I think the confusion stems from the word “gradual.” It seems there’s wide agreement that we have two dimensions of the AI timelines problem:
Growth rate pattern. This could be linear, polynomial, exponential, or hyperbolic, and perhaps include a shift between two or more trends. Choice of coefficients matters too. Linear growth with a high slope could reach the threshold faster than exponential growth with small coefficients.
AI difficulty
Paul’s description of “gradualism” as stated actually does make a statement about both dimensions, though it’s also somewhat ambiguous:
There will be a complete 4 year interval in which world output doubles, before the first 1 year interval in which world output doubles. (Similarly, we’ll see an 8 year doubling before a 2 year doubling, etc.)
US GDP last doubled from 1998-2021, a 23-year interval. Paul’s statement seems to imply that a doubling can occur in no less than 25% the time of its predecessor. Under this assumption, we’d have at least 3 doublings left, over the course of at least 8 years, before doublings can occur in less than a year. This still allows AI takeoff by 2030; it just suggest that we’ll be getting a warning shot over the next few years.
Another way to frame this, then, is that “For any choice of AI difficulty, faster pre-takeoff growth rates imply shorter timelines.”
This statement is literally and obviously true, and avoids the counterintuitive aspect introduced by the word “gradual.”
Another way to frame this, then, is that “For any choice of AI difficulty, faster pre-takeoff growth rates imply shorter timelines.”
I agree. Notably, that sounds more like a conceptual and almost trivial claim.
I think that the original claims sound deeper than they are because they slide between a true but trivial interpretation and a non-trivial interpretation that may not be generally true.
I think the confusion stems from the word “gradual.” It seems there’s wide agreement that we have two dimensions of the AI timelines problem:
Growth rate pattern. This could be linear, polynomial, exponential, or hyperbolic, and perhaps include a shift between two or more trends. Choice of coefficients matters too. Linear growth with a high slope could reach the threshold faster than exponential growth with small coefficients.
AI difficulty
Paul’s description of “gradualism” as stated actually does make a statement about both dimensions, though it’s also somewhat ambiguous:
US GDP last doubled from 1998-2021, a 23-year interval. Paul’s statement seems to imply that a doubling can occur in no less than 25% the time of its predecessor. Under this assumption, we’d have at least 3 doublings left, over the course of at least 8 years, before doublings can occur in less than a year. This still allows AI takeoff by 2030; it just suggest that we’ll be getting a warning shot over the next few years.
Another way to frame this, then, is that “For any choice of AI difficulty, faster pre-takeoff growth rates imply shorter timelines.”
This statement is literally and obviously true, and avoids the counterintuitive aspect introduced by the word “gradual.”
I agree. Notably, that sounds more like a conceptual and almost trivial claim.
I think that the original claims sound deeper than they are because they slide between a true but trivial interpretation and a non-trivial interpretation that may not be generally true.