I’m surprised at how hard it is for me to think of counterexamples.
I thought surely whale populations due to the slow generation time, but it looks like humpback whale populations have already recovered from whaling, and blue whales will get there before long.
Thinking again—in my baseball example, gravity is pulling the ball into the domain of applicability of the constant acceleration model.
Maybe what’s special about the exponential growth model is it implies escape from its own domain of applicability, in time that grows slowly (logarithmically) with the threshold.
I’m surprised at how hard it is for me to think of counterexamples.
I thought surely whale populations due to the slow generation time, but it looks like humpback whale populations have already recovered from whaling, and blue whales will get there before long.
Thinking again—in my baseball example, gravity is pulling the ball into the domain of applicability of the constant acceleration model.
Maybe what’s special about the exponential growth model is it implies escape from its own domain of applicability, in time that grows slowly (logarithmically) with the threshold.