When the thinking or writing has got stuck, and work on the next book (if that’s what it ever becomes) is stalled for a while, one entirely harmless diversion on the internet is to go along to math.stackexchange.com to see if I can usefully answer any logic questions. If you don’t know the site, it is the junior partner of the stunningly useful research-level mathoverflow.net which operates mostly beyond my pay grade.
Some of the questions on math.se are pretty confused stuff, or are from students trying their luck in getting others to do their homework for them. But such questions usually get closed down quickly. And there are enough questions which — even if hardly novel — are interesting enough to keep me going back to the site and having a shot at answering them. For some recent efforts with an unusually philosophical flavour, see this (on whether we can prove mathematical induction is sound), or this (on defining functions in set theory) or this (on whether there currently exists a set of Olympics 2016 winners). Or if you want something more techie (and don’t know the footnotes in my Gödel book!) you might like this proof from Rosza Péter that there are recursive but not primitive recursive functions which aren’t fast growing.
It might be fun to contribute, but is it worth the small-but-not-neglible effort? I’ve just checked my “profile” on math.se as you do: the whole enterprise is gamified, there are reputation points to be accrued, badges to be won, … sad eh? (Well, no, not sad — the whole point is that the voting up and down of answers for accuracy, clarity, helpfulness is what makes the site reliably useful). And what’s just really struck me is the Impact score. That’s the number of times people have read answers of mine that got positive votes (I think that’s how it basically works — though obviously no one is counting the quality of the reading!). The score is ~352K.
That’s a lot of readings. But it is not a wildly exceptional total (there are some very impressive expositors who contribute frequently to math.se and whose impact score is in the millions). So I’ve nothing especial to boast about here. Rather, it just brings home how very heavily used a site like math.se is. I imagine that this is very much on the basis of student-to-student recommendation, as in my experience lecturers can be distinctly sniffy about this sort of thing. But quite wrongly, I think. As a reader I’ve certainly learnt a lot of fiddly points of category theory there by searching around when stuck. Grad students and beyond can learn from the exercise of writing crisp cogent solutions to problems (and should surely be encouraged to do so, within reason). And old hands in their retirement, with little taste for golf or gardening, can continue to satisfy their pedagogic urges and find a grateful audience out there (much larger than any audience they were ever paid to teach!). What’s not to like?