Iâm skeptical of an âexponentials generally continueâ prior which is supposed to apply super-generally. For example, hereâs a graph of world population since 1000 AD; itâs an exponential, but actually there are good mechanistic reasons to think it wonât continue along this trajectory. Do you think itâs very likely to?
I donât personally have well-developed thoughts on population growth, but note that âpopulation growth wonât continue to be exponentialâ is a prediction with a notoriously bad track record.
It has? The empirical track record has been slowing global population growth, which peaked 60 years ago:
The population itself also looks pretty linear for the last 60 years, given 1B/â~12 years rate:
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I think the general story is something like this:
The (observable) universe is a surprisingly small place when plotted on a log scale. Thus anything growing exponentially will hit physical ceilings if projected forward long enough: a population of 1000 humans growing at 0.9% pa roughly equal the number of atoms in the universe after 20 000 years.
(Even uploading digital humans onto computronium only gets you a little further on the log scale: after 60 000 years our population has grown to 2E236, so ~E150 people per atom, and E50 per planck volume. If that number is not sufficiently ridiculous, just let the growth run for a million more years and EE notation starts making sense (10^10^x).)
There are usually also âpracticalâ ceilings which look implausible to reach long before youâve exhausted the universe: âIf this stock keeps doubling in value, this company would be 99% of the global market cap in X yearsâ, âEven if the total addressable consumer market is the entire human population, people arenât going to be buying multiple subscriptions to Netflix each.â, etc.
So ~everything is ultimately an S-curve. Yet although âthis trend will start capping out somewhereâ is a very safe bet, âcalling the inflection pointâ before youâve passed it is known to be extremely hard. Sigmoid curves in their early days are essentially indistinguishable from exponential ones, and the extra parameter which ~guarantees they can better (over?)fit the points on the graph than a simple exponential give very unstable estimates of the putative ceiling the trend will âcap outâ at. (cf. 1, 2.)
Many important things turn on (e.g.) âscaling is hitting the wall ~nowâ vs. âscaling will hit the wall roughly at the point of the first dyson sphere data centerâ As the universe is a small place on a log scale, this range is easily spanned by different analysis choices on how you project forward.
Without strong priors on âinflecting soonâ vs. âinflecting lateâ, forecasts tend to be volatile: is this small blip above or below trend really a blip, or a sign weâre entering a faster/âslow regime?
(My guess is the right ur-prior favours âinflecting soonâ weakly and in general, although exceptions and big misses abound. In most cases, you have mechanistic steers you can appeal to which give much more evidence. Iâm not sure AI is one of them, as it seems a complete epistemic mess to me.)
In particular, Iâm not trying to make a strong claim about exponentials specifically, or that things will line up perfectly, etc.
(Fwiw, though, it does seem possible that if we zoom out, recent/ânear-term population growth slow-downs might be functionally a ~blip if humanity or something like it leaves the Earth. Although at some point youâd still hit physical limits.)
Iâm skeptical of an âexponentials generally continueâ prior which is supposed to apply super-generally. For example, hereâs a graph of world population since 1000 AD; itâs an exponential, but actually there are good mechanistic reasons to think it wonât continue along this trajectory. Do you think itâs very likely to?
I donât personally have well-developed thoughts on population growth, but note that âpopulation growth wonât continue to be exponentialâ is a prediction with a notoriously bad track record.
It has? The empirical track record has been slowing global population growth, which peaked 60 years ago:
The population itself also looks pretty linear for the last 60 years, given 1B/â~12 years rate:
#
I think the general story is something like this:
The (observable) universe is a surprisingly small place when plotted on a log scale. Thus anything growing exponentially will hit physical ceilings if projected forward long enough: a population of 1000 humans growing at 0.9% pa roughly equal the number of atoms in the universe after 20 000 years.
(Even uploading digital humans onto computronium only gets you a little further on the log scale: after 60 000 years our population has grown to 2E236, so ~E150 people per atom, and E50 per planck volume. If that number is not sufficiently ridiculous, just let the growth run for a million more years and EE notation starts making sense (10^10^x).)
There are usually also âpracticalâ ceilings which look implausible to reach long before youâve exhausted the universe: âIf this stock keeps doubling in value, this company would be 99% of the global market cap in X yearsâ, âEven if the total addressable consumer market is the entire human population, people arenât going to be buying multiple subscriptions to Netflix each.â, etc.
So ~everything is ultimately an S-curve. Yet although âthis trend will start capping out somewhereâ is a very safe bet, âcalling the inflection pointâ before youâve passed it is known to be extremely hard. Sigmoid curves in their early days are essentially indistinguishable from exponential ones, and the extra parameter which ~guarantees they can better (over?)fit the points on the graph than a simple exponential give very unstable estimates of the putative ceiling the trend will âcap outâ at. (cf. 1, 2.)
Many important things turn on (e.g.) âscaling is hitting the wall ~nowâ vs. âscaling will hit the wall roughly at the point of the first dyson sphere data centerâ As the universe is a small place on a log scale, this range is easily spanned by different analysis choices on how you project forward.
Without strong priors on âinflecting soonâ vs. âinflecting lateâ, forecasts tend to be volatile: is this small blip above or below trend really a blip, or a sign weâre entering a faster/âslow regime?
(My guess is the right ur-prior favours âinflecting soonâ weakly and in general, although exceptions and big misses abound. In most cases, you have mechanistic steers you can appeal to which give much more evidence. Iâm not sure AI is one of them, as it seems a complete epistemic mess to me.)
I tried to clarify things a bit in this reply to titotal: https://ââforum.effectivealtruism.org/ââposts/ââiJSYZJJrLMigJsBeK/ââlizka-s-shortform?commentId=uewYatQz4dxJPXPiv
In particular, Iâm not trying to make a strong claim about exponentials specifically, or that things will line up perfectly, etc.
(Fwiw, though, it does seem possible that if we zoom out, recent/ânear-term population growth slow-downs might be functionally a ~blip if humanity or something like it leaves the Earth. Although at some point youâd still hit physical limits.)