Oxford Equilibrium: A Two-Slope Optimal Timing Problem
+ the Malthusian Model of [orchard]
Contents:
Hey
! I’m back on the plane—which means another ‘catch-up’-style post.
Oxford Equilibrium: A Two-Slope Optimal Timing Problem
Friends have noticed I’ve pushed back Oxford graduation a couple of times by now. First, I changed course PPE -> MathPhil; then, I rusticated, & have been roaming around America since. 2025 -> 2026 -> 2027.
I love my studies; I really do. When I started them, the world looked very different: GPT-3 Playground iirc. You couldn’t find a good LM to fluently discuss course material with for love nor money. ChatGPT came out in March 2023–moreover, GPT-4 did. It wasn’t a game-changer for me back then. These days, it’s the personalized tutor I didn’t know I needed. I arrived at Oxford with a hell of a lot of gaps. I didn’t close them quickly, in part because I opted into an alienated-hermit type of existence: I didn’t attend a lecture at the Mathematical Institute until the second year of my mathematics degree. But LMs kept improving all this time. Now they’re good enough to discuss topology with me–including in Voice Mode, which I’ll write another post advocating use of at some point.
I think I’m getting better at math faster than LMs are improving. One might be tempted to push back another year, s.t. they can properly accompany me through functional analysis. But–there’s a competing gradient to consider!
Oxford is getting hotter, & each summer exam season is less bearable than the last
OK, so that’s true given global warming & lack of A/C. Thermal regulation is a genuinely decision-relevant problem–you will not want to be there in 2030. It’s no Singapore.
But OK, there might be more interesting & general effects to consider in the course of this essay.
Consider:
Opportunity cost of being in school rises as you can do more with AI outside it
‘# of years to use skills for good’ decreases as we approach full automation
‘# of years to enjoy being mathematically competent / expressing yourself with math’ decreases as you approach the year of your own death
Whatever’s driving the competing curve–sensible intellectual/professional considerations or, let’s be real, it getting too damn hot in Oxford–we can model equilibrium timing like this:
This is especially relevant at colleges that allow several years of leave. The learning experience is likely to become more joyous as AI technology improves, so if learning certain material is a ‘bucket-list wish’, consider balancing the benefits of delaying with the costs of having less time to enjoy wielding, being shaped by, & expressing yourself through that knowledge.
My Favorite Equilibrium
The Malthusian model of [orchard]
Duncan once asked “What’s your favorite equilibrium?”
At [orchard], we had a set weekly snack budget. $50/week, I want to say?
Attendance varied—from ~10 to ~40. So we cycled through roughly these states:
