[JoshCole]

Your consideration about the limits is somewhat aligned with how I think about things, but I think you need to take one further step before things will snap into clarity and the entire discussion will become dissolved.

You have a world state in your mental model of the Turing Machine state, right? That is why you talk about a specific Turing Machine as if you could look at it from outside it. What do you think you get when you pause, not from within the Turing Machine, but in the space of Turing Machines implied by your observation so far?

How many programs do you think I could write which would output "Hello" midway through the computation? One? Two? Could I suggest to you that there are an infinite number of such potential programs? The observation space corresponds with a sort of superposition of potential world states.

It is worse than that though. Your observation space? It contains more statements as more computation takes place. Eventually it has to be abstracted or it isn't computationally reducible. So there are actually more than one observation per information state. When you think about things from within the universe, even though chair is atoms, you are better off having the superposition of chair being highly variable. It corresponds to many different things.

So when you are entering decision problems you are in actuality in multiple potential universes, in multiple potential observation spaces, and you can't even tell one way or another except by expanding the computation.

[JoshCole]

> Eventually it has to be abstracted or it isn't computationally reducible.

This should be "Eventually it should be abstracted or else you are at risk of being computationally reducible." I was trying to say it isn't computationally reduced in the unabstracted form, but didn't use the words precisely enough.