For some reason, erasure seems to be intimately tied to information and how we define it. I think this is because we decide, or choose, what information is (i.e. what is relevant), because we can imagine this information that we choose, doesn't exist, or it can, or has been erased. I think that without the concept of erasure, or non-existence, of information, it would be difficult if not impossible to "know" what information is. We can't say with certainty what computation is, but we can say it's a process that changes information.
Information exists independently of us. For it's existence (and erasure) it's irrelevant if we consider it relevant.
Yes, but how does the universe erase information? It's easy for us to do this individually, we can just forget something. My "axiom" is that information can only exist if it can be erased, with the corollary that erasure requires energy from the environment. Cut to the chase--does a black hole erase information?
I've had a look at Turing machines, and at quantum eraser experiments. Turing machines specify a tape with symbols on it and a read/write head that can move left or right. This tape must include 'blanks'and the TM must be able to write blanks, which means they are a symbol in the tape alphabet. A distinction is made between this tape alphabet, and the so-called input alphabet which excludes the blank symbol. A blank tape is equivalent to an empty memory. Erasing information in quantum experiments generally means an additional measurement.
In accordance to black holes erasing information what connections are you making here to the "blank tape"? Further even if it would be possible to erase information how would you be sure only one copy of that information exist?
