Journal Article
Structure from appearance: topology with shapes, without points

A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies are built with shapes, which are formalized as unanalyzed objects without points, and with structures defined from their parts. An interpretative, aesthetic dimension is introduced according to which the topological structure of a shape is not inherited from an ambient space but is induced based on how its appearance is interpreted into parts. The proposed approach provides a more natural, spatial framework for studies on the mathematical structure of design objects, in art and design. More generally, it shows how mathematical constructs (here, topology) can be built directly in terms of objects of art and design, as opposed to a more common opposite approach, where objects of art and design are subjugated to canonical mathematical constructs.

Title
Publication TypeJournal Article
Year of Publication2020
AuthorsHaridis A
JournalJournal of Mathematics and the Arts
Volume14
Issue3
Pagination199-238
Date Published02/2020
Type of ArticleOriginal research article
KeywordsMathematics of Shapes, Point-free Topology, Shape Grammars, Shape Topology, Structural Description
Abstract

A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies are built with shapes, which are formalized as unanalyzed objects without points, and with structures defined from their parts. An interpretative, aesthetic dimension is introduced according to which the topological structure of a shape is not inherited from an ambient space but is induced based on how its appearance is interpreted into parts. The proposed approach provides a more natural, spatial framework for studies on the mathematical structure of design objects, in art and design. More generally, it shows how mathematical constructs (here, topology) can be built directly in terms of objects of art and design, as opposed to a more common opposite approach, where objects of art and design are subjugated to canonical mathematical constructs.

URLhttps://doi.org/10.1080/17513472.2020.1723828
DOI10.1080/17513472.2020.1723828
Refereed DesignationRefereed