Research on the physics of language with particular emphasis on the quantum mechanical properties of syntax

2014 Fiscal Year Research-status Report

• Project/Area Number: 26370446
• Research Institution: Yokohama National University
• Principal Investigator: R・A Martin 横浜国立大学, 環境情報研究院, 准教授 (30302342)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: 生成文法 / ミニマリストプログラム / 品詞 / ファーストマージ / アダマール積 / 量子力学 / 国際研究者交流 / 米国

Outline of Annual Research Achievements

In this first year of this project, R.A. Martin (PI) has worked extensively together with Juan Uriagereka (Overseas Collaborative Researcher), as well as some other faculty and graduate students in physics and mathematics at the University of Maryland, to develop a new theory of lexical categories and the first-merge (the operation by which a lexical head forms a constituent with its complement) component of the grammar. One of the core ideas we have developed as a result of this research is that the traditional privative features N and V, which are used to yield the four major word classes (noun, verb, adjective and preposition), are in fact scalar values, where N corresponds to the real numbers and V to the imaginary numbers. A major consequence of this idea is that we can treat first-merge as matrix multiplication (Hadamard products), which we demonstrate is not only an interesting and natural way to formalize the operation, but also explains a number of otherwise mysterious facts about possible types of categories a given lexical head can take as a complement. Although this initial step of the project is not quite yet complete (we are in the process of finalizing the paper at the time of this report), we believe that what we have come up with so far represents significant progress on these issues, about which little has been said to date. As we work to wrap up this paper, we are preparing to start the next phase of the project, which is to work out a theory of specifiers and other instances of merger that go beyond first-merge, which we believe involve tensor products.

Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

The project is essentially progressing according to the original plan. Although we have not yet been able to make much headway concerning the mathematical analysis of chains and entanglement, this is because we discovered that there was much more involved in accounting for the initial "base" component of the grammar than we had originally envisioned. Therefore, we decided to invest a large amount of time to working out the details of these initial conditions for chain formation in as much detail as possible, which has also led to results beyond our original expectations. Although we were not able to finish it within the 2014 fiscal year, a paper dealing with this first stage of the project is almost complete, and we plan to submit it to a refereed academic journal within the couple of months. In addition to the above mentioned research activities, Martin has been actively involved over the last several months of the academic year, together with Douglas Saddy (U. of Reading) and Massimo Piattelli-Palmarini (U. of Arizona), in planning the first symposium on the physics of language, which we plan to hold in Japan during the 2015 fiscal year as one of the main research activities of the current project. This major international symposium is intended to serve as a forum to disseminate our interim results and to discuss our on-going work in the project with leading scholars from around the world. We expect it to be one of the highlights of the project, and crucial to its success.

Strategy for Future Research Activity

In the second and third years of the project, Martin and Uriagereka will continue to work together extensively, turning attention to a model of specifiers and chains. As some point during each of the remaining years, Martin will visit the University of Maryland for several days to one week in order to hold several research meetings with Uriagereka and other collaborators at the same university. The main use of funds during the 2015 academic year, however, will be to hold a large international symposium on the physics of language. The current plan is to invite between 7 and 9 collaborating overseas researchers (including some advanced doctoral students) to participate in this symposium. Funds will be used for travel expenses and/or honoraria for these invited scholars, as well as other general costs of running the symposium. In the third and final year of the project, Martin and Uriagereka will strive to complete a monograph that deals with the nature of the lexicon, the initial (first-merge) component of syntax, and the transformational (chain) component of syntax within a theoretical model that makes crucial use of principles of of quantum physics and quantum computation.

Causes of Carryover

Martin had originally intended to visit the University of Maryland to work with Uriagereka on the current research project, this plan had to be postponed due to Uriagereka’s schedule. Also, as the planning for the international symposium on the physics of language has proceeded, we decided that it was in our best interest, in terms of the success of the project, to invite 7 to 9 overseas scholars, which is a larger number than originally envisioned. Thus some funds originally allocated for use in the current fiscal year were intentionally reserved for this purpose, by cutting back on other expenses deemed less crucial in light of how our research is progressing.

Expenditure Plan for Carryover Budget

The funds carried over to the next fiscal year will primarily be used to pay for the costs of hosting an international symposium on the physics of language, including invited speakers' travel expenses and honoraria, as well as general running costs of the symposium. Funds will also be used to support a research visit to the University of Maryland by Martin.