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.
EDIT Rest in peace. Fire Upon the Deep was great.
EDIT Rest in peace. Fire Upon the Deep was great.
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.
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.