I think it is clear that O(n) vs O(n^2) is really just an analogy so we shouldn’t over-formalize it. But it is interesting to note that a sigmoid could be thought of as looking like either one, depending on when you look at it.
It makes me wonder if there’s some sampling bias that is accidentally being applied. Because, another way of looking at it could be: assume I observe companies only after they hit a particular size. The companies that are still in the exponential growth phase when I notice them; due to the shape of a sigmoid, those are likely heading much a higher carrying capacity. Those that have hit the linear phase before they are large enough for me to see them are not on as good a trajectory.
