To all those saying it is impossible: The point you are making about it being impossible is as moot as the one those that fear AI are making. From logical point of view, singularity (a moment when AI has modified itself to the point beyond our capacity of control or even understanding) seems possible. I don't see a way for us to tell what will happen when it hits. One needs to remember that AI itself may not be evil,…
I understand that a singularity by definition can never be reached. It's like the speed of light or absolute zero; infinity just out of reach no matter how much energy you spend trying to get there.
In math, a singularity is an unusual point, not sure if it can't be reached. I think it's used in different areas to describe different things. For example, if you model water in a channel, after some time the waves accumulate and you get a vertical water profile, the depth is not more a function, the mathematical model collapse, but in real life the water just make some nice crashing effect.