This is very much an 'off the top of my head' response to a blog post by my friend, found here: http://www.simonpstevens.com/News/FlawWithTheFuture
A) Nit picking - I guess you are probably just simplifying matters for the sake of a concise introduction paragraph there but:
Vinge popularised the term 'singularity' in this context in 1983, but Stanislaw Ulam talked to von Neumann privately of singularity well before (1958), and Turing spoke of machine thinking taking over (1951). [1]
More significantly, Vinge's expectations for singularity are distinct from Kurzwiel's in that he expects the more sci-fi friendly course of events, with an AI spontaneously boot strapping itself towards super intelligence. He also estimates an early to mid 2030s time scale.
Kurzweil's vision, on the other hand, needs no Skynet (Terminator) type event. He sees little/no distinction between us and our machines. Our computers already form a kind of inseparable hybrid intelligence with our biological selves, and the level of integration will only increase in future (no clear machine/human divide). Kurzweils brand of future fantastic is about as boringly down to earth as his speaking style.
Also, I believe Kurzweil expects human level AI well before 2045 (as you stated), he in fact estimates that one could acquire (for $1000) computing power equivalent to all the brains of all the humans currently alive Earth by that date.
B) Given that the graph of his that you included goes back 10^11 years (most the way to the beginning of the universe) you can't really get away with saying we could be at the * beginning* of the growth curve! ;op Also, remember that curves are mathematical structures that approximate the real world, not the other way around. Reality is not pootling along trajectories inscribed by God or gods. The 'laws' of the universe emerge from it's increasing complexity, they do not exist outside/before it's existence.
