Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography : leaves 176-178. / Ph.D.

According to some (e.g. Friston, 2010) predictive processing (PP) models of cognition have the potential to offer a grand unifying theory of cognition. The framework defines a flexible architecture governed by one simple principle - minimise error. The process of Bayesian inference used to achieve this goal results in an ongoing flow of prediction that both makes sense of perception and unifies it with action. Such a provocative and appealing theory naturally has caused ripples in philosophical circles, prompting several commentaries (e.g. Hohwy, 2012; Clark, 2016). This thesis tackles one outstanding philosophical problem in relation to PP - the question of mental representation. In attempting to understand the nature of mental representations in PP systems I touch on several contentious points in philosophy of cognitive science, including the explanatory power of mechanisms vs. dynamics, the internalism vs. externalism debate, and the knotty problem of proper biological function. Exploring these issues enables me to offer a speculative solution to the question of mental representation in PP systems, with further implications for understanding mental representation in a broader context. The result is a conception of mind that is deeply continuous with life. With an explanation of how normativity emerges in certain classes of self-maintaining systems of which cognitive systems are a subset. We discover the possibility of a harmonious union between mechanics and dynamics necessary for making sense of PP systems, each playing an indispensable role in our understanding of their internal representations.

Images of Oceania and Polynesia have traditionally been exoticised and romanticised by Western representations of a "paradise" populated by primitive natives with grass skirts and ukuleles. However, the movement towards political independence in the 1960s and 1970s has seen the emergence of a corpus of indigenous representations that depict and portray the real situation. These indigenous representations speak of subjugation and moreover testify to the debilitating effects colonialism has on cultural identities. The geographical area covered by this thesis is Western Polynesia, specifically the Pacific Island nations of Fiji, Tonga and Western Samoa and is concerned with literary representations. The thesis examines significant developments and trends in the creative writing of indigenous and migrant writers in these three countries of Western Polynesia: Western Samoa, Tonga and Fiji, seeing these literary representations from within as a writing out of multi-faceted aspects of the shifting identities of Pacific peoples in a post-colonial world. The introduction focuses on the historical colonial/post-colonial context of Western Polynesian writing and the socio-political imperatives for change which have had an impact on these writers and the texts they have produced. It also discusses the literary and anthropological representation of these Islanders from the 'outside', from the perspective of a European hegemonic self, forming the 'orientalist' stereotypes against which the initial texts written by the Pacific's colonised 'others' in the early 1970's reacted so strongly. Chapter One sets out the conceptual framework within which these texts will be discussed and analysed, beginning with indigenous and local concepts which indigenous and migrant Pacific Islanders use to connect and accommodate different 'ways of seeing' this representative body of literature, then moving on to other theorists concerned with literary representation and post-coloniality. Chapters Two to Nine explore the writing of these three countries, beginning with the fiction of Albert Wendt, one of the major writers from Western Polynesia who has an established regional and international literary reputation, and then progressing to focus on other selected representative writers of the three countries, including those in the early stages of attempting publication. The thesis concludes by discussing the texts from all three countries and tying them together in the various thematic strands of cultural clash, the widening of borders, the quest for self-definition and national identity in the contemporary Pacific, reiterating major points and examining possible future directions in Western Polynesian writing. The study takes an interdisciplinary approach to the critical analysis of Western Polynesian literature, maintaining the importance of seeing them as important forms of cultural communication in post-colonial contexts, as literary representations from the inside, writing out of a cultural consciousness which values the various 'pasts' of Polynesia as definitive 'maps' which provide the grids and bridges which Pacific Islanders in this part of Oceania can utilise to mediate their experiences and articulate their identities, to fit the widening boundaries of the Pacific into a post-colonial global context.

A persistent issue of debate in the area of 3D object recognition concerns the nature of the experientially acquired object models in the primate visual system. One prominent proposal in this regard has expounded the use of object centered models, such as representations of the objects' 3D structures in a coordinate frame independent of the viewing parameters [Marr and Nishihara, 1978]. In contrast to this is another proposal which suggests that the viewing parameters encountered during the learning phase might be inextricably linked to subsequent performance on a recognition task [Tarr and Pinker, 1989; Poggio and Edelman, 1990]. The 'object model', according to this idea, is simply a collection of the sample views encountered during training. Given that object centered recognition strategies have the attractive feature of leading to viewpoint independence, they have garnered much of the research effort in the field of computational vision. Furthermore, since human recognition performance seems remarkably robust in the face of imaging variations [Ellis et al., 1989], it has often been implicitly assumed that the visual system employs an object centered strategy. In the present study we examine this assumption more closely. Our experimental results with a class of novel 3D structures strongly suggest the use of a view-based strategy by the human visual system even when it has the opportunity of constructing and using object-centered models. In fact, for our chosen class of objects, the results seem to support a stronger claim: 3D object recognition is 2D view-based.

This dissertation focuses on the particular ways in which early modern English playwrights connect geographical territory depicted in charts, travel, and colonial literature to the female body. By examining the rhetorical methods that both male and female writers employ, I demonstrate how the emerging imperial discourse relies upon the idea that through marriage, women represent and convey territory for their male relatives. But as physical embodiments of family wealth and property that serve as crucial links between males, these women can subvert this use of their bodies in order to formulate a site of resistance to masculine modes of mapping that penetrate, explore, and chart both territory and bodies. Beginning with depictions of Queen Elizabeth and English geography, I investigate plays from the 1570s to the 1670s that reflect and reshape Elizabeth's cartography of her virgin body. In my consideration of Christopher Marlowe's Tragedie of Dido, Queene of Carthage, and Tamburlaine, I argue that although Dido and Zenocrate serve to represent their homelands and legitimize its conquest by their men, the two queens upset this rhetoric when they delineate their own geographic re-imaginings. Elizabeth Cary's The Tragedie of Mariam and The History of the Life, Reign, and Death of Edward II reveal how both Mariam and Isabel are inscribed by the same colonial rhetoric that imagines the women to be fertile land that can only be properly civilized by men. The next chapter reveals how Thomas Heywood's works reflect and legitimize the growing importance of trade rather than outright conquest in English overseas expansion. In If You Know Not Me, You Know No Bodie and The Fair Maid of the West, Heywood's Queen Elizabeth and her counterpart Bess Bridges demonstrate how any woman's virginity becomes a commodity to be used and traded as a representation of English virtue. The final chapter examines how Margaret Cavendish in Loves Adventures and Bell in Campo reclaims the body as a site of potential resistance by redeploying the rhetoric of virginity and cartography. The coda calls for continued investigation into the uses of geographic rhetoric through the example of Queen Anne.

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Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to produce invariants in tensor products of minuscule representations. For each web, a configuration space of points in the affine Grassmannian is constructed. This configuration space gives a natural way of calculating the invariant vectors coming from webs. In the case of G = SL_3, non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0). In the case of G = SL_n, a sufficient condition for a set of webs to yield a basis is given. Using this condition and a generalization of a technique by Westbury, a basis is constructed for SL_n. Due to the geometric Satake correspondence there exists another natural basis of invariants, the Satake basis. This basis arises from the underlying geometry of the affine Grassmannian. There is an upper unitriangular change of basis from the basis constructed above to the Satake basis. An example is constructed showing that the Satake, web and dual canonical basis of the invariant space are all different. The natural action of rotation on tensor factors sends invariant space to invariant space. Since the rotation of web is still a web, the set of vectors coming from webs is fixed by this action. The Satake basis is also fixed, and an explicit geometric and combinatorial description of this action is developed.

This thesis presents work on analytical reasoning with external representations (ERs) using problems similar to those used in the US GRE college-entrance examination. The work investigates the factors associated with effective ER use in situations where subjects select, construct and reason with their own ERs. Practically all previous work has tended to focus solely upon performance rather than process. In this thesis the emphasis is upon cognitive processes during the entire time-course of reasoning with ERs, from problem comprehension through to answer selection. A background to the work is provided by 2 comprehensive reviews of: 1.) previous research on ERs and reasoning and 2.) the cognitive and semantic properties of ERs. Results from three empirical studies are reported. The first study examined a large corpus of 'workscratchings' produced by subjects as they solved paper and pencil-based analytical reasoning problems under test conditions. The workscratching ERs showed great diversity between and within subjects and across a range of problems. They included lists, various kinds of table, set diagrams, node and arc diagrams, first-order and propositioned logic, plans and natural language. It is shown that problem-solving performance is related to the type of ER used in the solution. The second study utilised a computer-based system (switchERI). The system administered analytical reasoning problems and provided a. range of ER construction environments for the subject to choose and switch between. User-system interactions were recorded dynamically during problem solving. This methodology permitted microanalyses of the cognitive events at each stage during the time-course of problem solving. A process account of analytical reasoning with ERs is developed in which five major stages are identified - problem comprehension, ER selection, ER construction, read-off from the ER and answer selection/responding. A range of common slips and misconceptions are identified at each stage. The results show, inter alia, that subjects whose responses are consistent with their ERs perform better than subjects whose responses are inconsistent with their ERs even if the ER is partially incorrect. The data from the workscratching analysis and switchERI study informed the design of' switchERII, a second system. SwitchERII incorporates a. representation of the semantics of Euler's Circles, dynamically parses the user's representation and provides feedback and advice. A third study was conducted with the switchERII system. Few, if any, studies to date have attempted to relate subjects' prior knowledge of ER formalisms to their reasoning performance. Subjects' prior knowledge of ER formalisms was assessed in both switchER studies. It was observed that subjects' performance on representation interpretation tasks does not necessarily predict their performance in conditions where they select and construct their own representations. The reasons for the decoupling are discussed. Data from all three studies show that subjects often utilise multiple representations in their solutions, either concurrently or serially via. ER switching. Two distinctly different types of switching were observed. One kind ('thrashing') is associated with poorer performance and reflects less comprehensive prior knowledge, inability to select au appropriate ER and hazy problem comprehension. Judicious switching, on the other hand, is associated with high levels of problem comprehension and skilled matching of the ERs' properties to changing task demands. It is claimed that effective reasoning with ERs involves complex interactions between at least three factors: (a.) within-subject variables such as the subject's representational repertoire (prior knowledge) and representational modality preferences (cognitive style); (b.) skill at overcoming a variety of barriers to comprehension and an ability to discern the salient attributes and characteristics of different problem types and (c.) an understanding of the semantic and cognitive properties of graphical and non-graphical ERs coupled with an ability to match those properties to the problem's task demands. It is suggested that the role of externalisation in reasoning with ERs may be to facilitate the swapping of information between cognitive subsystems. A mechanism by which the use of diagrammatic ERs may facilitate self-explanation is also proposed. The thesis concludes with an argument in favour of a domain-independent 'ER curriculum'. It is suggested that direct instruction in the use of a range of ERs might equip students with wider representational repertoires and hence allow them more scope to indulge their representational preferences. Finally, several directions for future work are proposed. These include extending the representational semantics of switchERII, evaluating various types of system feedback and implementing a mechanism for checking for slips during read-off from ERs.

Let l be a prime and let q be a prime power not divisible by l. Put G=GI[subscript n](F[subscript q])and fix a representation pi of G over a sufficiently large finite field, k, of characteristic l, so that pi is cuspidal but not supercuspidal. We compute the W(k)[G]-endomorphism ring of the projective envelope of pi under the assumption that l>n. / text

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