Posted by ecto 21 hours ago
No. That is quite literally exponential growth, basically by definition. If x(t) is a growing value, then x'(t) is it's growth, and x''(t) its acceleration. If x influences x'' , say by a linear relation
x''(t) = x(t)
You get exponentials out as the solutions. Not hyperbolic.
I always thought of the exponential as the pole of the function "amount of work that can be done per unit time per human being", where the pole comes about from the fact that humans cease to be the limiting factor, so an infinity pops out.
There is no infinity in practice, of course, because even though humans should be made independent of the quantity of extractable work, you'll run into other boundaries instead, like hardware or resources like energy.
I’m going to lose it the day this becomes vernacular.
Catastrophizing can be unhealthy and unproductive, but for those among us that can affect the future of our societies (locally or higher), the results of that catastophizing helps guide legislation and "Overton window" morality.
... I'm reminded of the tales of various Sci-Fi authors that have been commissioned to write on the effects of hypothetical technologies on society and mankind (e.g. space elevators, mars exploration)...
That said, when the general public worries about hypotheticals they can do nothing about, there's nothing but downsides. So. There's a balance.