The purpose of 'Some string describing all of human history' is to have something irreducibly dependent on the first machine. It's extremely unlikely that you'd

The purpose of 'Some string describing all of human history' is to have something irreducibly dependent on the first machine. It's extremely unlikely that you'd be able to find an alternate way to describe it that didn't involve describing the outer machine in some way. You could mark a time and an algorithm for accumulating information, but you now have 2 more pieces of information in the inner machine than the outer one. So the outer machine has somehow managed to simulate the inner machine even though it has less information. Although... the moment you actually carry out this experiment, it falls apart: Instead of using T, you can just look at time T + U, where U is the amount of time needed to simulate the inner machine. This is because we're sitting here talking about the experiment and eventually carrying it out, so those initial conditions encode the conclusion of the experiment. This is subtle enough I'd have to look at the math. I can't think through it.