It seems like some trends (GDP, for example) are on a superexponential trajectory. I’d be very interested to see this analysis done for that stuff too. Do you think the qualitative results would be the same—it’s hard to tell, best strategy is to try to guess the form of the dampening term?
I don’t know, that’s one of the things I’m interested in. I guess the situation is something like: There are a bunch of positive feedback loops and a bunch of negative feedback loops. For most of human history, the positives have outweighed the negatives, and the result has been a more or less steady straight line on a log-log plot. Though the slope of the line changes from period to period, presumably because at some times the positive feedback loops are a lot stronger than the negative and at other times only a little.
We know that eventually growth will be limited by the lightspeed expansion of a sphere. Before that, growth might be limited to e.g. a one-month doubling time because that’s about as fast as grass can reproduce, or maybe a one-hour doubling time because that’s about as fast as microorganisms can reproduce? Idk. Maybe nanotech could double even faster than that.
The question is whether there’s any way to look at our history so far, our trajectory, and say “Aha! We seem to be past the inflection point!” or something like that. By analogy to the exponentials case you’ve laid out, my guess is the answer is “no,” but I’m hopeful.
Thanks for this!
It seems like some trends (GDP, for example) are on a superexponential trajectory. I’d be very interested to see this analysis done for that stuff too. Do you think the qualitative results would be the same—it’s hard to tell, best strategy is to try to guess the form of the dampening term?
Possibly. What would be the equivalent of a dampening term for a superexponential? A further growth term?
I don’t know, that’s one of the things I’m interested in. I guess the situation is something like: There are a bunch of positive feedback loops and a bunch of negative feedback loops. For most of human history, the positives have outweighed the negatives, and the result has been a more or less steady straight line on a log-log plot. Though the slope of the line changes from period to period, presumably because at some times the positive feedback loops are a lot stronger than the negative and at other times only a little.
We know that eventually growth will be limited by the lightspeed expansion of a sphere. Before that, growth might be limited to e.g. a one-month doubling time because that’s about as fast as grass can reproduce, or maybe a one-hour doubling time because that’s about as fast as microorganisms can reproduce? Idk. Maybe nanotech could double even faster than that.
The question is whether there’s any way to look at our history so far, our trajectory, and say “Aha! We seem to be past the inflection point!” or something like that. By analogy to the exponentials case you’ve laid out, my guess is the answer is “no,” but I’m hopeful.
It’s generally possible to see where the inflection point is, when we’re past it.
Ah, right, of course. Well, what about when the trend is noisy though? With periods of slower and faster growth?
What about “Aha! We are clearly nowhere near the inflection point!”?