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Mathematics requires precise inferences about abstract objects inaccessible to perception. How is this possible? One proposal is that mathematical reasoning, while concerned with entirely abstract objects, nevertheless relies on neural resources specialized for interacting with the world-in other words, mathematics may be grounded in spatial or sensorimotor(More)
The notes and articles in this series are progress reports on work being carried on by students and faculty in the Department. Because these papers are not finished products, readers are asked not to cite from them without noting their preliminary nature. The authors welcome any comments and suggestions that readers might offer. Yamashita and Chang (2001)(More)
Many animals can be trained to perform novel tasks. People, too, can be trained, but sometime in early childhood people transition from being trainable to something qualitatively more powerful-being programmable. We argue that such programmability constitutes a leap in the way that organisms learn, interact, and transmit knowledge, and that what facilitates(More)
In an effort to focus on tractable problems, computational natural language understanding systems have typically addressed language phenomena that are amenable to combinatorial approaches using static and stereotypical semantic representations. Although such approaches are adequate for much of language, they're not easily extended to capture humans' more(More)
We report on two experiments that ask when and under what linguistic conditions comprehenders construct detailed shape representations of mentioned objects, and whether these can change over the course of a sentence when new information contradicts earlier expectations. We used Japanese because the verb-final word order of Japanese presented a revealing(More)
Interactions between number and space, exemplified by the SNARC (Spatial-Numerical Association of Response Codes) effect, are often taken as evidence for a privileged spatial representation of number. Naturally, research on the spatial representation of number has typically focused on spatial tasks. But in order to make inferences about numerical cognition(More)
We have recently demonstrated our hashed oct-tree N-body code (HOT) scaling to 256k processors on Jaguar at Oak Ridge National Laboratory with a performance of 1.79 Petaflops (single precision) on 2 trillion particles. We have additionally performed preliminary studies with NVIDIA Fermi GPUs, achieving single GPU performance on our hexadecapole inner loop(More)