Abstract
Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima (Artif Intell Rev 15: 5–27, 2001), is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s (informal) framework as a tool to analyse the occurrence and properties of them. I consider a number of different examples from mathematical practice that illustrate a variety of uses of free rides in mathematics. Analysing these examples I find that mathematical free rides are sometimes based on syntactic and semantic properties of diagrams.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Synthese |
| Vol/bind | 199 |
| Nummer | 3-4 |
| Sider (fra-til) | 10475-10498 |
| Antal sider | 24 |
| ISSN | 0039-7857 |
| DOI | |
| Status | Udgivet - dec. 2021 |