Me: Our finite universe simply cannot continue our exponential growth rates for a million years. For trillions of years thereafter, possibilities will be known and fixed, and for each person rather limited.

One example of configuration space that could plausibly never run out is mathematical theorems. It takes relatively few atoms to write down absolutely mind-boggling theorems. As math progresses, these get easier to understand and work with, and presumably we'd work on harder theorems. As we do, it doesn't take many more atoms of notation to write he harder theorems. The complexity and interest of a theorem seems to be more than exponential in the size of the notation, for good theorems.

Another possible example is genetic information. Both literal genes, and organizational patterns of a culture. Like mathematical theorems, the complexity hidden in a small amount of information seems to be high, more than exponentially high.

Maybe these are still not enough to prevent an end of progress over the long haul. They deserve some careful attention, though. And anyway, even if it's just matter that stagnates, Robin's argument is still well worth taking to heart. We're living in a golden age.

As unbelievable as 4% growth for a trillion years is, your argument is really just that: an argument from incredulity. If such incredible growth is so obviously impossible, then it should be easy to explain exactly why.

Re: "Our finite universe simply cannot continue our exponential growth rates for a million years. For trillions of years thereafter, possibilities will be known and fixed, and for each person rather limited."

If the "person" has a brain the size of a planet then "known", "fixed" and "limited" would most-likely be a strange and inaccurate way of describing their "possibilities".

This is very similar to what occurred to me when I was in the middle of writing a similar comment to your original post as Mr Caplan.

Does anyone have any thoughts on how to approach memory archiving in this scenario? If we can't find ways to somehow expand the amount of matter at our disposal to create more memory storage capacity at an equal or greater rate than we accumulate memories, we would presumably be eventually forced to die or delete old memories. While this might stop us from becoming bored when we run out of new experiences, I'm curious as to what sort of mechanism could be created to deal with this situation.

Answering my own question: It seems that relative utility is multiplicative (in the way Robin implicitly assumes) as long as the pairwise equivalences are scale invariant, and indifference is transitive.

I'm aware of ways in which each of these fails when applied to human preference, but I don't know how much those failures affect Robin's argument (that exponential growth must end even if resources grow cubically)

This points out the potential for a phase transition of prosperity measured by growth in experience (Gross Domestic Experience?) to prosperity measured in terms of percent of potential experience actually experienced.

We may not be creating any new virtual realities, but nobody will have the time to live all the great ones already available. Sounds great to me.

Robin, you're implicitly assuming that relative utility (whether measured probabilistically or via relative durations) is multiplicative - so that if someone thinks experience A0 equal in desirability to a 1/1.04 chance at experience A1, or to experiencing A1 for 1/1.04 the duration of A0, and A1 stands in the same relation to A2, etc, then it will necessarily be the case that they would be indifferent to experiencing A0 for a year vs. A440 (if I did my math correctly) for one second, and also vs. having a 1 in 31.6 million chance of experiencing A440 for a year.

Is there any reason to believe that peoples' utility really works this way?

To follow up, maybe that is the solution to Fermi's Paradox. We see no aliens because they have all entered black holes to experience an infinite future.

It is not clear that the universe is strictly finite. The volume inside a black hole can be infinite, which implies infinite entropy. You can't get to the infinite entropy from the outside, but maybe you can by entering the black hole. It may appear to be finite from the outside, but it may not be finite from the inside.

Since this is a sci-fi topic might aswell take it to another level.

Our finite universe simply cannot continue our exponential growth rates for a million years. For trillions of years thereafter, possibilities will be known and fixed, and for each person rather limited.

Some smart economist quipped that there's a chance we're living in a virtual reality. If we are in one, why can't the rules be changed? One of the dangers of making absolute statements is not taking into account exogenous factors. Happens all the time in the market even when people have thought they thought of everything (eg. discrete multivariate distributions applied to real estate).

If we are not in a virtual reality or something similar (), which "seems" likely, growth will stop at some point, but the real question is what kind of life do the people (or whatever beings) enjoy.

Instant and arch1, a lack of growth does not at all imply a bad life. Growth could continue for a while and then stop at a high level and then capacities could stay high forever after. Not such a bad outcome at all. But still, growth does end.

I find Instant Karma's point to be a good one. Why would the eventual leveling off of growth in our technological capabilities alone (or perhaps in our achievable utility per second) necessarily limit a person's possibilities in a meaningful sense?

If a person's Acme9000 VR library has on tap, say, 10^10000 years' worth of profoundly distinct, absurdly high utility-per-second experiences, do we say that this person's "possibilities are limited" because that person is not constantly upgrading the experience quality to that achievable using Acme9001, Acme9002, etc?

I suppose we do if we are selling Acme9001. But it seems to me that any meaningful discussion of the Acme9000 owner's limitations should only start around year 10^9997 or so - which is to say, an immense span of time after Robin's exponential growth rates and Bryan's growth of quality of VR life had ceased.

(Having said this I admit that I find the whole discussion, in which we are throwing around notions such as utility per second, kind of awkward; it seems to miss what's important, but I haven't thought it through well enough to to do more than report my unease:-)

We all need to think bigger and get out of our current GDP paradigm.

Once we are millions or billions of times wealthier, with broader ranges of better experience, why do we need to create more experiences? We can spend the next few trillion years experiencing and sharing the ones we already created.

Let me restate: the scarce factor is experience. I think we will have enough to keep us busy for the next few trillion years. After that, well we can ask Robin then.

## Limits of Imagination

One example of configuration space that could plausibly never run out is mathematical theorems. It takes relatively few atoms to write down absolutely mind-boggling theorems. As math progresses, these get easier to understand and work with, and presumably we'd work on harder theorems. As we do, it doesn't take many more atoms of notation to write he harder theorems. The complexity and interest of a theorem seems to be more than exponential in the size of the notation, for good theorems.

Another possible example is genetic information. Both literal genes, and organizational patterns of a culture. Like mathematical theorems, the complexity hidden in a small amount of information seems to be high, more than exponentially high.

Maybe these are still not enough to prevent an end of progress over the long haul. They deserve some careful attention, though. And anyway, even if it's just matter that stagnates, Robin's argument is still well worth taking to heart. We're living in a golden age.

As unbelievable as 4% growth for a trillion years is, your argument is really just that: an argument from incredulity. If such incredible growth is so obviously impossible, then it should be easy to explain exactly why.

Re: "Our finite universe simply cannot continue our exponential growth rates for a million years. For trillions of years thereafter, possibilities will be known and fixed, and for each person rather limited."

If the "person" has a brain the size of a planet then "known", "fixed" and "limited" would most-likely be a strange and inaccurate way of describing their "possibilities".

This is very similar to what occurred to me when I was in the middle of writing a similar comment to your original post as Mr Caplan.

Does anyone have any thoughts on how to approach memory archiving in this scenario? If we can't find ways to somehow expand the amount of matter at our disposal to create more memory storage capacity at an equal or greater rate than we accumulate memories, we would presumably be eventually forced to die or delete old memories. While this might stop us from becoming bored when we run out of new experiences, I'm curious as to what sort of mechanism could be created to deal with this situation.

Answering my own question: It seems that relative utility is multiplicative (in the way Robin implicitly assumes) as long as the pairwise equivalences are scale invariant, and indifference is transitive.

I'm aware of ways in which each of these fails when applied to human preference, but I don't know how much those failures affect Robin's argument (that exponential growth must end even if resources grow cubically)

Peter de Blanc: While we are nitpicking, the speed of light, together with the holographic principle limits us to quadratic growth.

Robin and Arch,

This clarifies the issue for me.

This points out the potential for a phase transition of prosperity measured by growth in experience (Gross Domestic Experience?) to prosperity measured in terms of percent of potential experience actually experienced.

We may not be creating any new virtual realities, but nobody will have the time to live all the great ones already available. Sounds great to me.

Robin, you're implicitly assuming that relative utility (whether measured probabilistically or via relative durations) is multiplicative - so that if someone thinks experience A0 equal in desirability to a 1/1.04 chance at experience A1, or to experiencing A1 for 1/1.04 the duration of A0, and A1 stands in the same relation to A2, etc, then it will necessarily be the case that they would be indifferent to experiencing A0 for a year vs. A440 (if I did my math correctly) for one second, and also vs. having a 1 in 31.6 million chance of experiencing A440 for a year.

Is there any reason to believe that peoples' utility really works this way?

The speed of light limits you to cubic growth, not linear growth.

To follow up, maybe that is the solution to Fermi's Paradox. We see no aliens because they have all entered black holes to experience an infinite future.

It is not clear that the universe is strictly finite. The volume inside a black hole can be infinite, which implies infinite entropy. You can't get to the infinite entropy from the outside, but maybe you can by entering the black hole. It may appear to be finite from the outside, but it may not be finite from the inside.

Since this is a sci-fi topic might aswell take it to another level.

Our finite universe simply cannot continue our exponential growth rates for a million years. For trillions of years thereafter, possibilities will be known and fixed, and for each person rather limited.

Some smart economist quipped that there's a chance we're living in a virtual reality. If we are in one, why can't the rules be changed? One of the dangers of making absolute statements is not taking into account exogenous factors. Happens all the time in the market even when people have thought they thought of everything (eg. discrete multivariate distributions applied to real estate).

If we are not in a virtual reality or something similar (), which "seems" likely, growth will stop at some point, but the real question is what kind of life do the people (or whatever beings) enjoy.

Robin,Yes, growth does end (as long as one person can't control ever more resources, which seems likely at present). But why does that matter?

Instant and arch1, a lack of growth does not at all imply a bad life. Growth could continue for a while and then stop at a high level and then capacities could stay high forever after. Not such a bad outcome at all. But still, growth does end.

I find Instant Karma's point to be a good one. Why would the eventual leveling off of growth in our technological capabilities alone (or perhaps in our achievable utility per second) necessarily limit a person's possibilities in a meaningful sense?

If a person's Acme9000 VR library has on tap, say, 10^10000 years' worth of profoundly distinct, absurdly high utility-per-second experiences, do we say that this person's "possibilities are limited" because that person is not constantly upgrading the experience quality to that achievable using Acme9001, Acme9002, etc?

I suppose we do if we are selling Acme9001. But it seems to me that any meaningful discussion of the Acme9000 owner's limitations should only start around year 10^9997 or so - which is to say, an immense span of time after Robin's exponential growth rates and Bryan's growth of quality of VR life had ceased.

(Having said this I admit that I find the whole discussion, in which we are throwing around notions such as utility per second, kind of awkward; it seems to miss what's important, but I haven't thought it through well enough to to do more than report my unease:-)

We all need to think bigger and get out of our current GDP paradigm.

Once we are millions or billions of times wealthier, with broader ranges of better experience, why do we need to create more experiences? We can spend the next few trillion years experiencing and sharing the ones we already created.

Let me restate: the scarce factor is experience. I think we will have enough to keep us busy for the next few trillion years. After that, well we can ask Robin then.