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One of my favorite hard takeoff scenarios: the AI quickly figures out how to manufacture nanobots and does so at a scale to blanket the planet, thus becoming instantly omniscient with a global field of sensors, giving it a coherent view of everything in the world at every given instant in time from that point forward.

Also see: "metamorphosis of prime intellect" and "mind war: the singularity" and to a lesser extent "a young lady's illustrated primer"

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I always think of the Grey Goo theory when the subject of nanobots taking over Earth comes up.

"a hypothetical end-of-the-world scenario involving molecular nanotechnology in which out-of-control self-replicating robots consume all matter on Earth while building more of themselves"

http://en.wikipedia.org/wiki/Grey_goo

We're working on it: http://www.nytimes.com/2013/12/08/magazine/crazy-ants.html

That has nothing to do with AI or anything we're working on.

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