The Argument for Democracy

This chapter defends an epistemic argument for democracy, namely the argument that the rule of the many is better at aggregating knowledge and, in the version presented here, at producing better decisions than the rule of the few. This argument builds on the formal properties of two key democratic decision-making mechanisms of democracy, namely inclusive deliberation on equal grounds and majority rule with universal suffrage. Properly used in sequence and under the right conditions, these two mechanisms ensure that no information and viewpoint is ignored and maximize the cognitive diversity brought to bear on collective political problems and predictions. Building on existing formal results by Lu Hong and Scott Page, the chapter introduces the “Number Trumps Ability” theorem, which formalizes the intuition that many minds are smarter than just a few. Under the right conditions systems governed by democratic decision-procedures can be expected to deliver greater epistemic performance than less inclusive and egalitarian systems.

Trajective Locomotion

This chapter examines the perceptual and aesthetic properties of the “follow shot,” a tracking shot that follows a human subject on foot from behind. Analyzing two films that conspicuously explore the follow shot as their core stylistic principle, Alan Clarke’s Elephant (1989) and Gus Van Sant’s Elephant (2003), this chapter shows how the formal properties of the follow shot—the camera’s forward movement, its denial of the subject’s face, and its sense of being tethered to its subject—are crucial to each film’s meditation on violence and human agency. By visually emphasizing the forward movement of its subjects while denying access to their interiorities (via the face), the follow shot attunes its viewers to its subject’s agency as a sense of pure “towardness” devoid of psychological insight, an effect the chapter calls “trajectivity.” Such a mode of representing subjectivity, the chapter argues, opposes cinematic traditions that rely on a seamless relation between psychological motivation, human expression, and human action. In doing so, the chapter offers a revised film theoretical account of the relation between camera movement, expression, and ethics.

HANS ABRAHAMSEN AND A RECURRENT ‘CHILDLIKE’ RHYTHM

Hans Abrahamsen has reused the same rhythm across four pieces spanning 33 years: in his Ten Studies, for solo piano, and Six Pieces, for horn trio (both from 1984), in Schnee (2008) and in Three Pieces, for orchestra (2017). Because self-borrowing is crucial to Abrahamsen's compositional practice, this rhythm provides a case study in his compositional priorities, particularly in the role canonic techniques play in his music. Although the rhythm's formal properties lend it a marked asymmetry at the foreground, it is presented in Schnee as part of a canon with highly symmetric pitch materials. But despite this apparent conflict between symmetries and asymmetries, Abrahamsen's music freely combines different approaches to the rhythm, as long as it is linked to a high-register shimmer, suggesting that Abrahamsen's noted uses of canons are largely for textural ends.

Towards an Extrinsic Formalization of Featherweight Java in Agda

Featherweight Java is one of the most popular calculi which specify object-oriented programming features. It has been used as the basis for investigating novel language functionalities, as well as to specify and understand the formal properties of existing features for languages in this paradigm. However, when considering mechanized formalization, it is hard to find an implementation for languages with complex structures and binding mechanisms as Featherweight Java. In this paper we formalize Featherweight Java, implementing the static and dynamic semantics in Agda, and proving the main safety properties for this calculus.

Decidable Subtyping for Path Dependent Types

<p>Path dependent types form a central component of the Scala programming language. Coupled with other expressive type forms, path dependent types provide for a diverse set of concepts and patterns, from nominality to F-bounded polymorphism. Recent years have seen much work aimed at formalising the foundations of path dependent types, most notably a hard won proof of type safety. Unfortunately subtyping remains undecidable, presenting problems for programmers who rely on the results of their tools. One such tool is Dotty, the basis for the upcoming Scala 3. Another is Wyvern, a new programming language that leverages path dependent types to support both first class modules and parametric polymorphism. In this thesis I investigate the issues with deciding subtyping in Wyvern. I define three decidable variants that retain several key instances of expressiveness including the ability to encode nominality and parametric polymorphism. Wyvfix fixes types to the contexts they are defined in, thereby eliminating expansive environments. Wyvnon-μ removes recursive subtyping, thus removing the key source of expansive environments during subtyping. Wyvμ places a syntactic restriction on the usage of recursive types. I discuss the formal properties of these variants, and the implications each has for expressing the common programming patterns of path dependent types. I have also mechanized the proofs of decidability for both Wyvfix and Wyvμ in Coq.</p>

Decidable Subtyping for Path Dependent Types

<p>Path dependent types form a central component of the Scala programming language. Coupled with other expressive type forms, path dependent types provide for a diverse set of concepts and patterns, from nominality to F-bounded polymorphism. Recent years have seen much work aimed at formalising the foundations of path dependent types, most notably a hard won proof of type safety. Unfortunately subtyping remains undecidable, presenting problems for programmers who rely on the results of their tools. One such tool is Dotty, the basis for the upcoming Scala 3. Another is Wyvern, a new programming language that leverages path dependent types to support both first class modules and parametric polymorphism. In this thesis I investigate the issues with deciding subtyping in Wyvern. I define three decidable variants that retain several key instances of expressiveness including the ability to encode nominality and parametric polymorphism. Wyvfix fixes types to the contexts they are defined in, thereby eliminating expansive environments. Wyvnon-μ removes recursive subtyping, thus removing the key source of expansive environments during subtyping. Wyvμ places a syntactic restriction on the usage of recursive types. I discuss the formal properties of these variants, and the implications each has for expressing the common programming patterns of path dependent types. I have also mechanized the proofs of decidability for both Wyvfix and Wyvμ in Coq.</p>

Formal aspects of parametrized topological complexity and its pointed version

The notion of parametrized topological complexity, introduced by Cohen, Farber and Weinberger, is extended to fiberwise spaces which are not necessarily Hurewicz fibrations. After exploring some formal properties of this extension we also introduce the pointed version of parametrized topological complexity. Finally, we give sufficient conditions so that both notions agree.

"It‘s Hard to Keep Track": Mapping a Shifting Nation in Dylan Horrocks‘s Hicksville

<p>Using an art form that justifiably lays claim to both visual and literary genealogies—the graphic novel—Dylan Horrocks's Hicksville advances, rather than strictly challenges, many of the discussions which have informed the local manufacture of art and literature. My purpose in this thesis is to explore Horrocks's deployment of the critical perspectives of both art historical and literary discourse as they have developed from the pre-colonial to the twenty-first century in New Zealand, especially those associated with cultural nationalism. Hicksville claims a particular relation to the existing traditions within both art-historical and literary lines wherein they are conjoined in practice; integrated into the formal properties of Horrocks's work, the traditional concerns of local art and literature are not only subject matter but guide Horrocks‘s approach to narrative. The tension between art and place—the responsibility of the artist to the nation and its referents—appears in Hicksville as a structuring device rather than polemic via its concern with the economisation of art—or global capitalism—as it bears upon particular places and art practices. Yet Horrocks‘s handling of this theme upholds neither aestheticism nor populism. Rather, he invites the reader to make sense of extensive references to a range of artistic figures, from Heaphy to Hergé to Hotere, in a way that accounts for their equal force. Hicksville thus deliberately destabilises the joint histories of art and literary history to pointed effect, valuing its range of artistic and cultural inheritances—whether the visual or literary, the highbrow or lowbrow—for how they can remind us that contemporary artistic accounts of New Zealand must also consider the various ways the country has been constructed throughout its wider</p>

"It‘s Hard to Keep Track": Mapping a Shifting Nation in Dylan Horrocks‘s Hicksville

<p>Using an art form that justifiably lays claim to both visual and literary genealogies—the graphic novel—Dylan Horrocks's Hicksville advances, rather than strictly challenges, many of the discussions which have informed the local manufacture of art and literature. My purpose in this thesis is to explore Horrocks's deployment of the critical perspectives of both art historical and literary discourse as they have developed from the pre-colonial to the twenty-first century in New Zealand, especially those associated with cultural nationalism. Hicksville claims a particular relation to the existing traditions within both art-historical and literary lines wherein they are conjoined in practice; integrated into the formal properties of Horrocks's work, the traditional concerns of local art and literature are not only subject matter but guide Horrocks‘s approach to narrative. The tension between art and place—the responsibility of the artist to the nation and its referents—appears in Hicksville as a structuring device rather than polemic via its concern with the economisation of art—or global capitalism—as it bears upon particular places and art practices. Yet Horrocks‘s handling of this theme upholds neither aestheticism nor populism. Rather, he invites the reader to make sense of extensive references to a range of artistic figures, from Heaphy to Hergé to Hotere, in a way that accounts for their equal force. Hicksville thus deliberately destabilises the joint histories of art and literary history to pointed effect, valuing its range of artistic and cultural inheritances—whether the visual or literary, the highbrow or lowbrow—for how they can remind us that contemporary artistic accounts of New Zealand must also consider the various ways the country has been constructed throughout its wider</p>