The feelings that are motivating it aren't really specific to any field, so I suppose it's "any research I could plausibly do as an amateur without spending too much resources on it". I'm not specifically planning now to set out and do an easy-for-an-amateur research paper, the main thought driving it is that at some point I might find a question interesting enough to research it on my own, gwern-style, and then if it's plausible to do so I would want to get whatever work I do up to publishable standards for extra nerd cred.

I only also mentioned Erdos numbers because of a tangent thought of "hey, I'm in the rationalsphere, if I got other rationalsphere people involved in such a project and at least one of them was someone with a finite Erdos number, I'd get one too". And then by the time I was typing up that comment I had a tab open on this, although I also can't play an instrument (yet) and have never acted (yet).