ABSTRACT
This chapter owes its existence, in multiple ways, to Jim Greeno. Its proximate cause is the present conference on intellectual practices. This meeting is only the latest in a long series of conversations and events in which Jim and I have explored the notion of what it is to understand and do mathematics, science, …, or anything else, for that matter. The discussions have been far reaching, as seems fitting when one’s task is to understand the ways the mind works. Here, motivated by some of the not-worked-out suggestions in a recent paper of Jim’s, I am going to stretch even farther than usual. These efforts should be understood as an exercise in the spirit of a tried-and-true problem-solving heuristic—consider extreme cases.
