I think you are correct with respect to my estimate of α and the associated model I was using. Sorry about my error here. I think I was fundamentally confusing a few things in my head when writing out the comment.
I think your refactoring of my strategy is correct and I tried to check it myself, though I don’t feel confident in verifying it is correct.
Your estimate doesn’t account for the conversion between algorithmic improvement and labor efficiency, but it is easy to add this in by just changing the historical algorithmic efficiency improvement of 3.5x/year to instead be the adjusted effective labor efficiency rate and then solving identically. I was previously thinking the relationship was that labor efficiency was around the same as algorithmic efficiency, but I now think this is more likely to be around algo_efficiency2 based on Tom’s comment.
Neat, thanks a ton for the algorithmic-vs-labor update—I appreciated that you’d distinguished those in your post, but I forgot to carry that through in mine! :)
And oops, I really don’t know how I got to 1.6 instead of 1.5 there. Thanks for the flag, have updated my comment accordingly!
The square relationship idea is interesting—that factor of 2 is a huge deal. Would be neat to see a Guesstimate or Squiggle version of this calculation that tries to account for the various nuances Tom mentions, and has error bars on each of the terms, so we both get a distribution of r and a sensitivity analysis. (Maybe @Tom Davidson already has this somewhere? If not I might try to make a crappy version myself, or poke talented folks I know to do a good version :)
I think you are correct with respect to my estimate of α and the associated model I was using. Sorry about my error here. I think I was fundamentally confusing a few things in my head when writing out the comment.
I think your refactoring of my strategy is correct and I tried to check it myself, though I don’t feel confident in verifying it is correct.
Your estimate doesn’t account for the conversion between algorithmic improvement and labor efficiency, but it is easy to add this in by just changing the historical algorithmic efficiency improvement of 3.5x/year to instead be the adjusted effective labor efficiency rate and then solving identically. I was previously thinking the relationship was that labor efficiency was around the same as algorithmic efficiency, but I now think this is more likely to be around algo_efficiency2 based on Tom’s comment.
Plugging this is, we’d get:
λβ(1−p)=rq(1−p)=ln(3.52)0.4ln(4)+0.6ln(1.6)(1−0.4)=2ln(3.5)ln(2.3)(1−0.4)=2⋅1.5⋅0.6=1.8
(In your comment you said ln(3.5)ln(2.3)=1.6, but I think the arithmetic is a bit off here and the answer is closer to 1.5.)
Neat, thanks a ton for the algorithmic-vs-labor update—I appreciated that you’d distinguished those in your post, but I forgot to carry that through in mine! :)
And oops, I really don’t know how I got to 1.6 instead of 1.5 there. Thanks for the flag, have updated my comment accordingly!
The square relationship idea is interesting—that factor of 2 is a huge deal. Would be neat to see a Guesstimate or Squiggle version of this calculation that tries to account for the various nuances Tom mentions, and has error bars on each of the terms, so we both get a distribution of r and a sensitivity analysis. (Maybe @Tom Davidson already has this somewhere? If not I might try to make a crappy version myself, or poke talented folks I know to do a good version :)