Also, although these posts always devolve into AI discussions (because of the math-algebra thing), I'd like to point out that it's not the only possible path to the singularity.
Human/Machine merge is also possible, simply being at your computer raises your IQ by several points because you have access to google and wikipedia etc to research your points and present evidence with. There are machines already that read brainwaves, I remember reading about a company in france that is devolping typing software based on brainwaves and that it works (as in, it can read each letter of the alphabet just from you thinking about it) but is still too slow to be commercially viable.
Here's a blurb about a brainwave controlled videogame demonstration
http://www.technovelgy.com/ct/Science-F ... wsNum=1915Interfaces with machines are only going to get more complex and sophisticated, the mouse and keyboard is as primitive as the hand-crank on a Model T.
There is also the postulation that the internet might 'wake up', that is a bit out there to consider even for me but there
is a significant amount of AI already being performed all the time on the net, if you don't think so you don't understand what it takes to generate your google search in 0.25 seconds.
Which brings me to another point, AI itself is a shifting goal, loosely defined as 'whatever it is machines can't do right now'. Chess was originally held up as beyond the capability of AI, now it's trivial, and is of course no longer considered even a qualification.
I called Qwest a little while ago to pay my bill, I dealt with a machine, it took my credit card information and paid my bill, without me using the keypad
at all. I spoke to the machine, it understood my voice (without first being 'trained' like those toy robots you may seen), and processed complex information correctly.