Very interesting post. I’m interested in this argument about atoms and growth.
“Let’s say the world economy is currently getting 2% bigger each year.5 This implies that the economy would be doubling in size about every 35 years.6
If this holds up, then 8200 years from now, the economy would be about 3*1070 times its current size.
There are likely fewer than 1070 atoms in our galaxy,7 which we would not be able to travel beyond within the 8200-year time frame.8
So if the economy were 3*1070 times as big as today’s, and could only make use of 1070 (or fewer) atoms, we’d need to be sustaining multiple economies as big as today’s entire world economy per atom.”
I find this connection between GDP and atoms a bit obscure. It might also seem weird to think that today there is more GDP in $ than there are stars in the Milky Way, but these two things don’t seem comparable to me. There are 10^50 atoms on Earth (apparently). Maybe we only have access to 10^18 of these atoms or something. World GDP is 10^18 Zimbabwean cents. So, each atom is producing one Zimbabwean cent of value. I don’t know whether this is or isn’t plausible.
Really what we’re concerned about is whether we can extract subjective wellbeing from different arrangements of atoms. Once we start thinking about digital minds and VR, I don’t have a strong intuition about how much subjective wellbeing we can squeeze out of a given number of atoms.
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.”
What does “have access to” mean? There are >10^37 atoms making up human bodies. And dollars can buy physical stuff, and you might expect this to be somewhat weighted in PPP adjustments between now and the distant future.
I agree that it’s not quite clear how to interpret these things, but I don’t think it’s as nonsensical as you’re implying.
(thinking aloud a bit here) An analogy might be that Jeff Bezos has 78 organs. His net worth is $200bn. So there is $3bn of output for each of his organs. I just don’t know at what number it becomes implausible that his average organ could sustain a certain level of output. And this generally seems like a weird way to think about the limits on Bezos’ output. This seems structurally similar to the atoms point.
To push further on this… a natural response is to say “it only seems implausible that Bezos’ liver could have this economic value because you’re considering an organ in the abstract. But once his liver is combined with the rest of his Bezos and the influence he can have on the rest of the world, it stops being implausible”. This is true but then the same point applies to collections of atoms. I don’t know of a non-question begging way round this.
Another point is—how much economic value can you extract from an atom? I have no idea how you would go about answering that question without making some other substantive arguments about the limits to growth. This suggests that the atoms argument is a weak steer on limits to growth.
My interpretation of the argument is not that it is equating atoms to $. Rather, it invokes whatever computations are necessary to produce (e.g. through simulations) an amount of value equal to today’s global economy. Can these computations be facilitated by a single atom? If not, then we can’t grow at the current rate for 8200 years.
Digital content requires physical space too, just relatively small amounts. E.g., physical resources/atoms are needed to make the calculations associated with digital interactions. At some point the number of digital interactions will be capped, and the question will be how much they can be made better and better. More on the latter here: https://www.cold-takes.com/more-on-multiple-world-size-economies-per-atom/
I feel quite out of my depth here, so there is a real possibility that much of what follows in ill-informed...
Regarding “Digital content requires physical space too, just relatively small amounts. E.g., physical resources/atoms are needed to make the calculations associated with digital interactions.” — I wonder if we could look at historical amounts of physical resources/atoms dedicated to making calculations associated with economic interactions to see to what extent the amount has scaled with the increase in the size of the world economy. My intuition is that they are not really tethered; it seems like in a digital world there are possibly infinite ways to consolidate transactions and representations of value so that they require fewer resources/atoms.
I think that I am also hung up on what constitutes value and whether it is value that really increases or simply the numbers we use to represent value (perhaps this ventures into monetary value theory?). I’m under the impression that the numbers we used to represent value will necessarily increase because our economic system is inflationary.
Another small note: In the article you linked in your comment, you state that “the world economy that year included that second of your life, plus the rest of your year and many other people’s years.” I thought that the world economy would contain only strictly economic activities, and that there could be “single best moments of life” that are not included in the world economy (e.g., looking at the night sky and seeing a shooting star). Maybe this isn’t relevant to your point in the article.
Very interesting post. I’m interested in this argument about atoms and growth.
“Let’s say the world economy is currently getting 2% bigger each year.5 This implies that the economy would be doubling in size about every 35 years.6
If this holds up, then 8200 years from now, the economy would be about 3*1070 times its current size.
There are likely fewer than 1070 atoms in our galaxy,7 which we would not be able to travel beyond within the 8200-year time frame.8
So if the economy were 3*1070 times as big as today’s, and could only make use of 1070 (or fewer) atoms, we’d need to be sustaining multiple economies as big as today’s entire world economy per atom.”
I find this connection between GDP and atoms a bit obscure. It might also seem weird to think that today there is more GDP in $ than there are stars in the Milky Way, but these two things don’t seem comparable to me. There are 10^50 atoms on Earth (apparently). Maybe we only have access to 10^18 of these atoms or something. World GDP is 10^18 Zimbabwean cents. So, each atom is producing one Zimbabwean cent of value. I don’t know whether this is or isn’t plausible.
Really what we’re concerned about is whether we can extract subjective wellbeing from different arrangements of atoms. Once we start thinking about digital minds and VR, I don’t have a strong intuition about how much subjective wellbeing we can squeeze out of a given number of atoms.
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.”
What does “have access to” mean? There are >10^37 atoms making up human bodies. And dollars can buy physical stuff, and you might expect this to be somewhat weighted in PPP adjustments between now and the distant future.
I agree that it’s not quite clear how to interpret these things, but I don’t think it’s as nonsensical as you’re implying.
Fair cop on the access to atoms numbers.
(thinking aloud a bit here) An analogy might be that Jeff Bezos has 78 organs. His net worth is $200bn. So there is $3bn of output for each of his organs. I just don’t know at what number it becomes implausible that his average organ could sustain a certain level of output. And this generally seems like a weird way to think about the limits on Bezos’ output. This seems structurally similar to the atoms point.
To push further on this… a natural response is to say “it only seems implausible that Bezos’ liver could have this economic value because you’re considering an organ in the abstract. But once his liver is combined with the rest of his Bezos and the influence he can have on the rest of the world, it stops being implausible”. This is true but then the same point applies to collections of atoms. I don’t know of a non-question begging way round this.
Another point is—how much economic value can you extract from an atom? I have no idea how you would go about answering that question without making some other substantive arguments about the limits to growth. This suggests that the atoms argument is a weak steer on limits to growth.
My interpretation of the argument is not that it is equating atoms to $. Rather, it invokes whatever computations are necessary to produce (e.g. through simulations) an amount of value equal to today’s global economy. Can these computations be facilitated by a single atom? If not, then we can’t grow at the current rate for 8200 years.
I’m struggling to see why the world’s economy would be limited by the number of atoms in our galaxy when much of the economy seems to exist digitally.
Perhaps someone could clarify to what degree the “size of the economy” requires physical space.
Digital content requires physical space too, just relatively small amounts. E.g., physical resources/atoms are needed to make the calculations associated with digital interactions. At some point the number of digital interactions will be capped, and the question will be how much they can be made better and better. More on the latter here: https://www.cold-takes.com/more-on-multiple-world-size-economies-per-atom/
Thank you for the response, Holden!
I feel quite out of my depth here, so there is a real possibility that much of what follows in ill-informed...
Regarding “Digital content requires physical space too, just relatively small amounts. E.g., physical resources/atoms are needed to make the calculations associated with digital interactions.” — I wonder if we could look at historical amounts of physical resources/atoms dedicated to making calculations associated with economic interactions to see to what extent the amount has scaled with the increase in the size of the world economy. My intuition is that they are not really tethered; it seems like in a digital world there are possibly infinite ways to consolidate transactions and representations of value so that they require fewer resources/atoms.
I think that I am also hung up on what constitutes value and whether it is value that really increases or simply the numbers we use to represent value (perhaps this ventures into monetary value theory?). I’m under the impression that the numbers we used to represent value will necessarily increase because our economic system is inflationary.
Another small note: In the article you linked in your comment, you state that “the world economy that year included that second of your life, plus the rest of your year and many other people’s years.”
I thought that the world economy would contain only strictly economic activities, and that there could be “single best moments of life” that are not included in the world economy (e.g., looking at the night sky and seeing a shooting star). Maybe this isn’t relevant to your point in the article.
I’d appreciate any thoughts in response!