In short, we are approaching what many have called the singularity.
Not really. The singularity requires an intelligence explosion. A perfectly acceptable alternative route is human-intelligence augmentation, via some or all of biological hacking (genetic or otherwise), chemical hacking, and tool use. The former two are plausible but not yet off the ground, but regarding tool-based augmentation I think we're seeing meaningful, if preliminary, progress. (Then again, I think literacy counts in this bin.)
I think the key question is whether you think the self-amplifying returns of technology that we're already seeing will extend sustainably to amplifying intelligence (either human or artificial).
The trendy "rapture of the nerds" version of the singularity does.
The original definition is technology advancing at a faster rate than humans are capable of integrating and managing it. It was identified while trying to identify existential threats to humanity.
It's fascinating watching a warning about future dangers get repackaged by AI focused futurists into a utopian neo-religion.
"Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion,' and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make." - I. J. Good, 1965
However, I am not convinced the schools are entirely contradictory, even with their strong claims.
For example,
- Accelerating Change school: this is mainly a (historical) trajectory claim based on positive feedback loop of technology. It does not seem to make any strong (maximum) claims about even trajectories beyond the point of strong AI.
- Event Horizon school: this is a forecastability claim that the repurcussions of AI or intelligence enhancement significantly beyond current human intelligence is unknowable until you get there.
- Intelligence Explosion school: this is a positive feedback claim that the most you can tell when human intelligence is surpassed is that further intelligence gains, be it by enhancement or AI, will feedback on itself to create further and faster change.
These claims seem to agree with each other on fundamental aspects of technology and intelligence.
In addition, in my opinion, it would not take too much imagination to combine the separate claims into a unified Singularity model.
That said, the school delineation is itself a useful tool.