Are you saying there’s a devil in my details that makes it wrong? I don’t think so. Can you tell me a tricky thing that world can do that makes my code for agent worse than yours?
About “not obvious how world depends on agent’s output,” here’s a only very slightly more tricky thing agent can do, that is still not as tricky as looking for all proofs of length less than n. It can write a program agent-1 (is this what Nesov is getting at?) that always outputs 1, then compute world(agent-1). It can next write a program agent-2 that always outputs 2, then compute world(agent-2). On and on up to agent-en. Then have agent output the k for which world(agent-k) is largest. Since world does not depend on any agent’s source code, if agent outputs k then world(agent) = world(agent-k).
Again this is just a careful way of saying “ask world what’s the best agent can get, and do that.”
Are you saying there’s a devil in my details that makes it wrong? I don’t think so. Can you tell me a tricky thing that world can do that makes my code for agent worse than yours?
About “not obvious how world depends on agent’s output,” here’s a only very slightly more tricky thing agent can do, that is still not as tricky as looking for all proofs of length less than n. It can write a program agent-1 (is this what Nesov is getting at?) that always outputs 1, then compute world(agent-1). It can next write a program agent-2 that always outputs 2, then compute world(agent-2). On and on up to agent-en. Then have agent output the k for which world(agent-k) is largest. Since world does not depend on any agent’s source code, if agent outputs k then world(agent) = world(agent-k).
Again this is just a careful way of saying “ask world what’s the best agent can get, and do that.”