-Alto Brigida terrane, and they probably also constitute significant parts of the Alto Pajeu and Rio Capibaribe terranes. They are only slightly older than early stages of Brasiliano plutonism, with detrital zircon ages at least as young as 620 Ma; most T(DM) ages range from 1.2 to 1.6 Ga. Brasiliano plutons range from ca. 640 to 540 Ma, and their T(DM) ages range from 1.2 to 2.5 Ga. Previous workers have shown significant correlations among U-Pb ages, Sm-Nd model ages, petrology, and geochemistry, and we are able to reinforce and extend these correlations. Stage I plutons formed 640 -610 Ma and have T(DM) ages less than 1.5 Ga. Stage 11 (610-590 Ma) contains few plutons, but coincides with the peak of compressional deformation, metamorphism, and formation of migmatites. Stage III plutons (590 to ca. 575 Ma) have older T(DM) ages (ca. 1.8-2.0 Ga), as do Stage IV plutons (575 to ca. 550 Ma; T(DM) from 1.9 to 2.4 Ga). Stage III plutons formed during the transition from compressional to transcurrent deformation, while Stage IV plutons are mainly post-tectonic. Stage V plutons (550-530 Ma) are commonly undeformed (except along younger shear zones) and have A-type geochemistry. The five stages have distinct geochemical properties, which suggest that the tectonic settings evolved from early, arc-related magma-genesis (Stage I) to within-plate magma-genesis (Stage V), with perhaps some intermediate phases of extensional environments. (C) 2011 Elsevier Ltd. All rights reserved.

Tectonothermal evolution and exhumation history of the Paleozoic Proto-Andean Gondwana margin crust: The Famatinian Belt in NW Argentina

We studied the P-T-t evolution of a mid-crustal igneous-metamorphic segment of the Famatinian Belt in the eastern sector of the Sierra de Velasco during its exhumation to the upper crust. Thermobarometric and geochronological methods combined with field observations permit us to distinguish three tectonic levels. The deepest Level I is represented by metasedimentary xenoliths and characterized by prograde isobaric heating at 20-25 km depth. Early/Middle Ordovician granites that contain xenoliths of Level I intruded in the shallower Level II. The latter is characterized by migmatization coeval with granitic intrusions and a retrograde isobaric cooling P-T path at 14-18 km depth. Level II was exhumed to the shallowest supracrustal Level III, where it was intruded by cordierite-bearing granites during the Middle/Late Ordovician and its host-rock was locally affected by high temperature-low pressure HT/LP metamorphism at 8-10 km depth. Level III was eventually intruded by Early Carboniferous granites after long-term slow exhumation to 6-7 km depth. Early/Middle Ordovician exhumation of Level II to Level III (Exhumation Period I,0.25-0.78 mm/yr) was faster than exhumation of Level III from the Middle/Late Ordovician to the Lower Carboniferous (Exhumation Period II, 0.01-0.09 mm/yr). Slow exhumation rates and the lack of regional evidence of tectonic exhumation suggest that erosion was the main exhumation mechanism of the Famatinian Belt. Widespread slow exhumation associated with crustal thickening under a HT regime suggests that the Famatinian Belt represents the middle crust of an ancient Altiplano-Puna-like orogen. This thermally weakened over-thickened Famatinian crust was slowly exhumed mainly by erosion during similar to 180 Myr. (C) 2010 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

Denudation history of the Bocaina Plateau, Serra do Mar, southeastern Brazil: Relationships to Gondwana breakup and passive margin development

The Bocaina Plateau, which is situated on the eastern flank of the continental rift of southeastern Brazil, is the highest part of the Serra do Mar. Topographic relief in this area is suggested to be closely related to its complex tectono-magmatic evolution since the breakup of Western Gondwana and opening of the South Atlantic Ocean. Apatite fission track ages and track length distributions from 27 basement outcrops were determined to assess these hypotheses and reconstruct the denudation history of the Bocaina Plateau. The ages range between 303 +/- 32 and 46 +/- 5 Ma, and are significantly younger than the stratigraphic ages. Mean track lengths vary from 13.44 +/- 1.51 to 11.1 +/- 1.48 mu m, with standard deviations between 1.16 and 1.83 mu m. Contrasting ages within a single plateau and similar ages at different altitudes indicate a complex regional tectonothermal evolution. The thermal histories inferred from these data imply three periods of accelerated cooling related to the Early Cretaceous continental breakup, Early Cretaceous alkaline magmatism, and the Paleogene evolution of the continental rift of southeastern Brazil. The oldest fission track ages (>200 Ma) were obtained in the Serra do Mar region, suggesting that these areas were a long-lived source of sediments for the Parana, Bauru, and Santos basins. (C) 2010 International Association for Gondwana Research. Published by Elsevier B.V. All rights reserved.

The Development of Dalton`s Atomic Theory as a Case Study in the History of Science: Reflections for Educators in Chemistry

The inclusion of the history of science in science curricula-and specially, in the curricula of science teachers-is a trend that has been followed in several countries. The reasons advanced for the study of the history of science are manifold. This paper presents a case study in the history of chemistry, on the early developments of John Dalton`s atomic theory. Based on the case study, several questions that are worth discussing in educational contexts are pointed out. It is argued that the kind of history of science that was made in the first decades of the twentieth century (encyclopaedic, continuist, essentially anachronistic) is not appropriate for the development of the competences that are expected from the students of sciences in the present. Science teaching for current days will benefit from the approach that may be termed the ""new historiography of science"".

Structuralism and the Applicability of Mathematics

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.