I don't believe that prediction is based on trend-extrapolation. Nothing like that has ever happened, so there's no trend to draw from.
You are right about the singularity, but the underlying trend extrapolation is that of technical progress and, specifically, of software getting smarter.
Nowadays people got used to rapid technical progress and often consider it, um, inevitable. A look at history should disabuse one of that notion, though.
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