Assuming no faster-than-light travel and no exotic matter, a civilization which survives the Great Filter will always be contained in its future light cone, which is a sphere expanding outward with constant speed c. So the total volume available to the civilization at time t will be V(t) ~ t^3. As it gets larger, the total resources available to it will scale in the same way, R(t) ~ V(t) ~ t^3.
Suppose the civilization has intrinsic growth rate r, so that the civilization’s population grows as P(t) ~ r^t.
Since resources grow polynomially and population grows exponentially in t, as t goes to infinity the resources per person R(t) / P(t) ~ t^3 / r^t goes to zero. And since there is presumably a lower limit on the resources required to support one member of the civilization, r must approach 1 as t goes to infinity. This could mean, for instance, that each person has only one child before dying, or that everybody is immortal and never has children.
Of course these conclusions are pretty well-known round here, but I thought the scaling argument was neat and I haven’t seen it before.
This seems likely to be a problem even if we get FAI, since certainly some people’s CEVs include having children, and even with a starting population of a single person with such values, we’ll run up against resource limits, if the premises hold. (I suppose those future people lucky enough to live under FAI will just have to dry their tears with million-utilon bills.)
Another thought: Perhaps we could use relativity to get around this. If we expand outward at the speed of light, subjective time for people close to the edge will be greatly reduced, so each person could grow up, travel to the frontier at near lightspeed, and have their 2 children or whatever. To the rest of us I think this’ll look like increasingly many people crammed at the edge of the sphere, through length contraction. (I haven’t studied relativity, so this might be wrong.)
I like Eliezer’s solution better. Rather than wait until exponential population growth eats all the resources, we just impose population control at the start and let every married couple have a max of two children. That way, population grows at most linearly (assuming immortality).
Broadly speaking, I’m suspicious of social solutions to problems that will persist for geological periods of time. If we’re playing the civilization game for the long haul, then the threat of overpopulation could simply wait out any particular legal regime or government.
That argument goes hinky in the event of FAI singleton, of course.
Wouldn’t this conclusion require that indivudals and their resources are not resources to other individuals? A society that doesn’t share their lives in some way is not a community. If you share “the internet” among the number that use it the resultant amount of information migth be quite low, but that doesn’t mean that people don’t have access to information. In the same way if one chunk of energy is used in one way, it migth fullfill more wishes than just one person. What this means is you either need to cooperate or compete. The only one that can have the universe to himself without contention is the lone survivor. But if you are in a populated universe politics becomes necceary and it sphere widens.
Assuming no faster-than-light travel and no exotic matter, a civilization which survives the Great Filter will always be contained in its future light cone, which is a sphere expanding outward with constant speed c. So the total volume available to the civilization at time t will be V(t) ~ t^3. As it gets larger, the total resources available to it will scale in the same way, R(t) ~ V(t) ~ t^3.
Suppose the civilization has intrinsic growth rate r, so that the civilization’s population grows as P(t) ~ r^t.
Since resources grow polynomially and population grows exponentially in t, as t goes to infinity the resources per person R(t) / P(t) ~ t^3 / r^t goes to zero. And since there is presumably a lower limit on the resources required to support one member of the civilization, r must approach 1 as t goes to infinity. This could mean, for instance, that each person has only one child before dying, or that everybody is immortal and never has children.
Of course these conclusions are pretty well-known round here, but I thought the scaling argument was neat and I haven’t seen it before.
This seems likely to be a problem even if we get FAI, since certainly some people’s CEVs include having children, and even with a starting population of a single person with such values, we’ll run up against resource limits, if the premises hold. (I suppose those future people lucky enough to live under FAI will just have to dry their tears with million-utilon bills.)
Another thought: Perhaps we could use relativity to get around this. If we expand outward at the speed of light, subjective time for people close to the edge will be greatly reduced, so each person could grow up, travel to the frontier at near lightspeed, and have their 2 children or whatever. To the rest of us I think this’ll look like increasingly many people crammed at the edge of the sphere, through length contraction. (I haven’t studied relativity, so this might be wrong.)
I like Eliezer’s solution better. Rather than wait until exponential population growth eats all the resources, we just impose population control at the start and let every married couple have a max of two children. That way, population grows at most linearly (assuming immortality).
Broadly speaking, I’m suspicious of social solutions to problems that will persist for geological periods of time. If we’re playing the civilization game for the long haul, then the threat of overpopulation could simply wait out any particular legal regime or government.
That argument goes hinky in the event of FAI singleton, of course.
Wouldn’t this conclusion require that indivudals and their resources are not resources to other individuals? A society that doesn’t share their lives in some way is not a community. If you share “the internet” among the number that use it the resultant amount of information migth be quite low, but that doesn’t mean that people don’t have access to information. In the same way if one chunk of energy is used in one way, it migth fullfill more wishes than just one person. What this means is you either need to cooperate or compete. The only one that can have the universe to himself without contention is the lone survivor. But if you are in a populated universe politics becomes necceary and it sphere widens.