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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!
One reason we shouldn’t be too surprised that most scientific progress is recent, years-wise is that a very simple model of scientific progress might be that you need X people (or X smart, literate people etc) thinking for Y moments to have a Z% chance of coming up with a scientific insight.
And if you measure time anthropically rather than geologically, estimates suggest that >~20% of people who have ever lived were born after 1650. The fraction is likely higher if you measure by human-moments rather than number of humans (since dead infants don’t make many scientific insights), and higher still if you only count literate or otherwise knowledgeable humans with ample free time.
Yeah I crunched the numbers on this and the majority of human life years came after about 1300 (obviously very roughly)
Thank you for writing this.
After I first read all the material on Cold Takes (well, I skimmed it—but only because you asked me to!) I figured that I wouldn’t bother to keep up with new stuff as it comes out; what good would it do me? It was written for a general audience and I am not a general audience.
That attitude lasted until around the third time I found myself linking to or quoting from your blog as a starting point for conversations with the vastly inferentially removed. And, I’ve known about the blog less than a week.
Needless to say I’ll be keeping up with what you write.
The argument here by appealing to too few atoms in the galaxy as a limit to economic growth is poor physics. The fundamental limit to economic value is that of information density.
Most of the galaxy (and universe) is entirely devoid of matter. Visible matter is exceedingly rare. But not energy. And energy may be assembled into economically valuable patterns, most clearly as information. E.g. a radio transmission of an opera to listeners does not require consumption of atoms.
An upper bound for information density is given by https://en.wikipedia.org/wiki/Bekenstein_bound and it is exceedingly large, so large that there isn’t a fundamental limit on the time frames considered here.
Likewise, appeals to limits to energy emitted from all stars is considerably lower than the total energy content of the galaxy, by tremendous orders of magnitude.
As this article is looking at the far-term future, then outlandish possibilities (to us) must also be considered; a very far advanced civilization might consist mostly of a dance of electromagnetic radiation. Indeed we’re clearly on that path with wifi/5G.
TLDR: economic growth hasn’t a fundamental limit per the arguments here.
I’ve never heard of the Bekenstein bound; thanks for this sharing this additional way to estimate the limits of economic efficiency.
This doesn’t seem right. Specifically it seems like the Bekenstein bound might be larger than the limit Holden discusses in his post, but not so large as to not be reachable with Business As Usual exponential growth in a short timeframe.
Can we quantify what the Bekenstein bound actually is here to check? Here’s my attempt:
Using the Earth as the system and the equation from Wikipedia, it looks like the Bekenstein bound is 9.82*10^74 bits. (Let me know if this is incorrect.) There are 10^50 atoms in Earth, so that’s 10^25 bits/atom.
For our galaxy, it looks like the number is 8*10^36, assuming again that I set up the math right. Holden’s claim is that the limit to economic efficiency is likely less than the efficiency of an economy that is a factor of 10^70 times larger than today’s world economy and that uses less than 10^70 atoms.
Note however that (a) there’s not enough time to colonize the galaxy in 8,200 years even at the speed of light and (b) economic growth during colonization of the galaxy is quadratic, not exponential, since it is limited by the speed of light expansion of civilization. So given these two considerations, I think it makes more sense to look at the Earth-system rather than the Galaxy-system.
Using the Earth as the system instead, the similar claim would be that the maximum size economy that could be sustained by the Earth would be an economy less than 10^50 times as large as today’s world economy.
At 2% annual economic growth, it would take 5,813 years for the economy to grow by a factor of 10^50.
If we make the very conservative claim that today’s economy only uses 1 bit of information [1], then to grow the economy by a factor of 10^75 would presumably mean that the resulting economy would have at least 10^75 bits (I think this is a reasonable assumption; let me know if it’s not), i.e. the Bekenstein bound for the Earth.
At 2% annual growth, it would take 8,720 years to grow the economy by this factor, i.e. definitely still in the range of time frames considered in this post.
In reality, our current world economy uses more than 1 bit, and the Bekenstein bound would presumably thus be reached before the economy is able to grow by a factor of 10^75. E.g. Maybe the actual maximum factor according to the Bekenstein bound might be closer (on a log scale) to 10^50 than 10^75 (?). I have no idea and would be interested in hearing from anyone who thinks they do have a way to estimate this.
The calculations for total bits in the systems is correct: 9.82*10^74 bits (earth) and 4×10^106 bits (galaxy). The bit limit grows quadratically as you expand out the radius and energy-mass content.
12,395 years of 2% growth to achieve the the upper bound of the galaxy’s information content given perfect mass-energy efficiency.
Stepping back, this exercise in extrapolating 2% growth to extremes can be reduced to just the mathematical statement that any exponential growth will exceed a (constant or sub-exponentially growing) limit in finite time. Yes… QED.
Solutions like expanding this future-humanity’s Boltzmann-economy at a 2% radius per year get you to faster-expansion than the speed of light quickly. Quadratic (or similar orders) is probably the best one can do in the long run.
TLDR: in bits, exponential growth at a fixed growth rate forever of an economy is impossible (ad absurdum), but something like quadratic growth forever is not impossible.
An important point that I don’t think we’ve said yet is that information density is of course not the same as economic productivity.
What would the Gross Galactic Product be of a maximally-efficient galaxy economy that had reached the 4×10^106 bit information density limit? It would necessarily be close to $10^106 or close to 10^106 times greater than the size of today’s GWP, right?
Similarly, if annual GWP increases at 2%/year, that does not necessarily mean that the economy’s information density (or perhaps more accurately, the information density of the system the economy is enclosed in) is increasing at close to 2%/year, does it?
I avoided the ‘productivity’ or ‘economic value’ to focus on something physically tangible. Markets put an objective value on those, but there’s no physical laws to help here.
Generally you’d expect the marginal value of information to fall as more information is created. Aristotle’s works vs another youtube video or terrabytes of system logs. The information-density-value-efficiency gets lower as you get bigger. Our own hard drive’s content is a good additional example: probably <5% of the contents are high value, contrast to when we all had much smaller storage (e.g. 2.5 inch floppy drives).
That said, this is analogous to diminishing marginal value (or returns) to scale in economic activity.
Efficiency of any economic system with respect to fundamental resource usage (information, energy) probably is almost certainly declining in scale. Friction adds up.
I miss a clear definition of economic growth here, and the discussion strongly reminds me of the environmental resources focused critique of growth that has started with 1970′s Club of Rome—Limits to Growth, there might be value to examine the huge literature around that topic that has been produced ever since on such topics.
Economic growth = increase in market value, is a typical definition.
Market value can increase if we paint the grey houses pink, or indeed if we design good computer games, or if we find great drugs to constantly awe use in insanely great ways without downsides. Or maybe indeed if we can duplicate/simulate brains which derive lot of value, say, literally out of thin air—and if we decide to take into account their blissful state also in our growth measure.
If we all have our basic needs met, and are rich way beyond it, willingness to pay for some new services may become extremely huge; even for the least important services—merely as we have nothing to do with our wealth, and as we’re willing to pay so little on the margin for the traditional ‘basic’ goods who are (in my scenario assumed to be) abundant and cheaply produced.
So the quantitative long-run extent of “economic growth” then becomes a bit an arbitrary thing: economic growth potentially being huge, but the true extra value possibly being limited.
‘Economic growth’ may therefore be too intangible, too arbitrary a basis for discussing the nature of long-run fate of human (or what ever supersedes us) development.
Maybe we should revert back to directly discussing limits to increase in utility (as come comments here already do).
Could you provide some evidence that this rate of growth is unusual in history? I mean it wouldn’t shock me if we looked back at the last 5000 years and saw that most societies real production grew at similar rates during times of peace/tranquility but that resulted in small absolute growth that was regularly wiped out by invasion, plague or other calamity. In which case the question becomes whether or not you believe that our technological accomplishments make us more resistant to such calamities (another discussion entirely).
Moreover, even if we didn’t see similar levels of growth in the past there are plenty of simple models which explain this apparent difference as the result of a single underlying phenomenon. For instance, consider the theory that real production over and above subsistence agricultural level grows at a constant rate per year. As this value was almost 0 for the past 5,000 years that growth wouldn’t be very noticeable until recently. And this isn’t just some arbitrary mathematical fit but has a good justification, e.g., productivity improvements require free time, invention etc.. etc.. so only happens in the percent of people’s time not devoted to avoiding starving.
Also, it’s kinda weird to describe the constant rate of growth assumption as business as usual but then pick a graph where we have an economic singularity (flat rate of growth gives a exponential curve which doesn’t escape to infinity at any finite time). Having said all that, sure it seems wrong to just assume things will continue this way forever but it seems equally unjustified to reach any other conclusion.
A bit late to the discussion here, but I wanted to re-emphasize the slightly nearer term limits that Holden brought up by Tom Murphy in his “Do The Math” blog, first presented a decade ago:
https://dothemath.ucsd.edu/2011/07/galactic-scale-energy/
This is formalized in Chapters 1&2 in a textbook he just released: https://escholarship.org/uc/item/9js5291m
The argument goes 1) there is a finite amount of energy available, limited by solar capacity, 2) decoupling of energy from the economy is ultimately limited; we can only grow non-energy intense parts of the economy so much as a percentage of the overall economy, 3) space colonization is extremely difficult if not impossible given how inhospitable space is, and therefore 4) economic growth will eventually cease given limited energy and resources.
He also mentions thermodynamic limits to surface heat rejection via blackbody radiation. We may be able to get around that by moving most computation to space. Though I imagine that being a harder collective action problem to solve than climate change presently.
Galactic expansion through digital minds may be a possibility that gets around the human biological limits to space expansions, but it’s unclear that the timing will line up conveniently. Our rate of economic expansion may hit hard energy and resources limits before a galactic digital mind expansion, regardless of whether it is possible.
Ultimately I don’t see how it’s possible to get around the energy limitations. As long as there are energy requirements for people—biological or otherwise—then it doesn’t seem possible to indefinitely shrink the energy intensity of the economy to an arbitrarily small value.
Do we really imagine the future of the economy to be increasingly faster trading of multi-trillion dollar cat holograms? Is that humanity’s destiny?
GDP is a very leaky measure for growth in this context. To see this, consider a utopian scenario with dirt cheap fusion energy powered Star Trek replicators. The marginal cost of most traded goods drops to near zero and GDP tanks (setting aside services). You have for traditional industry writ large a similar dynamic to that napster triggered for the music industry.
Assuming we don’t all die sometime soon and things ‘carry on’ the solution is likely to lie at least in part, eventually, in giving up on trying to summarise all of technology in a scalar value.
On another note, as a piece of futurism we see here that technology / the economy is predicted to either:
Get much bigger.
Get much smaller.
Stay about the same.
Do something else.
This covers just about every possibility, so it can’t constitute much evidence on which to update.
[edit: tidied up]
Jeremy Rifkin discusses this possibility in The Zero Marginal Cost Society
Might get hold of it and confirm my biases :D.
I feel fairly confident though that this argument doesn’t hinge too much on a particular technology such as IoT (as I see in the blurb). To unnecessarily recapitulate: something like the above argument on GDP falls out as the consequence of marginal costs being driven to zero. By whatever means, and relying only on micro 101 theory. In the limit, GDP will provide very little information about utility. There’ll be a lot of good, cool stuff in the world which will be free.
What do you think of a “Matrix” scenario where instead of bothering to capture the entire universe, humans achieve just enough to create a sustainable virtual simulation for a billion people, and then disconnect from the real world forever as AGI robots manage the server farms? Would be especially easy with digital humans, but seems doable with physical humans too.
This might be worth rewording for clarity.
In the stagnation scenario the economy will not reach the “maximum size” permitted by the laws of physics (using a given amount of matter, e.g. the solar system), so saying “we’ll reach the economy’s ‘maximum size’” is confusing and could easily be misinterpreted. (I understand you’re using the phrase “maximum size” to mean “the largest size that it actually reaches” but I imagine others could easily interpret it to mean “maximum size possible.”)
Suggested rewording: “stagnation: growth will slow and stop before the economy reaches its maximum size, i.e. before the economy reaches the limits of efficiency given the laws of physics.”
It seems you already covered this in the extra notes at the end, but I imagine the real graph could look more like this :)
I think humanity entering the digital space could allow growth to keep going much further. We could potentially encode a human into 10^(20-30) atoms.
The footnotes are broken here and don’t show the preview (which is a very helpful feature for the cold takes article).
Loved your analogy of the plane on the runway. This describes well a feeling I’ve had and it can sometimes be lonely! Thanks for the important work you’re doing.