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James_Miller comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong
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It's all connected. You probably need different laws of logic to get a magical device or to allow for people to "instantly conceive of and communicate arbitrarily large numbers." See EY's Universal Fire where he wrote "If you stepped into a world where matches failed to strike, you would cease to exist as organized matter. Reality is laced together a lot more tightly than humans might like to believe."
The laws of logic don't prohibit minds with infinite states from existing, nor do they prohibit waves with infinite frequencies existing, nor eyes that can detect infinite variation in frequency. These aren't properties of our world, but they don't contradict logic. "It's all connected somehow, but I can't show how" - seems a bit like magical thinking.