On teaching, via Robert Talbert:
Look at the course you teach most often. If you had the power to remove one significant topic from that course, what would it be, and why?
I have a high degree of autonomy in most of the courses I teach, so power isn't the limiting factor for me. Time is a challenge to making big changes, of course. Gumption is probably what I need most right now. Summer is a great time for me to think about this, both for my compiler course this fall and programming languages next spring.
On research, via Kris Micinski:
i remember back to Dana Scott's lecture on the history of the lambda calculus where he says, "If Turing were alive today, I don't know what he'd be doing, but it wouldn't be recursive function theory." I think about that a lot.
Now I am, too. Seriously. I'm no Turing, but I have a few years left and some energy to put into something that matters. Doing so will require some gumption to make other changes in my work life first. I am reaching a tipping point.
I have been enjoying a few of James Propp's essays recently. Last month he wrote about the creation of zero. In Who Needs Zero, he writes:
But in mathematics, premature attempts to reach philosophical clarity can get in the way of progress both at the individual level and at the cultural level. Sometimes you have to just start talking before you understand what you're talking about.
This reminded me of a passage by Iris Murdoch in Metaphysics as a Guide to Morals, which I encountered in one of Robin Sloan's newsletters:
The achievement of coherence is itself ambiguous. Coherence is not necessarily good, and one must question its cost. Better sometimes to remain confused.
My brain seems hardwired to seek out and create abstractions. Perhaps it's just a deeply ingrained habit. Even so I am a pragmatist at heart. As Propp says, "Zero is as zero does."
Allowing oneself to remain confused, to forge ahead without having reached clarity yet, is essential to doing research, or to learning anything at all, really.