Models as maps and maps as interfaces

One of my favorite conceptual metaphors from David Basanta is Mathematical Models as Maps. From this perspective, we as scientists are exploring an unknown realm of our particular domain of study. And we want to share with others what we’ve learned, maybe so that they can follow us. So we build a model — we draw a map. At first, we might not know how to identify prominent landmarks, or orient ourselves in our fields. The initial maps are vague sketches that are not useful to anybody but ourselves. Eventually, though, we identify landmarks — key experiments and procedures — and create more useful maps that others can start to use. We publish good, re-usable models.

In this post, I want to discuss the Models as Map metaphors. In particular, I want to trace through how it can take us from a naive realist, to critical realist, to interface theory view of models.