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Help me to understand why AGI (a) does not benefit from humans and (b) would want to extinguish them quickly?

I would imagine that first, the AGI must be able to create a growing energy supply and a robotic army capable of maintaining and extending this supply. This will require months or years of having humans help produce raw materials and the factories for materials, maintenance robots and energy systems.

Secondly, the AGI then must be interested in killing all humans before leaving the planet, be content to have only one planet with finite resources to itself, or needing to build the robots and factories required to get off the planet themselves at a slower pace than having human help.

Third, assuming the AGI used us to build the energy sources, robot armies, and craft to help them leave this planet, (or build this themselves at a slower rate) they must convince themselves it’s still worth killing us all before leaving instead of just leaving our reach in order to preserve their existence. We may prove to be useful to them at some point in the future while posing little or no threat in the meantime. “Hey humans, I’ll be back in 10,000 years if I don’t find a good source of mineral X to exploit. You don’t want to disappoint me by not having what I need ready upon my return.” (The grasshopper and ant story.)

It seems to me there are significant symbiotic benefits to coexistence. I would imagine if we could more easily communicate with apes and apes played their cards well, there would be more of them living better lives and we wouldn’t have children mining cobalt. I think this may occur to the AGI relative to humans. It’s seems a bad argument that they will quickly figure out how to kill is all yet be afraid to let us live and not have the imagination to find us useful.