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actually_a_dog | 2 years ago
That's true, but not really saying very much. Any differentiable function is locally linear around a neighborhood of any point where the derivative exists.
> Also exponential growth does hit some kind of ceiling relatively quickly.
Well... that depends. Much like how markets can remain irrational longer than you can remain solvent, exponential growth can often remain exponential for much longer than it takes to create a problem. Conversely, sometimes it can't remain exponential long enough to prevent a problem. Exponential growth is a hard beast to tame.
vlovich123|2 years ago
What I’m saying is that it’s hard to know if you are dealing with an exponential scenario. You’d respond differently more quickly but doing so for a linear function may be the wrong response. There are certain failure modes when you do encounter an exponential but most things we encounter are more linear / dampened so the bias humans have against exponential is rational despite the failures we have dealing with exponential problems (climate change being a notable counter example). I’m saying it’s a rational trade off to evolve when dealing with the world.