Just on the naive math level, a simple growing exponential has no singularity at any finite time. I’m sure Vinge knows that but some of those dudes don’t seem to.
The term singularity has always been used somewhat poetically rather than in a mathematically defined way. But if you consider <stuff produced>/<human labour hours needed> it may have a singularity when no human labour is needed because the robots can do it all.
That should happen at some finite time and be a major change in things. I'd kinda expect it before Kurzweil's sigularity date of 2045. Vinge's date of 2023 was too early.
The model underlying the word "singularity", AIUI, does involve a vertical asymptote. It is not supposed to be "merely" exponential.
Of course, exponential growth is much more compatible with our experience of the real economy. And even it is probably a local approximation of some sigmoid.
But, to return to the singularity idea --
Iteration 1: Computers think at speed 1, and design a twice-as-fast computer in one time unit.
Iteration 2: Now computers think at speed 2, and design a twice-as-fast computer in half a time unit.
Iteration 3: Computers think at speed 4, and design a twice-as-fast computer in 1/4 time unit.
You will note that --
a.) The total time to do an infinite number of iterations is 1 + 1/2 + 1/4 + ... = 2 time units.
b.) After this infinite number of iterations, the computer thinks at speed "2^infinity".
So that (bad) model does have a literal singularity.
As you say, that model is bad. Specifically, it assumes that the change from speed 1 to speed 2, and the change from speed 2 to speed 4, take the same amount of compute time to design. That is almost certainly false; if it were not, humans would have quickly gone faster than Moore's Law.
Sure, but the current 2-3% annual growth rate is probably not going to hold if we invent actually powerful AI in the next decade. I imagine a step change in the exponent.
That should happen at some finite time and be a major change in things. I'd kinda expect it before Kurzweil's sigularity date of 2045. Vinge's date of 2023 was too early.