I agree. I did not depict The Singularity itself in my graphs, because Kurzweil generally does not either. He instead shows projected exponentials as evidence

I agree. I did not depict The Singularity itself in my graphs, because Kurzweil generally does not either. He instead shows projected exponentials as evidence for The Singularity happening: http://www.kurzweilai.net/the-law-of-accelerating-returns http://www.kurzweilai.net/the-law-of-accelerating-returns My first point is really just that the exponential is not hyperbolic. It's tempting to see an exponential graphs and think the value is rising against some invisible wall, like it is going to infinity. But of course it is not. My second point was between the linear-exponential shooting skywards or the log-exponential rising incrementally which is "more real"? In the case of computer capacity I claim the incremental one is real, it reflects how we experience the increases. None of this really speaks to whether the Singularity will happen or not. I'm just saying if it happens it won't be because of some upward surge in computing capacity just prior to The Singularity. Because no such surge is predicted.