Lautman and the Reality of Mathematics

Working in he 1930s, Albert Lautman described with extraordinary clarity the new understanding of mathematics of that time. He delighted in the multiple manifestations of a common idea in different mathematical fields. However, he took the common idea to belong not to mathematics itself, but to an 'ideal reality' sitting above mathematics. I argue in this paper that now that we have a mathematical language which can characterize these common ideas, we need not follow Lautman to adopt his form of Platonism. On the other hand, Lautman should be much better known than he is for pointing philosophy towards this most important feature of mathematics

Modal homotopy type theory

Chapter IV of a book which looks to demonstrate what philosophy can gain from the new formal language of modal homotopy type theory. Here I explore how we should understand the addition of modalities to homotopy type theory. This chapter will sit between modified versions of http://philsci-archive.pitt.edu/13448/ and http://philsci-archive.pitt.edu/11809/

Crystal structures of some complexes of group IB ethynyl compunds

Interest in these compounds centred on the bonding between the ethynyl groups and the metal atoms. The structures were determined by heavy atom techniques, and refined by the method of least squares, using three-dimensional data. Phenylethynyl(trimethylphosphine)copper(l), Me(_3)PCuC≡CPh, is tetrameric. The centresymmetric molecules are nearly flat, apart from the phosphine groups. The four copper atoms form a zig-zag chain, with Cu...Cu distances 2.45, 2.69, 2.4-5 Ǻ. Two phosphine groups are attached to each terminal copper atom. Two of the ethynyl groups lie on a line through the two inner copper atoms, to which they are σ-bonded. The other two are each 'side-on' bonded to an inner copper atom, with the bond to the phenyl group distorted away from the copper atom. Their terminal carbon atoms each form a bridge bond with two further copper atoms in the chain. Neglecting any copper- copper interaction, the coordination around the inner copper atoms is approximately trigonal, and around the terminal copper atoms, tetrahedral. Phenylethynyl(trimethylphosphine)silver(I), Me(_3)PAgCsC≡h , has silver atoms in infinite, almost straight, chains, with Ag...Ag = 3.03 Ǻ. Alternate silver atoms lie on centres of symmetry, and are σ-bonded to two ethynyl groups. These are 'side-on' bonded to adjacent silver atoms, which lie on two-fold axes, and which are bonded to two phosphine groups. The 'side-on' bonding is not symmetrical. (Ag-C = 2.55, 3.04 Ǻ.) The silver atoms are alternately in linear, and approximately tetrahedral, coordination. Phenylethynyl(isopropylamine)gold(I), (^i)PrfNH(_2)AuC≡CPh, has gold atoms in infinite zig-zag chains, related in pairs by two-fold axes. Au. ..Au = 3.72 2 Ǻ. along the chains, 3.27 Ǻ. Between chains. Each gold atom is linearly coordinated to an ethynyl carbon and an amine nitrogen atom, lying in the plane of the zig-zag. The arrangement excludes association through gold-ethynyl interaction, the shortest intermolecular distances being gold- gold or gold-nitrogen contacts

Quantum coherence in trapped ions

The techniques of ion trapping have been indispensable for the study of single particles and have greatly increased our understanding of the physical world. With a high degree of control over single quantum systems made possible by recent technical developments, trapped ion researchers are now looking to observe increasingly complex quantum dynamics. There is nothing fundamentally limiting the size such systems can scale to, if the remaining engineering challenges can be overcome, and there is consequently enormous potential for our understanding of physical processes on the boundary between simple quantum and large scale classical effects. The transition between quantum and classical dynamics is characterised by decoherence, which reduces the purity of quantum states as they couple to the environment. Investigation into the mechanisms of decoherence requires the development of novel tools for its classification, which motivates the experiments presented in this work. These show that multi-level coherence in the motional state of a trapped ion can be verified from interference patterns which extend the Ramsey technique. The metric uses simple operations and is shown not to be able to produce false positives, making it of interest in the study of coherence in noisy intermediate scale systems. The motional state of a trapped ion cannot be directly measured, and the scheme shows it is possible to extract information about a quantum system coupled to the measurement basis. Coherence between quantum states can enhance information processing and sensing, which is driving the development of techniques for preserving coherence in the presence of noise. This motivates the project begun in this thesis, which is to design and implement control fields for robust ion trap quantum logic. The rapid progress in the scale of ion trap devices expected in the coming years means new leaps in our understanding of the physical world could happen at any moment.Open Acces

Knowledge management in international development charities

This thesis investigates the effectiveness and potential longevity of Knowledge Management in three international development charities, in order to compare their experiences with the commercial context in which Knowledge Management originated. By this means, the research explores how well, or otherwise, Knowledge Management can be fitted into a different setting. It also throws significant light on the transfer of business practices more generally. Chapter one assesses the evolution of the discipline Knowledge Management. It also provides key information about International Development Charities. Chapter two identifies the theoretical foundations of Knowledge Management as a prescription for organisational effectiveness, together with recommended best practices. Two environmental factors are emphasised: the role of information technology and, given the historic link to Japanese workstyles, ideas about organisational `culture'. In chapter three, the methodology for practical enquiry, derived from organisational system theory, is presented, and the problems in assessing effectiveness are discussed. Chapters four and five provide the substantive outcome of the fieldwork. Patterns that emerge from the data are drawn together in chapter six, highlighting the selective nature of Knowledge Management in application and demonstrating both similarities to and divergences from the original concept. In particular, there are specific challenges posed by the international reach of development charities. The overall conclusions in chapter seven confirm that Knowledge Management undoubtedly chimes with the broad aims of international charities. At the same time, the transferability of Knowledge Management depends crucially upon its adaptability to the organisations' aims, resources, and `culture'. Where it is accepted that knowledge handling is needed to build organisational capacity, then Knowledge Management can provide a framework which, when combined with technological advances, is a tool, rather than the answer, for international charities engaged in the continuing struggle to abolish poverty

A Qualitative Study of Undergraduate Instrumentalists Teaching Elementary General Music Education

The central purpose of this multiple-case study was to describe the professional identities of six general music teachers who identified as instrumentalists as undergraduates. The study builds upon research addressing why students choose music education (Bergee, et al., 2001; Bright, 2006; Gillespie & Hamann, 1999; Lee, 2003; Madsen & Kelly, 2002) and the reasons some instrumentally "tracked" students may choose general music (Anderson-Nickel, 1997; Robinson, 2010). This study investigated tensions between the participants' instrumental backgrounds and the professional demands of general music teaching, and the role of those tensions in shaping professional identities. The conceptual framework is grounded in the work of Gee (2000) who suggests that the existence of identities requires interpretive systems through which individuals and institutions interact. The study describes tensions between institutional identities and core identities as important to the process of participants' professional identity development. Participants were general music teachers, 24 - 51 years of age, from different undergraduate institutions and who teach in different regions of the country. Semi-structured interviews, participant essays, transcripts, notebooks, and institutional websites were used for data collection. Participants' stories represent both narrative inquiry and case study approaches to qualitative research. Data analysis included a process of recontextualization (Coffey & Atkinson, 1996) to facilitate the production of narratives and coding techniques in individual and cross-case analysis. Cross-case analysis revealed seven emergent themes: (1) concerns about "perceived limitations" (Robinson, 2010, p. 41) of ensemble teaching as an important factor in the choice to teach general music, (2) the structure and requirements of directing a band as a factor in a turn toward working with younger students, (3) the unique structure of general music classes as a source of initial challenge, (4) a given curriculum or scope and sequence as something of value, (5) vocal teaching as a unique challenge for some instrumentally-trained general music teachers, (6) changes in self-identification as linked to agreements between institutional identities and core identities, and (7) professional positionality in relation to students, not colleagues. The concluding section offers suggestions for future research and implications for undergraduate music programs and school systems

Discovery of a lipid synthesising organ in the auditory system of an insect

Weta possess typical Ensifera ears. Each ear comprises three functional parts: two equally sized tympanal membranes, an underlying system of modified tracheal chambers, and the auditory sensory organ, the crista acustica. This organ sits within an enclosed fluid-filled channel–previously presumed to be hemolymph. The role this channel plays in insect hearing is unknown. We discovered that the fluid within the channel is not actually hemolymph, but a medium composed principally of lipid from a new class. Three-dimensional imaging of this lipid channel revealed a previously undescribed tissue structure within the channel, which we refer to as the olivarius organ. Investigations into the function of the olivarius reveal de novo lipid synthesis indicating that it is producing these lipids in situ from acetate. The auditory role of this lipid channel was investigated using Laser Doppler vibrometry of the tympanal membrane, which shows that the displacement of the membrane is significantly increased when the lipid is removed from the auditory system. Neural sensitivity of the system, however, decreased upon removal of the lipid–a surprising result considering that in a typical auditory system both the mechanical and auditory sensitivity are positively correlated. These two results coupled with 3D modelling of the auditory system lead us to hypothesize a model for weta audition, relying strongly on the presence of the lipid channel. This is the first instance of lipids being associated with an auditory system outside of the Odentocete cetaceans, demonstrating convergence for the use of lipids in hearing