'Yes, the century is an ashen sun': poem and subject in the philosophy of Alain Badiou

This thesis examines the relation between philosophy, the poem and the subject in the mature philosophy of Alain Badiou. It investigates Badiou’s decisive contribution to these questions primarily by means of comparison, especially to Martin Heidegger, Philippe Lacoue-Labarthe and Theodor Adorno, as well as by analysing Badiou’s readings of poems and prose by Paul Celan and Samuel Beckett respectively as sites of potential dialogue with his immediate predecessors. The thesis stresses the importance of French philosophy’s German heritage, emphasising not only Badiou’s radical departure from Heidegger and his legacy, but also the former’s wholesale rejection of philosophies that would, in the wake of twentieth-century violence and beyond, proclaim their own end or completion. The thesis argues Badiou’s innovative readings of Celan and Beckett to be crucial to understanding this endeavour: for Badiou, both writers use the poem to affirm novel conceptions of subjectivity capable of transcending the historical conditions of their presentation. The title quotation from Badiou’s The Century, ‘Yes, the century is an ashen sun’, anticipates both the affirmative nature of these subjective figures, and their presience, beyond the bounds of a twentieth-century ‘ashen sun’ pervaded by melancholy, for the ‘new suns’ of the twenty-first. The thesis is in four chapters. The first chapter unfolds the central concepts of Badiou’s departure from Heidegger using Paul Celan’s poems to focus the enquiry. It is guided by two of Badiou’s most condensed declarations about the poem, that, firstly, ‘the modern poem harbours a central silence’, and secondly, that ‘Celan completes Heidegger’. The second chapter exposes the political implications of Heidegger’s writings on Friedrich Hölderlin and the role of the subject therein, offering at its close some thoughts about what Badiou calls, following Philippe Lacoue-Labarthe, the poem’s ‘becoming-prose’. It concludes by drawing the poem and politics into relation by way of the philosophical category of the subject. The third chapter reads Badiou’s concept of ‘anabasis’ against Heidegger’s ‘homecoming’ in order to think the possibility of a collective political subject’s formation in the wake of Auschwitz. The final chapter examines the imbrication of the Two of love and the ‘latent poem’ in Badiou’s reading of Samuel Beckett’s late prose, contrasting this ‘affirmative’ reading of Beckett to Theodor Adorno’s earlier emphases on negation. Following its investigations of subjectivity, poem and prose throughout, the thesis concludes by returning to the title quotation in order to unfold the particular relations between subject, affirmation and negation Badiou’s philosophy enacts, and to offer further routes forward for research regarding Badiou’s philosophy and aesthetic figuration.

Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.