I was surprised that the instrumental convergence hypothesis had been proven
I’d like people to in general be much more careful about describing mathematical results in this way. The instrumental convergence hypothesis is not a mathematical fact, and so it cannot be proven; what can be done, and what’s done here, is to write down toy models in which something we’re prepared to call instrumental convergence happens, but more work needs to be done to answer questions like 1) how sensitive the result is to changes in the toy model and 2) what relevance we expect the toy model to have to reality.
Separately, I expect instrumental convergence to happen pretty robustly across a wide class of toy models, and for this fact to be pretty relevant to reality.
You’re right, thanks. I wasn’t sure whether I wanted to qualify that statement, given that I clarified that the proof made assumptions soon after. I’ll make the edit.
I’d like people to in general be much more careful about describing mathematical results in this way. The instrumental convergence hypothesis is not a mathematical fact, and so it cannot be proven; what can be done, and what’s done here, is to write down toy models in which something we’re prepared to call instrumental convergence happens, but more work needs to be done to answer questions like 1) how sensitive the result is to changes in the toy model and 2) what relevance we expect the toy model to have to reality.
Separately, I expect instrumental convergence to happen pretty robustly across a wide class of toy models, and for this fact to be pretty relevant to reality.
You’re right, thanks. I wasn’t sure whether I wanted to qualify that statement, given that I clarified that the proof made assumptions soon after. I’ll make the edit.