catastrophists: when evolution was gradually improving hominid brains, suddenly something clicked - it stumbled upon the core of general reasoning - and hominids went from banana classifiers to spaceship builders. hence we should expect a similar (but much sharper, given the process speeds) discontinuity with AI.
gradualists: no, there was no discontinuity with hominids per se; human brains merely reached a threshold that enabled cultural accumulation (and in a meaningul sense it was culture that built those spaceships). similarly, we should not expect sudden discontinuities with AI per se, just an accelerating (and possibly unfavorable to humans) cultural changes as human contributions will be automated away.
I found the extended Fire/Nuclear Weapons analogy to be quite helpful. Here's how I think it goes:
In 1870 the gradualist and the catastrophist physicist wonder about whether there will ever be a discontinuity in explosive power
It seems like the AGI Gradualist sees the example of humans like my imagined Nukes Gradualist sees the sun, i.e. just a scale up of what we have now. While the AGI Catastrophist sees Humans as my imagined Nukes Catastrophist sees the sun.
The key disanalogy is that for the Sun case, there's a very clear 'impossibility proof' given by the Nukes Catastrophist that the sun couldn't just be a scale up of existing chemical and gravitational energy sources.