Topological Concepts and Language: A Report of Research in Progress
by
Bill Barton
Dept. Mathematics, The University of Auckland
Coauthors: Ivan Reilly

Collaboration between a long-time research topologist and a researcher interested in mathematics and culture has given rise to a project aimed at determining whether there are differences in the way research topologists from different language-groups understand the fundamental concepts of their field. The linguistic bases of any such differences are also being explored.

The problems of such research are largely methodological, and a number of possible instruments for detecting differences are being developed. Three instruments (using concept-mapping, teaching metaphors, and reaction to a historical account of topology) have been trialled. One of these has been found to be impractical, the other two are being further refined. A new instrument based on reactions to a developing subfield of topology is now being developed and will be trialled during 1999. In addition to testing instruments, some lessons have been learned about how they may be best administered.

As part of the pilot research many topologists have been drawn into discussion about this research, its assumptions, its methods, its likely results, and the implications of any findings. The findings are interesting both in themselves, and in relation to recent literature in linguistics and the anthropology of mathematics.

Participants in this conference are invited to participate in the research, in both this trialling stage, and/or as subjects. Discussion and debate on the issues are welcomed.

AMS subject classifications: 01A99, 54-03

Keywords: topological concepts, language, culture

Date received: January 12, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caca-07.