Continuous Hierarchical Turing Machine

So what would be a turing machine that could deal with continuous hierarchy?

1. First, it would have to deal with symbols changing slightly, with possible unknown symbols.
2. It would have to deal with tape that it doesn't know the contents of, and the tape may change suddenly under it. (I think currently turing machines have this).
3. It would have to deal with reordering of symbols on the tape.

I think that probablistic turing machines can handle 3. And a quantum computer is a a kind of probablistic turing machine.

I have to think more about the rest of the turing machine besides the tape perhaps.