Algebraic Properties of Parikh Matrices of Binary Picture Arrays

A word is a finite sequence of symbols. Parikh matrix of a word is an upper triangular matrix with ones in the main diagonal and non-negative integers above the main diagonal which are counts of certain scattered subwords in the word. On the other hand a picture array, which is a rectangular arrangement of symbols, is an extension of the notion of word to two dimensions. Parikh matrices associated with a picture array have been introduced and their properties have been studied. Here we obtain certain algebraic properties of Parikh matrices of binary picture arrays based on the notions of power, fairness and a restricted shuffle operator extending the corresponding notions studied in the case of words. We also obtain properties of Parikh matrices of arrays formed by certain geometric operations

The social occupations of modernity : philosophy and social theory in Durkheim, Tarde, Bergson and Deleuze

This thesis explores the relationship between occupations and the ontology of the social. I begin by drawing a distinction between the messianic and the modern as concentrated in the affective transformation of vocation into occupation. I then, in the Introduction, sketch an ontic-ontological contrast proper to the modern, between modernity, as the collective problematization of social diversity, and the contemporary, as the plural ground of need which provides a source for these problematizations. I argue that this distinction will enable me to shed new light on the occupational as a distinctly modern event. In Part I, I begin by providing a reading of Durkheim in which I argue that the occupational is to be understood ontologically, but no longer by means of the theorization of society and social types. This kind of theorization, exemplified in Durkheim's concept of solidarity, contains a fundamental ambiguity between this concept's ontological senses of original diversity and of unity in diversity. Durkheim's thought is thus first intelligible in terms of an implicit evolutionary sense of coherence or `need of wholeness.' However, the explicit evolutionary framework and its central typological difference between the mechanical and organic is an attempt to resolve the ambiguity that must fail because it addresses primarily a distinction of obligation rather than a distinction of need. Obligation is shown to be a concept of facticity which overcodes and obscures the distinction of need. I then go on to argue that sociality can be better accounted for in terms of a continuity of social becoming which is revealed in a perspective of modernity purged of the modernist tendency to metaphorize this continuity in terms such as `solidity' (Durkheim) and `flow' (Tarde). This perspective is the irreducibly plural perspective of the contemporary, which, I conclude Part I by suggesting, lies in a sense of merging with a social outside. In Part II, I turn to investigate the outside by discussing the social thought of Bergson and Deleuze. Bergson's thought is presented as an alternative to the deductivesociologistic approaches of Durkheim and Tarde, because it attempts to critically affirm the smooth duration of social continuity. However, I argue that the notion of `open society' that Bergson presents is still too tied to a model of rare spirituality and hence to the messianic perspective. I then proceed to a social-theoretical analysis of Deleuze's oeuvre, in order to show how he uses elements of a thought of continuity from Tarde (microsociology) and from Bergson (multiplicity), but that he is able to transcend the family-model-centeredness of Tarde and the rare-spiritual-modelcenteredness of Bergson, by theorizing non-modelled figures of transformative affective multiplicity inscribed within the actual, ie. `full particularities'. In my concluding chapter, I show how the intellectual trajectory which takes us from Durkheim to Deleuze can be analysed as a movement from a doctrine or relatively passive notion of social externality towards a more active social image of the outside. In particular, I am concerned to show how this image of the outside can be recontextualized in terms of a movement of occupation that can be thought of as always combining a sense of the contemporary with a sense of modernity

The pornographical: a mimetic ethics of bodies

This thesis is situated across the fields of contemporary political philosophy, critical theory and feminist/gender studies. It argues that the notion of an ‘ana-aesthetic’ is required in order to provide a fuller sense of the conceptual nuances regarding pornography. The ‘ana-aesthetic’ is suggested as the ground and surface economy for this ‘unsayable something’ that is so much a part of the everyday common senses of contemporary life and art. Distinct from the ‘anti-aesthetic’, the ‘ana-aesthetic’ utilises a discursive methodology, and in sidestepping the usual moral entanglements found in attempts to analyse sexually explicit and often misogynistic pornographies, this thesis shows how the ‘ana-aesthetic’ surface of ‘the pornographical’ generates a mimetic and bodily ethics. ‘The pornographical’ is discussed in terms of its techne of comic humour, as a way of creating substance without lapsing into abyssal logics of lack; and the manner in which sexual meaning of fantasy is pleasurable, forming compressed data. The comic is suggested as something found, a cultural ‘ready-made’ gesture, of pleasure, produced through an economic expenditure of ideational mimetics (upon cathexis). This thesis suggests that through the comic, ‘the pornographical’ creates mimetic economies of witnessing. ‘The pornographical’ occupies a strange cultural position in its relationship to both the body and to technology. It is this relationship that gives ‘the pornographical’ its paradoxical ‘ana-linguistic’/’a-radical’ (without a ‘root’) structure, that generates a way of thinking that is related to and also embodies and mediates the body, without positing sexuality as an essentialism

MA

thesisMy thesis derives its impetus and its structure from the work and thought of Gregory Bateson. My aim is to demonstrate the ongoing vitality of his ecology of Mind by tracing the connections between his work and that of Gilles Deleuze, Félix Guattari, and Alain Badiou. Part I represents a broad overview of Bateson's major works, emphasizing his theories of abduction and recursivity as critical philosophical concepts. Bateson's notion of abduction as a third investigatory methodology suggests a means for connecting his work to that of other theorists. A pioneer of cybernetics, his probing of the recursive role of information feedback and of the pragmatic interface between organisms and their environment can be read as a meta-model for a multiperspectival approach to environmental issues and texts. Part II explores the differences and the reiterative similarities in the work of Bateson, the French writing team of Félix Guattari and Gilles Deleuze, and contemporary French philosopher Alain Badiou. Using mathematical notation as metaphoric semiotics, I argue that a theoretical multiplicity moves rhizomatically between and across the very permeable boundaries that may be drawn between these theorists, and that the emerging connections describe a pregnant holism. Part III moves to employ the insights of this theoretical analysis in a more pragmatic application of these shared insights and concerns. In a recent journal article. Dr. Robert Cox urged the environmental communication community to define itself as a crisis discipline. Bateson's vision for ecological holism was predicated on respecting the dangers inherent in ad hoc intervention in systems whose interconnectivity may be little perceived when defined in causal and linear terms. The dangers of rhetorically limiting the semantics of environmental communication to a heuristic rather than a holistic approach are further explored using the work of Deleuze, Guattari and Badiou. This section provides a discursive and diacritical response to Dr. Cox's proposals. My thesis concludes with the recognition of the depth of Gregory Bateson's vision and of the contemporaneity still vibrant in his perspectives. Bateson is in many ways the exemplar of an environmental humanities scholar, and I weave that thread into my concluding remarks

A Multifaceted Performance Model for the Multiple Percussion Performance Practice: Performance Analysis of Select Works toward Developing a Graduate Curriculum

The purpose of this document is to articulate the various dimensions of the solo multiple percussion performance practice, the primary objective being to construct appropriate graduate curricula. It was found that the necessary skills and concepts could be categorized into four dimensions that make up the multi-faceted model: (1) equipment and setup, (2) notational style, (3) technical demands, and (4) conceptual performance. Requisite skills were posited from performance analyses of over fifty solo works that range from intermediate to advanced difficulty. Representative works are described that might effectively introduce and challenge these requisite skills and concepts, as are exemplary pieces that require their mastery. One piece that I performed for recital within my doctoral program was selected for each dimension to provide experiential details: The Anvil Chorus is used to describe equipment and setup, Psappha for notational style and devices, Thirteen Drums for technical facility, and Tunnels for the performance concept. I conclude the document with sample program curricula suggested for master’s and doctoral level, as well as curricula specific to each dimension of the performance model. It is my hope that the percussion instructor will use this model to analyze their own inventory and to include future additions to the literature for creating an effective and comprehensive graduate multiple percussion curriculum