my side quest into applied domain / principles of a domain / philosophy of a domain led to a search for “triple loop learning” to see if it existed (I knew about double), and yes, it does. It even matches the time-scales I reasoned out for applied (single loop) / principles (double loop) / philosophy (triple loop). Didn’t expect to end up with that result but now that I see it, I see it.
So, back to “tool”, “domain” “wilderness”. A tool needs two or more domains to do work upon. But the tool can be applied onto two or more domains on the same domain. That is to say, a domain’s “applied” (task / do / action) can “input” and “output” multiple “variables” that can interface with a tool that also takes “multiple inputs and outputs” and do work in real time with it.
So ‘a tool interfaces two or more domains’ can work on the same domain just as it would on multiple domains. In the case of mathematics, tools rarely leave the domain of mathematics. But boy there are many subdomains in mathematics that are not easily compatible with each other even they they ultimately can be with the right tools.
So a domain can shift in hierarchy. It can be a wilderness (background) that’s assumed most of the time upon which these domains play. Or it can be considered a subdomain on a domain as many levels of sub are needed. Hierarchies can nest. subdomains can also follow different, non-hierarchical, non-nesting relationships as they’re each ultimately domains with their relationships specified in a broader domain’s philosophy (or principles)