[ExI] Axes on a graph

[Tom Nowell]

Some time ago, I made a post which I think I called "curves on a graph". I liked discussing how our different interpretations of technological progress meant people came up with different curves of technological progress, some leading to singularity/spike/acceleration/etc. and some to other conclusions. I was inspired at the time by Max More's "surge and singularity scenarios"
http://strategicphilosophy.blogspot.com/2009/06/how-fast-will-future-arrive-how-will.html

Now thinking about that "why the singularity will never happen" column has led me to ponder a different area - how much time will the steepest part of the graph be spread over? Imagine you are drawing a graph with time on the x axis and technological progress on the y axis. Following Kurzweil or Broderick, you look at accelerating rates of progress and come up with an exponential curve (or not, if you prefer one of Max's alternative scenarios). Now, there's a very steep part which seem to resemble a hyperbolic curve (hence the resemblance to a mathematical singularity). Assuming technology can't progress infinitely and there's a levelling off somewhere between weakly godlike and strongly godlike, how much time does this huge leap occur over?

Some have the idea of it being superfast - day 1: "Hey, my AI is self-improving", day 10 "Hey, who ordered the computer-controlled electron microscopes and oligonucleotide assembly gear?", day 30 "Hey, why is the planet turning to computronium?" whereas some scenarios have the process of uploading/AI developing, society changing/collapsing as more intelligences become non-biological and over years a post-singularity world emerging. 

What I'm interested in is this - are there any credible figures to suggest upper or lower limits to singularity speed? How much time would the singularity spread over, and would any biological humans be able to adapt or would it completely future-shock us all?

Tom