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.
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.