| 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. |