[actually_a_dog]

Yeah, unfortunately, I believe that one side effect of the human (sensory) nervous system having a logarithmic response curve is that humans are bad at understanding exponential processes. If you look at an exponential function on a log scale, you get a graph that looks linear. But, that's what fools people into thinking exponential processes are tame and easy to control.

[vlovich123]

Well that and it’s hard to distinguish if you’re early in exponential growth or linear. Also exponential growth does hit some kind of ceiling relatively quickly.

I think that’s an easier explanation for why we’re biased against it that isn’t necessarily tied to why the brain uses a logarithmic response curve. The latter could be because it provides better dampening to random excitations (ie the brain doesn’t have to expend as much energy dealing with them at the cost of missing signal in lower energy levels). Of course it could be this is why we’re bad with exponential but that seems like a larger leap to make.

[actually_a_dog]

> Well that and it’s hard to distinguish if you’re early in exponential growth or linear.

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]

> 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.

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.