Bit ironic given the model’s alleged finding…
Singularities are model breakdowns. A singularity simply says our current methods cease to work in this region. Within the context of a recursively self-improving intelligence with an unknown bound, “singularity” is probably a good description of our current socioeconomic system.
And it's definitely supposed to imply some kind of historical discontinuity not a change in convexity.
But thinking about the geometry of this problem helps understand why people aren't adjusting well to this. While we're walking on the curve, we look at the rate of change of the curve and say, "well, yeah, of course, dy/dx is 5 at this point and was 1 at the point a few years ago, because the curve is getting steeper" but we're always going to feel this way as things rip off into the stratosphere because dy/dx(e^x) = e^x.
From standing on the curve the curve is notably seeper, but the steepness totally makes sense to you. It's only when you look back 10 years or so that you think "wait a second, holy hell, I couldn't have imagined this!"
The first time I really (I mean really) thought about the singularity and AI was in roughly 2014. I mean, yea, I'd thought about things before that, but yeah, before the Humans need not apply video, I'd never actually given it much thought. I think back to myself 10 - 15 years or so ago, when I was just starting to tackle real programming projects, and was just starting to get decent at writing code, there is no way on earth that I would have imagined that a little over a decade later, Navier-Stokes would be solved by a computer program and the vast majority of my work would be playing sooth sayer to increasingly complicated piles of linear algebra.