Nice! Yep this is a great analysis and checks out for me. I think it’s really valuable to back-out qualitative stories to support the conclusions of these models. Thanks very much.
I think it’s possible to get more sceptical of >10 years in <1 year by saying:
Even if r >> 1 today, that’s not strong evidence r will remain >1 until we’re very near effective limits. E.g. suppose r = 4 today, and effective limits of tech are 15 OOMs away. There’s a good chance r falls below r after a few OOMs of progress. But my model assumes that r would remain above 1 until we’re very close to limits. So my model is too aggressive.
This relates to you saying “It’s very unclear how to model this, but let’s say you need a bit of extra margin for both the upper bound and for r — maybe you need the upper bound to allow for like 11 years of progress (because the last year might be slow) and for r to be greater than 1.5 (so the speed of progress has time to gather up a bit of momentum before it goes below 1).” Plausibly you need to add more margin than you’ve done there for this to go through. (Though as you point out in another comment, it’s plausible my values for limits are too conservative.)
Nice! Yep this is a great analysis and checks out for me. I think it’s really valuable to back-out qualitative stories to support the conclusions of these models. Thanks very much.
I think it’s possible to get more sceptical of >10 years in <1 year by saying:
Even if r >> 1 today, that’s not strong evidence r will remain >1 until we’re very near effective limits. E.g. suppose r = 4 today, and effective limits of tech are 15 OOMs away. There’s a good chance r falls below r after a few OOMs of progress. But my model assumes that r would remain above 1 until we’re very close to limits. So my model is too aggressive.
This relates to you saying “It’s very unclear how to model this, but let’s say you need a bit of extra margin for both the upper bound and for r — maybe you need the upper bound to allow for like 11 years of progress (because the last year might be slow) and for r to be greater than 1.5 (so the speed of progress has time to gather up a bit of momentum before it goes below 1).” Plausibly you need to add more margin than you’ve done there for this to go through. (Though as you point out in another comment, it’s plausible my values for limits are too conservative.)