>> The big error is assuming the the accelleration will continue at the same rate it currently is. It won't.
Or maybe it will.
I don't think technology (and corresponding societal change) will ever happen so fast that it's like engaging warp drive as the term "singularity" seems to imply, but...
The logic of a technological singularity, or at least of accelerating change, is based on HOW/WHY this is going to happen, not just a naÃve extrapolation of what is currently happening.
In particular, it's inevitable from what we now understand about the brain we'll eventually be able to achieve human level AI, and with ongoing advances in our understanding of the brain as well as in neural-net based machine learning, it does seem that this will happen sooner rather than later (in the next 50 years, say, possibly quite a bit sooner).
The logic of the singularity/accelerating change, which seems hard to deny (notwithstanding my warp drive comment) is that once we get to humal level AI, it's going to get beyond (and WAAAAY beyond) human level in a hurry, for a variety of reasons:
1) Throw more compute power at it and it'll think faster/deeper. e.g. Play grandmaster level chess (or geopolitical strategy, or whatever ) with instantaneous response rather than pondering on it.
2) Fusion of intelligence and computer technology. Imagine if your brain had perfect recall and access to the entirety of human knowledge, data, etc. Imagine if your ability to chunk knowledge in 7 +/- pieces was replaced by an ability to reason in way more complex terms.
3) AI will improve itself. The first human level AI (maybe thinking faster via fast hardware, maybe with better memory, etc, etc) can learn about it's own design, the human brain, and just like it's own human creators and design a more powerful AI 2.0, which will design AI 3.0
Now consider the combination of these better and better AI designs running on faster and faster hardware... It's not hard to imagine an acceleration of AI capability.
Now consider this AI not only having the human sensory inputs of vision, hearing, etc, but also growing to include any source of data you care to give it such as the content of every daily newspaper in the world, every daily tweet, the output of every publically accessible webcam, the output of every weather balloon
So, a super-human intelligence, running at highly accelerated speed, with the ability to sense (and likely predict via causal relations it has learnt) the entire world...
Now, presumably (as is already happening) folk will be worried about the possibilities and try to put safeguards in place, but humans are fallible and technology advances anyway. All it takes is a few bugs for a sufficiently powerful AI running on a computer somewhere to learn how to hack computer based factories, power stations, weapons systems, household robots, you name it... and if/'when this happens, good luck trying to outwit it to regain control.
Now, this may not all happen at disorientating warp speed, but it'll happen fast enough. Technology in 20-30 years time will look just as much like science fiction as todays would have done 20-30 years ago, but we're reached a point where AI is going to be part of the mix, and because it will be self-improving it's going to happen fast once we get to that point.