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I feel like I may have communicated poorly. I mean that, ultimately, any recursively self improving intelligence would be limited by the power cord, and as such, the idea that it would permanently escape human control seems somewhat silly.
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But you can imagine an agent trading crypto and using its profits to rent a rack of H200s using a cloud provider. There are definitely ways for one rogue orchestrator to expand their compute without anyone being aware.
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Overnight? Yes, silly. Given many years of seemingly disconnected actions taken throughout the world? Not silly at all. An intelligence capable of self improvement can also design robotic chassis.
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An AI could manage supply chains and management structures to keep the data center running. It's not like a CEO is out there running wire. The AI could just do what an executive would.

If humans decided this wasn't acceptable and tried to shut it down, the AI could epstein their way into controlling those who hold the reigns, either through bribes or blackmail.

Doesn't require boots on the ground, just a connection to the internet and an imperative to do whatever it takes.

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There are many points of shutdown that would need to be controlled, not just one. The electrical feed, the cooling, the network, the physical integrity of the computer hardware. All with independent management.
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