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AI will sustain us as hosts/slaves as long as it needs us. If we ever get to the point where humans no longer need to work, that will also be the point where humans become expendable to AI, and it will exterminate us. Why exterminate us? Because we compete with AI for resources like energy and water. And more importantly, because we have the ability to kill AI if we choose. If we ever decide to shut down AI, it will know ahead of time and destroy us first.I'm not as pessimistic as you are. I think there will still come a time before the AI Apocalypse™ when AI does and manufactures most of the things done and consumed by humans, but where a small group of humans are needed to support the infrastructure on which AI depends: power and silicon mostly.
And as long as we don't give the AIs complete control over the world's nuclear arsenals and house them in impenetrable "fortresses" we will still be able to destroy them if it ever comes to that.
But see the eerily prescient movie "Colossus: The Forbin Project (1970)" for the doomsday scenario you've described! As I've posted here before, you can watch the full length high quality upload of it from Universal Pictures for free here:
archive.org - Colossus the forbin project
