One important question for the long-term future is whether we can expect accelerating growth in the near future (see e.g. this <@recent report@>(@Modeling the Human Trajectory@)). For AI alignment in particular, the answer to this question could have a significant impact on AI timelines: if some arguments suggested that it would be very unlikely for us to have accelerating growth soon, we should probably be more skeptical that we will develop transformative AI soon.
So far, the case for accelerating growth relies on one main argument that the author calls the _Hyperbolic Growth Hypothesis_ (HGH). This hypothesis posits that the growth _rate_ rises in tandem with the population size (intuitively, a higher population means more ideas for technological progress which means higher growth rates). This document explores the _empirical_ support for this hypothesis.
I’ll skip the messy empirical details and jump straight to the conclusion: while the author agrees that growth rates have been increasing in the modern era (roughly, the Industrial Revolution and everything after), he does not see much support for the HGH prior to the modern era. The data seems very noisy and hard to interpret, and even when using this noisy data it seems that models with constant growth rates fit the pre-modern era better than hyperbolic models. Thus, we should be uncertain between the HGH and the hypothesis that the industrial revolution triggered a one-off transition to increasing growth rates that have now stabilized.
Planned opinion:
I’m glad to know that the empirical support for the HGH seems mostly limited to the modern era, and may be weakly disconfirmed by data from the pre-modern era. I’m not entirely sure how I should update—it seems that both hypotheses would be consistent with future accelerating growth, though HGH predicts it more strongly. It also seems plausible to me that we should still assign more credence to HGH because of its theoretical support and relative simplicity—it doesn’t seem like there is strong evidence suggesting that HGH is false, just that the empirical evidence for it is weaker than we might have thought. See also Paul Christiano’s response.
The growth rate of output per person definitely has been roughly constant in developed countries (esp. the US) in the 20th century. In the doc, I’m instead talking about the growth rate of total output, globally, from about 1600 to 1950.
(So the summary may give the wrong impression. I ought to have suggested a tweak to make it clearer.)
Although, is it the case that growth(GDP) increased during the modern era (ie, growth(population) has been rising)? My recollection is that the IR was a structural break, with g jumping from 0.5% to 2% (or something).
The world GDP growth rate also seems to have been increasing during the immediate lead-up to the Industrial Revolution, as well as during the following century, although the exact numbers are extremely uncertain. The growth rate most likely stabilized around the middle of the 20th century.
Nit: Maybe you mean something stronger than transformative AI here? I don’t know if it makes sense to me that future explosive growth should tell us much about timelines for transformative AI as traditionally defined (as a transition comparable to the agricultural or industrial revolution). If we know that neither past transition caused explosive growth, it feels like we should think it’s quite plausible that transformative AI will have only a moderate impact on the growth rate.
On my read of this doc, everyone agrees that the industrial revolution led to explosive growth, and the question is primarily about whether we should interpret this as a one-off event, or as something that is likely to happen again in the future, so for all viewpoints it seems like transformative AI would still require explosive growth. Does that seem right to you?
My impression is that everyone agrees that the Industrial Revolution led to an increase in the growth rate, but that the Hyperbolic Growth Hypothesis (HGH) disagrees with the Series Of Exponentials Hypothesis on whether that increase in the growth rate was trend-breaking.
Put differently, the HGH says that as far as the growth rate is concerned, the Industrial Revolution wasn’t special—or if it was, then it must attribute this to noise. According to the HGH, the growth rate has been increasing all the time according to the same hyperbolic function, and the industrial revolution was just a part of this trend. I.e. only one “growth mode” for all of history, rather than the industrial revolution ushering in a new growth mode.
By contrast, on the Series Of Exponential view, the Industrial Revolution did break the previous trend—we had exponential growth both before and after, but with different doubling times.
I agree with this, but it seems irrelevant to Asya’s point? If it turned out to be the case that we would just resume the trend of accelerating growth, and AI was the cause of that, I would still call that transformative AI and I would still be worried about AI risks, to about the same degree as I would if that same acceleration was instead trend-breaking.
Yes, sorry, I think I was too quick to make a comment and should have paid more attention to the context. I think the claims in my comment are correct, but as you say it’s not clear what exactly they’re responding to, and in particular I agree it’s not relevant to Asya’s point on whether to use ‘explosive’.
I think everyone agrees that the industrial revolution led to an increase in the growth rate. I think ‘explosive’ growth as Roodman talks about it hasn’t happened yet, so I would avoid that term.
Planned summary for the Alignment Newsletter:
Planned opinion:
I think this is a misunderstanding. The common view is that the growth rate has been constant in the modern era.
The growth rate of output per person definitely has been roughly constant in developed countries (esp. the US) in the 20th century. In the doc, I’m instead talking about the growth rate of total output, globally, from about 1600 to 1950.
(So the summary may give the wrong impression. I ought to have suggested a tweak to make it clearer.)
Right, growth(GDP) > growth(GDP per capita) when growth(population)>0.
Although, is it the case that growth(GDP) increased during the modern era (ie, growth(population) has been rising)? My recollection is that the IR was a structural break, with g jumping from 0.5% to 2% (or something).
The world GDP growth rate also seems to have been increasing during the immediate lead-up to the Industrial Revolution, as well as during the following century, although the exact numbers are extremely uncertain. The growth rate most likely stabilized around the middle of the 20th century.
Nit: Maybe you mean something stronger than transformative AI here? I don’t know if it makes sense to me that future explosive growth should tell us much about timelines for transformative AI as traditionally defined (as a transition comparable to the agricultural or industrial revolution). If we know that neither past transition caused explosive growth, it feels like we should think it’s quite plausible that transformative AI will have only a moderate impact on the growth rate.
On my read of this doc, everyone agrees that the industrial revolution led to explosive growth, and the question is primarily about whether we should interpret this as a one-off event, or as something that is likely to happen again in the future, so for all viewpoints it seems like transformative AI would still require explosive growth. Does that seem right to you?
My impression is that everyone agrees that the Industrial Revolution led to an increase in the growth rate, but that the Hyperbolic Growth Hypothesis (HGH) disagrees with the Series Of Exponentials Hypothesis on whether that increase in the growth rate was trend-breaking.
Put differently, the HGH says that as far as the growth rate is concerned, the Industrial Revolution wasn’t special—or if it was, then it must attribute this to noise. According to the HGH, the growth rate has been increasing all the time according to the same hyperbolic function, and the industrial revolution was just a part of this trend. I.e. only one “growth mode” for all of history, rather than the industrial revolution ushering in a new growth mode.
By contrast, on the Series Of Exponential view, the Industrial Revolution did break the previous trend—we had exponential growth both before and after, but with different doubling times.
I agree with this, but it seems irrelevant to Asya’s point? If it turned out to be the case that we would just resume the trend of accelerating growth, and AI was the cause of that, I would still call that transformative AI and I would still be worried about AI risks, to about the same degree as I would if that same acceleration was instead trend-breaking.
Yes, sorry, I think I was too quick to make a comment and should have paid more attention to the context. I think the claims in my comment are correct, but as you say it’s not clear what exactly they’re responding to, and in particular I agree it’s not relevant to Asya’s point on whether to use ‘explosive’.
I think everyone agrees that the industrial revolution led to an increase in the growth rate. I think ‘explosive’ growth as Roodman talks about it hasn’t happened yet, so I would avoid that term.
Ah, fair point, I’ll change “explosive” to “accelerating” everywhere.