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Emile comments on Formalizing Newcomb's - Less Wrong
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Why can't God Almighty be modelled mathematically?
Omega/God is running the universe on his computer. He can pause any time he wants (for example to run some calculations), and modify the "universe state" to communicate (or just put his boxes in).
That seems to be close enough to 4). Unlike with 3), you can't use the same process as Omega (pause the universe and run arbitrary calculations that could consider the state of every quark).
No God Almighty needed for your example, just an intelligence that's defined to be more powerful than you. If your computational capacity is bounded and the other player has much more, you certainly can't apply any perfectly rational decision concept. The problem is now about approximation. One approximation I've mentioned several times already is believing powerful agents with a 100% track record of truth. Sound reasonable? That's the level of discussion you get when you introduce bounds.