Eyeballing the graphs you produced, it looks like the singularities you keep getting are hyperbolic growth, which we already have in real life (compare log(world GDP) to your graph of log(projects completed) - their shapes are almost identical).
So far as I can tell, what you’ve shown is that you almost always get a big speedup of hyperbolic growth as AI advances but without discontinuities, which is what the ‘continuous takeoff’ people like Christiano already say they are expecting.
AI is just another, faster step in the hyperbolic growth we are currently experiencing, which corresponds to a further increase in rate but not a discontinuity (or even a discontinuity in rate).
So perhaps this is evidence of continuous takeoff still being quite fast.
Yes, thanks! I mostly agree with that assessment,* though as an aside I have a beef with the implication that Bostrom, Yudkowsky, etc. expect discontinuities. That beef is with Paul Christiano, not you. :)
So far the biggest update this has been for me, I think, is that it seems to have shown that it’s quite possible to get an intelligence explosion even without economic feedback loops. Like, even with a fixed compute/money budget—or even with a fixed number of scientists and fixed amount of research funding—we could get singularity. At least in principle. This is weird because in practice I am pretty sure I remember reading that the growth we’ve seen so far can be best explained via an economic feedback loop: Better technology allows for bigger population and economy which allows for more scientists and funding which allows for better technology. So I’m a bit confused, I must say—my model is giving me results I would have predicted wouldn’t happen.
*There have been a few cases where the growth didn’t look hyperbolic, but rather like a steady exponential trend that then turns into a singularity. World GDP, by contrast, has what looks like at least three exponential trends in it, such that it is more parsimonious to model it as hyperbolic growth. I think.
I should add though that I haven’t systematically examined these graphs yet, so it’s possible I’m just missing something—e.g. it occurs to me right now that maybe some of these graphs I saw were really logistic functions rather than hyperbolic or exponential-until-you-hit-limits. I should make some more and look at them more carefully.
Eyeballing the graphs you produced, it looks like the singularities you keep getting are hyperbolic growth, which we already have in real life (compare log(world GDP) to your graph of log(projects completed) - their shapes are almost identical).
So far as I can tell, what you’ve shown is that you almost always get a big speedup of hyperbolic growth as AI advances but without discontinuities, which is what the ‘continuous takeoff’ people like Christiano already say they are expecting.
So perhaps this is evidence of continuous takeoff still being quite fast.
Yes, thanks! I mostly agree with that assessment,* though as an aside I have a beef with the implication that Bostrom, Yudkowsky, etc. expect discontinuities. That beef is with Paul Christiano, not you. :)
So far the biggest update this has been for me, I think, is that it seems to have shown that it’s quite possible to get an intelligence explosion even without economic feedback loops. Like, even with a fixed compute/money budget—or even with a fixed number of scientists and fixed amount of research funding—we could get singularity. At least in principle. This is weird because in practice I am pretty sure I remember reading that the growth we’ve seen so far can be best explained via an economic feedback loop: Better technology allows for bigger population and economy which allows for more scientists and funding which allows for better technology. So I’m a bit confused, I must say—my model is giving me results I would have predicted wouldn’t happen.
*There have been a few cases where the growth didn’t look hyperbolic, but rather like a steady exponential trend that then turns into a singularity. World GDP, by contrast, has what looks like at least three exponential trends in it, such that it is more parsimonious to model it as hyperbolic growth. I think.
I should add though that I haven’t systematically examined these graphs yet, so it’s possible I’m just missing something—e.g. it occurs to me right now that maybe some of these graphs I saw were really logistic functions rather than hyperbolic or exponential-until-you-hit-limits. I should make some more and look at them more carefully.