An experimental and theoretical tool for studying the language of geometric concepts

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Engineering and Management Program

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Dhariwal, Manuj

Advisor dc:contributor.advisor

• Laura Schulz and Joshua Tenenbaum.

• Engineering and Management Program.
• System Design and Management Program.
• Integrated Design and Management Program.
• Electrical Engineering and Computer Science.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/120899

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/120899