[todd8]

This isn’t obvious to me. It doesn’t have to simulate itself in real time. It may not be able to simulate itself simulating itself. There may be proof of this using a diagonalization proof.

Consider programs that are quines, programs are able to output the exact source code of the program. See [1].

And there are abstract computers that can produce any computable output. These are called Universal Turing Machines, see [2]. UTMs can be specified with a remarkably small number of internal states, see [3].

I’m not saying you are wrong, but computability is full of unintuitive results, and the answer may be more subtle than what is revealed by “just thinking about it”.

[1] https://en.m.wikipedia.org/wiki/Quine_(computing)

[2] https://en.m.wikipedia.org/wiki/Universal_Turing_machine

[3] https://en.m.wikipedia.org/wiki/Wolfram%27s_2-state_3-symbol...

[simonh]

It needs to be able to store a complete representation of different versions of it's own state, in it's own state.