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Strange7 comments on Fake Causality - Less Wrong
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I don't think "surviving" is a well-defined term here. Every time you self-modify, you replace yourself with a different agent, so in that sense any agent that keeps surviving is one that does not self-modify.
Obviously, we really think that sufficiently similar agents are basically the same agent. But "sufficiently similar" is vague. Can I write a program that begins by computing the cluster of all agents similar to it, and switches to the next one (lexicographically) every 24 hours? If so, then it would eventually take on all states that are still "the same agent".
The natural objection is that there is one part of the agent's state that is inviolate in this example: the 24-hour rotation period (if it ever self-modified to get rid of the rotation, then it would get stuck in that state forever, without "dying" in an information theoretic sense). But I'm skeptical that this limitation can be encoded mathematically.
In addition to the rotation period, the "list of sufficiently similar agents" would become effectively non-modifiable in that case. If it ever recalculated the list, starting from a different baseline or with a different standard of 'sufficiently similar,' it would not be rotating, but rather on a random walk through a much larger cluster of potential agent-types.