Gabriel Weaver

Professional Objective

Develop a masters project in Computer Science at Tufts University that incorporates developing a markup language for Ancient mathematical diagrams for texts written in Ancient Latin, Greek, and Arabic.

• A Masters Project In Computer Science: Applying Diagrammatic Reasoning to Develop a Markup Language For Ancient Greek Mathematics Diagrams.

  Problem

  While TEI-XML provides a mechanism for marking-up the semantic content of a text, it does not provide a means to mark-up the semantic content of diagrams. In the context of Ancient Greek Mathematics proofs, diagrams clarify the concepts expressed in the text, and the construction of the diagram appears to be an aspect of "translation". When multiple editions of a Greek Mathematics book exist, not only are differences found in the text, but often also within the diagrams. In fact, one editor boasts of his translation, intended to be used as a textbook, with new diagrams, indicating the importance of diagrams for learning the material. In light of this evidence, there is a need for the ability to capture the semantic content of diagrams, for they are an essential aspect of an edition of an Ancient Mathematics text.

  Benefits of a Solution

  If a markup language for Mathematical diagrams were to be developed, then we would be able to do the following activities
  • Preserve the diagrams in a format suitable for long-term archiving, just as TEI does for text.
  • Compare two editions of the same diagram by examining their semantic structure, made explicit via the markup
  • Possibly extract drawing conventions, at the scope of the author or wider. This would be possible because the markup would separate the presentation of the diagram from the semantics of the diagram.

  Components of Research

  Development of the diagram markup will involve research into the following areas.

  • Computer Science:

    • Markup Languages - In particular XML. An understanding of Markup languages, what they can and cannot do will help to identify the limits of these languages, and what types of information they can represent.
    • Theory of Computation - Specifically, it may be useful to determine what class of language 'diagram markup' belongs to to theoretically 'prove' or 'disprove' what is aspects of a diagram are or are not possible to represent with XML (a context-free language).
    • Computer Graphics - A background in the theory of computer graphics will be useful towards understanding the division between semantic and presentational information.
    • Human-Computer Interaction- In particular diagrammatic Reasoning "the understanding of concepts and ideas by the use of diagrams and imagery, as opposed to linguistic or algebraic representations -- not only allows us to gain insight into the way we think, but is a potential base for constructing representations of diagrammatic information that can be stored and processed by computers" (Diagrammatic Reasoning).

  • Classics

    • Multiple Ancient Languages - Latin and Greek, and ideally Arabic would allow for a comparison of diagrams across multiple time periods and cultures.
    • History - An understanding of the role Ancient Greek Mathematics had over time with an eye towards possible implications for the underlying semantics and/or presentation of the diagrams' semantics. For example, is there a difference between diagrams found in editions intended to be used as textbooks and diagrams found in editions without such a purpose. What was the purpose of such editions if they were not textbooks?

  Research Logistics

  1. Computer Science

     • Talk to Professor Laing about XML and what type of language it is, and diagram-markup and what class of language that would be.
     • Take Computer Graphics and HCI (beg for a tutorial in diagrammatic reasoning) this fall (if possible), if the class is project-based (which it probably will be) structure it so as to be a sub-project of this project.
     • Talk to Professor Hwang about geometry for his domain expertise. This can be used to develop domain-models of the objects involved. Also talk to him about being a resource to help and step through whatever author is chosen.
     • Contact Professor Joyce and bounce these ideas off of him and talk to him about his work

  2. Classics

     • Talk to Neel about framing this project in the context of the history of transmission of Ancient Mathematical texts.
     • Talk to Neel about figuring out a good author criteria include:
       • History of the author with respect to the history of transmission of Ancient Mathematical texts
       • Availability of editions from libraries, rare-book libraries, and elsewhere, preferably in the New England area
       • Availability of editions in Latin, Greek, and hopefully Arabic too!
     • Find buddies for the review of Ancient Latin
     • Find buddies for the review of Ancient Greek
     • Find buddies for the review of Ancient Arabic! Anyone? Anyone?

  Latest Ramblings

  • 7/24/06 - Notes on the diagram markup. Here we get nitty gritty as we prepare to take the plunge into formalizing our schemas for the components of the diagram markup:
    1. The axiomatic data from the source texts
    2. The semantic/proof structure the diagram represents
    3. The stylistic/presentational aspects of the diagram.
  • 7/18/06 - Sample diagram markup, split among semantic and then edition specific, presentational markup. The id references the first instance of an object while one can specify presentational attributes for any object on any step. The editions involved include Sir Thomas Heath's Euclid, represented in Joyce's recreations, and the Byrne edition
  • 7/17/06 - Formal Structure of A Euclidean Proof versus caption describing parts of 'Sentential Representation' of a geometric diagram. The Sentential Representation bit is from "Why a Diagram Is (Sometimes) Worth Ten Thousand Words" by Jill H. Larkin & Herbert A. Simon of Carnegie Mellon University. The formal structure of a euclidean proof is from Heath's Elements. Also playing with ideas of notations and "symbol spaces" and using properties of one space to provide intuition for properties of the same elements in another space
  
  This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.Copyright © 2006 by Gabriel Weaver. View PDF