I find this connection between GDP and atoms a bit obscure.
Anecdotally, I’ve found this connection between GWP and atoms to be an effective intuition pump. Nearly everyone I’ve talked to seems to intuitively agree that “sustaining multiple economies as big as today’s entire world economy per atom” is unrealistic (whether on a solar system or galactic scale), and that the real limit imposed by the laws of physics is likely lower.
That said, that this is intuitive to people doesn’t show that the physical limits on the size of the economy are indeed below this point.
For example, in the Overcoming Bias comment section, Toby Ord pointed out (in 2009):
It is indeed conjectured that there are finitely many distinguishable states in any particular region of space. However:
(1) this is a conjecture, and may turn out to be false (though most people who know about it think it is probably true).
(2) all finite sets of finite numbers have a finite bound, but this doesn’t mean that we know what it is, or how fast it can grow as the size of the volume increases. Thus, it is a bound in some sense, but not of the type robin is looking for.
(3) perhaps some arrangements of matter within a volume of spacetime have infinite value.
Point 2 seems important, since it seems plausible that there are economies of scale with consciousness, where e.g. an optimal digital mind that uses a million times as much computation as an optimal digital mind that uses as much computation as the human brain could have much, much greater than a million times as much welfare as the smaller digital mind. (Note that I say this is plausible, but I don’t know whether I should put ~10% or ~90% credence to this being true and would love to know more.)
And while point 3 seems unlikely to me, what do I know—I’d guess we don’t know enough to definitely rule this out.
So with all this said, I too would like to identify better ways to estimate the limits on the physical limits to size of the economy. Surely there are better ways to estimate this than just thinking about “economies as big as today’s entire world economy per atom” and making the intuitive judgment call that that the limits are likely less than that level of efficiency.
We argue for some more fundamental reasons for limited growth, and specifically (and I think fully) address William Kiley’s point 3.
I also think that we can make some strong claims about the bound implied by optimal human brain emulation based on fundamental physics to find a fairly pessimistic upper bound on exponential growth past 10k years. (We looked at 100k years in our example, but we also talked about far, far smaller than 2% growth.)
Thanks for this, it helped shore things up for me, and I think it’s maybe valuable enough to link to in the main piece with short disclaimer e.g. “Does the value/atoms stuff seem weird or unintuitive to you? Read more here”
Currently I have the high end of the range set to 10^15 trillion 2020US$, which is 10^13 times as large as the economy is today. Metaculus currently gives 20% credence to the economy being larger than that in 2200. (My forecast is more pessimistic.)
For reference, if we turned the entire mass of the Earth into human brains, there would be about 5*10^14 times more human brains than there are human brains today. (I’m using this as a reference for a large economy. My assumption is that a solar-system-size economy that produces as much value as that many brains is quite efficient, though not necessarily at or near the limit of what’s physically possible.)
Additionally note that 50 years of near-speed-of-light galaxy colonization we’ll be able to reach an additional 1,000 stars and with 150 years of that we’ll be able to reach 7,594 stars (I think WolframAlpha undercounts the number of stars that actually exist, but not by an order of magnitude until you get out to further distances). So that means the economy could potentially be ~3-4 orders of magnitude larger by 2200 than the largest economy our solar system can support.
(Note: I’ve asked a moderator on Metaculus to adjust the high end of the range up from 10^15 to 10^30 trillion 2020$ so that we can capture the high end of peoples’ estimates for how large the economy can get.)
(Note that at 30% annual economy growth (the threshold for what Open Phil calls explosive economic growth), the economy can reach 10^15 trillion USD in a mere 115 years starting at the economy’s current size. Again, Metaculus gives a 20% chance that this size economy or greater will exist in 2200. Metaculus gives a 30% chance that the economy will be greater than 10^15 trillion USD in 2200. From this I’d speculate that Metaculus would give roughly 10% to >10^20, and roughly 5% to >10^25. Hopefully we’ll be able to see this exactly more precisely once the high end of the range is increased to 10^30.)
(Final note: Only about a dozen unique people have made forecasts on the 2200 GWP Metaculus question so far, so the forecasts are likely very speculative and could probably be improved a lot with more research.)
(UPDATE: Changing ranges on Metaculus questions after forecasts have been made apparently isn’t possible, so instead I’ve created a second version of the question with a range going up to 10^29 trillion 2020 US$ (it should be approved by moderators and visible within a couple days). Hopefully this is high enough to capture >98% of Metaculus’ probability mass.)
Thanks for all the thoughts on this point! I don’t think the comparison to currency is fair (the size of today’s economy is a real quantity, not a nominal one), but I agree with William Kiely that the “several economies per atom” point is best understood as an intuition pump rather than an airtight argument. I’m going to put a little thought into whether there might be other ways of communicating how astronomically huge some of these numbers are, and how odd it would be to expect 2% annual growth to take us there and beyond.
One thought: it is possible that there’s some hypothetical virtual world (or other configuration of atoms) with astronomical value compared to today’s economy. But if so, getting to that probably involves some sort of extreme control and understanding of our environments, such as what might be possible with digital people. And I’d expect the path to such a thing to look more like “At some point we figure out how to essentially escape physical constraints and design an optimal state [e.g., via digital people], causing a spike (not necessarily instantaneous, but quite quick) in the size of the economy” than like “We get from here to there at 2% growth per year.”
Anecdotally, I’ve found this connection between GWP and atoms to be an effective intuition pump. Nearly everyone I’ve talked to seems to intuitively agree that “sustaining multiple economies as big as today’s entire world economy per atom” is unrealistic (whether on a solar system or galactic scale), and that the real limit imposed by the laws of physics is likely lower.
The only concrete exception I’m aware of is Bryan Caplan in the Limits to Growth post you linked me to last month.
That said, that this is intuitive to people doesn’t show that the physical limits on the size of the economy are indeed below this point.
For example, in the Overcoming Bias comment section, Toby Ord pointed out (in 2009):
Point 2 seems important, since it seems plausible that there are economies of scale with consciousness, where e.g. an optimal digital mind that uses a million times as much computation as an optimal digital mind that uses as much computation as the human brain could have much, much greater than a million times as much welfare as the smaller digital mind. (Note that I say this is plausible, but I don’t know whether I should put ~10% or ~90% credence to this being true and would love to know more.)
And while point 3 seems unlikely to me, what do I know—I’d guess we don’t know enough to definitely rule this out.
So with all this said, I too would like to identify better ways to estimate the limits on the physical limits to size of the economy. Surely there are better ways to estimate this than just thinking about “economies as big as today’s entire world economy per atom” and making the intuitive judgment call that that the limits are likely less than that level of efficiency.
I’ve just put up a post with more discussion of this point: https://www.cold-takes.com/more-on-multiple-world-size-economies-per-atom/
It seems like this is partly covering the same ground as my paper with Anders; https://philpapers.org/rec/MANWIT-6
We argue for some more fundamental reasons for limited growth, and specifically (and I think fully) address William Kiley’s point 3.
I also think that we can make some strong claims about the bound implied by optimal human brain emulation based on fundamental physics to find a fairly pessimistic upper bound on exponential growth past 10k years. (We looked at 100k years in our example, but we also talked about far, far smaller than 2% growth.)
Thanks for this, it helped shore things up for me, and I think it’s maybe valuable enough to link to in the main piece with short disclaimer e.g. “Does the value/atoms stuff seem weird or unintuitive to you? Read more here”
Yeah I would think with VR and digital minds, it’s a lot less clear whether there are diminishing returns from matter to subjective wellbeing.
One way I thought of to try to better identify what the physical limits on the size of the economy are likely to be is to ask on Metaculus What will real Gross World Product be in 2200, in trillions of 2020 US$?.
Currently I have the high end of the range set to 10^15 trillion 2020US$, which is 10^13 times as large as the economy is today. Metaculus currently gives 20% credence to the economy being larger than that in 2200. (My forecast is more pessimistic.)
For reference, if we turned the entire mass of the Earth into human brains, there would be about 5*10^14 times more human brains than there are human brains today. (I’m using this as a reference for a large economy. My assumption is that a solar-system-size economy that produces as much value as that many brains is quite efficient, though not necessarily at or near the limit of what’s physically possible.)
Additionally note that 50 years of near-speed-of-light galaxy colonization we’ll be able to reach an additional 1,000 stars and with 150 years of that we’ll be able to reach 7,594 stars (I think WolframAlpha undercounts the number of stars that actually exist, but not by an order of magnitude until you get out to further distances). So that means the economy could potentially be ~3-4 orders of magnitude larger by 2200 than the largest economy our solar system can support.
(Note: I’ve asked a moderator on Metaculus to adjust the high end of the range up from 10^15 to 10^30 trillion 2020$ so that we can capture the high end of peoples’ estimates for how large the economy can get.)
(Note that at 30% annual economy growth (the threshold for what Open Phil calls explosive economic growth), the economy can reach 10^15 trillion USD in a mere 115 years starting at the economy’s current size. Again, Metaculus gives a 20% chance that this size economy or greater will exist in 2200. Metaculus gives a 30% chance that the economy will be greater than 10^15 trillion USD in 2200. From this I’d speculate that Metaculus would give roughly 10% to >10^20, and roughly 5% to >10^25. Hopefully we’ll be able to see this exactly more precisely once the high end of the range is increased to 10^30.)
(Final note: Only about a dozen unique people have made forecasts on the 2200 GWP Metaculus question so far, so the forecasts are likely very speculative and could probably be improved a lot with more research.)
(UPDATE: Changing ranges on Metaculus questions after forecasts have been made apparently isn’t possible, so instead I’ve created a second version of the question with a range going up to 10^29 trillion 2020 US$ (it should be approved by moderators and visible within a couple days). Hopefully this is high enough to capture >98% of Metaculus’ probability mass.)
Thanks for all the thoughts on this point! I don’t think the comparison to currency is fair (the size of today’s economy is a real quantity, not a nominal one), but I agree with William Kiely that the “several economies per atom” point is best understood as an intuition pump rather than an airtight argument. I’m going to put a little thought into whether there might be other ways of communicating how astronomically huge some of these numbers are, and how odd it would be to expect 2% annual growth to take us there and beyond.
One thought: it is possible that there’s some hypothetical virtual world (or other configuration of atoms) with astronomical value compared to today’s economy. But if so, getting to that probably involves some sort of extreme control and understanding of our environments, such as what might be possible with digital people. And I’d expect the path to such a thing to look more like “At some point we figure out how to essentially escape physical constraints and design an optimal state [e.g., via digital people], causing a spike (not necessarily instantaneous, but quite quick) in the size of the economy” than like “We get from here to there at 2% growth per year.”