As you note, whether you use exponential or logistic assumptions is essentially decisive for the long-run importance of increments in population growth. Yet we can rule out exponential assumptions which this proposed âCharlemagne effectâ relies upon.
In principle, boundless forward compounding is physically impossible, as there are upper bounds on growth rate from (e.g.) the speed of light, and limitations on density from the amount of available matter in a given volume. This is why logistic functions, not exponential ones, are used for modelling populations in (e.g.) ecology.
Concrete counter-examples to the exponential modelling are thus easy to generate. To give a couple:
A 1% constant annual growth rate assumption would imply saving one extra survivor 4000 years ago would have result in a current population of ~ 2* 10 ^17: 200 Quadrillion people.
A âconservativeâ 0.00001% annual growth rate still results in populations growing one order of magnitude every ~25 million years. At this rate, you end up with a greater population than atoms in the observable universe within 2 billion years. If you run until the end of the stelliferous era (100 trillion years) at the same rate, you end up with populations on the order of 10^millions, with a population density basically 10^thousands every cubic millimetre.
I think itâs worth mentioning that what youâve said is not in conflict with a much-reduced-but-still-astronomically-large Charlemagne Effect: youâve set an upper bound for the longterm effects of nearterm lives saved at <<<2 billion years, but that still leaves a lot of room for nearterm interventions to have very large long term effects by increasing future population size.
That argument refers to the exponential version of the Charlemagne Effect; but the logistic one survives the physical bounds argument. OP writes that they donât consider the logistic calculation of their Charlemagne Effect totally damning, particularly if it takes a long time for population to stabilise:
However, note that even in the models where the Charlemagne Effect weakens, it is not necessarily completely irrelevant. In the logistic model I created, the Charlemagne Effect is about 10,000 times less strong â but on the humongous scales of future people, this wouldnât necessarily disqualify TNIs from competition with TLIs. Under future population scenarios with a carrying capacity, the Charlemagne Effect will be disproportionately weaker the sooner we either reach or start oscillating around a carrying capacity.
If that happens in the very early days of humanityâs future (e.g. 10% or less of the way through), then the Charlemagne Effect will be much less important. But if it happens later, then the Charlemagne Effect will have mattered for a large chunk of our future and thus be important for our future as a whole.
Thanks for reading the post, and your feedback! I think David Mears did a good job responding in a way aligned with my thinking. I will add a few additional points:
I donât think we can really know how future population will grow. To name one scenario aligned with exponential growth I cite in my post, Greaves and MacAskill discuss the possibility of space colonization that could lead to expansion possibilities that could stretch on for millions or billions of years:
âAs Greaves and MacAskill argue, it is feasible that future beings could colonize the estimated over 250 million habitable planets in the Milky Way, or even the billions of other galaxies accessible to us.[25] If this is the case, there doesnât seem to be an obvious limit to human expansion until an unavoidable cosmic extinction event.â
Second, itâs possible that even if growth doesnât exponentially grow, it could at various times have cyclic growth (booms and busts) or exponential decline. As I discuss, in both of these cases where there is not a carrying capacity, the Charlemagne Effect would still hold.
Third, we canât know how long humanity will continue on. For example, the average mammal species has a âlifespanâ of 1 million years. Plus humans are uniquely capable of creating existential catastrophe that could greatly shorten our species lifespan. In these cases, exponential growth may not be unrealistic.
Last, I will point out that you could very well be right that in the future population growth follows a logistic curve, and/âor humans continue on for billions of years. But there is some significant probability these conditions donât hold, just as we canât be certain that working to mitigate existential risk from AI, pandemics, etc. will prevent human extinction. Thus, within an expected value calculation of long term value, the Charlemagne Effect should still apply as long as there is some chance that the necessary conditions for it would exist.
Thanks for the post.
As you note, whether you use exponential or logistic assumptions is essentially decisive for the long-run importance of increments in population growth. Yet we can rule out exponential assumptions which this proposed âCharlemagne effectâ relies upon.
In principle, boundless forward compounding is physically impossible, as there are upper bounds on growth rate from (e.g.) the speed of light, and limitations on density from the amount of available matter in a given volume. This is why logistic functions, not exponential ones, are used for modelling populations in (e.g.) ecology.
Concrete counter-examples to the exponential modelling are thus easy to generate. To give a couple:
A 1% constant annual growth rate assumption would imply saving one extra survivor 4000 years ago would have result in a current population of ~ 2* 10 ^17: 200 Quadrillion people.
A âconservativeâ 0.00001% annual growth rate still results in populations growing one order of magnitude every ~25 million years. At this rate, you end up with a greater population than atoms in the observable universe within 2 billion years. If you run until the end of the stelliferous era (100 trillion years) at the same rate, you end up with populations on the order of 10^millions, with a population density basically 10^thousands every cubic millimetre.
I think itâs worth mentioning that what youâve said is not in conflict with a much-reduced-but-still-astronomically-large Charlemagne Effect: youâve set an upper bound for the longterm effects of nearterm lives saved at <<<2 billion years, but that still leaves a lot of room for nearterm interventions to have very large long term effects by increasing future population size.
That argument refers to the exponential version of the Charlemagne Effect; but the logistic one survives the physical bounds argument. OP writes that they donât consider the logistic calculation of their Charlemagne Effect totally damning, particularly if it takes a long time for population to stabilise:
Hi Greg,
Thanks for reading the post, and your feedback! I think David Mears did a good job responding in a way aligned with my thinking. I will add a few additional points:
I donât think we can really know how future population will grow. To name one scenario aligned with exponential growth I cite in my post, Greaves and MacAskill discuss the possibility of space colonization that could lead to expansion possibilities that could stretch on for millions or billions of years:
âAs Greaves and MacAskill argue, it is feasible that future beings could colonize the estimated over 250 million habitable planets in the Milky Way, or even the billions of other galaxies accessible to us.[25] If this is the case, there doesnât seem to be an obvious limit to human expansion until an unavoidable cosmic extinction event.â
Second, itâs possible that even if growth doesnât exponentially grow, it could at various times have cyclic growth (booms and busts) or exponential decline. As I discuss, in both of these cases where there is not a carrying capacity, the Charlemagne Effect would still hold.
Third, we canât know how long humanity will continue on. For example, the average mammal species has a âlifespanâ of 1 million years. Plus humans are uniquely capable of creating existential catastrophe that could greatly shorten our species lifespan. In these cases, exponential growth may not be unrealistic.
Last, I will point out that you could very well be right that in the future population growth follows a logistic curve, and/âor humans continue on for billions of years. But there is some significant probability these conditions donât hold, just as we canât be certain that working to mitigate existential risk from AI, pandemics, etc. will prevent human extinction. Thus, within an expected value calculation of long term value, the Charlemagne Effect should still apply as long as there is some chance that the necessary conditions for it would exist.