An experimental and theoretical tool for studying the language of geometric concepts
Thesis: S.M. in Engineering and Management, Massachusetts Institute of Technology, System Design and Management Program, 2018.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2019
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| Online Access: | http://hdl.handle.net/1721.1/120899 |
| _version_ | 1826197117986668544 |
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| author | Dhariwal, Manuj |
| author2 | Laura Schulz and Joshua Tenenbaum. |
| author_facet | Laura Schulz and Joshua Tenenbaum. Dhariwal, Manuj |
| author_sort | Dhariwal, Manuj |
| collection | MIT |
| description | Thesis: S.M. in Engineering and Management, Massachusetts Institute of Technology, System Design and Management Program, 2018. |
| first_indexed | 2024-09-23T10:42:46Z |
| format | Thesis |
| id | mit-1721.1/120899 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T10:42:46Z |
| publishDate | 2019 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1208992022-09-01T02:18:20Z An experimental and theoretical tool for studying the language of geometric concepts Dhariwal, Manuj Laura Schulz and Joshua Tenenbaum. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Engineering and Management Program System Design and Management Program. Massachusetts Institute of Technology. Integrated Design and Management Program Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Engineering and Management Program. System Design and Management Program. Integrated Design and Management Program. Electrical Engineering and Computer Science. Thesis: S.M. in Engineering and Management, Massachusetts Institute of Technology, System Design and Management Program, 2018. Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018. Cataloged from PDF version of thesis. Includes bibliographical references (pages 65-66). In this thesis, I propose concretizing the Piagetian view of children as 'gifted learners' to children as 'gifted language builders', who construct and learn many languages to reduce their uncertainty about the world. These include languages such as, the language of geometry, the language of music & rhythm, even a child playing with blocks (eg: LEGO) is actually learning or rather building a language for themselves. As a specific case, I introduce an experimental paradigm and tool, Finding GoDot, for studying the cognitive language of geometry. Using the above lens, I model constructive actions as a language, specifically looking at the task of drawing shapes. Next, majority of this thesis deals with the problem of calculating the entropy and redundancy of such a language for which there is no readily available language data. For this, I utilize Shannon's insight of accessing our implicit statistical knowledge of the structure of a language by converting it to a reduced text form, through a prediction experiment. I generalize Shannon's experiment design to make it applicable for a wide variety of languages, beyond just text-based, especially those lacking existing language data. Finally, I compute entropy (average information per letter) values for individual shapes to show evidence of subjects using a rich forward model to mentally simulate incomplete shapes, thus gaining information about the underlying shape more than is visible. I also share results on bounds for the entropy and redundancy of the proposed language of actions for generating shape drawings. by Manuj Dhariwal. S.M. in Engineering and Management S.M. 2019-03-11T19:36:42Z 2019-03-11T19:36:42Z 2018 2018 Thesis http://hdl.handle.net/1721.1/120899 1088894032 eng MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission. http://dspace.mit.edu/handle/1721.1/7582 66 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Engineering and Management Program. System Design and Management Program. Integrated Design and Management Program. Electrical Engineering and Computer Science. Dhariwal, Manuj An experimental and theoretical tool for studying the language of geometric concepts |
| title | An experimental and theoretical tool for studying the language of geometric concepts |
| title_full | An experimental and theoretical tool for studying the language of geometric concepts |
| title_fullStr | An experimental and theoretical tool for studying the language of geometric concepts |
| title_full_unstemmed | An experimental and theoretical tool for studying the language of geometric concepts |
| title_short | An experimental and theoretical tool for studying the language of geometric concepts |
| title_sort | experimental and theoretical tool for studying the language of geometric concepts |
| topic | Engineering and Management Program. System Design and Management Program. Integrated Design and Management Program. Electrical Engineering and Computer Science. |
| url | http://hdl.handle.net/1721.1/120899 |
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