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"