A lot of this depends on the subtleties of the laws of physics. I think the best solution is to end death now; if the math doesn’t work out in our favour, we can always just slow down subjective time and build our own exponentials.
A lot of this depends on the subtleties of the laws of physics.
Oh sure. In any case, the “exponential growth in a Euclidean space” scenario wouldn’t work because we wouldn’t be able to maintain constant forward acceleration indefinitely, if everything around us was moving backwards at close to light speed.
I think the best solution is to end death now; if the math doesn’t work out in our favour, we can always just slow down subjective time and build our own exponentials.
The last bit may not be possible. There’s a finite limit to the amount of information one can store in a given region of space (or else the amount of mass-energy needed to represent it would collapse into a black hole). So to have exponentially many people, you’ll always need an exponential amount of space, whatever you do to subjective time.
If we slow down subjective time at an always increasing rate, we could ensure that the amount of people that we can support increases at the same rate as the amount of people we need to support.
I see. That does the keep space requirements down, but subjectively we’d be moving along this graphical timeline at constant speed. I don’t how much computation is possible in the ‘Dark Era’. (Perhaps only a finite amount?)
I don’t know if that’s more or less of a problem than death or limiting births. That is a question for a FAI; while we may be able to solve it, only an AI would need to. I doubt that the concept of personal identity will even survive the singularity, so this could easily end up not mattering.
Oh sure. I regard the above purely as a mathematical curiosity.
It doesn’t provide exponential growth for very long, because the people at the frontier of this expanding hyperbolic sphere would reach the heat death of the universe alarmingly soon. At least, I think that’s what would happen, assuming the universe will end in a heat death (as opposed to a Big Rip or Big Crunch).
ETA: Actually, that only defeats the ‘exponential growth in a Euclidean space’ scenario. But still, I agree that we can’t blithely assume current physics.
A lot of this depends on the subtleties of the laws of physics. I think the best solution is to end death now; if the math doesn’t work out in our favour, we can always just slow down subjective time and build our own exponentials.
Oh sure. In any case, the “exponential growth in a Euclidean space” scenario wouldn’t work because we wouldn’t be able to maintain constant forward acceleration indefinitely, if everything around us was moving backwards at close to light speed.
The last bit may not be possible. There’s a finite limit to the amount of information one can store in a given region of space (or else the amount of mass-energy needed to represent it would collapse into a black hole). So to have exponentially many people, you’ll always need an exponential amount of space, whatever you do to subjective time.
If we slow down subjective time at an always increasing rate, we could ensure that the amount of people that we can support increases at the same rate as the amount of people we need to support.
I see. That does the keep space requirements down, but subjectively we’d be moving along this graphical timeline at constant speed. I don’t how much computation is possible in the ‘Dark Era’. (Perhaps only a finite amount?)
I don’t know if that’s more or less of a problem than death or limiting births. That is a question for a FAI; while we may be able to solve it, only an AI would need to. I doubt that the concept of personal identity will even survive the singularity, so this could easily end up not mattering.
Oh sure. I regard the above purely as a mathematical curiosity.
It doesn’t provide exponential growth for very long, because the people at the frontier of this expanding hyperbolic sphere would reach the heat death of the universe alarmingly soon. At least, I think that’s what would happen, assuming the universe will end in a heat death (as opposed to a Big Rip or Big Crunch).
ETA: Actually, that only defeats the ‘exponential growth in a Euclidean space’ scenario. But still, I agree that we can’t blithely assume current physics.