GDP growth is measured in money, a measure of value. Value does not have to be backed by a proportional amount of matter (or energy, space or time) because we can value things as much as we like—more than some constant times utilon per gram second.
Suppose I invent an algorithm that solves a hard problem and sell it as a service. The amount people will be willing to pay for it—and the amount the economy grows—is determined by how much people want it and how much money there is, but nobody cares how many new atoms I used to implement it. If I displace older, less efficient algorithms, then I produce value while reducing the number of atoms (or watts) backing the economy!
Material goods and population size can’t keep growing forever, but value can. Many recent developments that produced a lot of value, like radio, computing, and the Internet, didn’t do it by using proportionally more atoms. An algorithm is a convenient example but this applies to non-digital services just as much.
This is not a novel argument but I can’t recall it’s source or name.
As a concrete example, let’s imagine that sending an email is equivalent to sending a letter. Let’s ignore the infrastructure required to send emails (computers, satellites, etc) vs. letters (mail trucks, post offices, etc), and assume they’re roughly equal to each other. Then the invention of email eliminated the vast majority of letters, and the atoms they would have been made from.
Couple this with the fact that emails are more durable, searchable, instantaneous, free, legible, compatible with mixed media, and occupy only a miniscule amount of physical real estate in the silicon of the computer, and we can see that emails not only reduce the amount of atoms needed to transmit a letter, but also produce a lot more value.
In theory, we might spend the next several thousand years not only finding ways to pack more value into fewer atoms, but also enhancing our ability to derive value from the same good or service. Perhaps in 10,000 years, checking my email will be a genuine pleasure!
In fact, come to think of it, this is the thesis of More from Less by Andrew McAffee, who points out that in numerous categories of material products, we’ve seen global GDP growing while using less material resources, in both relative and absolute terms.
Edit: though see multiple 1-star reviews from non-anonymous Amazon reviewers with economics PhDs who say the core premise of McAffee’s book is incorrect. Sounds like there is better research out there than he presents in this book.
An alternative point of view is in Decoupling Debunked, which seems to feed into degrowth literature. Makes me worry that both McAffee’s and this piece will suffer from the same issues we find when we look for a consensus viewpoint among economists on the effect of the minimum wage.
We find that relative decoupling is frequent for material use as well as GHG and CO2 emissions but not for useful exergy, a quality-based measure of energy use. Primary energy can be decoupled from GDP largely to the extent to which the conversion of primary energy to useful exergy is improved. Examples of absolute long-term decoupling are rare, but recently some industrialized countries have decoupled GDP from both production- and, weaklier, consumption-based CO2 emissions.
There’s a few one-star Amazon reviews for the book that suggest McAfee’s data is incorrect or misleading. Here’s a quote from one of them, which seems like a solid counterargument to me:
“However, on the first slide on page 79, he notes that the data excludes impact from Import/export of finished goods. Not raw materials but finished goods. He comments that Net import is only 4% of GDP in the US. Here he makes a (potentially) devastating error – (potentially) invalidating his conclusion.
While Net imports is indeed around 4% of GDP, the gross numbers are Exports at approx. +13% and Imports at approx. −17%. So any mix difference in finished goods in Export and Import, can significantly change the conclusion. It so happens that US is a major Net importer of finished goods e.g. Machinery, electronic equipment and autos (finished goods, with materials not included above in the consumption data). Basically, a big part of US’ consumption of cars, washing machines, computers etc. are made in Mexico, China etc. They contain a lot of materials, not included in the graphs, upon which he builds his conclusion/thesis. So quite possibly, there is no de-coupling.”
I still think the argument holds in this case, because even computer software isn’t atom-less. It needs to be stored, or run, or something somewhere.
I don’t doubt that you could drastically reduce the number of atoms required for many products today. For example, you could in future get a chip in your brain that makes typing without a keyboard possible. That chip is smaller than a keyboard, so represents lots of atoms saved. You could go further, and have that chip be an entire futuristic computer suite, by reading and writing your brain inputs and outputs directly it could replace the keyboard, mouse, monitors, speakers, and entire desktop, plus some extra stuff, like also acting as a VR Headset, or video game console, or whatever. Lets say you manage to squeeze all that into a single atom. Cool. That’s not enough. For this growth to go on for those ~8000 years, you’d need to have that single-atom brain chip be as valuable as everything on Earth today. Along with every other atom in the galaxy.
I think at some point, unless the hottest thing in the economy becomes editing humans to value specific atoms arbitrary amounts (which sounds bad, even if it would work), you can’t get infinite value out of things. I’m not even sure human minds have the capability of valuing things infinitely. I think even with today’s economy, you’d start to hit some asymptotes (i.e. if one person had everything in the world, I’m not sure what they’d do with it all. I’m also not sure they’d actually value it any more than if they just had 90% of everything, except maybe the value on saying “I have it all”, which wouldn’t be represented in our future economy)
And still, the path to value per atom has to come from somewhere, and in general it’s going to be making stuff more useful, or smaller, but there’s only so useful a single atom can be, and there’s only so small a useful thing can be. (I imagine some math on the number of ways you could arrange a set of particles, multiplied by the number of ways a particular arrangement could be used, as an estimate. But a quick guess says that neither of those values are infinite, and, I expect that number to be dominated by ways of arranging particles, not by number of uses, considering that even software on a computer is actually different arrangements of the electrons.)
So I guess that’s the heart of it to me, there’s certainly a lot more value we can squeeze out of things, but if there’s not literally infinite, it will run out at some point, and that ~8000 year estimate is looking pretty close to whatever the limit is, if it’s not already over it.
Please see my other reply here. Yes, value is finite, but the number of possible states of the universe is enormously large, and we won’t explore it in 8000 years. The order of magnitude is much bigger.
(Incidentally, our galaxy is ~ 100,000 light years across; so even expanding to cover it would take much longer than 8000 years, and that would be creating value the old-fashioned way by adding atoms, but it wouldn’t support continued exponential growth. So “8000 years” and calculations based off the size of the galaxy shouldn’t be mixed together. But the order-of-magnitude argument should work about as well for the matter within 8000 light-years of Earth.)
In much the same way, estimates of value and calculations based on the number of permutations of atoms shouldn’t be mixed together. There being a googleplex possible states in no way implies that any of them have a value over 3 (or any other number). It does not, by itself, imply that any particular state is better than any other. Let alone that any particular state should have value proportional to the total number of states possible.
Restricting yourself to atoms within 8000 light years, instead of the galaxy, just compounds the problem as well, but you noted that yourself. The size of the galaxy wasn’t actually a relevant number, just a (maybe) useful comparison. It’s like when people say that chess has more possible board states than there are atoms in the observable universe times the number of seconds since the Big Bang. It’s not that there’s any specifically useful interaction between atoms and seconds and chess, it’s just to recognize the scale of the problem.
Value is not obviously bounded by atoms, yes. However, GDP measures production of value. And, the entities producing value are made of atoms. Today these entities are humans. In the future, they might be something much more efficient. However, it seems at least plausible that their efficiency (i.e. rate of value production per atom) is somehow bounded by physics.
The rate of value production per atom can be bounded by physics. But the amount of value ascribed to the thing being produced is only strictly bounded by the size of the number (representing the amount of value) that can be physically encoded, which is exponential in the number of atoms, and not linear.
size of the number (representing the amount of value) that can be physically encoded, which is exponential in the number of atoms
The natural numbers that can be physically encoded are not bounded by an exponent of the number of bits if you don’t have to be able to encode all smaller numbers as well in the same number of bits. If you define a number, you’ve encoded it, and it’s possible to define very large numbers indeed.
The configuration does change, it’s just that the change is not about the amount of matter. If there are configurations absurdly more positively or negatively valuable than others, that just makes the ordinary configurations stop being decision relevant, once discerning the important configurations becomes feasible.
So, you imagine that the rate at which new “things” are produced hits diminishing returns, but every new generation of things is more valuable than the previous generation s.t. exponential growth is maintained. But, I think this value growth has to hit a ceiling pretty soon anyway, because things can only be that much valuable. Arguably, nothing is so valuable that you can be Pascal-mugged into paying 1000 USD for someone promising to produce it by magic. Hence, the maximally valuable thing is worth no more than 1000 USD divided by the tiny probability that a Pascal mugger is telling the truth. I admit that I don’t know how to quantify this, but it does point at a limit to such growth.
you imagine that the rate at which new “things” are produced hits diminishing returns
The rate at which new atoms (or matter/energy/space more broadly) are added will hit diminishing returns, at the very least due to speed of light.
The rate at which new things are produced won’t necessarily hit diminishing returns because we can keep cannibalizing old things to make better new things. Often, re-configurations of existing atoms produce value without consuming new resources except for the (much smaller) amount of resources used to rearrange them. If I invent email which replaces post mail I produce value while reducing atoms used.
this value growth has to hit a ceiling pretty soon anyway, because things can only be that much valuable
Eventually yes, but I don’t think they have to do hit a ceiling soon, e.g. in a timeframe relevant to the OP. Maybe it’s probable they will, but I don’t know how to quantify it. The purely physical ceiling on ascribable value is enormously high (other comment on this and also this).
Like you, I don’t know what to make of intuition pumps like your proposed Pascal’s Ceiling of Value. Once you accept that actual physics don’t practically limit value, what’s left of the OP is a similar-looking argument from incredulity: can value really grow exponentially almost-forever just by inventing new things to do with existing atoms? I don’t know that it will keep growing, but I don’t see a strong reason to think it can’t, either.
I think it’s more than an argument from incredulity.
Let’s try another angle. I think that most people would prefer facing a 10−6 probability of death to paying 1000 USD. I also think there’s nothing so good that a typical person would accept a 1−10−6 probability of everyone dying to get it with the remaining probability of 10−6. Moreover, a typical person is “subulititarian” (i.e. considers n people dying at most n times as bad as themself dying). Hence, subjective value is bounded by 1000×106×106×1010=1025 USD. Combined with physics, this limits GPD growth on a relevant timeframe.
I think that most people would prefer facing a 10e-6 probability of death to paying 1000 USD.
The sum of 1000 USD comes from the average wealth of people today. Using (any) constant here encodes the assumption that GDP per capita (wealth times population) won’t keep growing.
If we instead suppose a purely relative limit, e.g. that a person is willing to pay a 1e-6 part of their personal wealth to avoid a 1e6 chance of death, then we don’t get a bound on total wealth.
Let U(W) denotes the utility of a person with wealth W, Umax the maximal utility of a person (i.e. limW→∞U(W)) and ¯W the median wealth of a modern person. My argument establishes that
Umax≤U(¯W)+dUdW∣W=¯W⋅$1025
But, can we translate this to a bound on GDP? I’m not sure.
Part of the problem is, how do we even compare GDPs in different time periods? To do this, we need to normalize the value of money. Standard ways of doing this in economics involve using “universally valuable” goods such as food. But, food would be worthless in a future society of brain emulations, for example.
I propose using computational resources as the “reference” good. In the hypothetical future society you propose, most value comes from non-material goods. However, these non-material goods are produced by some computational process,. Therefore, buying computational resources should always be marginally profitable. On the other hand, the total amount of computational resources is bounded by physics. This seems like it should imply a bound on GDP.
I propose using computational resources as the “reference” good.
I don’t understand the implications of this, can you please explain / refer me somewhere? How is the GDP measurement resulting from this choice going to be different from another choice like control of matter/energy? Why do we even need to make a choice, beyond the necessary assumption that there will still be a monetary economy (and therefore a measurable GDP)?
In the hypothetical future society you propose, most value comes from non-material goods.
That seems very likely, but it’s not a necessary part of my argument. Most value could keep coming from material goods, if we keep inventing new kinds of goods (i.e. new arrangements of matter) that we value higher than past goods.
However, these non-material goods are produced by some computational process,. Therefore, buying computational resources should always be marginally profitable. On the other hand, the total amount of computational resources is bounded by physics. This seems like it should imply a bound on GDP.
There’s a physical bound on how much computation can be done in the remaining lifetime of the universe (in our future lightcone). But that computation will necessarily take place over a very very long span of time.
For as long as we can keep computing, the set of computation outputs (inventions, art, simulated-person-lifetimes, etc) each year can keep being some n% more valuable than the previous year. The computation “just” needs to keep coming up with better things every year instead of e.g. repeating the same simulation over and over again. And this doesn’t seem impossible to me.
The nominal GDP is given in units of currency, but the value of currency can change over time. Today’s dollars are not the same as the dollars of 1900. When I wrote the previous comment, I thought that’s handled using a consumer price index, in which case the answer can depend on which goods you include in the basket. However, actually real GDP is defined using something called the GDP deflator which is apparently based on a variable “basket” consisting of those goods that are actually traded, in proportion to the total market value traded in each one.
AFAIU, this means GDP growth can theoretically be completely divorced from actual value. For example, imagine there are two goods, A and B, s.t. during some periods A is fashionable and its price is double the price of B, whereas during other periods B is fashionable and its price is double the price of A. Assume also that every time a good becomes fashionable, the entire market switches to producing almost solely this good. Then, every time the fashion changes the GDP doubles. It thus continues to grow exponentially while the real changes are just circling periodically on the same place. (Let someone who understands economics correct me if I misunderstood something.)
Given the above, we certainly cannot rule out indefinite exponential GDP growth. However, I think that the OP’s argument that we live in a very unusual situation can be salvaged by using a different metric. For example, we can measure the entropy per unit of time produced by the sum total of human activity. I suspect that for the history so far, it tracks GDP growth relatively well (i.e. very slow growth for most of history, relatively rapid exponential growth in modern times). Since the observable universe has finite entropy (due to the holographic principle), there is a bound on how long this phenomenon can last.
“Many recent developments that produced a lot of value, like radio, computing, and the Internet, didn’t do it by using proportionally more atoms.”
There are vacuum electronic tube production facilities (late 18th century onward), many billion dollar semiconductor factories (late 1970s onward), and piles and piles of electronic waste that say this isn’t true.
By “proportionately more” I meant more than the previous economic-best use of the same material input, which the new invention displaced (modulo increasing supply). For example, the amount of value derived by giving everyone (every home? every soldier? every car?) a radio is much greater than any other value the same amount of copper, zinc etc. could have been used for before the invention of radio. We found a new way to get more value from the same material inputs.
For material outputs (radio sets, telegraph wire, computers), of course material inputs are used. But the amount of value we get from the inputs is not really related to, or bounded by, the amount of input material. A new way of using material can have an arbitrarily high value-produced-to-materials-consumed ratio.
I’ll run with your example of semiconductor factories. A factory costs between $1-20 billion to build. The semiconductor industry has a combined yearly revenue of $500 billion (2018). Doesn’t sound like a huge multiplier so far.
But then consider that huge amounts of modern technology (= value) require semiconductors as an input. The amount of semiconductor industry inputs, and material waste byproducts, was similar in 1990 and 2020 (same order of magnitude). But the amount of value enabled by using those semiconductors was enormously larger in 2020. Whole new markets were created thanks to the difference in capability between 1990 semiconductors ($100 per megabyte DRAM) and 2020 ($0.003 per MB). Smartphones, PCs, modern videogames, digital video and audio, digital cameras, most of the way the Internet and Web are used today; but also all modern devices with chips inside, from cars to satellites; the list is almost endless.
All of these require extra inputs besides semiconductors, and those inputs cost time and money. But the bill of materials for a 2020 smartphone is smaller and cheaper than that of an early 1990 cellphone, while the value to the owner is much greater. (A lot of the value comes from software and digital movies and music, which don’t consume atoms in the relevant sense, because they can be copied on demand.)
Thank you for clarifying the definition you’re using for “proportionately more”.
Two points come to mind:
The material waste products of the electronics ecosystem between 1990s and now has shifted from mass/toxic atoms (cathode-ray tubes/lead, mercury) to less mass but more rare(er) earth elements such as indium and cobalt. 1 The problem of “this can’t go on” may not be limited by total of all atoms but by total of electronically important elements that can be mined “sustainably” on earth. All atoms are not equal. As you’re probably aware, “rare earth” is not always about the total amount of atoms of said element in the earth but of how the element is dispersed (or not) and, thus, how “easily” it can be mined. (“easily” includes physical as well as political impediments2)The electronic waste stream efforts are very likely to shift from dealing with mass/toxicity to harvesting the rare earth elements from electronic waste. I can imagine the trade-off graph between all of the costs of more pit mines in more politically diverse areas for harvesting virgin rare earth elements vs harvesting electronic waste. I can’t imagine either being anywhere close to all of the atoms on earth much less the entire universe. Orders of magnitude seem likely but I could be persuaded otherwise.
The idea of “modern technology (=value)” seems to have a presumption of that value being only positive. When I see that kind of blanket statement about technology I am reminded of the 2012 cover of The MIT Technology Review with Buzz Aldrin saying “You promised me Mars colonies. Instead, I got Facebook”. No argument from me that use of atom-light applications are valued in the stock market. No argument from me regarding the excitement/”value” of block-chain and it’s use of more electricity than many countries. Humans used to be pretty thrilled about tulips, too. Maybe the point of downsides of modern technology, including the exploitation of human nature wrt self-image (Instagram), in-group/out-group (Facebook), metabolic balance (Ultra-Processed Food), and attention (video games), fall to the stagnation/collapse buckets of the OP.
The second point plays into the first: modern technology value of human nature exploitation diverts technology from going off-planet to get more electronically important atoms.
I hope the two links can be followed. I’m new to this commenting tool. I’m open to advice if I’ve linked incorrectly (or inelegantly).
The OP’s argument is general: it says essentially that (economic) value is bounded linearly by the number of atoms backing the economy. Regardless of how the atoms are translated to value. This is an impossibility argument. My rebuttal was also general, saying that value is not so bounded.
Any particular way of extracting value, like electronics, usually has much lower bounds in practice than ‘linear in the amount of atoms used’ (even ignoring different atomic elements). So yes, today’s technology that depends on ‘rare’ earths is bounded by the accessible amount of those elements.
But this technology is only a few decades old. The economy has been growing at some % a year for much longer than that, across many industries and technological innovations that have had very different material constraints from each other. And so, while contemporary rare-earth-dependent techniques won’t keep working forever, the overall trend of economic growth could continue far beyond any one technology’s lifespan, and for much longer than the OP projects.
Technology and other secular change doesn’t always increase value; often it is harmful. My argument is that economy can keep growing for a long time, not that it necessarily will, or that all (or even most) changes over time are for the best. And GDP is not a good measure of human wellbeing to begin with; we’re measuring dollars, not happiness, and when I talk about “utility” I mean the kind estimated via revealed preferences.
Seriously, what is this piece? It smacks of scientism, trying to force economic growth into some kind of important metric that augurs limits on the future. (“Of course we won’t leave the galaxy within 8200 years”? “This is all based on pretty basic observations”???)
Clearly there are only there possible scenarios (stagnate, explode, collapse), which parallels the same kind of pure mathematics that big bang theorists work with? How about taking a page out of economics, “the market can stay irrational longer than you can stay solvent”?
Money has barely existed in the same form for the last century, much less the last 8000 years. GDP as a metric is even worse; from wikipedia: “[GDP] focuses on flows, not stocks. As a result, an economy can run down its assets yet, at the same time, record high levels of GDP growth”
We keep reinventing political and cultural systems every few hundred years, why would our current frameworks even make sense 8000 years out?
Breaking out of your provably-complete set of end state scenarios, what if all that impossible economic wealth becomes concentrated in the hands of Bezos? Or we decide at 2000 years out that this is untenable; what actions could we take? Is it unavoidable, the way global warming seems to be?
It seems more important to talk about the details here, or provide something of interest, otherwise this is just advanced shitposting about “the end is coming”, complete with clickbait title. Wtf?
GDP growth is measured in money, a measure of value. Value does not have to be backed by a proportional amount of matter (or energy, space or time) because we can value things as much as we like—more than some constant times utilon per gram second.
Suppose I invent an algorithm that solves a hard problem and sell it as a service. The amount people will be willing to pay for it—and the amount the economy grows—is determined by how much people want it and how much money there is, but nobody cares how many new atoms I used to implement it. If I displace older, less efficient algorithms, then I produce value while reducing the number of atoms (or watts) backing the economy!
Material goods and population size can’t keep growing forever, but value can. Many recent developments that produced a lot of value, like radio, computing, and the Internet, didn’t do it by using proportionally more atoms. An algorithm is a convenient example but this applies to non-digital services just as much.
This is not a novel argument but I can’t recall it’s source or name.
As a concrete example, let’s imagine that sending an email is equivalent to sending a letter. Let’s ignore the infrastructure required to send emails (computers, satellites, etc) vs. letters (mail trucks, post offices, etc), and assume they’re roughly equal to each other. Then the invention of email eliminated the vast majority of letters, and the atoms they would have been made from.
Couple this with the fact that emails are more durable, searchable, instantaneous, free, legible, compatible with mixed media, and occupy only a miniscule amount of physical real estate in the silicon of the computer, and we can see that emails not only reduce the amount of atoms needed to transmit a letter, but also produce a lot more value.
In theory, we might spend the next several thousand years not only finding ways to pack more value into fewer atoms, but also enhancing our ability to derive value from the same good or service. Perhaps in 10,000 years, checking my email will be a genuine pleasure!
In fact, come to think of it, this is the thesis of More from Less by Andrew McAffee, who points out that in numerous categories of material products, we’ve seen global GDP growing while using less material resources, in both relative and absolute terms.
Edit: though see multiple 1-star reviews from non-anonymous Amazon reviewers with economics PhDs who say the core premise of McAffee’s book is incorrect. Sounds like there is better research out there than he presents in this book.
An alternative point of view is in Decoupling Debunked, which seems to feed into degrowth literature. Makes me worry that both McAffee’s and this piece will suffer from the same issues we find when we look for a consensus viewpoint among economists on the effect of the minimum wage.
A more optimistic 2020 peer reviewed article on decoupling, “A systematic review of the evidence on decoupling of GDP, resource use and GHG emissions, part II: synthesizing the insights”, claims:
There’s a few one-star Amazon reviews for the book that suggest McAfee’s data is incorrect or misleading. Here’s a quote from one of them, which seems like a solid counterargument to me:
“However, on the first slide on page 79, he notes that the data excludes impact from Import/export of finished goods. Not raw materials but finished goods. He comments that Net import is only 4% of GDP in the US. Here he makes a (potentially) devastating error – (potentially) invalidating his conclusion.
While Net imports is indeed around 4% of GDP, the gross numbers are Exports at approx. +13% and Imports at approx. −17%. So any mix difference in finished goods in Export and Import, can significantly change the conclusion. It so happens that US is a major Net importer of finished goods e.g. Machinery, electronic equipment and autos (finished goods, with materials not included above in the consumption data). Basically, a big part of US’ consumption of cars, washing machines, computers etc. are made in Mexico, China etc. They contain a lot of materials, not included in the graphs, upon which he builds his conclusion/thesis. So quite possibly, there is no de-coupling.”
Thanks very much for pointing this out. I hadn’t seen these rebuttals before.
I still think the argument holds in this case, because even computer software isn’t atom-less. It needs to be stored, or run, or something somewhere.
I don’t doubt that you could drastically reduce the number of atoms required for many products today. For example, you could in future get a chip in your brain that makes typing without a keyboard possible. That chip is smaller than a keyboard, so represents lots of atoms saved. You could go further, and have that chip be an entire futuristic computer suite, by reading and writing your brain inputs and outputs directly it could replace the keyboard, mouse, monitors, speakers, and entire desktop, plus some extra stuff, like also acting as a VR Headset, or video game console, or whatever. Lets say you manage to squeeze all that into a single atom. Cool. That’s not enough. For this growth to go on for those ~8000 years, you’d need to have that single-atom brain chip be as valuable as everything on Earth today. Along with every other atom in the galaxy.
I think at some point, unless the hottest thing in the economy becomes editing humans to value specific atoms arbitrary amounts (which sounds bad, even if it would work), you can’t get infinite value out of things. I’m not even sure human minds have the capability of valuing things infinitely. I think even with today’s economy, you’d start to hit some asymptotes (i.e. if one person had everything in the world, I’m not sure what they’d do with it all. I’m also not sure they’d actually value it any more than if they just had 90% of everything, except maybe the value on saying “I have it all”, which wouldn’t be represented in our future economy)
And still, the path to value per atom has to come from somewhere, and in general it’s going to be making stuff more useful, or smaller, but there’s only so useful a single atom can be, and there’s only so small a useful thing can be. (I imagine some math on the number of ways you could arrange a set of particles, multiplied by the number of ways a particular arrangement could be used, as an estimate. But a quick guess says that neither of those values are infinite, and, I expect that number to be dominated by ways of arranging particles, not by number of uses, considering that even software on a computer is actually different arrangements of the electrons.)
So I guess that’s the heart of it to me, there’s certainly a lot more value we can squeeze out of things, but if there’s not literally infinite, it will run out at some point, and that ~8000 year estimate is looking pretty close to whatever the limit is, if it’s not already over it.
Please see my other reply here. Yes, value is finite, but the number of possible states of the universe is enormously large, and we won’t explore it in 8000 years. The order of magnitude is much bigger.
(Incidentally, our galaxy is ~ 100,000 light years across; so even expanding to cover it would take much longer than 8000 years, and that would be creating value the old-fashioned way by adding atoms, but it wouldn’t support continued exponential growth. So “8000 years” and calculations based off the size of the galaxy shouldn’t be mixed together. But the order-of-magnitude argument should work about as well for the matter within 8000 light-years of Earth.)
In much the same way, estimates of value and calculations based on the number of permutations of atoms shouldn’t be mixed together. There being a googleplex possible states in no way implies that any of them have a value over 3 (or any other number). It does not, by itself, imply that any particular state is better than any other. Let alone that any particular state should have value proportional to the total number of states possible.
Restricting yourself to atoms within 8000 light years, instead of the galaxy, just compounds the problem as well, but you noted that yourself. The size of the galaxy wasn’t actually a relevant number, just a (maybe) useful comparison. It’s like when people say that chess has more possible board states than there are atoms in the observable universe times the number of seconds since the Big Bang. It’s not that there’s any specifically useful interaction between atoms and seconds and chess, it’s just to recognize the scale of the problem.
Value is not obviously bounded by atoms, yes. However, GDP measures production of value. And, the entities producing value are made of atoms. Today these entities are humans. In the future, they might be something much more efficient. However, it seems at least plausible that their efficiency (i.e. rate of value production per atom) is somehow bounded by physics.
The rate of value production per atom can be bounded by physics. But the amount of value ascribed to the thing being produced is only strictly bounded by the size of the number (representing the amount of value) that can be physically encoded, which is exponential in the number of atoms, and not linear.
The natural numbers that can be physically encoded are not bounded by an exponent of the number of bits if you don’t have to be able to encode all smaller numbers as well in the same number of bits. If you define a number, you’ve encoded it, and it’s possible to define very large numbers indeed.
Great point, thanks!
To me, just ascribing more value to things without anything material about the situation changing sounds like inflation, not real growth.
The configuration does change, it’s just that the change is not about the amount of matter. If there are configurations absurdly more positively or negatively valuable than others, that just makes the ordinary configurations stop being decision relevant, once discerning the important configurations becomes feasible.
So, you imagine that the rate at which new “things” are produced hits diminishing returns, but every new generation of things is more valuable than the previous generation s.t. exponential growth is maintained. But, I think this value growth has to hit a ceiling pretty soon anyway, because things can only be that much valuable. Arguably, nothing is so valuable that you can be Pascal-mugged into paying 1000 USD for someone promising to produce it by magic. Hence, the maximally valuable thing is worth no more than 1000 USD divided by the tiny probability that a Pascal mugger is telling the truth. I admit that I don’t know how to quantify this, but it does point at a limit to such growth.
The rate at which new atoms (or matter/energy/space more broadly) are added will hit diminishing returns, at the very least due to speed of light.
The rate at which new things are produced won’t necessarily hit diminishing returns because we can keep cannibalizing old things to make better new things. Often, re-configurations of existing atoms produce value without consuming new resources except for the (much smaller) amount of resources used to rearrange them. If I invent email which replaces post mail I produce value while reducing atoms used.
Eventually yes, but I don’t think they have to do hit a ceiling soon, e.g. in a timeframe relevant to the OP. Maybe it’s probable they will, but I don’t know how to quantify it. The purely physical ceiling on ascribable value is enormously high (other comment on this and also this).
Like you, I don’t know what to make of intuition pumps like your proposed Pascal’s Ceiling of Value. Once you accept that actual physics don’t practically limit value, what’s left of the OP is a similar-looking argument from incredulity: can value really grow exponentially almost-forever just by inventing new things to do with existing atoms? I don’t know that it will keep growing, but I don’t see a strong reason to think it can’t, either.
I think it’s more than an argument from incredulity.
Let’s try another angle. I think that most people would prefer facing a 10−6 probability of death to paying 1000 USD. I also think there’s nothing so good that a typical person would accept a 1−10−6 probability of everyone dying to get it with the remaining probability of 10−6. Moreover, a typical person is “subulititarian” (i.e. considers n people dying at most n times as bad as themself dying). Hence, subjective value is bounded by 1000×106×106×1010=1025 USD. Combined with physics, this limits GPD growth on a relevant timeframe.
The sum of 1000 USD comes from the average wealth of people today. Using (any) constant here encodes the assumption that GDP per capita (wealth times population) won’t keep growing.
If we instead suppose a purely relative limit, e.g. that a person is willing to pay a 1e-6 part of their personal wealth to avoid a 1e6 chance of death, then we don’t get a bound on total wealth.
Let U(W) denotes the utility of a person with wealth W, Umax the maximal utility of a person (i.e. limW→∞U(W)) and ¯W the median wealth of a modern person. My argument establishes that
Umax≤U(¯W)+dUdW∣W=¯W⋅$1025
But, can we translate this to a bound on GDP? I’m not sure.
Part of the problem is, how do we even compare GDPs in different time periods? To do this, we need to normalize the value of money. Standard ways of doing this in economics involve using “universally valuable” goods such as food. But, food would be worthless in a future society of brain emulations, for example.
I propose using computational resources as the “reference” good. In the hypothetical future society you propose, most value comes from non-material goods. However, these non-material goods are produced by some computational process,. Therefore, buying computational resources should always be marginally profitable. On the other hand, the total amount of computational resources is bounded by physics. This seems like it should imply a bound on GDP.
I don’t understand the implications of this, can you please explain / refer me somewhere? How is the GDP measurement resulting from this choice going to be different from another choice like control of matter/energy? Why do we even need to make a choice, beyond the necessary assumption that there will still be a monetary economy (and therefore a measurable GDP)?
That seems very likely, but it’s not a necessary part of my argument. Most value could keep coming from material goods, if we keep inventing new kinds of goods (i.e. new arrangements of matter) that we value higher than past goods.
There’s a physical bound on how much computation can be done in the remaining lifetime of the universe (in our future lightcone). But that computation will necessarily take place over a very very long span of time.
For as long as we can keep computing, the set of computation outputs (inventions, art, simulated-person-lifetimes, etc) each year can keep being some n% more valuable than the previous year. The computation “just” needs to keep coming up with better things every year instead of e.g. repeating the same simulation over and over again. And this doesn’t seem impossible to me.
The nominal GDP is given in units of currency, but the value of currency can change over time. Today’s dollars are not the same as the dollars of 1900. When I wrote the previous comment, I thought that’s handled using a consumer price index, in which case the answer can depend on which goods you include in the basket. However, actually real GDP is defined using something called the GDP deflator which is apparently based on a variable “basket” consisting of those goods that are actually traded, in proportion to the total market value traded in each one.
AFAIU, this means GDP growth can theoretically be completely divorced from actual value. For example, imagine there are two goods, A and B, s.t. during some periods A is fashionable and its price is double the price of B, whereas during other periods B is fashionable and its price is double the price of A. Assume also that every time a good becomes fashionable, the entire market switches to producing almost solely this good. Then, every time the fashion changes the GDP doubles. It thus continues to grow exponentially while the real changes are just circling periodically on the same place. (Let someone who understands economics correct me if I misunderstood something.)
Given the above, we certainly cannot rule out indefinite exponential GDP growth. However, I think that the OP’s argument that we live in a very unusual situation can be salvaged by using a different metric. For example, we can measure the entropy per unit of time produced by the sum total of human activity. I suspect that for the history so far, it tracks GDP growth relatively well (i.e. very slow growth for most of history, relatively rapid exponential growth in modern times). Since the observable universe has finite entropy (due to the holographic principle), there is a bound on how long this phenomenon can last.
There’s some discussion of this in a followup post.
“Many recent developments that produced a lot of value, like radio, computing, and the Internet, didn’t do it by using proportionally more atoms.”
There are vacuum electronic tube production facilities (late 18th century onward), many billion dollar semiconductor factories (late 1970s onward), and piles and piles of electronic waste that say this isn’t true.
By “proportionately more” I meant more than the previous economic-best use of the same material input, which the new invention displaced (modulo increasing supply). For example, the amount of value derived by giving everyone (every home? every soldier? every car?) a radio is much greater than any other value the same amount of copper, zinc etc. could have been used for before the invention of radio. We found a new way to get more value from the same material inputs.
For material outputs (radio sets, telegraph wire, computers), of course material inputs are used. But the amount of value we get from the inputs is not really related to, or bounded by, the amount of input material. A new way of using material can have an arbitrarily high value-produced-to-materials-consumed ratio.
I’ll run with your example of semiconductor factories. A factory costs between $1-20 billion to build. The semiconductor industry has a combined yearly revenue of $500 billion (2018). Doesn’t sound like a huge multiplier so far.
But then consider that huge amounts of modern technology (= value) require semiconductors as an input. The amount of semiconductor industry inputs, and material waste byproducts, was similar in 1990 and 2020 (same order of magnitude). But the amount of value enabled by using those semiconductors was enormously larger in 2020. Whole new markets were created thanks to the difference in capability between 1990 semiconductors ($100 per megabyte DRAM) and 2020 ($0.003 per MB). Smartphones, PCs, modern videogames, digital video and audio, digital cameras, most of the way the Internet and Web are used today; but also all modern devices with chips inside, from cars to satellites; the list is almost endless.
All of these require extra inputs besides semiconductors, and those inputs cost time and money. But the bill of materials for a 2020 smartphone is smaller and cheaper than that of an early 1990 cellphone, while the value to the owner is much greater. (A lot of the value comes from software and digital movies and music, which don’t consume atoms in the relevant sense, because they can be copied on demand.)
Thank you for clarifying the definition you’re using for “proportionately more”.
Two points come to mind:
The material waste products of the electronics ecosystem between 1990s and now has shifted from mass/toxic atoms (cathode-ray tubes/lead, mercury) to less mass but more rare(er) earth elements such as indium and cobalt. 1 The problem of “this can’t go on” may not be limited by total of all atoms but by total of electronically important elements that can be mined “sustainably” on earth. All atoms are not equal. As you’re probably aware, “rare earth” is not always about the total amount of atoms of said element in the earth but of how the element is dispersed (or not) and, thus, how “easily” it can be mined. (“easily” includes physical as well as political impediments2)The electronic waste stream efforts are very likely to shift from dealing with mass/toxicity to harvesting the rare earth elements from electronic waste. I can imagine the trade-off graph between all of the costs of more pit mines in more politically diverse areas for harvesting virgin rare earth elements vs harvesting electronic waste. I can’t imagine either being anywhere close to all of the atoms on earth much less the entire universe. Orders of magnitude seem likely but I could be persuaded otherwise.
The idea of “modern technology (=value)” seems to have a presumption of that value being only positive. When I see that kind of blanket statement about technology I am reminded of the 2012 cover of The MIT Technology Review with Buzz Aldrin saying “You promised me Mars colonies. Instead, I got Facebook”. No argument from me that use of atom-light applications are valued in the stock market. No argument from me regarding the excitement/”value” of block-chain and it’s use of more electricity than many countries. Humans used to be pretty thrilled about tulips, too. Maybe the point of downsides of modern technology, including the exploitation of human nature wrt self-image (Instagram), in-group/out-group (Facebook), metabolic balance (Ultra-Processed Food), and attention (video games), fall to the stagnation/collapse buckets of the OP.
The second point plays into the first: modern technology value of human nature exploitation diverts technology from going off-planet to get more electronically important atoms.
I hope the two links can be followed. I’m new to this commenting tool. I’m open to advice if I’ve linked incorrectly (or inelegantly).
The OP’s argument is general: it says essentially that (economic) value is bounded linearly by the number of atoms backing the economy. Regardless of how the atoms are translated to value. This is an impossibility argument. My rebuttal was also general, saying that value is not so bounded.
Any particular way of extracting value, like electronics, usually has much lower bounds in practice than ‘linear in the amount of atoms used’ (even ignoring different atomic elements). So yes, today’s technology that depends on ‘rare’ earths is bounded by the accessible amount of those elements.
But this technology is only a few decades old. The economy has been growing at some % a year for much longer than that, across many industries and technological innovations that have had very different material constraints from each other. And so, while contemporary rare-earth-dependent techniques won’t keep working forever, the overall trend of economic growth could continue far beyond any one technology’s lifespan, and for much longer than the OP projects.
Technology and other secular change doesn’t always increase value; often it is harmful. My argument is that economy can keep growing for a long time, not that it necessarily will, or that all (or even most) changes over time are for the best. And GDP is not a good measure of human wellbeing to begin with; we’re measuring dollars, not happiness, and when I talk about “utility” I mean the kind estimated via revealed preferences.
Seriously, what is this piece? It smacks of scientism, trying to force economic growth into some kind of important metric that augurs limits on the future. (“Of course we won’t leave the galaxy within 8200 years”? “This is all based on pretty basic observations”???)
Clearly there are only there possible scenarios (stagnate, explode, collapse), which parallels the same kind of pure mathematics that big bang theorists work with? How about taking a page out of economics, “the market can stay irrational longer than you can stay solvent”?
Money has barely existed in the same form for the last century, much less the last 8000 years. GDP as a metric is even worse; from wikipedia: “[GDP] focuses on flows, not stocks. As a result, an economy can run down its assets yet, at the same time, record high levels of GDP growth”
We keep reinventing political and cultural systems every few hundred years, why would our current frameworks even make sense 8000 years out?
Robin Hanson’s [This is the Dream Time](https://www.overcomingbias.com/2009/09/this-is-the-dream-time.html) has a similar idea, but actually gives enough material to engage with.
Breaking out of your provably-complete set of end state scenarios, what if all that impossible economic wealth becomes concentrated in the hands of Bezos? Or we decide at 2000 years out that this is untenable; what actions could we take? Is it unavoidable, the way global warming seems to be?
It seems more important to talk about the details here, or provide something of interest, otherwise this is just advanced shitposting about “the end is coming”, complete with clickbait title. Wtf?