8 research outputs found
Metaphor and mathematics
Traditionally, mathematics and metaphor have been thought of as disparate: the former rigorous, objective, universal, eternal, and fundamental; the latter imprecise, derivative, nearly - if not patently - false, and therefore of merely aesthetic value, at best. A growing amount of contemporary scholarship argues that both of these characterizations are flawed. This dissertation shows that there are important connexions between mathematics and metaphor that benefit our understanding of both. A historically structured overview of traditional theories of metaphor reveals it to be a notion that is complicated, controversial, and inadequately understood; this motivates a non-traditional approach. Paradigmatically shifting the locus of metaphor from the linguistic to the conceptual - as George Lakoff, Mark Johnson, and many other contemporary metaphor scholars do - overcomes problems plaguing traditional theories and promisingly advances our understanding of both metaphor and of concepts. It is argued that conceptual metaphor plays a key role in explaining how mathematics is grounded, and simultaneously provides a mechanism for reconciling and integrating the strengths of traditional theories of mathematics usually understood as mutually incompatible. Conversely, it is shown that metaphor can be usefully and consistently understood in terms of mathematics. However, instead of developing a rigorous mathematical model of metaphor, the unorthodox approach of applying mathematical concepts metaphorically is defended
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The Development of Non-Symbolic Probability Judgments
Uncertainty plays a role in a variety of early learning processes such as numerical reasoning, language learning, and causal reasoning. Furthermore, adults experience probabilistic data in the course of numerous tasks every day. Thus, the ability to make accurate predictions about future events is a foundational skill which serves both child and adult. Researchers have studied the development of probabilistic reasoning for decades, providing data to suggest that , until early adolescence, children are incapable of accurately predicting future outcomes based on proportion. An equally long scholarly lineage has also provided evidence that adults rely on inaccurate heuristics and biases when reasoning about probability. If prediction is so vitally important to human judgment and decision making, why does the empirical literature suggest humans have impoverished decision making skills when reasoning about uncertainty? What mental representations do humans really on to calculate probability? How do these mental representations change with age and experience? The current dissertation seeks to answer these questions by studying simple probability judgments made by children and adults. The empirical evidence provided here suggests that children and adults draw on analog magnitude representations of number in order to enumerate sets of outcomes. Furthermore, although both children and adults sometimes use inaccurate heuristics, children rely on these heuristics less with age and adults seem to use them when they perceive two outcomes to be equally likely. In chapter 2, I present findings from a series of experiments employing a non-symbolic ratio magnitude comparison task to investigate the relationship between number approximation, ratio processing, and probability estimation in adults. Empirical results reveal that performance on a probability discrimination task improves as the ratio of the two proportions increases and psychophysical modeling revealed that both numerical and non-numerical stimulus features such as field area, size, and sparsity influence probability estimation. Additionally, these findings reveal that probability estimation is influenced by formally incorrect heuristic decision rules or strategies. Furthermore, findings from two follow-up experiments indicate that these strategies are not influenced by the amount of time participants are given to compute probability and that they persist even when participants are informed that the use of this strategy is not always accurate. While previous research has investigated the influence of ratio processing and heuristic bias on probabilistic decision making, this series of experiments marks the first attempt to systematically investigate both the psychophysical properties of probability estimation and the factors which influence adults' use of heuristic decision rules in a non-symbolic probability discrimination task. Chapter 3 presents the findings from two experiments designed to investigate the developmental trajectory of children’s probability approximation abilities. These results indicate that probability judgments improve with age, become more accurate as the distance between two ratios increases, and that children’s perceived probability is influenced by the same psychophysical properties reported for adults (i.e. the size of the objects and the perceived numerosity of target objects). Older children’s performance suggested the correct use of proportions for estimating probability; but in some cases, children relied on heuristic shortcuts. Together, these results suggest that children’s non-symbolic probability judgments show a clear distance effect, and that the acuity of probability estimations increases with age. In chapter 4, I push this research further by investigating the influence of feedback on children’s use of heuristic decision rules. Results from two experiments reveal that children's use of heuristics can be overridden with the proper amount and type of feedback. Together, our findings indicate that children use heuristic decision rules to reason about the outcome of future events but that children can override the use of heuristics if they are provided with enough feedback on trials which conflict with their strategy. These results help shed light on the development of probabilistic reasoning and may lead to improved assessments of children's quantitative reasoning. Together, the results reported in this dissertation suggest that human probabilistic reasoning is not as impoverished as previous research might suggest. Although children and adults sometimes use inaccurate heuristic decision rules to aid their decision-making, they are also capable of accurately calculating probability based on proportion. Furthermore, children can learn to reformulate their calculations of probability based on feedback and reach a more sophisticated understanding of the proportional nature of probability. These findings have broad implications for a variety of domains such as cognitive development, numerical reasoning, decision-making, strategy selection, and mathematics education
Identifying the First Person
Wide agreement exists that self-ascriptions that one would express with the first-person pronoun differ in kind from those one would express with other self-designating expressions such as proper names and definite descriptions. At least some first-person self-ascriptions, many argue, are nonaccidental—that is, they involve no self-identification, and hence in making them one cannot accidentally misidentify the subject of the ascription. I examine the support for this claim throughout the literature, paying particular attention to Sydney Shoemaker\u27s proposal that self-ascriptions are nonaccidental in virtue of being immune to error through misidentification relative to the first-person pronoun. According to Shoemaker, such immunity results from the special way in which one is introspectively aware of the psychological property or state ascribed, a way that leaves no room for questions to arise as to whether oneself is its bearer. I contend that though it may seem from the point of view of consciousness that we are directly and immediately aware of the states of our bodies and minds as our own, both theoretical and empirical considerations strongly suggests that we have no such direct awareness. Proprioception and introspection prove in the end to be better described as types of informed, conscious self-interpretation. Taking inspiration from Dennett, Rosenthal, and Nozick, I offer the naive proposal as an alternative that explains all self-ascriptions in terms of one\u27s relying upon a battery of commonsense self-specifying beliefs to interpret both which state or property one has and who has it. As a result, first-person self-ascriptions differ from others only in degree and not in kind, and self-misidentification always remains a possibility—even when self-ascribing properties with the first-person pronoun
TransStates: Conceptual Art in Eastern Europe and the Limits of Utopia.
This dissertation explores the utopian and metaphysical aspirations found in the pockets of collective creativity that drove Conceptual art in Eastern Europe in the 1960s and 1970s. It does so by focusing on two groups of artists from the places that defined the limits of relative freedom and unfreedom in Cold War Eastern Europe: the former Yugoslavia and the former USSR. Thus, I trace the trajectories of philosophical and stylistic developments in the work of the OHO collective, which worked in Ljubljana (Slovenia) from 1965-1971 and the work of the duo of Vitaly Komar and Alexander Melamid which they did between 1972 and 1980, before and immediately after their emigration from Moscow to the U.S.
In narrating the groups’ histories and addressing the existing narratives about them, I pay particular attention to the way the groups’ work was tied to both local forms of protest and desire for self-governed spaces of freedom, as well as to a larger global shift in both the production and display of art taking place in the 1960s and 1970s. Moreover, I argue that within the global Conceptual shift of which these collectives were part, their practices were singularly representative of the preoccupations broadly shared by artists in Eastern Europe. In both cases, the oeuvres encompassed diverse media and spoke to multiple audiences, both actual and imagined, often using similar tropes. Even more
importantly, in both cases, the groups’ projects were driven by a desire to respond to utopian aspirations through artistic practice, self-consciously modeling through art the possibilities of personal politics in one’s particular time and place. It is in these responses to the utopian impulse that one also finds the stark contrast between OHO and Komar and
Melamid, who define the far opposite ends of the spectrum of good and bad faith in utopia. In doing so, they offer insight both into the wide array of roles that unofficial art sought to play in Cold War Eastern Europe and into the limits to which utopianism could still be reconciled with artistic practice in the wake of the Conceptual shift.Ph.D.History of ArtUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/89756/1/ksenya_1.pd
Face perception: an approach to the study of autism
The autistic child's ability to identify others' faces and their
expressions was investigated in comparison with the ability of non-autistic
children. A study of the children's ability to identify
peers' from isolated facial areas revealed that the autistic children
were abnormally good at this task. Reasons for these findings were
investigated in a series of experiments which revealed that the
autistic children were also abnormally good at recognising inverted
faces and inverted text. The conclusion was drawn that the autistic
children's performance was due to their possessing a perceptual
integration deficit which prevents them seeing stimuli like faces and
words as meaningful wholes. This was investigated further by tests
of their ability to discern facial expression and the results of these
studies supported the above conclusion. Tests of the children's ability
to lip read revealed that the autistic children also had problems with
between modality perceptual integration. Studies of their ability
to produce facial expressions showed them to be poor at both
spontaneous and elicited expressions. Further, whilst they were as
good as controls at copying facial expression, they were less able to
make use of visual feedback to improve their attempts. This was seen
as further evidence for a perceptual integration deficit. Finally, a
computerised study of autistic children's eye movements whilst viewing
live facial expressions and other stimuli supported much of the previous
findings, adding the finding that they had abnormally brief visual
fixation times and that they engaged in very few feature-to-feature
gaze shifts. The results were discussed and found to favour a theory
in which the autistic child's problems with social and communicative
competence are linked to his problems with perceptual integration.
The possession versus the use of abilities was discussed, as was
possible sites of neurological damage, and the possibility that
autistic children lack some vital usually 'innate' abilities and
propensities