And one way to tackle this is to investigate a more concrete question: what’s the base rate of any technology having a big discontinuity?

A significant historical example was the development of nuclear weapons. Over thousands of years, the energy density of explosives didn’t increase by much. Then within a few years, it got thousands of times better.

I haven't listened to the podcast yet, so apologies if this is elaborated further, but are nuclear weapons really a good example in terms of impact? The firebombing of Tokyo killed 100,000 in a single night. The Hiroshima bombing was a new method but the destruction was similar in scale. (Keep in mind also that nuclear weapons weren't missiles at first.)

I can't think of any truly discontinuous technological developments if measured by impact. Taking ~5 years to develop a proof of concept into something useful (as with airplanes) doesn't really count as a discontinuity, in my opinion.