I’ve just been re-reading Robin Milner’s Tutorial on the Polyadic pi-Calculus, a text I struggled with about a year ago. This time around I’ve been able to follow the notation, and even complete one of the exercises to provide a proof - using three “structural congruence laws” - that (vx)P is equivalent to P where x is not a free name of P.

That’s a significant advance in understanding, for me: it means I can do a type of formal mathematics (albeit to only the most piddling degree) that a year ago I could get no purchase on at all.

This is really encouraging: it means the the slow progress I’ve been making with TaPL in particular is paying off, even if it is still slow. It means that I’m not intrinsically incapable of ever learning to use such mental tools, or simply too impatient to ever find using them rewarding. On the contrary, I got a real kick out of writing out the proof.

I’ve always wondered about the humility and self-deprecation often shown by people struggling to master difficult subjects. It’s always seemed quite foreign to me: when I was studying English, and reading philosophy and theology and whatever else in that line I could get my hands on, the matter at hand never seemed that difficult to me - it never made me doubt my own abilities. But mathematics is hard for me in a way that Derrida never was, in a way that makes even minor successes seem far from inevitable. I still haven’t got to the end of the pi calculus tutorial, and it’s quite possible that just over the next page something will appear that totally defeats me.

That is a type of novelty that is both precious and intimidating; you approach it gingerly, rather than rushing enthusiastically towards it. Perhaps through mathematics I can cultivate a small garden of discipline amid the wild dissipation of my thoughts.