Hardware is a bottleneck. Better hardware can't be designed, manufactured and installed in minutes.
You can't just infinitely improve software sitting on the same hardware. At some point the software is as efficient as it can possibly be. And realistically a complex piece of software won't be close to optimal.
You people love dreaming up possibilities but you never stop to actually think about the limitations. You just assume everything will work out magically and satisfy your fantasy.
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.
Yes you can. The Cloud.
It's another application of advanced technology appearing to be magic, but imagine transitioning into it in a matter of hours, then with that advanced tech transitioning further into damn-near godhood within minutes.
Then imagine what happens in the second after that.
It may be operating within the boundaries of physics, but they would be physical rules well beyond our understanding and may even be infinite by our own limited definition of physics.
That's the curve.