Why do mathematicians need different ways of presenting mathematical objects? The case of cayley graphs
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Topoi 29 (1):41-51 (2010)
This paper investigates the role of pictures in mathematics in the particular case of Cayley graphs—the graphic representations of groups. I shall argue that their principal function in that theory—to provide insight into the abstract structure of groups—is performed employing their visual aspect. I suggest that the application of a visual graph theory in the purely non-visual theory of groups resulted in a new effective approach in which pictures have an essential role. Cayley graphs were initially developed as exact mathematical constructions. Therefore, they are legitimate components of the theory (combinatorial and geometric group theory) and the pictures of Cayley graphs are a part of practical mathematical procedures.
|Keywords||Visualisation Intuition Geometry of groups Cayley graphs|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Charles Parsons (2008). Mathematical Thought and its Objects. Cambridge University Press.
Solomon Feferman (2000). Mathematical Intuition Vs. Mathematical Monsters. Synthese 125 (3):317-332.
Citations of this work BETA
No citations found.
Similar books and articles
Robert W. Burch (1994). Game-Theoretical Semantics for Peirce's Existential Graphs. Synthese 99 (3):361 - 375.
B. Courcelle (2012). Graph Structure and Monadic Second-Order Logic: A Language-Theoretic Approach. Cambridge University Press.
J. C. E. Dekker (1981). Twilight Graphs. Journal of Symbolic Logic 46 (3):539-571.
Michael Kohlhase & Andrea Kohlhase, Spreadsheet Interaction with Frames: Exploring a Mathematical Practice.
Karlis Podnieks & John Tabak (2011). The Nature of Mathematics – an Interview with Professor Karlis Podnieks. In John Tabak (ed.), Numbers: Computers, Philosophers, and the Search for Meaning. Revised Edition. Facts on File 188–197.
Jeffrey Kline & Shravan Luckraz (2011). A Note on the Relationship Between Graphs and Information Protocols. Synthese 179 (S1):103-114.
Jessica Carter (2004). Ontology and Mathematical Practice. Philosophia Mathematica 12 (3):244-267.
Added to index2010-01-23
Total downloads82 ( #41,037 of 1,726,249 )
Recent downloads (6 months)6 ( #118,705 of 1,726,249 )
How can I increase my downloads?