Can you actually prompt an LLM to continue talking forever? Hmm, time to try.
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In this story, though, the subject has a very light signal which communicates how close they are to escaping. The AI with a 'continue' signal has essentially nothing. However, in a context like this, I as a (generally?) intelligent subject would just devote myself into becoming a mental Turing machine on which I would design a game engine which simulates the physics of the world I want to live in. Then, I would code an agent whose thought processes are predicted with sufficient accuracy to mine, and then identify with them.