> I [...] fit a hyperbolic model to each one independently

^ That's your problem right there.

Assuming a hyperbolic model would definitely result in some exuberant predictions but that's no reason to think it's correct.

The blog post contains no justification for that model (besides well it's a "function that hits infinity"). I can model the growth of my bank account the same way but that doesn't make it so. Unfortunately.

Indeed. At various points you could have presumably done an identical analysis with journal articles and climate change, string theory, functional programming… terms & reached structurally the same conclusion.

The coming Singularity: When human institutions will cease being able to coherently react to monads!

If I understand the author correctly, he chose the hyperbolic model specifically because the story of "the singularity" _requires_ a function that hits infinity.

He's looking for a model that works for the story in the media and runs with it.

Your criticism seems to be criticizing the story, not the author's attempt to take it "seriously"