I'm glad to see people like you that understand that computers are ultimately machines that we put electric current (limited by our infrastructure) in to, and even with optimal efficiency (which we are no where close to), some math comes out. This year we all learned that a lot of what we thought was human thought can be expressed as math. Cool. But we can't scale that any higher than the physical input to the computer, and the physical heat dissipation that we can handle either. A 100% occupancy computing device is effectively a radiator.
So singularity people think 2 fallacies:
1. That it is possible to write an exponential function that somehow scales to asymptotic
2. That it is possible to write software that is so energy efficient that its output somehow exceeds the power draw
1 can be redefined to say "effectively" vertical. Ok. Cool motive, not a singularity.
2 can be handled by pumping more and more power in to the machine and building new nuclear plants to do so. This is what Microsoft is doing today.