# Drawing space: mathematicians’ kinetic conceptions of eigenvectors

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## Abstract

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of eigenvectors depends strongly on both time and motion—hence, on physical interpretations of mathematical abstractions—which are dimensions of thinking that are typically deliberately absent from formal, written definition of the concept. We shall also show how gesture and talk contribute differently and uniquely to mathematical conceptualisation and further elaborate the claim that diagrams provide an essential mediating role between the two.

## Keywords

Language Metaphor Gesture Diagram Motion Time Conceptual mathematics Linear algebra## Notes

### Acknowledgements

This research has been supported by the Social Sciences and Humanities Research Council of Canada. We would like to thank the mathematicians who participated in this study. We would also like to thank David Pimm for his feedback on previous versions. We extend our acknowledgements as well to three anonymous reviewers and to Norma Presmeg for her guidance in our revisions.

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